EUROPA-TECHNICAL BOOK SERIES
for the Metalworking Trades
Ulrich Fischer
Roland Gomeringer
Max Heinzler
Roland Kilgus
Friedrich Naher
Stefan Oesterle
Heinz Paetzold
Andreas Stephan
Mechanical and
Metal Trades
Handbook
2nd English edition
Europa-No.: 1910X
VERLAG EUROPA LEHRMITTEL · Nourney, Vollmer GmbH & Co. KG
Dusselberger StraBe 23 . 42781 Haan-Gruiten • Germany
Original title:
Tabellenbuch Metall, 44th edition, 2008
Authors:
Ulrich Fischer
Roland Gomeringer
Max Heinzler
Roland Kilgus
Friedrich Naher
Stefan Oesterle
Heinz Paetzold
Andreas Stephan
Dipl.-lng. (FH)
Dipl.-Gwl.
Dipl.-lng. (FH)
Dipl.-Gwl.
Dipl.-lng. (FH)
Dipl.-lng.
Dipl.-lng. (FH)
Dipl.-lng. (FH)
Reutlingen
MeBstetten
Wangen im Allgau
Neckartenzlingen
Balingen
Amtzell
Muhlacker
Kressbronn
Editor:
Ulrich Fischer, Reutlingen
Graphic design:
Design office of Verlag Europa-Lehrmittel, Leinfelden-Echterdingen, Germany
The publisher and its affiliates have taken care to collect the information given in this book to the best of their ability.
However, no responsibility is accepted by the publisher or any of its affiliates regarding its content or any statement
herein or omission there from which may result in any loss or damage to any party using the data shown above.
Warranty claims against the authors or the publisher are excluded.
Most recent editions of standards and other regulations govern their use.
They can be ordered from Beuth Verlag GmbH, Burggrafenstr. 6, 10787 Berlin, Germany.
The content of the chapter "Program structure of CNC machines according to PAL" (page 386 to 400) complies with
the publications of the PAL Prufungs- und Lehrmittelentwicklungsstelle (Institute for the development of training and
testing material) of the IHK Region Stuttgart (Chamber of Commerce and Industry of the Stuttgart region).
English edition: Mechanical and Metal Trades Handbook
2nd edition, 2010
654321
All printings of this edition may be used concurrently in the classroom since they are unchanged, except for some
corrections to typographical errors and slight changes in standards.
ISBN 13 978-3-8085-1913-4
Cover design includes a photograph from TESNBrown & Sharpe, Renens, Switzerland
All rights reserved. This publication is protected under copyright law. Any use other than those permitted by law
must be approved in writing by the publisher.
© 2010 by Verlag Europa-Lehrmittel, Nourney, Vollmer GmbH & Co. KG, 42781 Haan-Gruiten, Germany
http://www.europa-lehrrnittel.de
Translation: Techni-Translate, 72667 Schlaitdorf, Germany; www.techni-translate.com
Eva Schwarz, 76879 Ottersheim, Germany; www.technische-uebersetzungen-eva-schwarz.de
Typesetting:YellowHand GbR, 73257 Kiingen, Germany; www.yellowhand.de
Printed by: Media Print lnformationstechnologie, D-33100, Paderborn, Germany
3
Preface
1 Mathematics
M
The Mechanical and Metal Trades Handbook is well-suited
for shop reference, tooling, machine building, maintenance
and as a general book of knowledge. It is also useful for educational purposes, especially in practical work or curricula
and continuing education programs.
9-32
Target Groups
p
• Industrial and trade mechanics
• Tool & Die makers
• Machinists
• Millwrights
• Draftspersons
• Technical Instructors
• Apprentices in above trade areas
• Practitioners in trades and industry
• Mechanical Engineering students
33- 56
3 Technical
drawing
TD
57 - 114
Notes for the user
The contents of this book include tables and formulae in
eight chapters, including Tables of Contents, Subject Index
and Standards Index.
The tables contain the most important guidelines, designs,
types, dimensions and standard values for their subject
areas.
Units are not specified in the legends for the formulae if several units are possible. However, the calculation examples
for each formula use those units normally applied in practice.
Designation examples, which are included for all standard
parts, materials and drawing designations, are highlighted
by a red arrow(= ).
The Table of Contents in the front of the book is expanded
further at the beginning of each chapter in form of a partial
Table of Contents.
The Subject Index at the end of the book (pages 417-428) is
extensive.
The Standards Index (pages 407-416) lists all the current
standards and regulations cited in the book. In many cases
previous standards are also listed to ease the transition from
older, more familiar standards to new ones.
We have thoroughly revised the 2nd edition of the "Mechanical and Metal Trades Handbook" in line with the 44th edition
of the German version "Tabellenbuch Metall". The section
dealing with PAL programming of CNC machine tools was
updated (to the state of 2008) and considerably enhanced.
4 Material science
MS
115-200
5 Machine
elements
ME
201 - 272
6 Production
Engineering
PE
273-344
7 Automation and
Information Technology
345- 406
A
8 International material
comparison chart.
Standards 407-416
S
Special thanks to the Magna Technical Training Centre for
their input into the English translati on of this book. Their
assistance has been extremely valuable.
The authors and the publisher will be grateful for any suggestions and constructive comments.
Spring 2010
Authors and publisher
4
Table of Contents
9
1 Mathematics
1.1
Numerical tables
Square root, Area of a circle ......... 10
Sine, Cosine ......... ......... ... . 11
Tangent, Cotangent ............... . 12
1.2 Trigonometric Functions
Definitions ........................ 13
Sine, Cosine, Tangent, Cotangent .... 13
Laws of sines and cosines ........... 14
Angles, Theorem of intersecting
lines ............................ . 14
1.3 Fundamentals of Mathematics
Using brackets, powers, roots ....... 15
Equations ......................... 16
Powers of ten, Interest calculation .... 17
Percentage and proportion
calculations ................ . .. . ... 18
1.4 Symbols, Units
Formula symbols, Mathematical
symbols .. .. ... ................... 19
SI quantities and units of
measurement ..................... 20
Non-SI units ...................... 22
1.5
1.6
1.7
1.8
1.9
Centroids
Centroids of lines ......... .. ....... 32
Centroids of plane areas .... ........ 32
33
2 Physics
Motion
Uniform and accelerated motion ..... 34
Speeds of machines ................ 35
2.2 Forces
Adding and resolving force vectors ... 36
Weight, Spring force .... .... .... ... 36
Lever principle, Bearing forces ....... 37
Torques, Centrifugal force ........... 37
2.3 Work, Power, Efficiency
Mechanical work .................. 38
Simple machines .................. 39
Power and Efficiency ... ..... ...... . 40
2.4 Friction
Friction force ................ . . . ... 41
Coefficients of friction .... .......... 41
Friction in bearings ................ 41
2.5 Pressure in liquids and gases
Pressure, definition and types ....... 42
Buoyancy .. ...... ... .............. 42
Pressure changes in gases ..... .. ... 42
2.6 Strength of materials
Load cases, Load types ............. 43
Safety factors, Mechanical
strength properties ................. 44
Tension, Compression,
Surface pressure ........ .......... 45
Shear, Buckling ......... .. .... .... . 46
Lengths
Calculations in a right triangle ....... 23
Sub-dividing lengths, Arc length ..... 24
Flat lengths, Rough lengths ......... 25
Areas
Angular areas .. ... .... ............ 26
Equilateral triangle, Polygons,
Circle ................... . ........ 27
Circular areas ..... ........ ........ 28
Volume and Surface area
Cube, Cylinder, Pyramid ........... . 29
Truncated pyramid, Cone,
Truncated cone, Sphere ............. 30
Composite solids .................. 31
Mass
General calculations .......... . ..... 31
Linear mass density ................ 31
Area mass density ................. 31
2.1
2.7
2.8
Bending, Torsion .................. 47
Shape factors in strength ........ . .. 48
Static moment, Section modulus,
Moment of inertia .................. 49
Comparison of various
cross-sectional shapes ............. 50
Thermodynamics
Temperatures, Linear
expansion, Shrinkage ...... ...... .. 51
Quantity of heat ................... 51
Heat flux, Heat of combustion ....... 52
Electricity
Ohm's Law, Conductor resistance .... 53
Resistor circuits ................... 54
Types of current ................... 55
Electrical work and power ........... 56
5
Table of Contents
57
3 Technical drawing
3.1
3.2
3.3
3.4
3.5
Basic geometric constructions
Lines and angles ................... 58
Tangents, Circular arcs, Polygons .... 59
Inscribed circles, Ellipses, Spirals ..... 60
Cycloids, Involute curves, Parabolas .. 61
Graphs
Cartesian coordinate system ........ 62
Graph types ...................... . 63
Drawing elements
Fonts ............................ 64
Preferred numbers, Radii, Scales ..... 65
Drawing layout ................... . 66
Line types ........ .. .. .. . .. ....... 67
Representation
Projection methods ........ ........ 69
Views .. ...... ............ ........ 71
Sectional views .............. ...... 73
Hatching .............. ........ .. . 75
Entering dimensions
Dimensioning rules ................ 76
Diameters, Radii, Spheres, Chamfers,
Inclines, Tapers, Arc dimensions ..... 78
Tolerance specifications ............ 80
Types of dimensioning ............. 81
Simplified presentation in drawings . . 83
3.6
Machine elements
Gear types ............ ......... ... 84
Roller bearings .................... 85
Seals ............................. 86
Retaining rings, Springs .... ........ 87
3.7 Workpiece elements
Bosses, Workpiece edges . ........ .. 88
Thread runouts, Thread undercuts ... 89
Threads, Screw joints .............. 90
Center holes, Knurls, Undercuts ...... 91
3.8 Welding and Soldering
Graphical symbols ................. 93
Dimensioning examples ............ 95
3.9 Surfaces
Hardness specifications in drawings .. 97
Form deviations, Roughness .. ... ... 98
Surface testing, Surface indications .. 99
3.10 ISO Tolerances and Fits
Fundamentals ............ ........ 102
Basic hole and basic shaft systems .. 106
General Tolerances, Roller
bearing fits ...... . ......... ...... 110
Fit recommendations ..... ......... 111
Geometric tolerancing .... ..... .... 112
GD & T (Geometric
Dimensioning & Tolerancing) .......113
115
4 Materials science
4.1
4.2
4.3
4.4
4.5
4_6
Materials
Material characteristics of solids .... 116
Material characteristics of liquids
and gases ....................... 117
Periodic table of the elements ...... 118
Designation system for steels
Definition and classification of steel . 120
Material codes, Designation ........ 121
Steel types, Overview ... . ....... 126
Structural steels ..... ........ . .... 128
Case hardened, quenched and tempered, nitrided, free cutting steels ... 132
Tool steels .... ........ ........... 135
Stainless steels, Spring steels ... ... 136
Finished steel products
Sheet, strip, pipes ............... .. 139
Profiles .... . ..................... 143
Heat treatment
Iron-Carbon phase diagram ...... .. 153
Processes . . . . . . . . . . . . . . . . . . . . . . . . 154
Cast iron materials
Designation, Material codes ... ..... 158
Classification ..................... 159
Cast iron ........................ 160
Malleable cast iron, Cast steel ...... 161
4.7
Foundry technology
Patterns, Pattern equipment . .. .... . 162
Shrinkage allowances,
Dimensional tolerances ..... .. . . . .. 163
4.8 Light alloys, Overview of Al alloys .. 164
Wrought aluminum alloys ......... 166
Aluminum casting alloys ........... 168
Aluminum profiles ................ 169
Magnesium and titanium alloys ..... 172
4.9 Heavy non-ferrous metals,
Overview ........... ... ... ....... 173
Designation system ............ .. . 174
Copper alloys ..... .............. . 175
4.10 Other metallic materials
Composite materials,
Ceramic materials ..... . .. .. . . .... 177
Sintered metals .................. 178
4.11 Plastics, Overview . . ............ 179
Thermoplastics ................... 182
Thermoset plastics, Elastomers ..... 184
Plastics processing ................ 186
4.12 Material testing methods,
Overview ..... ..... ....... . . . 188
Tensile testing . ... ................ 190
Hardness test .. . .......... ....... 192
4.13 Corrosion, Corrosion protection .. 196
4.14 Hazardous materials ......... .. . 197
6
Table of Contents
201
5 Machine elements
5.1
Threads (overview) ............. 202
Metric ISO threads ........... .. ... 204
Whitworth threads, Pipe threads .... 206
Trapezoidal and buttress threads .... 207
Thread tolerances ..... .... ...... .. 208
5.2 Bolts and screws (overview) .... . 209
Designations, strength ............. 210
Hexagon head bolts & screws .. .. .. 212
Other bolts & screws .............. 215
Screw joint calculations ............ 221
Locking fasteners ..... .... ........ 222
Widths across flats, Bolt and
screw drive systems .............. 223
5.3 Countersinks .................. 224
Countersinks for countersunk
head screws ..................... 224
Counterbores for cap screws ....... 225
5.4 Nuts (overview) . . .. .......... .. 226
Designations, Strength .......... .. 227
Hexagon nuts .................... 228
Other nuts ....................... 231
5.5 Washers (overview) . ...... .... . 233
Flat washers ..................... 234
HV, Clevis pin, Conical spring washers . 235
5.6 Pins and clevis pins (overview) . .. 236
Dowel pins, Taper pins, Spring pins . 237
5.7
5.8
5.9
Drive elements
Belts ............................ 253
Gears ....................... . ... 256
Transmission ratios ....... .... . ... 259
Speed graph ..................... 260
5.10 Bearings
Plain bearings (overview) .. .. ...... 261
Plain bearing bushings ............ 262
Antifriction bearings (overview) ..... 263
Types of roller bearings . . . .. ....... 265
Retaining rings ............ . ..... . 269
Sealing elements ................. 270
Lubricating oils .......... ........ . 271
Lubricating greases .... . ..... .. ... 272
273
6 Production Engineering
6.1
Quality management
Standards, Terminology ........... 274
Quality planning, Quality testing .... 276
Statistical analysis .... ............ 277
Statistical process control .......... 279
Process capability ................. 281
Production planning
Time accounting according to REFA . 282
Cost accounting ....... . . . ...... .. 284
Machine hourly rates .............. 285
6.3 Machining processes
Productive time .................. 287
Machining coolants ............... 292
Cutting tool materials, Inserts,
Tool holders ..................... 294
Forces and power ................. 298
Cutting data: Drilling, Reaming,
Turning .......... .......... . ..... 301
Cutting data: Taper turning ......... 304
Cutting data: Milling ............... 305
Indexing ......................... 307
Cutting data: Grinding and honing .. 308
6.4 Material removal
Cutting data ...................... 313
Processes . . . . . . . . . . . . . . . . ........ 314
6.5 Separation by cutting
Cutting forces .................... 315
Grooved pins, Grooved drive studs,
Clevis pins ........... .......... .. 238
Shaft-hub connections
Tapered and feather keys ........ .. 239
Parallel and woodruff keys ........ . 240
Splined shafts, Blind rivets ......... 241
Tool tapers ....................... 242
Springs, components of jigs
and tools
Springs ......................... 244
Drill bushings .................... 247
Standard stamping parts ........... 251
6.6
6.7
6.2
6.8
Shearing ........................ 316
Location of punch holder shank ..... 317
Forming
Bending ...................... ... 318
Deep drawing .... . . .. . ........... 320
Joining
Welding processes ..... .. ......... 322
Weld preparation ................. 323
Gas welding . . ....... . .. ........ . 324
Gas shielded metal arc welding ..... 325
Arc welding ...................... 327
Thermal cutting .................. 329
Identification of gas cylinders ...... . 331
Soldering and brazing ............. 333
Adhesive bonding ................ 336
Workplace safety and environmental
protection
Prohibitive signs .................. 338
Warning signs .......... .......... 339
Mandatory signs,
Escape routes and rescue signs .... . 340
Information signs ................. 341
Danger symbols ..... ............. 342
Identification of pipe lines .......... 343
Sound and noise ................. 344
7
Table of Contents
7 Automation and Information Technology
7.1
7 .2
7.3
7.4
7 .5
Basic terminology for control
engineering
Basic terminology, Code letters,
Symbols ........ ........... .... . 346
Analog controllers ................ 348
Discontinuous and digital controllers .. 349
Binary logic . ...... .... ........... 350
Electrical circuits
Circuit symbols ........... ........ 351
Designations in circuit diagrams .... 353
Circuit diagrams .................. 354
Sensors ........ ................ . 355
Protective precautions ............. 356
Function charts and function diagrams
Function charts ................... 358
Function diagrams ........ ..... ... 361
Pneumatics and hydraulics
Circuit symbols ................... 363
Layout of circuit diagrams ......... 365
Controllers ....................... 366
Hydraulic fluids ... ................ 368
Pneumatic cylinders .. . ........ .... 369
Forces, Speeds, Power ............ 370
Precision steel tube ............... 372
Programmable logic control
PLC programming languages ..... .. 373
Ladder diagram (LD) . .... ......... 374
Function block language (FBL) ...... 374
8 Material chart, Standards
8.1
8.2
7.6
7.7
7 .8
345
Structured text (ST) ........ ....... 374
Instruction list ................... 375
Simple functions ................. 376
Handling and robot systems
Coordinate systems and axes ....... 378
Robot designs .................. .. 379
Grippers, job safety .......... ..... 380
Numerical Control {NC) technology
Coordinate systems ............... 381
Program structure according to DIN .. 382
Tool offset and Cutter compensation . 383
Machining motions as per DIN ..... .. 384
Machining motions as per PAL
(German association) . .. .......... . 386
PAL programming system for turning . 388
PAL programming system for milling . 392
Information technology
Numbering systems ............... 401
ASCII code ....................... 402
Program flow chart, Structograms .. 403
WORD- and EXEL commands ...... 405
407
International material
comparison chart ........ .... .. 407
DIN, DIN EN, ISO etc. standards .. 412
Subject index
417
8
Standards and other Regulations
Standardization and Standards terms
Standardization is the systematic achievement of uniformity of material and non-material objects, such as components, calculation methods, process flows and services for the benefit of the general public.
Standards term
Example
Explanation
Standard
DIN 7157
A standard is the published result of standardization, e.g. the selection of certain fits
in DIN 7157.
Part
DIN 30910-2
The part of a standard associat ed w ith other parts w ith the same main number. DIN
30910-2 for example describes sintered materials for filters, while Part 3 and 4
describe sintered materials for bearings and formed parts.
Supplement
DIN 743
Suppl. 1
A supplement contains information for a standard, however no additional specifications. The supplement DIN 743 Suppl. 1, for example, contains application
examples of load capacity calculations for shafts and axles described in DIN 743.
Draft
EDIN 6316
(2007-02)
A draft standard contains the preliminary finished results of a standardization;
this version of the intended standard is made available to the public for comments. For example, the planned new version of DIN 6316 for goose-neck
clamps has been available to the public since February 2007 as Draft E
DIN 6316.
Preliminary
standard
DIN V66304
(1991-12)
A preliminary standard contains the results of standardization which are not released
by DIN as a standard, because of certain provisos. DIN V 66304, for example, discusses a format for exchange of standard part data for computer-aided design.
Issue date
DIN 76-1
(2004-06)
Date of publication which is made public in the DIN publication guide; this is the
date at which time the standard becomes valid. DIN 76-1, which sets undercuts
for metric ISO threads has been valid since June 2004 for example.
Types of Standards and Regulations (selection)
Type
Abbreviation
Explanation
Purpose and contents
International
Standards
(ISO standards)
ISO
International Organization for
Standardization, Geneva (0 and S
are reversed in the abbreviation)
Simplifies the international exchange of
goods and services, as well as cooperation
in scientific, technical and economic areas.
European
Standards
(EN standards)
EN
European Committee for Standardization (Comite Europeen de
Normalisation), Brussels
DIN
DIN EN
German
Standards
(DIN standards)
DIN ISO
DIN EN ISO
DINVDE
Technical harmonization and the associat ed
reduction of trade barriers for the advancement of the European market and the coalescence of Europe.
Deutsches l nstitut fur Normung e.V., National standardization facilitates rationalBerlin (German Institute for
ization, quality assurance, environmental
Standardization)
protection and common understanding in
European standard for which the
economics, technology, science, manageGerman version has attained the sta- ment and public relations.
tus of a German standard.
German standard for which an international standard has been adopted
w ithout change.
European standard for which an
international standard has been
adopted unchanged and the German
version has the status of a German
standard.
Printed publication of the VOE, which
has the status of a German standard.
Verein Deut scher lngenieure e.V.,
These guidelines give an account of the curDusseldorf (Society of German
rent state of the art in specific subject areas
Engineers)
and contain, for example, concrete proceduVerband Deutscher Elektrotechniker ral guidelines for the performing calculations
or designi ng processes in mechanical or
e.V., Frankfurt (Organization of Gerelectrical engineering.
man Electrical Engineers)
VOi Guidelines
VOi
VOE printed
publications
VOE
DGQ publicalions
DGQ
Deutsche Gesellschaft fur Oualitiit e.V., Recommendations in the area of quality
technology.
Frankfurt (German Association for
Quality)
REFA sheets
REFA
Association for Work Design/Work
Structure, Industrial Organization and
Corporate Development REFA e.V.,
Darmstadt
Recommendations in the area of production and work planning.
Table of Co ntents
9
1 Mathematics
d
fi
A = n•d 2
4
1
2
1.0000
1.4142
3
1.732 1
0.7854
3.1416
7.0686
sine
=
cosine
=
tangent
=
cotangent
=
1.1
Square root, Area of a circle . . . .. .. .. . . . ... . .. 10
Sine, Cosine . ... . .... .. . . . . .. . .. . ... . ... ... 11
Tangent, Cotangent .... . ... . .. . . . . .. . .. ... .. 12
1.2
opposite side
hypotenuse
adjacent side
hypotenuse
opposite side
adjacent side
adjacent side
opposite side
1
X
X
I
X
1.4
I
1 kW • h = 3.6 • 106 W • s
I
6
1.6
Symbols, Units
Lengths
1.7
,~
d
1.9
r! "(/{ ~~
J .
I
:,.._
+--·--·--·
X
M ass
General calculations .. . .. ...... .. .. .. . ... . . . . 31
Linear mass density . . . .. . . .. .. .. .. .. ...... . . 31
Area mass density ... ... .... ..... .... .. ..... 31
km
~ ,
,
I ~
Volume and Surface area
Cube, Cy linder, Pyramid ... . .. . .............. 29
Truncated pyramid, Cone, Truncated cone, Sphere 30
Composite solids ...... . .. . . . .. . . .. .... . . . .. 31
1.8
m in -
Areas
Angular areas . . . . ... ... ... . ..... . .... . . . . . . 26
Equilateral triangle, Polygons, Circle .... . . ... . . 27
Circular areas . . ... . .... . . ... .... . ...... . .. . 28
~
x,
Using brackets, powers, roots .. . . ... . ... ... .. 15
Equations . . . . . ... .. .. .. .. . ... . . ... . . . . .. . . . 16
Powers of t en, Interest calculation ... .. . . . . . ... 17
Percentage and proportio n calculations ... .. . . . 18
Calculations in a right t riangle . . .... . .... . .... 23
Sub-dividing lengths, Arc length .. .. .. . . ... . . . 24
Flat lengt hs, Rough lengths .... . . . ... . . . . . .... 25
I \
i
Fundamentals of Mathematics
Form ula symbols, Mathematical symbols . .. . . . 19
SI quantities and units of measurement . ....... 20
Non-SI units ... ..... . .. . . ... . . ... ..... . . . .. 22
1.5
,.
Trigonometric Functions
Definitions . . ............ . ... . ... . . . . . . . . . .. 13
Sine, Cosine, Tangent, Cot angent . ... . ...... . .. 13
Laws of sines and cosines .. .. . . .. ... . .. ... . . . 14
Angles, Theorem of intersecting lines . . ... .. . .. 14
1.3
5 = -1 -(3 + 5)
-3 +-
Numerical tables
Centroids
Centroids of lines ...... ...... ... ... ... ... ... 32
Centroids of plane areas .. .... . .... . ... . .. .. . 32
10
M ath ematics: 1. 1 Numerical tables
d
{d"
A- n -d2
4
d
{d"
A - "-d2
2042.82
2 123.72
2206.18
2290.22
2375.83
101
102
103
104
105
10.0499
10.0995
10.1489
10.1980
10.2470
8011.85
8171 .28
8332.29
8494.87
8659.01
15 1
152
153
154
155
12.2882
12.3288
12.3693
12.4097
12.4499
17907.9
18 145.8
18385.4
18626.5
18869.2
7.4833
7.5498
7.6158
7.6811
7.7460
2463.01
2551.76
2642.08
2733.97
2827.43
106
107
108
109
110
10.2956
10.3441
10.3923
10.4403
10.488 1
8824.73
8992.02
9 160.88
9331.32
9503.32
156
157
158
159
160
12.4900
12.5300
12.5698
12.6095
12.6491
19 113.4
19359.3
19606.7
19855.7
20 106.2
61
62
63
64
65
7.8 102
7.8740
7.9373
8.0000
8.0623
2922.47
3019.07
3 117.25
3216.99
3318.31
111
112
113
114
115
10.5357
10.5830
10.630 1
10.677 1
10.7238
9676.89
9852.03
10028.7
10207.0
10386.9
161
162
163
164
165
12.6886
12.7279
12.767 1
12.8062
12.8452
20358.3
20612.0
20867.2
21 124.1
21 382.5
201.062
226.980
254.469
283.529
314.159
66
67
68
69
70
8.1240
8.1854
8.2462
8.3066
8.3666
3421.19
3525.65
3631.68
3739.28
3848.45
116
117
118
119
120
10.7703
10.8167
10.8628
10.9087
10.9545
10568.3
10751.3
10935.9
111 22.0
11309.7
166
167
168
169
170
12.8841
12.9228
12.9615
13.0000
13.0384
21 642.4
21904.0
22167.1
22431.8
22698.0
4.5826
4.6904
4.7958
4.8990
5.0000
346.361
380.133
415.476
452.389
490.874
71
72
73
74
75
8.4261
8.4853
8.5440
8.6023
8.6603
3959.19
4071 .50
4185.39
4300.84
4417.86
121
122
123
124
125
11.0000
11.0454
11.0905
11.1355
11. 1803
11 499.0
11 689.9
11 882.3
12076.3
1227 1.8
171
172
173
174
175
13.0767
13.1149
13.1529
13.1909
13.2288
22965.8
23235.2
23506.2
23778.7
24 052.8
26
27
28
29
30
5.0990
5.1962
5.2915
5.3852
5.4772
530.929
572.555
615.752
660.520
706.858
76
77
78
79
80
8.7178
8.7750
8.8318
8.8882
8.9443
4536.46
4656.63
4778.36
4901.67
5026.55
126
127
128
129
130
11.2250
11.2694
11.3137
11.3578
11.4018
12469.0
12667.7
12868.0
13069.8
13273.2
176
177
178
179
180
13.2665
13.3041
13.3417
13.3791
13.4164
24328.5
24605.7
24884.6
25164.9
25446.9
31
32
33
34
35
5.5678
5.6569
5.7446
5.8310
5.916 1
754.768
804.248
855.299
907.920
962.113
81
82
83
84
85
9.0000
9.0554
9.1104
9.1652
9.2195
5 153.00
5281.02
5410.61
5541.77
5674.50
131
132
133
134
135
11.4455
11.489 1
11.5326
11.5758
11.6190
13478.2
13684.8
13892.9
14102.6
14313.9
181
182
183
184
185
13.4536
13.4907
13.5277
13.5647
13.601 5
25730.4
26015.5
26302.2
26590.4
26880.3
36
37
38
39
40
6.0000
6.0828
6. 1644
6.2450
6.3246
1017.88
1075.21
1134.11
11 94.59
1256.64
86
87
88
89
90
9.2736
9.3274
9.3808
9.4340
9.4868
5808.80
5944.68
6082.12
6221.14
6361 .73
136
137
138
139
140
11.6619
11.7047
11.7473
11.7898
11.8322
14526.7
14741.1
14957.1
15174.7
15393.8
186
187
188
189
190
13.6382
13.6748
13.711 3
13.7477
13.7840
27171.6
27464.6
27759.1
28055.2
28352.9
41
42
43
44
45
6.403 1
6.4807
6.5574
6.6332
6.7082
1320.25
1385.44
1452.20
1520.53
1590.43
91
92
93
94
95
9.5394
9.5917
9.6437
9.6954
9.7468
6503.88
6647.61
6792.91
6939.78
7088.22
14 1
142
143
144
145
11.8743
11.9164
11.9583
12.0000
12.0416
15614.5
15836.8
16060.6
16286.0
16513.0
19 1
192
193
194
195
13.8203
13.8564
13.8924
13.9284
13.9642
28652.1
28952.9
29255.3
29559.2
29864.8
46
47
48
49
50
6.7823
6.8557
6.9282
7.0000
7.071 1
1661.90
1734.94
1809.56
1885.74
1963.50
96
97
98
99
100
9.7980
9.8489
9.8995
9.9499
10.0000
7238.23
7389.81
7542.96
7697.69
7853.98
146
147
148
149
150
12.0830
12.1244
12.1655
12.2066
12.2474
16741 .5
16971.7
17203.4
17436.6
17671.5
196
197
198
199
200
14.0000
14.0357
14.071 2
14.1067
14.142 1
30171.9
30480.5
30790.7
31 102.6
31415.9
d
{d"
A = n -d2
d
{d"
A = n-d2
2
3
4
5
1.0000
1.4142
1.732 1
2.0000
2.236 1
0.7854
3.14 16
7.0686
12.5664
19.6350
51
52
53
54
55
7.1414
7.211 1
7.280 1
7.3485
7.4162
6
7
8
9
10
2.4495
2.6458
2.8284
3.0000
3.1623
28.2743
38.4845
50.2655
63.6173
78.5398
56
57
58
59
60
11
12
13
14
15
3.3166
3.4641
3.6056
3.7417
3.8730
95.0332
113.097
132.732
153.938
176.715
16
17
18
19
20
4.0000
4.123 1
4.2426
4.3589
4.472 1
21
22
23
24
25
4
Table values of (d and A are rounded off.
4
-
-
4
11
Mathematics: 1. 1 Numerical tables
Values of Sine and Cosine Trigonometric Functions
sine 0° to 45°
de·
grees
sine 45• to 90•
de·
grees
minutes
-
minutes
0'
15'
30'
45'
60'
0.0175 as·
0.0349 88"
0.0523 87"
0.0698 86"
0.0872 as·
+
45°
46"
47•
48"
49•
0.7071
0.7193
0.7314
0.7431
0.7547
0.7102
0.7224
0.7343
0.7461
0.7576
0.7133
0.7254
0.7373
0.7490
0.7604
0.7163
0.7284
0.7402
0.7518
0.7632
0.7193
0.73 14
0.7431
0.7547
0.7660
94•
0.7660
0.7771
0.7880
0.7986
0.8090
0.7688
0.7799
0.7907
0.8013
0.8116
0.7716
0.7826
0.7934
0.8039
0.8141
0.7744
0.7853
0.7960
0.8064
0.8166
0.7771
0.7880
0.7986
0.8090
0.8 192
39"
39•
82°
8 1°
80"
50•
51°
52°
53•
54•
0.1865
0.2036
0.2207
0.2377
0.2546
0.1908 79•
0.2079 78°
0.2250
0.2419 76°
0.2588 75•
55•
56°
57•
58°
59•
0.8192
0.8290
0.8387
0.8480
0.8572
0.8216
0.8315
0.8410
0.8504
0.8594
0.8241
0.8339
0.8434
0.8526
0.8616
0.8266
0.8363
0.8457
0.8549
0.8638
0.8290
0.8387
0.8480
0.8572
0.8660
34•
33•
3 1°
30•
0.2672
0.2840
0.3007
0.3173
0.3338
0.2714
0.2882
0.3049
0.3214
0.3379
0.2756
0.2924
0.3090
0.3256
0.3420
74•
73°
72°
71°
70°
so· 0.8660
6 1° 0.8746
62° 0.8829
63° 0.8910
64" 0.8988
0.8682
0.8767
0.8850
0.8930
0.9007
0.8704 0.8725
0.8788 0.8809
0.8870 0.8890
0.8949 0.8969
0.9026 0.9045
0.8746
0.8829
0.8910
0.8988
0.9063
29•
28°
27°
26°
25°
0.3461
0.3624
0.3786
0.3947
0.4107
0.3502
0.3665
0.3827
0.3987
0.4 147
0.3543
0.3706
0.3867
0.4027
0.4187
0.3584 -69"
0.3746 68"
0.3907 67°
0.4067 66"
0.4226 65°
65° 0.9063
66" 0.9135
67° 0.9205
68" 0.9272
69° 0.9336
0.9081
0.9153
0.9222
0.9288
0.9351
0.9100
0.9171
0.9239
0.9304
0.9367
0.91 18
0.9188
0.9255
0.9320
0.9382
0.9135
0.9205
0.9272
0.9336
0.9397
24°
23°
22°
21·
20•
0.4226
0.4384
0.4540
0.4695
0.4848
0.4266
0.4423
0.4579
0.4733
0.4886
0.4305
0.4462
0.4617
0.4772
0.4924
0.4344
0.4501
0.4656
0.4810
0.4962
0.4384
0.4540
0.4695
0.4848
0.5000
64"
63°
62°
61°
60"
70°
7 1°
72°
73°
74°
0.9397 0.9412 0.9426
0.9455 0.9469 0.9483
0.9511 0.9524 0.9537
0.9563 0.9576 0.9588
0.9613 0.9625 0.9636
0.9441
0.9497
0.9550
0.9600
0.9648
0.9455
0.951 1
0.9563
0.9613
0.9659
19°
18°
17°
16°
1s ·
30•
31°
32°
33°
34•
0.5000
0.5150
0.5299
0.5446
0.5592
0.5038
0.5188
0.5336
0.5483
0.5628
0.5075 0.51 13
0.5225 0.5262
0.5373 0.5410
0.5519 0.5556
0.5664 0.5700
0.5150
0.5299
0.5446
0.5592
0.5736
59°
58°
57°
56°
55°
75°
76°
77°
78°
79•
0.9659
0.9703
0.9744
0.9781
0.9816
0.9670
0.9713
0.9753
0.9790
0.9825
0.9681
0.9724
0.9763
0.9799
0.9833
0.9692
0.9734
0.9772
0.9808
0.9840
0.9703
0.9744
0.9781
0.9816
0.9848
14°
13°
12°
11·
10°
35°
36"
37°
38"
39•
0.5736
0.5878
0.6018
0.6157
0.6293
0.5771
0.5913
0.6053
0.6191
0.6327
0.5807
0.5948
0.6088
0.6225
0.6361
0.5842
0.5983
0.6122
0.6259
0.6394
0.5878
0.6018
0.6157
0.6293
0.6428
54•
53°
52°
51°
50•
so• 0.9848
0.9856
0.9884
0.9909
0.9931
0.9950
0.9863
0.9890
0.9914
0.9936
0.9954
0.9870
0.9897
0.9920
0.9941
0.9958
0.9877
0.9903
0.9925
0.9945
0.9962
9•
40•
41°
42°
0.6428
0.6561
0.6691
0.6820
0.6947
0.6461
0.6593
0.6724
0.6852
0.6978
0.6494
0.6626
0.6756
0.6884
0.7009
0.6528
0.6659
0.6788
0.6915
0.7040
0.6561
0.6691
0.6820
0.6947
0.7071
49°
48"
47°
46°
45°
as• 0.9962
0.9966 0.9969 0.9973 0.9976
86° 0.9976 0.9979 0.9981 0.9984 0.9986
87° 0.9986 0.9988 0.9990 0.9992 0.9994
88° 0.9994 0.9995 0.9997 0.9998 0.99985
89" 0.99985 0.99991 0.99996 0.99999 1.0000
4•
3•
2·
1•
60'
45'
30'
15'
O'
t
+
0'
15'
30'
45'
0.0000
0.0 175
0.0349
0.0523
0.0698
0.0044
0.0218
0.0393
0.0567
0.0741
0.0087
0.0262
0.0436
0.0610
0.0785
0.0 131
0.0305
0.0480
0.0654
0.0828
9•
0.0872
0.1045
0.1219
0.1392
0.1564
0.0915
0.1089
0.1262
0.1435
0.1607
0.0958
0.1 132
0.1305
0.1478
0.1650
0.1002
0. 1175
0.1 349
0. 1521
0.1693
0.1045
0.1219
0.1392
0.1564
0.1736
10·
11•
12·
13°
14°
0.1736
0.1908
0.2079
0.2250
0.2419
0.1779
0.1951
0.2 122
0.2292
0.2462
0.1 822
0.1994
0.2164
0.2334
0.2504
15°
16°
17•
18°
19°
0.2588
0.2756
0.2924
0.3090
0.3256
0.2630
0.2798
0.2965
0.3132
0.3297
20·
2 1°
22°
23°
24°
0.3420
0.3584
0.3746
0.3907
0.4067
25°
26°
27°
28°
29•
o·
1·
2·
3•
4•
5•
6"
7•
a·
43•
44•
60'
83°
n·
m inutes
cosine 45° t o 90•
degrees
81° 0.9877
82° 0.9903
83° 0.9925
84" 0.9945
60'
45'
30'
15'
minutes
coalne O" to 45°
Table values of the trigonometric funct ions are rounded off to four decimal places.
0'
44•
43"
42°
4 1°
40°
37°
36"
35•
32°
a·
7°
6"
5•
o·
t
de·
grees
12
M athematics: 1. 1 Numerica l t ables
Values of Tangent and Cotangent Trigonometric Functions
de-
tangent 0° to 45°
g rees =
minutes
-!,
0'
o· 0.0000
grees = minutes
-
15'
30'
45'
60'
tangent 45° to 90°
de--
-!,
0'
15'
30'
45'
60'
1·
2•
3•
4•
0.0 175
0.0349
0.0524
0.0699
0.0044
0.0218
0.0393
0.0568
0.0743
0.0087
0.0262
0.0437
0.0612
0.0787
0.0 131
0.0306
0.0480
0.0655
0.0831
0.0175
0.0349
0.0524
0.0699
0.0875
59• 45°
88° 460
87• 47°
86· 40•
as• 49°
1.0000
1.0355
1.0724
1.1106
1.1504
1.0088
1.0446
1.0818
1.1204
1.1606
1.0176
1.0538
1.0913
1.1303
1.1708
1.0265
1.0630
1.1009
1.1403
1.1812
1.0355 4 40
1.0724 43"
1.1106 42"
1.1504 41°
1.1918 40°
50
50
70
so
90
0.0875
0.1051
0.1228
0.1405
0.1584
0.0919
0. 1095
0.1272
0.1450
0. 1629
0.0963
0.11 39
0. 13 17
0. 1495
0.1673
0.1007
0.1184
0.1361
0.1539
0.17 18
0.1 051 940 500
0. 1228 83° 51°
0.1 405 a2° 52°
0.1584 81° 530
0. 1763 so· 540
1.1918
1.2349
1.2799
1.3270
1.3764
1.2024
1.2460
1.2915
1.3392
1.3891
1.2 131
1.2572
1.3032
1.3514
1.4019
1.2239
1.2685
1.3151
1.3638
1.4150
1.2349
1.2799
1.3270
1.3764
1.4281
10°
11•
12°
13°
14°
0.1763
0.1944
0.2126
0.2309
0.2493
0.1 808
0. 1989
0.217 1
0.2355
0.2540
0.1853
0.2035
0.22 17
0.2401
0.2586
0.1899
0.2080
0.2263
0.2447
0.2633
0.1944
0.2 126
0.2309
0.2493
0.2679
79° 55°
78° 56°
1.4281
1.4826
1.5399
1.6003
1.6643
1.4415
1.4966
1.5547
1.6160
1.6808
1.4550
1.5108
1.5697
1.6319
1.6977
1.4687
1.5253
1.5849
1.6479
1.7 147
1.4826 340
1.5399 330
1.6003 32°
1.6643 31°
1.7321 30•
15°
16°
17°
18°
19°
0.2679
0.2867
0.3057
0.3249
0.3443
0.2726
0.2915
0.3 105
0.3298
0.3492
0.2773
0.2962
0.3153
0.3346
0.3541
0.2820
0.3010
0.3201
0.3395
0.3590
0.2867
0.3057
0.3249
0.3443
0.3640
74°
1.7321 1.7496
1.8040 1.8228
1.8807 1.9007
1.9626 1.9840
2.0503 2.0732
1.7675
1.8418
1.921 0
2.0057
2.0965
1.7856
1.8611
1.9416
2.0278
2. 1203
1.8040 29°
1.8807 2a0
1.9626 27°
2.0503 26°
2.1445 25°
20·
21°
22°
23°
24°
0.3640
0.3839
0.4040
0.4245
0.4452
0.3689
0.3889
0.4091
0.4296
0.4505
0.3739
0.3939
0.4142
0.4348
0.4557
0.3789
0.3990
0.4193
0.4400
0.4610
0.3839
0.4040
0.4245
0.4452
0.4663
69° 65°
68· 660
67° 67°
660 680
65° 590
2.1445
2.2460
2.3559
2.4751
2.6051
2.1692
2.2727
2.3847
2.5065
2.6395
2.1943
2.2998
2.4142
2.5386
2.6746
2.2199
2.3276
2.4443
2.57 15
2.7106
2.2460 24°
2.3559 23°
2.4751 22°
2.6051 21°
2.7475 200
25°
26°
27°
28°
29°
0.4663
0.4877
0.5095
0.5317
0.5543
0.4716
0.4931
0.5150
0.5373
0.5600
0.4770
0.4986
0.5206
0.5430
0.5658
0.4823
0.5040
0.5261
0.5486
0.5715
0.4877
0.5095
0.5317
0.5543
0.5774
540
63°
62°
6 1°
500
71°
720
73°
74°
2.7475
2.9042
3.0777
3.2709
3.4874
2.7852
2.9459
3.1240
3.3226
3.5457
2.8239
2.9887
3.1716
3.3759
3.6059
2.8636
3.0326
3.2205
3.4308
3.6680
2.9042
3.0777
3.2709
3.4874
3.7321
19°
18°
17°
16°
15°
30°
3 1°
32°
33°
340
0.5774
0.6009
0.6249
0.6494
0.6745
0.5832
0.6068
0.63 10
0.6556
0.6809
0.5890
0.6128
0.637 1
0.6619
0.6873
0.5949
0.6 188
0.6432
0.6682
0.6937
0.6009
0.6249
0.6494
0.6745
0.7002
59°
500
57°
56°
55°
75°
76°
77°
78°
79°
3.7321 3.7983
4.0108 4.0876
4.3315 4.4194
4.7046 4.8077
5.1446 5.2672
3.8667
4.1653
4.5107
4.9152
5.3955
3.9375
4.2468
4.6057
5.0273
5.5301
4.0108
4.3315
4.7046
5.1446
5.6713
14°
13°
12°
11°
35°
36°
37°
38°
39•
0.7002
0.7265
0.7536
0.7813
0.8098
0.7067
0.7332
0.7604
0.7883
0.8170
0.7133
0.7400
0.7673
0.7954
0.8243
0.7199
0.7467
0.7743
0.8026
0.8317
0.7265
0.7536
0.7813
0.8098
0.8391
540
53°
52°
5 1°
500
so·
400 0.8391 0.8466
41° 0.8693 0.8770
42° 0.9004 0.9083
430 0.9325 0.9407
440 0.9657 0.9742
0.8541
0.8847
0.9163
0.9490
0.9827
0.8617
0.8925
0.9244
0.9573
0.9913
0.8693
0.9004
0.9325
0.9657
1.0000
49°
400
47°
46°
45°
30'
15'
0'
60'
45'
m inutes
cotange nt 45° to 90°
77• 57°
76° 50•
75° 59°
so·
73° s 1°
72° 62°
710 63°
70° 54•
t
70°
36•
35°
10°
81°
82°
83°
040
5.6713
6.3138
7.1154
8.1443
9.5144
5.8197 5.9758 6.1402 6.3 138
6.4971 6.69 12 6.8969 7.1154
7.3479 7.5958 7.8606 8.1443
8.4490 8.7769 9.1309 9.5144
9.9310 10.3854 10.8829 11.4301
90
so
70
85°
860
87°
880
590
11.4301 12.0346 12.7062 13.4566 14.3007
14.3007 15.2571 16.3499 17.6106 19.0811
19.081 1 20.8188 22.9038 25.4517 28.6363
28.6363 32.7303 38.1885 45.8294 57.2900
57.2900 76.3900 114.5887 229.1817 00
40
30
20
10
oo
60'
45'
30'
15'
m inutes
de--
grees
390
38"
37°
cot angent o• to 45°
Table values of the trigonometric functions are rounded off to four decimal places.
O'
6°
50
t
de--
grees
13
Mathematics: 1.2 Trigonometric Functions
Trigonometric functions of right triangles
Definitions
Designations in a
right triangle
Application
Definitions of the
ratios of the sides
opposite side
hypotenuse
sin a =
adjacent side
hypotenuse
cos a =
opposite side
tangent
c hypo(enus~ a adjacent
=
adjacent side
~
]
side of fJ .__ _ _ _ __ __
tan a =
adjacent side
opposite side
cot a =
c hh~potenuse a opposite
side of a
a
.
I
b adjacent side of a
sine
=
cosine
=
cotangent =
b oppositl side of fJ
for <I: f3
for <l:a
a
sin P =
C
b
_Q
C
cos /3 = ~
-
C
C
a
ti
b
a
tan P =
b
a
cot/J =
ti
a
Graph of the trigonometric functions between 0° and 360°
Representation on a unit circle
Graph of t he trigonometric functions
90°
♦
ll
cot a{+)
cot (J(-l
I
+1
\/
~) j•o ~
.,:,
180°
111
>
0
~P<
-
270°
C:
'
0,.
360°
C
"'
IV
~,j
IV
V\V
r¥'' i"¥l¥T.
n,
I~
-
\/
ll
~ oo
I
The values of the trigonomet ric functions of angles> 90° can be derived from the values of the angles between 0° and
90° and then read from the t ables (pages 11 and 12). Refer to the graphed curves of the trigonometric functions for
the correct sign. Calculators w ith t rigonometric functions display both the value and sign for the desired angle.
Example: Relationships for Quadrant II
Relationships
Example: Function values for the angle 120° (a= 30° in the formulae)
sin (90° +a)= +cos a
sin (90° + 30°) = sin 120° = +0.8660
cos 30° = +0.8660
cos (90° + a) = -sin a
cos (90° + 30°) = cos 120° = -0.5000
- sin 30° = -0.5000
tan (90° + al = - cot a
tan (90°+30°)=tan 120° = - 1.7321
-cot 30°= -1.7321
Function values for select ed angles
90•
180°
270°
360°
Function
so·
180°
270°
360°
sin
0
+1
0
-1
0
tan
0
00
0
00
0
cos
+1
0
-1
0
+1
cot
00
0
00
0
00
Function
Relationships between the functions of an angle
sin2 a + cos2 a = 1
tan a • cot a = 1
t an a = sin a
cos a
cot a= cos a
sin a
cos a
Example: Calculation of t an a from sin a and cos a for a= 30°:
tan a= s ina/cosa = 0.5000/ 0.8660 • 0.5774
14
Mathematics: 1.2 Trigonometric Functions
Trigonometric functions of oblique triangles, Angles, Theorem of intersecting lines
Law of sines and Law of cosines
~
Law of sines
Law of cosines
a: b: c = sina: sin /l : siny
a2 = b 2 + c 2 - 2 . b. c • cosa
b2 = a2 + c 2 - 2. a• C • cosP
a
b
C
- -= - -=-sina sin /J siny
(
c 2 = a2 + b2 - 2 . a. b . cosy
Application in calculating sides and angles
Calculation of sides
usi ng the Law of sines
using the Law of cosines
Calculation of angles
using the Law of sines
using the Law of cosines
b-sina c -sina
a= - - - = - - sin/J
siny
a= ✓b2 + c2 - 2-b-c-cosa
.
a-sin{J a-siny
sma= - - - = - -b
c
cosa =
b = a-_sin{J = c -sin{J
sma
s ony
b = ✓a 2 +c2 -2-a- c-cos{J
sin /3 = b -sina = b-siny
cos{J =
c = ✓a 2 + b2 - 2-a -b -cosy
.
c -sina c -sin/J
smr = - - - = - -a
b
c=a-siny =b-siny
sin/J
sin a
8
C
cosy =
b2+c2-a2
2-b -c
a2+c2 - b2
2-a-c
a2+b2-c2
2-a-b
Types of angles
Corresponding angles
h I
gz
~
j
If two parallels g 1 and g 2 are intersected
by a straight line g, there are geometrical
interrelationships between the corresponding, opposite, alternate and adjacent angles.
I
I
I
I
I
a= {J
Opposite angles
I
{J = r5
Alternate angles
g,
I
a=r5
Adjacent angles
a + y= 180°
I
Sum of angles in a triangle
~
Sum of angles
in a triangle
In every triangle the sum of the interior
angles equals 180°.
I
a+{J+y= 180°
I
(
Theorem of intersecting lines
c,
~\\ ~i ~t
A
lb
b1
B
B,
If two lines extending fro m Point A are
intersected by two parallel lines BC and
B1C 1, the segment s of t he parallel lines
and the corresponding ray segments of
the lines extending fro m A form equal
ratios.
Theorem of intersecting
lines
a
a,
b
- =-
I
b,
[fil
C
=c,
I ~ =~
I
I
15
Mathematics: 1.3 Fundamentals
Using brackets, powers and roots
Calculations with brackets
Type
Explanation
Example
Factoring out
Common factors (divisors) in addition and subtraction are
placed before a bracket.
3· x + 5•X = x-(3+5) = 8 - x
Expanding
bracketed terms
Binomial
~ + ~=..!.·(3+ 5)
X X X
A fraction bar combines terms in the same manner as
brackets.
a+b -h = (a+b),!!_
2
2
A bracketed term is multiplied by a value (number, variable, another bracketed term). by multiplying each term
inside the brackets by this value.
5 - (b+ c) = 5b + 5c
(a+ b) • (c - d) = ac- ad+ be- bd
A bracket ed term is divided by a value (number, variable,
another bracketed term), by dividing each term inside the
bracket by this value.
(a+ b):c=a :c + b:c
formulae
A binomial formu la is a formula in which the term (a + b)
or (a - b) is multiplied by itself.
Muffiplication/division and
addition/subtracti-
In mixed equations, the bracketed term s must be solved
first. Then multiplication and division calculations are performed, and finally addit ion and subtraction.
on calculations
a- b
a
b
- 5- =5- 5
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
(a + b) • (a - b) = a2 - b 2
a • (3x - 5x) - b • ( 12y- 2y)
= a · (- 2xl - b • 10y
= -2ax- 10by
Powers
Definitions
a base;
x exponent;
y exponential value
Product of identical factors
Addition
a•= Y
a - a- a- a = a4
4 . 4 . 4 . 4 = 44 = 256
Subtraction
Powers w ith the same base and the same exponents are
treat ed like equal numbers.
Multiplication
Division
Powers w ith the same base are multiplied (divided) by
adding (subtracting) the exponents and keeping the base.
a4 • a2 =a . a• a - a- a · a = ;/'
Negative
exponent
Numbers w ith negative exponents can also be w ritten as
fractions. The base is then given a positive exponent and
is placed in the denominator.
m - 1 = _..!._ = ...!_
3a3 + 5 a3 - 4 a3
= a3 • (3 + 5 - 4) = 4a3
~ . 22 = 214+2) = ~ = 64
32 .,_ 33 = 312- 3) = :,1 = 1/3
m1
m
a-3 = ...!_
a3
Fractions in
exponents
Powers with fracti onal exponents can also be written as
roots.
Zero in
Every power w ith a zero exponent has the value of one.
exponents
4
a3 = ~
(m+ n) 0 = 1
a• .,. a4; 8 I4- 4t = 8 0 = 1
2° = 1
Roots
Definitions
x root's exponent;
a rad icand;
y root value
Signs
Even number exponents of the root give positive and
negative values, if the radicand is positive. A negat ive radicand results in an imaginary number.
~= ± 3
?./-9 = + 3i
Odd number exponents of the root give positive values if
the radicand is positive and negative values if t he radicand
is negative.
Addition
Subtraction
Identical root expressio ns can be added and subtracted.
Multiplication
Roots with the same exponents are multiplied (divided) by
taking the root of the product (quotient) of the radicands.
Division
✓
a +3 ✓
a-2 ✓
a= 2 ✓
a
16
Mathematics: 1.3 Fundamentals
Types of equations, Rules of transformation
Equations
Type
Explanation
Example
Variable
equation
Equivalent terms (formula terms of equal value ) form relationships between variables (see also, Rules of transformation).
v =n• d • n
(a+ b) 2 = a2 + 2ab+ b2
Compatible units
equation
Immediate conversion of units and constant s to an SI unit
in the result.
P = M •n . PinkW ~
9550'
'
n in 1/min and M in Nm
Only used in special cases, e.g. if engineering parameters
are specified or for simplification.
Single variable
equation
Calculation of t he value of a variable.
x+3=8
X=B - 3-5
Function
equation
Assigned function equation: y is a function of x wit h x as
the independent vari able; y as the dependent variable.
y = f (x)
~(- real numbers
The number pair (x,y) of a value table form the graph of
the function in the (x, y) coordinate system.
y = f (x) = b
Constant function
The graph is a line parallel to the x-axis.
-
-
Proportional function
y = f (x) = mx
The g raph is a straight line through the origin.
y = 2X
Linear function
y = f (x) = mx+ b
The graph is a st raight line with slope m and y intercept b
(example below).
y = 0.5x+1
Quadratic function
y = f (x) = x 2
Every quadrat ic
(example below).
linear
function
y:mx+b
function
example:
y- 0.5x+ 1
t: ~
,._
1
,/"
,,,_ 2 - 1
- 1
I
g raphs
as
a
parabola
quadratic
function
y:xz
m =0.5
b =1
1 2 3
x---
v= a 2x2 + a,x+ a0
\ti:7
-2 -1
-1
1 2
3
x ---
Rules of transformation
Equations are usually transformed to obtain an equation in which the unknown variable stands alone on the left side
of the equation.
The same number can be added or subtracted from bot h
sides.
In the equations x+ 5 = 15 and x+ 5-5 = 15-5, x has the
same value, i.e. the equations are equivalent.
x +5
= 15
x + 5 - 5 = 15- 5
X=10
y- c
=d
y - c+c =d+c
y = d+c
l- 5
Multiplication
Division
It is possible to multiply or divide each side of t he equation
by t he same number.
B· X = b
B· X b
~- = a
a
b
X
a
l+ a
Powers
The expressions on both sides of t he equations can be
raised to t he same exponential power.
Addition
Subtraction
✓
x = B+ b
l +c
I <l2
(-Jx)Z =(a+ b)2
x = a2 +2ab + b2
Roots
The root of the expressions on both sides of the equation
can be taken using the same root exponent.
x 2 = a+ b
(-Jx)2 = .Ja<lJ
X =±.Ja+b
If
17
Mathematics: 1.3 Fundam entals
'
Decimal multiples and factors of units, Interest calculation
Decimal multiples and factors of units
cf. DIN 1301-1 (2002-10)
SI units
Mathematics
Power of
ten
Name
10 18
,015
,012
,o9
106
103
102
,01
1o0
10-1
10-2
,o-3
10~
10-9
10-12
10-15
10-18
quintillio n
quadrillio n
trillion
bi llion
million
thousand
hundred
ten
one
1 000 000 000 000 000 000
1 000 000 000 000 000
1 000 000 000 000
1 000000000
1 000000
1 000
100
10
1
exa
peta
tera
giga
mega
kilo
hect o
deca
T
G
M
k
h
da
-
-
tenth
hundredt h
t housandth
millionth
billionth
t rillionth
quadrillionth
quintillionth
0.1
0.01
0.001
0.000 001
0.000 000 001
0.000 000 000 001
0.000 000 000 000 001
0.000 000 000 000 000 001
deci
centi
milli
micro
nano
pico
femto
atto
d
val ues
• 1
1
<1
..
>1
f
1
10 100 1000
I
f
I
I
,..
I
E
Examples
Meaning
Unit
1018 meters
10 15 meters
Em
Pm
TV
GW
MW
kN
hi
dam
m
p
1012 volts
109 watts
106 watts
103 newto ns
102 liters
101 meters
,oo meter
10·1 meters
10·2 meters
10·3 volts
dm
cm
mV
µA
nm
pF
fF
am
C
m
µ
n
p
f
a
10~ ampere
10-9 meters
10-12 farad
10· 15 farads
10-18 meters
Numbers greater t han 1 are expressed wit h positive exponents and num bers less t han 1 are expressed wit h negative exponents.
1
1000 100 10
.. ,
Prefix
Name
Character
M ultiplication f actor
Examples: 4300 = 4.3 • 1000 = 4.3 • 103
14638 = 1.4638 • 104
10-J , 0-2 10- 1 100 101 10 2 ,o3
0.07 = 1~ = 7 • 10-2
Simple interest
p
A
principle
amount accumulated
I
r
interest
interest rate per year
t
time i n days,
interest period
Interest
I
I=
1st example:
P = $2800.00; r = 6 ~ ; t = 1/ 2 a; I = ?
a
$ 84. 00
100%
I
1 interest year (1 a) = 360 days (360 d)
$2800.00-6!- - 0.5a
I =
P- r - t
100% • 360
360 d = 12 months
1 interest mont h = 30 days
2nd example:
P = $ 4800.00; r = 5.1~; r = 50d; I = ?
I =
$ 4800.00- 5.1% • 50 d
•
- $34.00
100% · 360 d
•
~
Compound interest calculation for o ne-time payment
p
A
pri nciple
amount accumulated
I
r
interest
interest rat e per year
n
q
time
compounding factor
Example:
P = $ 8000.00; n = 7years; r = 6.5%;A = ?
55
q =1 + - % = 1.065
100%
A = P • q" = $ 8000.00 . 1.0657 = $ 8000.00 - 1.553986
= S 12 431. 89
Amount accumulated
I
A = p . q"
I
Compounding factor
I
I
I
I
r
q = 1 + 100%
I
18
Mathematics: 1.3 Fundame ntals
Percentage calculation, Proportion calculations
Percentage calculation
Percent value
The percentage rate g ives the fraction of the base value in hundredths.
The base value is the val ue from which the percentage is to be calculated.
The percent value is t he amount representing the percentage of the base value.
P, percentage rate, in percent
Pv percent value
I
B., base value.
1st example:
P.=Bv·f':
V
I
1()()%
Percentage rate
Workpiece rough part weight 250 kg (base value); material loss 2%
(percentage rate); material loss in kg=? (percent value)
P. = Bv • P, = 250 kg• 2%
V
100%
100%
I
-1
5kg
P,. =.!3t_·100%
Bv
I
2nd example:
Rough weigh t of a casting 150 kg; weight after machining 126 kg;
weigh t percent rate(%) of material loss?
150 kg - 126 kg
P. =!',,__ · 100% =
• 100% = 16%
150kg
' Bv
l
Proportion calculations
-
Three steps for calculating direct proportional ratios
Example:
t
80
I Known data 160 elbow pipes weigh 330 kg.
Calculate the unit weight by dividing
2nd step: I
I
-
60
1st step:
~ 40
"i::
:::, 20
0
~
60 elbow pipes weigh 330 kg. What is the weight of
35 elbow pipes?
1 elbow pipe weighs
,.
100
200 kg 300
weig h t -
0
3rd step:
I
I
330 kg
60
I I
Calculate the total by multiplying
35 elbow pipes weigh
330 kg • 35 = 192_5 kg
60
---
Three steps for calculating inverse proportional ratios
Example:
t
2~0 I150
~ 100
_g so
0
0
I Known data I11 takes 3 workers 170 hours
Calculate the unit time by mult iplying
2nd step: I
I
'
~~
I
I
2
4
I
I
It takes 3 workers 170 hours to process one order. How m any
hours do 12 workers need to process t he same order?
I
I
It takes 1 worker 3 • 170 hrs
I
6 8 10 12 14
workers-
3rd step:
I
Calculate the total by d ividing
It takes12 workers
I
3 . 170 hrs= 42 5 hrs
12
•
Using the three steps for calculating direct and inverse proportions
Example:
660 workpieces are manufactured by 5 m achines i n 24 days.
1st application of 3 steps:
5 machines produce 660 workpieces in 24 days
1 machine produces 660 workpieces in 24 . 5 days
9 machines produce 660 workpieces in 24 . 5 days
9
How much time does it take for
9 m achines to produce
312 workpieces of the same
type?
2nd application of 3 steps:
9 machines produce 660 workpieces in 24 . 5 days
9
9 machines produce 1 workpiece in
~i,;0 days
2
9
9 machines produce 312 workpieces in
24-5 - 312
= 6.3 days
g. 660
19
M athematics: 1.4 Symbols, Units
Formula symbols, Mathematical symbols
Formula symbols
Formula
Meaning
symbol
cf. DIN 1304-1 (1994-03)
Formula
symbol
Meaning
Formula
symbol
Meaning
Length, Area, Volume, Angle
I
w
h
s
Length
Width
Height
Linear distance
r,R
d,D
A, s
V
Radius
Diameter
Area, Cross-sectional area
Volume
a,{!,y
D
Planar angle
Solid angle
Wave length
Force
Gravitational force, Weight
Torq ue
Torsional moment
Bending mo ment
Normal stress
Shear stress
Normal strain
Modulus of elasticity
G
µ,f
w
I
W,E
W.,E0
w,, E,
p
~
Shear modulus
Coefficient of friction
Section modulus
Second moment of an area
Work, Energy
Potential energy
Kinetic energy
Pow er
Efficiency
Frequency
Velocity
Angular velocity
a
g
a
Q,V,q,,
Acceleration
Gravitational acceleration
Angular acceleration
Volumet ric flow rate
,
Mechanics
m
rrl
m"
~
J
p
Pabs
Pamb
Pg
Mass
Linear mass density
A rea mass density
Density
Moment of inertia
Pressure
Absolute pressure
Ambient pressure
Gage pressure
F
fw,W
M
T
Mb
a
T
£
E
nme
t
T
n
Time, Duration
Cycle duration
Revolution frequency,
Speed
f,v
V, U
w
Electricity
Q
E
C
I
Electric charge, Quantity of
electricity
Electromotive force
Capacitance
Electric current
l
R
(l
y,x
Inductance
Resistance
Specific resistance
Electrical conductivity
X
z
"'N
Reactance
Impedance
Phase difference
Number of turns
Heat
r,e
/J. T, /J.t, MJ
t, ~
a1,a
Thermodynamic
t emperature
Temperat ure difference
Celsius temperature
Coefficient of linear
expansion
,
Q
a
k
Heat, Quant ity of heat
Thermal conductivity
Heat transition coefficient
Heat transmission
coefficient
,,,, a
H..,
Heat flow
Thermal diffusivity
Specific heat
Net calorific value
Luminous intensity
Radiant energy
a
C
Light. Electromagnetic radiation
E
llluminance
f
n
Focal length
Refractive index
I
Q,W
Acoustic pressu re
Acoustic velocity
lp
I
Acoustic pressure level
Sound intensity
4'
Acoustics
p
C
N
Mathematical symbols
Math.
symbol
~
=
...
""
=
*
~
<
s
>
~
+
- ,/, :, +
~
Spoken
approx. equals, around,
about
equivalent to
and so on, etc.
infinity
Loudness
Loudness level
cf. DIN 1302 (1999-121
Math.
symbol
a"
r
"r
equal to
not equal to
is equal to by definition
less than
!x i
J.
less than or equal to
greater than
g reater than o r equal to
plus
ti
-l:
minus
times, multiplied by
over, divided by, per, to
sigma {summation)
£Ix
I
II
C,
"
%
%o
Spoken
Math.
symbol
proportional
a to the n•th power, the n•th
power of a
square root of
n-th root of
log
lg
In
e
logarithm (general)
common logarithm
natur al logarithm
Euler number {e • 2.718281... )
absolute value of x
perpendicular to
is parallel to
parallel in the same direction
sin
cos
tan
cot
sine
cosine
tangent
cotangent
parallel in the opposite direction
angle
triangle
congruent to
0, 11, {}
delta x (difference between
two values)
percent, of a hundred
per mil, of a thousand
n
All
AB
a', a"
a,, a2
Spoken
parentheses, brackets
open and closed
pi (circle constant =-=
3.14159 ...J
line segment AB
arc AB
a prime, a double prime
a sub 1, a sub 2
20
Mathematics: 1.4 Symbols, Units
SI quantities and units of measurement
sI11 Base quantities and base units
e-
cf. DIN 1301-1 (2002-101, -2 (1978-021, -3 (1979-101
Electric
n-mo-
Amount of
substance
Luminous
intensity
kelvin
mole
candela
K
mol
cd
Length
Mass
lime
current
dynamic
temperature
Base
units
meter
kilogram
second
ampere
Unit
symbol
m
kg
s
A
quantity
11 The units for measurement are defined in the International System of Units SI (Systeme Int ernational d'Unites). It
is based on the seven basic units (SI units), from which other units are derived.
Base quantities, derived quantities and their units
Quantity
Unit
Name
!Symbol
Symbol
Relationship
Remarks
Examples of application
= 10 dm = 100 cm
= 1000 mm
1 mm = 1000µm
1 km = 1000 m
1 inch = 25.4 mm
In aviation and nautical applications
t he following applies:
1 international nautical mile = 1852 m
Length, Area, Volume, Angle
Length
I
A rea
A,
Volume
Plane
angle
(anglel
s
V
meter
m
1m
square meter
m2
1 m2
are
hectare
a
ha
cubic meter
m3
liter
I, L
1 m3
= 1000 dm3
= 1 000 000 cm 3
11 = 1 L = 1 dm3 = 10 di =
0.001 m 3
1 ml
= 1 cm3
Mostly for fluids and gases
seconds
'
1 rad = 1 m/m = 57.2957 .. 0 1 rad is the angle fo rmed by the intersection of a circle around the center of
= 180°/n
1 m radius w ith an arc of 1 m length.
10
= ; rad= 60'
In technical calculations instead of
1 0
a = 33° 17' 27.6", better use is a =
1'
= 1°/60 = 60"
33.291°.
1'
= 1'/60 = 1°/3600
Q
steradian
sr
1 sr
m
kilogram
gram
kg
g
1 kg
1g
megagram
Mg
t
a,{J, y ... radian
degrees
rad
0
minutes
Solid angle
Symbol Sonly for cross-sectional
= 10000 cm2
areas
= 1 000000 mm2
2
1a
= 100 m
1 ha
= 100 a = 10000 m 2 A re and hectare only for land
100 ha = 1 km 2
= 1 m2/m2
An object whose extension measures
1 rad in one direction and perpendicularly to this also 1 rad, covers a solid
angle of 1 sr.
Mechanics
Mass
metric t on
= 1000 g
- 1000 mg
1 metric t = 1000 kg= 1 Mg
0.2 g
= 1 ct
Mass in the sense of a scale result or a
weight is a quantity of t he type of mass
(unit kg).
Mass for precious stones in carat (ct).
Linear mass
density
m'
kilogram
per meter
kg/m
1 kg/m = 1 g/mm
For calculating the mass of bars, profiles, pipes.
Area mass
m'
kilogram
per square
kg/m2
1 kg/m 2 = 0.1 g/cm2
To calculate the mass of sheet metal.
kg/m3
1000 kg/m 3 = 1 metric t/m3
= 1 kg/dm 3
= 1 g/cm3
= 1 g/ml
= 1 mg/mm3
The density is a quantity independent
of location.
density
meter
Density
{!
kilogram
per cubic
met er
21
Mathematics: 1.4 Symbols, Units
SI quantities and units of measurement
Quantities and Units (continued)
Quantity
Symbol
Unit
Name
Remarks
Examples of application
Relationship
!Symbol
Mechanics
J
kilogram x
square
meter
kg - m 2 The following applies for a
homogenous body:
J =e- il - V
Force
F
newton
N
Weight
FG, G
M
newton x
N-m
Mb
meter
Moment
of inertia, 2nd
Moment of
mass
Torque
Bending mom.
Torsional
Momentum
The force 1 N effects a change in vel= 1 ~ = 1 .::!.
s
m
ocity of 1 m/s in 1 s in a 1 kg mass.
3
1 MN = 10 kN = 1000000 N
1N
2
1 N • m is the moment that a force of
1 N effects w ith a lever arm of 1 m.
kg- m/s 1 kg-m/s=1N - s
The momentum is the product of the
mass times velocity. It has the direction
of the velocity.
1 N - m = 1 kg •2m
s
T
p
kilogram x
meter
per second
Pressure
The moment of inertia (2nd m oment of
mass) is dependent upon the t otal
mass of the body as well as its form
and the position of the axis of rotation.
p
pascal
Pa
Mechanical
stress
O, T
newton
per square
millimeter
N/mm2
Second
moment of
area
I
meter to the
fourth power
centimeter
to the fourth
power
m•
1 Pa - 1 N/m 2 = 0.01 mbar
1 bar = 100000 N/m2
= 10 N/cm 2 = 105 Pa
1 mbar = 1 hPa
1 N/mm2 = 10 bar= 1 MN/m2
= 1 MPa
1 daN/cm2 =·0.1 N/mm2
Pressure refers to th e force per unit
area. For gage pressure the symbol p 9
is used (DIN 1314).
1 bar - 14.5 psi (pounds per square
inch)
1 m 4 = 100000000 cm4
Previously: Geomet rical moment of
inertia
cm4
Energy, Work,
Quantity of
heat
E,W joule
J
1 J = 1 N-m = 1 W-s
= 1 kg, m 2/s2
Joule for all forms of energy, kW - h
preferred for electrical energy.
Power
Heat flux
p
<P
watt
w
1W = 1 J/s=1N,m/s
= 1V-A = 1m2 -kgts3
Power describes the work which is
achieved w ithin a specific time.
t
seconds
minutes
hours
day
year
s
min
h
d
1 min= 60 s
1 h = 60 min = 3600s
1 d = 24 h = 86400 s
3 h means a time span (3 hrs.).
3h means a point in time (3 o'clock).
If points in time are w ritten in mixed
form, e. g. 3h24m10•, the symbol m in
can be shortened to m .
lime
Time,
Time span,
Duration
a
=1 cycle in 1 second.
Frequency
f, V
hert2
Hz
1 Hz = 1/s
1 Hz
Rotational
speed,
Rotational
freauencv
n
1 per second
1/s
1 per minute
1/min
= 60/min = 60 m in-1
1
1/min = 1 min- 1 = - 60s
The number of revolutions per unit of
time gives the revolution frequency,
also called rpm.
Velocity
V
meters per
second
meters per
mis
1 m/s
Nautical velocity in knots (kn):
1 kn = 1.852 km/h
1/s
= 60 m/min
= 3.6 km/h
m/m in 1 m/min=~
60 s
1m
kilomet ers per km/h
1 km/h
= 3.6s
hour
L
minute
miles per hour = 1 mile/h = 1 mph
1 mph - 1.60934 km/h
Angularvelocity
w
1 per second
radians per
second
1/s
rad/s
w =2 n • n
For a rpm of n = 2/s the angular velocity w = 4 ,r/s.
Acceleration
a, g
meters per
second
squared
m/s2
1 m/s2 = 1 m/s
1s
Symbol g only for acceleration due to
gravity.
g = 9.81 m/s2 ~ 10 mts2
"'
22
Mathematics: 1.4 Symbols, Units
SI quantities and units of measurement
Quantities and units (continued)
Quantity
Unit
Name
Symbol
Symbol
Remarks
Examples of application
Relationship
El-.:ity and Magnetism
Elec:tric CUITent
Elect romotive
force
Electrical
resistance
Electrical
conductance
I
E
ampere
volt
A
V
1 V = 1 W/ 1 A = 1 J/C
R
o hm
Q
1 Q = 1 V/1 A
G
siemens
s
1 S = 1 A/1 V = 1/Q
{!
ohmx
meter
siemens
per meter
Q-m 1cr6Q-m = 1 Q. mm2/m
Specific
resistance
Conductivity
y,x
Frequency
f
The movement of an electrical charge is
called current. The electromotive force
is equal to the potential difference bet·
ween two points in an electric field. The
reciprocal of the elect rical resistance is
called the electrical conductivity.
"
Sim
hertz
Hz
1 Hz
= 1/s
1000 Hz 1 kHz
Frequency of public elect ric utility:
EU 50 Hz, USA/Canada 60 Hz
1J
=1W-s= 1 N - m
1 kW • h = 3.6 MJ
1 W-h = 3.6 kJ
In atomic and nuclear physics the unit
eV (electron volt) is used.
for alternating current:
The angle between current and voltage
in inductive or capacitive load.
2
Electrical energy
w
joule
J
Phase
difference
\0
-
-
1 . !l-mm2
e= - '" - - m
1.
m
x = - in - - !l - mm2
e
COS,p = ...E_
U -1
Elect. field strength
Elect. charge
Elect. capacitance
inductance
E
Q
C
L
volts per meter Vim
coulomb
C
farad
F
henry
H
Power
Effective power
p
watt
IC =1A-1s;1A -h=3.6kC E= f._ C = Q
1F = 1 C/V
1 H = 1 V • s/A
a·
u· 0 = 1 • t
w
1 W = 1J/s = 1 N-m/s
= 1 V-A
In electrical power engineering:
Apparent power S in V • A
Kelv in (K) and degrees Celsius (°C) are
used for temperatures and temperature differences.
t = T - T0 ; T0 = 273.15 K
degrees Fahrenheit (°F): 1.8 °F = 1•c
Thermodynamics and Heat transfer
Thermodynamic
temperature
Celsius
temperature
r,e
kelvin
K
OK =-273.15°C
t, {/
degrees
Celsius
·c
o•c = 273.15 K
o•c = 32 °F
Quantity of
heat
Q
joule
J
1 J = 1W -s=1 N-m
1 kW · h = 3600000 J = 3.6 MJ
1 kcal " 4.1868 kJ
joule per
kilogram
Jo ule per
cubic meter
J/kg
1 MJ/kg = 1000000 J/kg
Hnet
J/m3
1 MJ/m3 = 1000000 J/m3
Thermal energy released per kg fuel
minus the heat of vaporization of the
water vapor contained in the exhaust
gases.
Net calorific
value
0 ' F = -17.77°C
Non-SI units
Length
Area
1 inch = 25.4 mm
1 foot =0.3048m
1 yard =0.9144m
1 nautical
m ile = 1.852 km
1 mile = 1.609 km
1 sq.in = 6.452 cm 2 1 cu.in
= 16.39 cm 3
1 sq.ft = 9.29 dm2 1 cu.ft
= 28.32 dm3
1 sq.yd = 0.8361 m 2 1 cu.yd
=764.6 dm3
1 US gallon = 3.785 dm3
Pressure
1 Imp. gallon = 4.536 dm3
1 barrel
= 158.8dm3
1 bar = 14.5 psi
Volume
Energy, Power
Mass
1 oz
= 28.35 g
1 PSh = 0.735kWh
1 lb
= 453.6 g
1 PS
= 735W
1 metric t = 1000 kg 1 kcal = 4186.8Ws
1 short ton= 907.2 kg 1 kcal = 1.166Wh
1 kpm/s = 9.807 W
1 carat
= 0.2g
1 Btu
= 1055 Ws
1 hp
= 745.7W
Prefixes of decimal factors and multiples
Prefix
pico
nano
micro
milli
centi
deci
deca
hect o
kilo
mega
giga
Prefix symbol
p
n
µ
m
C
d
h
k
M
G
T
Power of ten
10-12
10- 9
10-6
10-J
10-2
10-1
da
101
102
103
,as
109
1012
-
Factor
1 mm = 10-3 m = 1/1000 m ,
1 km = 1000 m,
Multiole
1 kg= 1000 g,
tera
-
1 GB (Gigabyte)= 1000000000 bytes
23
Mathematics: 1.5 Lengths
Calculations in a right triangle
The Pythagorean Theorem
In a right triangle the square of the hypotenuse is equal
to the sum of the squares of the two sides.
a
b
side
c
hypotenuse
side
Square of the
hypotenuse
I
c2 = a2 + b2
1st example:
c = 35 mm; a = 21 mm; b = ?
b = ,lc2-a2 =,/(35 mm)2 -(21 mml2 = 28mm
,2
2nd example:
Length of the
hypotenuse
1 c= ✓a4b2
CNC program with R = 50 mm and I - 25 mm.
K=?
c2 =a' +b2
Length of the sides
R2 = / 2 + K 2
K = ,!R2 - 12 = ,/502 mm2 - 252 mm2
a = ✓c2 -b2
K = 43.3mm
Euclidean Theorem (Theorem of sides)
The square over one side is equal in area to a rectangle
formed by the hypotenuse and the adjacent hypotenuse
segment.
a, b
sides
c
hypotenuse
p, q
hypotenuse segments
Example:
A rectangle with c = 6 cm and p = 3 cm should be
changed into a square wit h the same area.
C·Q
Square over the side
~
~
How long is the side of the square a?
C•p
a2 = c •P
a = F P = ,!6cm • 3cm =4.24cm
Pythagorean theorem of height
The square of height his equal in area to the rectangle of
the hypotenuse sections p and q.
h
p, q
q
heig ht
hypotenuse sections
Example:
Right triangle
p = 6 cm; q = 2 cm; h = ?
p-q
p
h' = p • q
h = ~ = ✓6cm-2cm = ✓12cm2 = 3.46cm
Square of the height
I
h2=p-q
24
Mathematics: 1.5 Lengths
Division of lengths, Arc length, Composite length
Sub-dividing lengths
Edge distance = spacing
I total length
p spacing
n number of holes
EKample:
I = 2 m; n = 24 holes; p = ?
p = - 1- = 2000mm = BOmm
n+ 1
24 + 1
total length
p spacing
Edge distance " spacing
p
p
p
number of holes
n
a, b edge distances
p
..."'
I
.
Example:
I-IH bl
p=~
1=1950 m m; a= 100mm; b = 50 mm;
n = 25 holes; p = ?
1- (a + bl 1950mm- 150mm
p =~=
25 - 1
Subdividing into pieces
75mm
bar length
s saw cutting w idth
z number of pieces Ir remaining length
15 piece length
I,
EKample:
I = 6000mm; 15 = 230 mm; s = 1.2 mm; z = ?;I, =?
6000
z =_ I _ =
mm
15 + s 230 mm+ 1.2 mm
I,
s
s
25. 95 = 25 pieces
I, = 1-z - (I, +s)=6000 mm-25 - (230 mm+ 1.2 mm)
= 220mm
Remaining length
I
l r = I - z • (/5 + s)
Arc length
EKample: Torsion spring
18 arc length
r radius
a angle at center
d d iameter
Arc length
l =n• r •a
a
180°
~Example:
r = 36 mm; a = 120"; 18 = ?
1 = " . r • a = " • 36 mm · 120"
•
180"
180°
75_36 mm
l = rt· d • a
a
3500
Composite length
D outside d iameter
dm mean diameter
11, 12 section lengths
a
angle at center
inside diameter
r thickness
L composite length
d
Example (com posite length, picture left):
D= 360 mm; t= 5 mm; a = 270°; 12 = 70 mm;
dm = ?; L = ?
dm=D- t = 360mm - 5mm = 355mm
,,
L
= 1, + 12 = 1l • dm. a + 12
360
= ". 355 mm. 2700 + 70 mm= 906.45mm
360"
Composite length
25
Mathematics: 1.5 Lengths
Effective length, Spring wire length, Rough length
Effective lengths
D
d
dm
t
I
a
Circular ring sector
outside diameter
inside diameter
mean diameter
t hickness
effective length
angle at center
Effective length
of a circular ring
I
I = re · dm
r~~::;:
Effective length of a
Example (circular ring sector):
D = 36 mm; t = 4 mm; a = 240°; dm =?; I = ?
Mean diameter
dm= D-t = 36 mm - 4mm = 32mm
1 = n-dm •a = n-32 mm -240"
360"
360"
6J.02mm
dm = d+ t
D
Spring wire length
Example: Compression spring
Effective length
of the helix
effective length of the helix
Dm mean coil diameter
number of active coils
l=:rc· Dm•i+
2-:rc• Dm
Example:
Dm = 16 mm; i = 8.5; / =?
l - n•Dm•i+2•1t·Dm
= rr • 16 mm • 8.5 + 2 • rr • 16 mm = 528 mm
Rough length of forged parts and pressed parts
When forming without scaling loss the volume of the rough
part is the same as t he volume of the finished part. If there
is scaling loss or burr formation, this is compensated by a
factor that is applied to the volume of the finished piece.
V8 volume of the rough part
V8 volume of the finished part
q addition factor for scaling loss o r loss due to burrs
A 1 cross-sectional area of the rough part
A2 cross-sectional area of the finished part
/1
initial length of the addition
/2
length of the solid forged part
Example:
scaling loss
A cylindrical peg d ~ 24 mm and /2 ~ 60 mm is pressed
onto a flat steel workpiece 50 x 30 mm. The scaling
loss is 10 %. What is the initial length /1 of the forged
addition?
v. = V0 - (1+q)
A 1 - / 1 = A2 · 12 • (l + q)
A2 • 12 • (1+q)
A,
rr . (24 mm)2 • 60 mm. (1 + 0.1)
4 - 50 mm - 30 mm
20mm
Volume without scaling loss
Volume with scaling
loss
Va= Ve· (1 + q)
26
Mathematics: 1.6 Areas
Angular areas
Square
A
/
area
length of side
d
length of diagonal
Area
A=/2
Example:
Length of diagonal
I= 14 mm; A = 7; d = ?
A = 12 = (14 mm) 2 ~ 196 mm2
d = fi_ - I= fi_ - 14 mm= 19.8 mm
I
d=fi-1
Rhombus (lozenge)
A
I
area
length of side
w w idth
Area
A=l • w
Example:
I = 9 mm; w = 8.5 mm; A = ?
A s / . W = 9 mm -8.5 mm =76.5mm2
Rectangle
A
w width
d length of diagonal
area
length
Example:
I= 12 mm; w= 11 mm; A = ?; d = ?
A = I- w = 12 mm• 11 mm = 132mm2
d = Jt 2 + w 2 = J(12 mm)2 + (11 mm)2 = J265 mm2
= 16.28 mm
Area
I
I
A=/- w
Length of diagonal
d=~
Rhomboid (parallelogram)
A
area
length
w width
Area
A=I• w
Example:
l=36mm; w = 15 mm;A =?
A = I• w = 36mm - 15mm = 540mm2
Trapezoid
A
11
12
area
longer length
shoner length
Im average length
w width
Area
A = ,, +12 •W
2
Example:
/ 1 = 23 mm; /2 = 20 mm; w = 17 mm; A = ?
A = 11 + t, · W= 23mm +20mm _17 mm
2
= 366.5 mm2
2
Triangle
A
area
length of side
w width
1-w
A=-
Example:
2
11 = 62 mm; w = 29 mm; A = 7
A= ~
2
Area
= 62mm • 29mm
2
B99mm2
Mathematics: 1.6 Areas
27
Triangle, Polygon, Circle
Equilateral triangle
area
Diameter of
Area
diameter of inscribed circle circumscribed circle
length ofside
I D=~ I= 2. d , ..
h height
0 diameter of circumscribed
circle
Exampla:
Diameter of
A
d
/
✓3.
,-A-=-~-_-✓
_3__/-2-
I = 42 mm; A = ?;
A =.!. . ./3 ./2 = .!. . ./3 -(42mml2
4
4
D
= 763.9 mm2
Regular polygons
.A
/
0
d
n
a
p
Diameter of
area
inscribed circle
Area
length of side
diameter of circumscribed
circle
,..___
d_=_-J_o_2___12__.I l,.__A_ =
_ _n _
-~_·_d_
diameter of inscribed circle
Diameter of
no. of vertices
angle at center
vertex angle
u_:: _r~
_: _ 2
_ :_ircl
-/ 2
c.....ir_c_
_e__.l
__.
r:~,:r 1
~ I
Example:
Hexagon with 0 = 80 mm;/=?; d= ?; A = ?
• ( -;,180") = 80mm-sm
• ( 180') = 40mm
I = O -s,n
6
d = J OL / 2 = J6400 mm2 - 1600 mm2 = 69.282 mm
A = n-1-d = 6- 40mm • 69.282 mm
4
4
41
56.92 mm2
Calculation of regular polygon using table values
No. of
Diameter of
circumscribed circle D ...
Area A ..
3
4
0.325 • 0 2
0.500 · 0 2
1.299-d2
1.000. d 2
0.433 • /2
1.000 · ,2
5
6
8
10
12
0.595 • 0 2
0.649 • 0 2
0.707 . 0 2
0.735 · 0 2
0.750 · 0 2
0.908 • d 2
0.866- d 2
0.829 . d 2
0.812 • d 2
0.804 · d 2
1.721 - 12
2.598 • 12
4.828 • 12
7.694 · ,2
11.196 - /2
1.154, /
1.414 . /
1.702. /
2.000. /
2.614. /
3.236 • /
3.864 . /
2.000 , d
1.414 - d
1.236 • d
1. 155 • d
1.082 . d
1.052 • d
1.035 - d
Example: Octagon w ith / = 20 mm
A = ?; 0 = ?
A q 4.828 • 12 = 4.828 , (20 mm)2 = 1931.2 mm2 ;
Diameter of
inscribed circle d ...
0.578, I
1.000 • I
1.376. /
1.732 • /
2.414 • /
3.078. /
3.732. /
Length of side I ~
0.500 • 0
0.707. 0
0.867. 0
0.707 • 0
1.732. d
1.000. d
0.809 • D
0.866 • 0
0.924 . 0
0.951 • 0
0.966, 0
0.588 • 0
0.500 • 0
0.383 • 0
0.309 • 0
0.259, 0
0.727 • d
0.577 • d
0.414 . d
0.325 • d
0.268- d
0 ~ 2.614. I= 2.614. 20 mm= 52.28 mm
Circle
A
d
area
diameter
C circumference
Example:
Area
n-d2
A =-4
d = 60 mm; A= ?; C = ?
Circumference
A = n,d2 = n• (60 mm)2 2827 mm•
4
4
C = n -d = n -60 mm = 188.5mm
28
Mathematics: 1.6 Areas
Circular sector, Circular segment, Circular ring, Ellipse
Circular sector
A
d
/0
chord length
area
diameter
arc length
r
a
Area
radius
angle at center
Example:
d = 48 mm; a= 110°; /8 = 7; A= 7
rt •r •a
Chord length
1t•24mm-110"
l 80"
46.1 mm
10 = l 80"
=
A =~
2
46.1 mm- 24mm
2
~
I~_ _
,=
_ _2_-_, _· _si_n_i _ _
S53mm2
r e lengt~
= n. r . a
a
180"
d
Circular segment
Circular segment with a :5180°
I
):
w w idth of segment
r radius
A
d
area
diamet er
/8
arc length
I
chord length
Example:
a
Area
angle at center
A = /0 -r -1- (r- wl
2
r= 30 mm ; a = 120°; I= 7; W= 7; A=?
Chord length
I •2•r -sin~- 2-30mm-sin l20" - 51.96 mm
2
2
/= 2 -r-sin~
w -~•tan~- S1.S6mm_tan l20" - 14.999mm- 15 mm
2
4
2
4
2
2
d
A• 1t·d -~-1-(r -w)
4 "!HJ'
2
Jf•(60mm)2 120" 51.96mm-OOmm - 15 mm)
_ _ _ 4_ _ ,-m_
2
1= 2 -,Jw-(2- r - w)
Height of segment
I
a
w = -- tan-
- 562.8 mm'
2
Radius
w /2
r =-+ - 2 8- w
4
w = r -J, 2-~
Circular ring
A area
D outside diameter
d inside diameter
Area
dm mean
diameter
w
w idth
Example:
0 = 160 m m ; d = 125 mm; A = 7
A - ~ -(0 - d
2
2
4
=7834 mm2
~-(1602 mm - 125 mm
2
) -
2
2
)
4
Ellipse
A area
D lengt h
Example:
d diameter
C Circumference
D = 65 mm; d = 20 mm; A = 7
A =" · D-d =" • 65mm-20mm
4
4
= 1021mm2
Area
- - - - -Jt
- -D
- -•d- - - .
A =- 4
Circumference
29
Mathematics: 1.7 Volume and Surface area
Cube, Square prism, Cylinder, Hollow cylinder, Pyramid
'
Cube
V volume
As surface area
Volume
length of side
Example:
Surface area
I = 20 mm; V = ?; As = ?
V = 13 = (20 mm)3 = 8000 mm3
A, = 6 . / 2 = 6 • (20 mm)2 = 2400 mm2
Square prism
V volume
As surface area
/ length of side
Volume
h height
w width
Surface area
Example:
l ~ 6cm; w ~ 3cm;h=2cm;V=?
V=I. w- h=6cm-3cm-2cm = 36cm 3
A 5 = 2 • (/ • w + I • h + w • h)
Cylinder
V volume
d diameter
h height
As surface area
Ac cylindrical surface area
Volume
Example:
Surface area
rc-d 2
V = - - •h
4
--<::
d = 14 mm; h= 25 mm; V= 7
I A· =1t·d·h+2·~ 1
V = 1t·d' -h
4
n- (14mm)2 _
4
25
mm
Cylindrical surface area
I
=3848mm 3
Ac =1t ·d•h
Hollow cylinder
V volume
A, surface area
D, d
h
diameter
Volume
height
Example:
--<::
0 = 42 mm; d = 20 mm; h • 80mm;
V=?
V = n-h ·(02 - d 2 )
4
= n-80mm -(422 mm2 - 202 mm2)
4
= 116703mm3
Surface area
As = re - {D + d) • [ i-(0-d) + h]
Pyramid
V volume
h height
h, slant height
length of base
/1 edge length
w width of base
Example:
Volume
1-w·h
V =-3
Edge length
l = 16mm;w= 21mm;h=45mm; V=?
V ='•w•h= 16mm - 21mm-45mm
3
3
= 5040mm 3
Slant height
30
Mathematics: 1.7 Volume and Surface area
Truncated pyramid, Cone, Truncated cone, Sphere, Spherical segment
Truncated pyramid
V
volume
t,. /2 lengths of
base
h1
A1 area of base
surface
A2 top surface
slant height
height
h
w 1, ""'2 widths
Volume
Example:
/ 1 =40 mm;/2 = 22 mm; w 1 = 28mm;
w2 = 15 mm; h = 50 mm; V = ?
Slant height
V = !!_ ·(A,+ Ai +,}A,- Ai)
3
50mm
r,:;;;;:;-;;;:;
= - - •11120+ 330 + vl 120. 330)mm2
3
= 34299mm3
Cone
V volume
Ac conical surface area
d
diameter
h
h5
height
slant height
Volume
1t-d2 h
V =-- ·4
3
Conical surface area
Example:
d=52mm;h=110mm; V = ?
V = n·d2 .!!.
4
3
n -(52mm)2 110mm
4
3
= nfI70mm3
Truncated cone
V volume
d
diameter
of top
height
slant height
Ac conical surface area
D
diameter
of base
h
h,
Volume
n- h
V = - ·(D2 +d2 +D-d)
12
I
Conical surface area
Example:
D= 100 mm; d= 62 mm; h=B0 mm; V=?
V = 1t•h (0 2 +d2 + D ·d)
12
= 1t -80mm -(1()()2 +622 + 100-62)mm2
12
= 419800mm 3
A c = ~·(O+d)
0
r
n:~:gJ:2 + (
¥f
Sphere
V volume
A, surface area
d
diameter of sphere
Volume
it. d3
Example:
V =--
6
d~9 mm; V = ?
Surface area
V= " ·d3_n -(9mm>3 = 382mm3
6
6
Spherical segment
'~
''
tTI
,
d
V volume
A 1 lateral surface area
A 5 surface area
Example:
d
h
d = 8 mm; h = 6 mm; V = ?
V = rr•h2•(~ -~)
= n . 6 2 mm2 · ( 8~m- 6~m)
= 226mm3
diameter of sphere
height
Volume
Surface area
I As=
1t • h • (2 • d- h)
Lateral surface area
Ai= 1t ·d•h
I
31
Mathematics: 1.8 Mass
Volumes of composite solids, Calculation of mass
Volumes of composite solids
Total volume
V total volume
V1, V2 partial volumes
Example:
Tapered sleeve; D = 42 mm; d = 26 mm;
d, = 16mm; h = 45mm; V = ?
V, =~- (D2 + d 2 + D -dl
12
45
= n- mm -(422 +262 +42 -26) mm2
12
= 41610mm3
V2 = n- d,2 -h = n- 162 mm2 -45mm = 9048 mm'
4
4
V = v, - V2 = 41610mm3 - 9048 mm3 = 32562 mm3
Calculation of mass
Mass, general
m mass
V volume
(!
density
Mass
Example:
Workpiece made of aluminum;
V = 6.4 dm3; £! = 2.7 kg/dm3; m = ?
m=V•(! = 6.4dm3 2.7 ~
dm3
= 17.28kg
Values for density of
solids, liquids and gases:
pages 116 and 117
_J
Linear mass density
, . kg
mm-
m mass
m' linear mass density
length
m
Linear mass density
I
m= m'-1
Example:
Steel bar with d = 15 mm;
m' = 1.39 kg/m; / = 3.86 m; m =?
m =m'- 1=1.39 ~-3.86m
m
= 5. 37kg
Application: Calculating
the mass of profile sections, pipes, w ires, etc.
using the table values for
m'
Area mass density
m mass
A area
m " area mass density
Area mass density
I
m = m"-A
Example:
Steel sheet
t = 1.5 mm; m' = 11.8 kg/m 2;
A = 7.5 m 2 ; m =?
m = m "- A = 11.8 k~•7.5m2
m
=88. Skg
Application: Calculating
the mass of sheet metal,
foils, coatings, etc using
the table values for m "
32
Mathematics: 1.9 Centroids
Centroids of Lines and Plane Areas
Centroids of lines
I, / 1 , /2
lengths of the lines
C, C1 , C2 centroids of the lines
x,,, x 1, x 2 hori zontal distances of the line centroids from the y-axis
Ye, y1, y2 vertical d istances of the line centroids from the x-axis
Line segment
I:
x,
Composite continuous lines
fc
x,
.I
y
General
Circular arc
r ./
Y, = -
f,;
c
/ -180°
Yc = - - lt•
[ O l ---\---=--- - - - r
•
I
'·
1;'
I
a
,2
+-·-
~
- -- -~ -
X
Semicircular arc
I Ye "" 0.6366 • r
= /1 . X1 + /2 • X2 + ...
X
I
C
J,+/2+ ...
Quarter circle arc
Calculation of I and /8 :
Page 28
Ye ss 0.9003 • r
Centroids of plane areas
A, A,, A 2 areas
C, C1, C2 centroids of the areas
x,,, x1, x2 horizontal distances of the area centroids from the y-axis
Ye, y,, y2 vertical distances of the area centroids from the x -axis
Rectangle
Triangle
Yc=
Circular sector
General
w
3
Composite areas
2-r-l
Yc=JT
yf--_ ___x..c
1 _ _ ___,
a
Semi-circle area
I Ye "" 0.4244 • r
I
A,
Quarter circle area
Ye "" 0.6002 • r
x,
X
Circular segment
f,;
/3
Ye = 12-A
Table of Contents
33
2 Physics
t~
2.1
Motion
Uniform and accelerated motion . ... ..... ... .. 34
Speeds of machines . . .. ..... . ..... . .. ....... 35
2.2
Forces
Adding and resolving force vectors ............ 36
Weight, Spring force ........................ 36
• Lever principle, Bearing forces .... ... ..... ... . 37
Torques, Centrifugal force ...... ... ...... ... .. 37
2.3
Work, Power, Efficiency
Mechanical work ............................ 38
Simple machines ... . . ...... .... . ...... . .... 39
Power and Efficiency ........................ 40
2.4
Friction
Friction force ......... . .......... ....... .... 41
Coefficients of friction .. .. ...... .. . .......... 41
Friction in bearings ..... ....... ... . .......... 41
2.5
Pressure in liquids and gases
Pressure, definition and types ................. 42
Buoyancy .................. . ............... 42
Pressure changes in gases ................... 42
2.6
Strength of materials
Load cases, Load types . . . . . . . . . . . . . . . . . . . . . . 43
Safety factors, Mechanical strength properties .. 44
Tension, Compression, Surface pressure .. ..... 45
Shear, Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Bending, Torsion .................. .. ........ 47
Shape factors in strength ... .............. ... 48
Static moment, Section modulus, Moment of inertia . 49
50
Comparison of various cross-sectional shapes
2.7
Thermodynamics
Temperatures, Linear expansion, Shrinkage ..... 51
Quantity of heat ... ........ ................. 51
Heat flux, Heat of combustion .. . ............. 52
2.8
Electricity
Ohm's Law, Conductor resistance ............. 53
Resistor circuits ............ . ................ 54
Types of current . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Electrical work and power . . . . . . . . . . . . . . . . . . . . 56
.,, 20
2
3
4 s 5
tim e f ~
A
I
.I J
34
Physics: 2.1 Motion
Uniform motion and uniformly accelerated motion
Uniform motion
LinMrmotion
Displacement-time diagram
v
t
s
velocity
time
d isplacement
Example:
v=48 km/h; S= 12 m; I m?
1!:':' = 60 ..!:':'._=3.6 km
s
min
h
Conversion: 48 km = 4BOOOm = 13.33!:':'
h
3600s
s
4 s 5
2
3
time f - - -
1 km = 16.667..!:':'._
h
min
t =~= ~ = 0.9 s
V
13.33m/S
= 0.2778!:':'
s
Circular motion
v
circumferential velocity,
cutting speed
n
r
rotational speed
radius
w
angular velocity
d
d iameter
Example:
Pulley, d= 250 mm; n= 1400 m in- 1;
V=?;w=]
1400
Conversion: n = 1400min- 1 =
= 23.33s- 1
60s
v = n • d • n = n .Q.25m-23.33s-1 = 18.3!!:'.
Circumferential
~
~
Angular
velocity
I
w =2 ·n• n
s
w =2 • n • n = 2 • n -23.33s- 1 = 146.6s-1
For a cutting speed of a circumferential velocity
see page 35.
Uniformly accelerated motion
U.-r acc.lerated motion
Velocity-time diagram
3
4 s 5
time f - - Displacement-time diagram
t"'
t erminal velocity (acceleration),
or initial velocity (deceleration)
s
a
displacement
acceleration
t
g
Object. free fall from s = 3 m; v = ?
a = 9 = 9.81~
s2
Conversion: v =80km = 80000m = 22.22!:':'
h
3600s
s
"'
00
4 s 5
3
time f - - -
v =~
v2
(22.22 m/s)2
5
=~
2-7m/s2
Displacement due to
acceleration/
deceleration
1
S=- · V·t
2
Vehicle, v = 80 km/h; a= 7 m/s2 ;
Braking distance s = ?
4
F::77
~
l~example:
2nd example:
8
The following applies
to acceleration from
rest or deceleration to
rest:
Terminal or initial
time
gravitational
acceleration
5
~
'o
v
v = ~= -h-9.81 m/s2 -3m = 7.7 !!:'.
12
m
-:::.,
E
~
The increase in velocity per second is called acceleration; and a decrease is deceleration. Free fall is
uniformly accelerated motion on which gravitational
acceleration g is acting.
s = .!. a· t 2
2
v2
S = --
2 -a
35.3m
35
Physics: 2.1 Motion
Speeds of machines
Feed rate
Turning
9
Feed rate
for drilling, turning
v1 feed rate
n
rotational speed
feed
f, feed per cutting edge
N number of cutting edges, o r
num ber of teeth on the pinion
P th read pitch
p pitch of rack and pinion
..
1st example:
Screw
drive
Cylindrical milling cutter, z = 8; f, = 0.2 mm;
n s 45/min; vr = 7
v 1 =n-f,-N= 45 _2_,0,2 mm . 8 = 72 m '."
mm
mm
~
I
v1 = n-f
Feed rate
for milling
I
v, = n-ft-N
,....,,,.,,,,,,.,.,..._ _...,
v,
2nd example:
Feed drive with threaded spindle,
P = 5 mm; n = 112/min; Vf = ?
n
Threaded spindle
with pitch P
Rack and
pinion
Feed rate
for screw drive
v 1 = n P = 112 _2_-5 m m = 560mm
min
min
3rd example:
Feed rate for
rack and pinion
Feed of rack and pinion,
n = 80/min; d= 75 mm; v1 =?
v 1 =n•d •n= n• 75 mm,80_2_
min
= 18850~ = 18.85 ~
min
min
z
v1 =n-d-n
Cutting speed. Circumferential velocity
v
cutting speed
circumferent ial velocity
d
n
d iameter
rotational speed
Ve
Cutting speed
Cutting speed
I
Ve= 1t • d • n
Example:
Turning, n = 1200/min; d = 35 mm; Ve=?
v. = n-d • n= n -0.035 m• 1200 _2_
.
mrn
Circumferential
velocity
I
v= n-d-n
= 132~
min
Circumferentia
velocity
11
Average speed of crank mechanism
El
•O
~
s
Va
n
s
average speed
number of double strokes
stroke length
Example:
Power hacksaw,
s = 280 mm; n = 45/min; Va = ?
v0 = 2-s- n= 2-0.28 m-45 _2_
= 25.2 ...!!!...
min
mm
Average speed
Va= 2 • s • n
36
Physics: 2.2 Forces
Types of forces
Adding and resolving forces
Chosen for the following
examples Mi= 10 mNm
~
F1, F2 component forces
F,
resultant force
vector magnitude
(length)
Mr scale of forces
Representing forces
Forces are represented by vectors.
The length / of the vector corresponds to the
magnitude of the force F.
Adding collinear forces acting in the same direction
Sum
Example: F1 =80N; F2 = 160N; F, =7
F, = F, + F2 = 80 N + 160 N = 240 N
Subtracting collinear forces acting in opposite directions
F,
Fr = F1 - F2
Example: F1 = 240 N; F2 = 90 N; F, = ?
F, =F,-F2 = 240 N - 90 N = 150N
I • f2• 1
Addition and resolution of forces
whose lines of action intersect
Addition
.o.iff
_e_r_e_n.ce
_ _ _ _ _.,
Solving a force diagram by
adding or resolving
(force vectors)
Example of graphical addition:
Shape of
the force
diagram
F1 = 120 N; F2 = 170 N; y = 118";
Mr= 10 N/mm; F, = ?; measured: / = 25 mm
F, =I• Mr = 25 mm - 10 N/mm =250 N
Resolution
Example of graphical resolution:
F, = 260 N; a = 90°; fJ = 15°; Mr = 10 N/mm;
F, = ?; F2 =?;measured: / 1 = 7 mm; /2 = 27 mm
F1 = / 1 •Mr= 7 mm. 10 N/mm = 70 N
F2 = /2 • Mr = 27 mm • 10 N/mm = 270 N
Required
trigonometric
function
Force diagram sine,
with right
cosine,
angles
tangent
Force diagram Law of sines,
w ith oblique Law of
angles
cosines
Forces of acceleration and deceleration
A force is required to accelerate or decelerate a mass.
acceleration force
a acceleration
F
Acceleration force
m mass
Example:
m = 50kg; a=3~; F = 7
F = m -a = 50kg-3 ~ = 150kg -~= 150N
s2
s2
_j
Weight
Gravity generates a weight force on a mass.
Fw weight
g gravitational
m
mass
acceleration
Example:
Weight
1 Fw = m-g
I-beam, m = 1200 kg; Fw = ?
Fw = m-g= 1200kg-9.81~ = 11772N
s
Calculation
page 31
of mass:
Spring force (Hooke's law)
F
ro~
"-
300
~200
~too
·"a. 0 111!::..L..::.:.J........l__J
~
0 10 20mm40
spring
displacement s ~
The force and corresponding linear expansion
of a spring are proportional w ithin the elastic range.
F spring force
s spring displacement
R spring constant
Spring force
I
F=R-s
Example:
Compression spring, R = B N/mm; s = 12 mm; F = ?
F = R•s = B ~
·12mm = 96N
mm
Change in spring force
I
t,.F = R- t,.s
37
Physics: 2.2 Forces
Torque, Levers, Centrifugal force
Torque and levers
Single-ended lever
The effective lever arm is the right angle distance Moment
between the fulcrum and the line of applicat ion of
the force. For disk shaped rotating parts the lever
arm corresponds to the radius r.
M
moment
F force
Lever principle
effective lever arm
I
LM1 sum of all counter-clockwise moments
LM, sum of all clockwise moments
I1
Two-ended lever
Example:
Angle lever, F1 = 30 N; / 1 = 0.15 m; /2 = 0.45 m;
F2 = 7
Lever principle with
only 2 applied forces
F, = F1 - /1 = 30 N -0.15m - l0N
/2
0.45m
Bearing forces
Example of bearing forces
I
8
Fa
A bearing point is treated as a fulcrum in calculating Lever principle
bearing forces.
FA, Fa bearing forces
/, / 1, / 2 effective
lever arms
F1, F2 forces
Example:
Overhead travelling crane, F1 = 40 kN; F2 = 15
kN; / 1 = 6 m; /2 = 8 m; / = 12 m; FA= 7
Solution: B is selected as fu lcrum point; the
bearing force FA is assumed on a singleended lever.
FA F1 -/1 +F2 -12 40kN -6m + 15kN -8m 30kN
I
12m
Bearing force at A
Torque in gear drives
z,
The lever arm of a gear is half of its reference diame- Torques
ter d . Different torques result if two engaging gears - - - - - - - - - - .
do not have the same number of teeth.
M, = Fi 1 • d,
Driving gear
Driven gear
Fi, t angential force
F12 tangential force
M, torque
M2 torque
d1 reference diameter
d2 reference diameter
z1 number of teeth
z2 number of teeth
n1 rotational speed
n2 rotational speed
gear ratio
2
Example:
Gears, i = 12; M 1 = 60 N • m; M2 = ?
M:, = i • M 1 = 12 • 60 N • m = 720 N · m
For gear ratios for gear drives see page 259.
Centrifugal force
Centrifugal force Fe when a mass is made to move
along a curvilinear pat h, e.g. a circle.
Centrifugal force
Fe centrifugal force w angular velocity
m mass
v circumferential velocity
r
radius
Example:
Turbine blade, m = 160 g; v = 80 m/s;
d = 400 mm; Fe = ?
F. = m -v2 = 0.16kg • (80 m/s>2 5120 kg• m =Sl20N
2
•
r
0.2 m
s
38
Physics: 2.3 Work, Power, Efficiency
Work and Energy
Mechanical work, lifting work and frictional work
Work is performed when a force act s along a distance.
F
Fw
Fa
Fr,
w
force in direction of travel
weight
friction force
normal force
work
force dist ance
s, h height of lift
µ
coefficient of
friction
.w. o_r_k_ _ _ _ _ _.,
W=F•s
s
Lifting work
1st e><ample:
Frictional work
F = 300 N; s = 4 m; W = ?
W = F- s = 300 N • 4 m = 1200 N · m ~ 1200 J
2nd e>1ample:
1J= 1N , 1m
Frictional work, Fr, = 0.8 kN; s = 1.2 m; µ = 0.4; W = ?
W = µ • FN , s = 0.4, 800 N , 1.2 m = 384 N , m = 384 J
kg . m2
=1W-s=1 - s2
1 kW· h = 3.6 MJ
Energie of position
En«gy of
position
Energie of position is stored work (energy of position,
spring energy).
E, W 0 energy of position
weight
F
force
Fw
R
spring constant
s, h travel, lift or fall
height, spring
displacement
Energy of position
E><ample:
Drop hammer, m = 30 kg; s ~ 2.6 m; W0 = ?
W0 = Fw ·S = 30 kg • 9.81~ • 2.6m = 765J
s
Kinetic energy
Linear motion
Kinetic energy is energy of motion.
ffl---.z::>"7Jlr-"I~
E, Wk kinetic energy or work
angular velocity
w
J
mass moment of inertia
Rotational motion (rotation)
E><ample:
v velocity
m mass
Drop hammer, m = 30 kg; s ~ 2.6 m; Wk = ?
} ~
Kinetic energy
of linear motion
Kinetic energy
of rotational motion
v= J2 - g-s= J2 -9.81 m/s2 -2.6 m = 7.14 m/s
$
w. = m-v2 = 30kg-(7.14m/s)2
2
2
765
J
Golden Rule of Mechanics
"What is gained in force is lost in distance·.
W1
F1
s1
Fw
h
input work
input force
displacement of
force F1
weight
height of lift
W2 output work
F2 output force
52 displacement of
force F2
1/
efficiency
E><ample:
Lifting device, Fw = 5 kN; h = 2 m; F = 300 N; s = ?
s = Fw•h = 5000 N -2 m ll.lm
F
300N
"Golden Rule"
of Mechanics
F1-s1=Fw-h
Allowing for
friction
39
Physics: 2.3 Work, Power, Efficiency
Simple machines
Fixed pulley11
Movable pulley11
F, =Fw
.;;
s1 = h
Block and tackle11
s1 = 2 • h
Inclined plane11
n
no. of load-bearing
ropes, pulleys
a angle of inclination
F, • s, = Fw • h
I
I
-<::
s1 = n- h
F, = Fw· sina
"
"'
W2=Fw •h
Bolt11
Wedge1I
/3
P
thread pitch
lever arm
For 1 full turn
angle of inclination
I
tan /3 incline
-<::
"
.;;
F, - _fi_
2 - tan/3
s, = 2 • 1t · /
L'.'.lLx=tan(J
s2 = s1 • tan/3
s,
W2 = F2-h
Gear winch11
Hoisting winch1'
d
d
no
I crank length
d drum
crank length
drum
diameter
number of turns
of the d rum
diameter
gear
ratio
Fw·d
F, •I = -2
h =rt •d ·no
-<::
W2 =Fw •h
I
I
Fvv · d
F,•l•i = - 2
j = Z2
z,
W2=Fw•h
1l The formulae apply to a hypothetical frictionless condition, wherein the output work w, is equal to the input work
W2.
40
Physics: 2.3 Work, Powe r, Efficiency
•
Power and Efficiency
Power in linear motion
Power is work per unit time.
P
W
v
power
work
velocity
Power
s
displacement in
the force direction
P=W
t
time
F-s
P=-
1st example:
t
Fo rklift, F = 15 kN; V= 25 m/min; P=?
25
P =F •v = 15000N, m = 6250 N-m = 6250W = 6.25kW
60s
s
P=F· V
2nd example:
Crane lifts a machine. m = 1.2 t; s = 2.5 m ;
t=4.5s;P=7
1W =1 ~
Fw= m, g= 1200 kg, 9.81 m/s2 = 11772 N
P = fw·s. 11 772 N -2.5m 6540W = 6.SkW
=
t
s
N ,m
1
s
1kW = 1.36 PS
4.5s
For power in pumps and cylinders see page 371.
Power in circular motion
P power
M torque
F tangential force
v velocity
s displacement in the force direction Power
t time
---------.
P =F· V
n rotational speed
w angular velocity
P =F·n·d•n
Example:
Belt drive, F= 1.2 kN; d = 200mm; n = 2800/min; P= ?
P= M-2 • n• n
P = F•n •d • n
= 1.2 kN · 11 • 0.2 m, 2800 = 35.2 kN. m = 35.2 kW
60s
s
Numerical equation:
Enter--> M in N . m, n in 1/min
Result --, P in kW
or:
Power
M-n
P=--
For cutting power in machine tools see pages 299 and 300.
9550
Efficiency
input
power
PM1=P1
output
power
P52=P2
Efficiency refers to the ratio of power or work output to the Efficiency
power or work input.
P1 input power
W1 input work
q total efficiency
P2
output power
W2
output work
q1, q2 partial efficiencies
Example:
Belt drive, P1 • 4 kW; P2 = 3 kW; q1 • 85%; q = ?; ~2 = ?
T/ = ! i = 3 kW = 0.7S;
P, 4kW
'Ii=.!!..= 0.75 = 0.88
1h 0.85
Efficiencies q (approximate valuesl
Brown coal power station
0.32
Coal power station
0.41
Natural gas power station
0.50
Gas turbine
0.38
Steam turbine (high pressure) 0.45
Water turbine
0.85
Cogeneration
0.75
0.27
Gasoline engine
Automobile diesel engine (partial load) 0.24
Automobile diesel engine (full load)
0.40
Large diesel engine (partial load)
0.33
Large diesel engine (full load)
0.55
Three phase AC motor
0.85
Machine tools
0.75
Screw thread
Pinion gear
0.30
0.97
Worm gear, i = 40
Friction drive
Chain drive
W ide V-belt drive
0.65
0.80
0.90
0.85
0.75
Hydrostatic transmission
41
Physics: 2.4 Friction
Types of friction, Coefficients of friction
Friction force
Static friction, sliding friction
[i ::~~
f N
L
I
Static friction, sliding friction
&
I
The resulting friction force is dependent on the normal
fo rce F,; and the
Friction force for static
• type of friction, i.e. static, sliding or rolling friction
and sliding friction
• frictional condition (lubrication condition):
dry, mixed or viscous friction.
FF =µ,·~
• surface ro ughness
• material pairing (materi al combination)
These effects are all incorporated into the experimentally
determined coefficient of friction µ..
Friction force
F,; normal force f coefficient of rolling friction
for rolling friction11
r radius
f'rc friction force µ coefficient of friction
FF
-
1st example:
Plain bearing, FN = 100 N; µ = 0.03; Frc = ?
f'rc = µ • FN = 0.03 • 100 N = 3 N
I
f -~
Fr-= -
I
I
r
Rolling friction
F,
~
2nd example:
Crane wheel on steel rail, F,; = 45 kN; d = 320 m m;
f = 0.5 mm; Frc =?
0.5 mm • 45000 N
F, = !..:!ii =
140.6N
160mm
r
~TY
I
1,1
11 caused by elastic
deformation between roller body
and rolling surface
Coefficients of friction (guideline values)
~of-friction,,. ~ of-ng frictionµ.
Material pairing
Example of application
dry
lubricated
dry
lubricated
steel/steel
st eel/cast iron
st eel/Cu-Sn alloy
steel/Pb-Sn alloy
vise guide
machine guide
shaft in solid plain bearing
shaft in multilayer plain bearing
0.20
0.20
0.20
0.15
0.10
0. 15
0. 10
0. 10
0.15
0.18
0.10
0.10
0.10-0.05
0.10-0.08
0.06-0.03 21
0.05- 0.03 21
steel/polyamide
steel/PTFE
steel/friction lining
steel/wood
shaft in PA plain bearing
low temperature bearing
shoe brake
part on an assembly stand
0.30
0.04
0.60
0.55
0.15
0.04
0.30
0.10
0.30
0.04
0.55
0.35
0.12- 0.03 21
0_0421
0.3-0.2
0.05
wood/wood
cast iron/Cu-Sn alloy
rubber/cast iron
rolling element/steel
underlay blocks
adjustment gib
belts on a pulley
anti-friction bearing31, guideway31
0.50
0.28
0.50
0.20
0.16
0.30
0.20
0. 10
0.20- 0.10
-
-
-
-
0.003-0.001
-
21 The significance of the material pairing decreases w ith increasing sliding speed and presence of mixed and v iscous
friction.
31 Calculation performed in spite of rolling movement, because it is typically simi lar t o calculations of static or sliding
friction.
Coefficients of rolling friction (guideline valuesl4I
Material pairing
Example of application
Coefficient of rolling friction f in mm
steel/steel
plastic/concrete
rubber/asphalt
steel w heel on a guide rail
caster wheel on concrete floor
car tires on the street
0.5
5
8
4 1 Data on coefficients
of rolling friction can
vary considerably in
technical literature.
Friction moment and friction power in bearings
FN
f V\
~ - JI
~
F, =µ-FN
M
FN
p
friction mo ment
normal force
friction power
µ
d
n
coefficient
of friction
d iameter
rotational speed
Example:
Steel shaft in a Cu-Sn plain bearing, µ = 0.05;
ft, = 6kN; d= 160 mm; M = ?
M =µ·fr.i·d = 0.05 - 6000 N. 0.16 m
2
2
24N •m
Friction moment
I
M= µ,-~ ·d
2
Friction power
I P=µ,- Fw n • d•
I
nl
42
Physics: 2.5 Pressure in liquids and gases
Types of pressure
Pressure
p
F
A
pressure
force
A
Pressure
area
F
p =-
A
Example:
F = 2 MN; pist on 0 d = 400 mm; p = 7
P=!:._= 2000000N
A
n • I40cm>2
Units of pressure
N
= 1 m2 = 0.00001 bar
1591~
= 159.lbar
cm2
1 Pa
4
For calculations on hydraulics and pneumatics see page 370.
1 bar = 10 ~
= 0.1 ~
cm2
mm2
1 mbar= 100Pa= 1 hPa
Gage pressure, air pressure, absolute pressure
2
+1
e bar
ct
e
::,
bar
g> ~
e
C.
0
_ll
~
;,l
,,,
"
0,,,
.0
The gage pressure is
positive, if Pabs > Pamb and
negative, if Pabs < Pamb (vacuum)
",,,
oc.
'5
Pe
gage pressure (excedens, excess)
Pamb air pressure (ambient, surroundings)
Pabs absolute pressure
t
air
pressure
-~ 0. cf Pamb
..
0
Pamb = 1.013 bar ~ 1 bar
!standard air pressure)
Example:
Car tires, Pe= 2.2 bar; Pamb = 1 bar; Pabs = ?
2'~5
p.,. = Pe + Pamb = 2.2 bar + 1 bar = 3.2 bar
- 1 ~ v a cuum
_J
Hydrostatic pressure, buoyancy
Pe hydrostatic pressure,
inherent pressure
(!
g
density of the liquid
g ravitational acceleration
Fa buoyant force
V displaced volume
h depth of liquid
Hydrostatic pressure
I
I
Pe = 9 · e-h
Buoyant force
Example:
-<::
What is the pressure in a water depth of 10 m?
FB=9 ·e-V
p = 9 ·t! • h = 9.81~ • 1000~ - 10m
•
s2
kg
= 98100 m _
52
m3
=98100Pa ~ 1bar
For density va lues, see page 117.
Pressure changes in gases
Compression
condition 1
condition 2
Fl
I
~
Boyle's Law
5 - -- - - - -
bar
t
~L........I.L.-...J.........1.----'---J
Condition 1
Pabs1 absolute pressure
v, volume
T,
absolute
temperature
Condition 2
Pabs2 absolute pressure
volume
V2
T2 absolute
temperature
Special cases:
Example:
A compressor aspirates V1 = 30 m 3 of air at
Pabs1 = 1 bar and t 1 = 15°C and compresses
it to V2 = 3.5 m3 and r2 = 150°C.
What is the pressure Pabs2?
Calculation of absolute t emperatures (page 511:
T, = t, + 273 = (15 + 273) K = 288 K
00
dml 5
volume V - - -
T2 = t2 + 273 = ( 150 + 273) K = 423 K
P...i P_ , • v, .T2
T1 -V2
1 bar-30m3 -423 K
12.6bar
288K . 3.5m3
constant temperature
I
Pabsl • V, = Pabs2 • V2
constant volume
I
43
Physics: 2.6 Strength of Materials
Load cases, Types of loading, Material properties, Stress limits
Load cases
dynamic loading
static loading
pulsating
lt=_
iM_
time ~
0
Load case I
Magnitude and direction of the load
remain the same, e.g. for a weight
load on columns.
J,
Load case II
The load increases to a maximum
value and then falls back to zero,
e. g. fo r crane cables and springs.
..... ~
20
time~
t" t
§.~
time~
0
lt f\AT
alternating
stationary
Load case Ill
The load alternates between a positive and a negative maximum value
of equal magnitude, e.g. for rotating
axles.
Types of loading, material properties, stress limits
Material properties
Type of load
Stress
Tension
tensile
V
Compression
6
Strength
:d
Shear
~
Torsion
H
:= .
Buckling
F
for plastic
deformation
stress
tensile
strength
yield strength
o,
Rm
Re
0.2%-y ield
point
Rpo.2
compression
st ress
compression
strength
Oe
Dee
Standard stress limits 01m
for load case
Deformation
I
II
nt
material
elongation ductile brittle
(steel) (cast
f
iron)
elongation
Rm
Re
at fracture
Rpo.2
A
pulsating
tensile
fatigue
strength
alternating
tensile
fatigue
strength
lltpuls
OtA
material
ductile brittle
(steel) (cast
iron)
pulsating
compressio n
fatigue
strength
alternat ing
compression
fatigue
strength
Ocpuls
OeA
pulsating
bending
fatigue
strength
alternating
bending
fatigue
strength
Obpuls
0 bA
-
-
p ulsating
torsional
fatigue
strength
alternating
torsional
fatig ue
strength
Ttpuls
TtA
-
-
natural
compression
yield point
compression set
OeF
fe
0.2%-offset compressive
y ield strength
fail ure
Oco.2
<ee
'
Bending
_;;:}
UmltvakMs
bending
stress
bending
strengt h
bending
lim it
def lection
Ob
Obe
ObF
f
0 ee
Def
Oco.2
bending
lim it
ObF
shear
stress
shear
strength
Ts
Tse
-
-
•se
torsional
stress
to rsional
strengt h
torsional
limit
angular
deflection
torsional
limit
Tt
Tie
,,.
'P
Ttf
buckling
stress
buckling
strength
Obu
ObuB
shear
strength
buckling
strengt h
-
-
ObuB
44
Physics: 2.6 Strength of Materials
Mechanical strength properties, Allowable stresses, Safety factors
Mechanical strength properties in static and dynamic loading1I
Type of load
Tension, Compression
Shear
I
I
II
•se
obF
Obpuls
Load case
I
II
Ill
Stress
limit o1im
R,,. R0 0.2
Ocf, Oco.2
Otpuls
Ocpuls
OcA
OtA
Bending
Torsion
Ill
I
II
Ill
DbA
ftF
ftpuls
ftA
2
Materi al
Stress limit Oiim i n N/mm
S235
S275
E295
E335
E360
235
275
295
335
365
235
275
295
335
365
150
180
210
250
300
290
340
390
470
550
330
380
410
470
510
290
350
410
470
510
170
200
240
280
330
140
160
170
190
210
140
160
170
190
210
120
140
150
160
190
C15
17Cr3
16MnCr5
20MnCr5
18Cr NiMo7-6
440
510
635
735
835
340
490
580
630
710
760
870
330
390
430
480
550
600
800
880
940
960
610
710
890
1030
1170
610
670
740
920
1040
370
390
440
540
610
250
290
360
420
470
250
290
360
420
470
210
220
270
310
350
C22E
C45E
C60E
46Cr2
41Cr4
50CrM o4
30CrNiMo8
440
510
635
735
835
340
490
580
650
800
900
1050
220
280
325
370
410
450
510
400
560
680
720
800
880
1000
490
700
800
910
1120
1260
1470
410
520
600
670
750
820
930
240
310
350
390
440
480
550
245
350
400
455
560
630
735
245
350
480
455
510
560
640
165
210
240
270
330
330
375
GS-38
GS-45
GS-52
GS-60
200
230
260
300
200
230
260
300
160
185
210
240
300
360
420
480
260
300
340
390
260
300
340
390
150
180
210
240
115
135
150
175
115
135
150
175
90
105
120
140
EN-GJS-400
EN-GJS-500
EN-GJS-600
EN-GJS-700
250
300
360
400
240
270
330
355
140
155
190
205
400
500
600
700
350
420
500
560
345
380
470
520
220
240
270
300
200
240
290
320
195
225
275
305
115
130
160
175
11 Values were determined using cylindrical samples having d"' 16 mm w ith polished surface. They apply to struc-
tural steels in no rmalized condition; case hardened steels for achieving core st rength after case hardening and
grain refinement; heat treatable steels in tempered condition.
The compression strength of cast i ron with flake graphite is De e ~ 4 • Rm,
Values according to DIN 18800 are to be used for structural steelwork.
Allowable stress for (pre-)sizing of machine parts
For safety reasons parts may only be loaded with a portion of the stress limit or;m which will
lead to permanent deformation, fracture or fatigue fracture.
0 811ow
allowable stress
V
safety factor (table below )
D 1im
stress limit depending on
type of loading and load case
Allowable stress
(preliminary design)
Example:
What is the allowable tensile stress o,anow for a hexagonal bolt ISO 4017 - M12 x 50 10.9, if a safety factor of 1.5 is required w ith static loading?
N
N
_ Otim _ 900N/mm2
- 600~
a 1;m - R. - 10 • 9 • 10 mm2 - 900 mm2 ; u,,allow
V
1.5
mm2
I
O'lim
aauow=-V
I
For mechanical strength properties for bolts see page 211.
Safety factors v for (pre-)sizing machine parts
I (static)
Load case
Type of material
Safety fact or v
ductile materials,
e. g. steel
1.2- 1.8
Hand Ill Cdynamic)
brittle materials,
e.g. cast iron
2.0- 4.0
ductile materials,
e.g. steel
3_ 411
brittle materials,
e.g. cast iron
3 -611
•1 The high margins of saf ety in part sizing relative to the stress limits are intended to compensate for yet unknown
strength-reducing effects due to part shape (for shape-related strength factors see page 48).
45
Physics: 2.6 St rength of Materials
Tensile stress, Compressive stress, Surface pressure
Tensile stress
The calculation of allowable stress only applies to static
loading (l oad case I).
F
,;--
R.
F
Rm tensile strength
tensile stress
tensile force
cross-sectional area
s
Ucallow allowable tensile stress
~R
F
o,= S
s~ *
a,
Tensile stress
yield strength
safety factor
Fallow allowable tensile force
V
Example:
I
sj
Allowable tensile stress
(S235JR, v = 1.8); Fallow = 13.7 kN; d = ?
for
steel
S = F811ow = 13700N - l05 mm2
a,, allow 130 N/mm2
c = 12 mm (accord ing to t able, page 10)
Re
---;:;-
0 t,allow =
for
For mechanical strengt h properties Re and R.-n see pages 130
to 138. For calculation of elastic elongation see page 190.
F
I
Allowable tensile force
Fallow= Ot,allow.
Round bar steel, a,_allow = 130 N/mm2
LU
I
F
er, = s
Rm
cast
O"t_allow = ----;:;-
iron
Compressive stress
~I ' \
oompression yield point
OcF
compressive stress
Oc
Oc,aI1ow allowable comp. stress
V
safety factor
r'--- _../
s...________
~
I
Compressive stress
The calculation of allowable st ress only applies to static
loading (l oad case I).
F
F
Oc= 5
Rack made of EN-GJL-300; S = 2800 mm2;
V :: 2.5; Fallow = 7
4 . 300N/mm2
-2800 mm2 = 1 344000N
2.5
For mechanical strength properties see page 44 and pages 160-161
S
I
Allowable
compressive force
Fallow= Oc,allow,
''
4- R
Faaow == Uc, allow . S = ~ .5
I
F
ere=
I
Example:
- - - - -~
'-- F
F
oompressive force
Fa11owallowable oomp. force
s cross-sectional area
Rm tensile strength
sj
Allowable
compressive stress
for
steel
ercF
erc,allow = - -
for
cast
iron
4 - Rm
V
ac, allow "' - -v-
Surface pressure
~
,.,,~
F
p
force
surface pressure
A
cont act surface,
projected area
Example:
Surface pressure
I
Two metal sheets, each 8 mm t hick, are joined with a
bolt DIN 1445-10h11 x 16 x 30. How g reat a force may
be applied g iven a maximum allowable surface pressure of 280 N/mm2?
F = p-A = 280 __!:!_ - 8mm • 10mm
mm2
= 22400N
F
p =A
I
Allowable surface pressure for joints with pins and bolts
made of steel (standard valuesl
Sliding fit smooth bolt
Fit with notched piece
Assembly type
Press fit smooth pin
Ill
I
II
Ill
I
II
Ill
Load case
I
II
Component material
allowable surface pressure in N/mm2
70
70
25
25
10
S235
100
35
50
30
25
105
75
40
75
55
30
30
10
E295
10
cast steel
85
60
30
60
45
20
30
25
15
70
50
25
50
35
20
40
30
cast iro n
40
30
20
10
40
30
15
30
15
CuSn, CuZn alloy
15
15
10
45
AICuMg alloy
65
45
25
35
20
For reference values for allowable soecific bearino load of various olain bearinQ materials see oaQe 261.
I
46
Physics: 2.6 Strength of Materials
Shear and buckling stress
Shear stress
The loaded cross-section must not shear.
shear stress
rs.allow allowable shear stress
Tse
shear strength
r5
Shear stress
F811ow allowable shear force
S
cross-sectional area
v
safety factor
Example:
Allowable
shear stress
Dowel pin 0 6 mm, single-shear loaded,
E 295, V = 3; Fallow = ?
singleshear
r allow = r sB = 390 N/mm2 130 ___!'±_
'
V
3
mn,2
S
= n , d2 = n-(6mm>2 = 2S.3 mm2
4
4
N
F - = S • r,a11ow = 28.3mm 2 -130 mm2 = 3679N
doubleshear
For mechanical strength properties r 1 8 and safety factors see page 44.
TsB
Ts, allow = -;-
Allowable shear force
I
Fallow= S • Ts.allow
Cutting of materials
The loaded cross-section must be sheared.
TsBmax max. shear strength
Rmmax max. tensile strength
F
S
F
shear area
cutting force
Maximum
shear strength
Example:
Punching a 3 mm thick steel sheet S235JR;
d = 16mm;F=?
Cutting force
Rmmax = 470 N/mm2 (Table page 130)
r sBmax ~ 0.8 • Rmmax= 0.8 • 470 N/mm 2 = 376 N/mm2
S =n · d-s = n -16mm -3mm= 150.8mm2
I
f =S·TsBmax
F = S • r,emax = 150.8 mm2 • 376 N/mm2 = 56701 N
= 56.7 kN
I.
[=rr•d
,
"'
For mechanical strength properties l\n ~
I(
for steel, see pag es 130 to 138
Buckling stress (Euler columns)
Load case and free buckling
lengths (Euler columns)
Load case
F
II
III
IV
F
F
F
Calculation for buckling of Euler columns applies only to
thin (profile) parts and within the elastic range of the
workpiece.
Allowable buckling
Fi,.,,anow allowable buckling force E Modulus of elasticity force
/
length
/ Moment of inertia
n 2 - E·I
/ 00
free buckling length
ftx, II = - - ,aow
l~u·V
v
safety factor (in machine construction ~ 3--10)
Example:
Beam IP8200, / = 3.5 m; clamped at both ends;
v = 10; l't,uallow = ?; E = 210000 N/mm2 = 21 , 106 N/cm 2
(table below); 111 = 2000 cm4
2
2 EI n -21-1<>6 2:.. .2ooocm4
Fb4- = ~
/bu· v
=
cm2
(0.5 • 350 cm>2 • 10
= 1.35-106 N = 1.35MN
free buckling lengths
100=2·1 100=1 100=0.1,/ lbu=0.5·1
11 for moments of inertia of an area (2nd moment), see pages
49 and 146-151. Special calculation methods are stipulated
for structural steel according to DIN 18800 and DIN 4114.
Modulus of elasticity Ein kN/mm2
steel
EN-GJL150
EN-GJL300
EN-GJS400
GS-38
EN-GJMW350-4
CuZn40
196-216
80-90
110-140
170-185
210
170
80-100
AlaHoy
1i alloy
112- 130
I
47
Physics: 2.6 Strength of Materials
Bending and torsional stress
Bending stress
Tensile and compressive stresses occur in a member
during bending. The maximum stress is calculated in
boundary areas of the member; they may not exceed
the allowable bending stress.
ob bending stress
Mb bending moment
W axial section modulus
F
f
bending force
deflection
Example:
Beam IPE-240, W = 324 cm3 (page 149); clamped at
one end; concentrated load F = 25 kN; / = 2.6 m; ob = 7
Ub=Mb
W
25000N -260 cm
324 cm3
Allowable bending
stress ob allow
from page 44
20061 _!:!__- 200 ~
cm2
mm2
Bending load cases in beams
Beam loaded with a concentrated load
Beam with a uniformly distributed load
fixed at one end
fixed at one end
F
F . /3
f =--
F. /3
f =- 8-E-I
3 • E -I
fixed at both ends
fixed at both ends
F. /
Mb = -
.....
F
12
F ./3
f= - - - 384 - E-I
F . /3
f = - - -192 • E • I
E Modulus of elasticity; values: page 46 f 2nd moment of inertia; formulae: page 49; values: pages 146 to 151.
F' Distributed load (load per unit length, e.g. N/cm)
/ Length of distributed load
Torsional stress
Mt torsional moment
W 0 polar section modulus
Tt
t o rsional stress
Torsional stress
Example:
Shaft, d = 32 mm; M 1 = 420 N • m ; r 1 = 7
W. = "·d3 = "·(32mm)3 6434mm3
P
16
16
M 1 420000 N • mm
N
•• = WP = 6434 mm3 65•3 mm2
For polar section moduli see pages 49 and 151
Allowable torsionalstress Tta11ow from page
44 o r page 48
48
Physics: 2.6 Strength of Materials
Shape factors in strength
Shape-related strength and allowable stress for dynamic loading
Shape-related strength is the fatigue strength of the cross-section of a dynamically loaded member w ith an additional allowance for the strength reducing effects of the component"s shape. Important factors include
• the shape of the component (presence of stress concentration)
• machining quality (surface roughness)
• stock dimensions (member thickness).
When compensating for the required safety factor t his yields the allowable stress needed to verify the strength of a member which is dynamically loaded.
b,
surface condition factor
05 shape-related strength
o 1;m stress l imit of the unnotched
size f actor
bi
cross-section, e.g. Oba or r tpuls (page 44)
stress concentration fact or
Pk
safety factor for fatigue fracture
VF
o (r)anow allowable stress
Shape-related strength
(dynamic loading)
c:rs = o-r1m ·b, · bi
/3k
Tg = rr,m ·b, ·bi
{Jk
Allowable stress
(dynamic loading)
Example:
0"5
Rotating axle, E335, transverse hole, surface roughness Rz - 25 µm,
rough part diameter d = 50 mm, safety factor v F = 1.7; as = ?; 0a11ow = ?
O"auow= -
I
= 280 N/mmZ (page 44); b 1= QB~ = 570 N/mm2 , diagram below);
Oz = 0.8 (diagram below); /Jk = 1.7 (table below)
C1bW ·b, ·Oz 280 NJmmZ -0.8 • 0.8
105N/mm2
"s
1.7
/Jk
"a11ow = osi"F =105 N/mm2 / 1.7 = 62N/mm2
0 bw
VF
rs
rauow = VF
v, for steel ~ 1.7
Stress concentration and stress concentration factors fJk for steel
Example: Stress distribution
for tensile loading
engineering
st r ess in
unnotched part
F
I
,II U1 tl
~~~ vs
Unnotc hed cross-sections have an uninterrupted distribution of forces and therefore a uniform stress distribution. Changes in cross-sections lead to concentrations
of lines of force where stresses are concentrated. The ensuing reduction of strength
is primarily influenced by the notch shape, but also by the notch sensitivity of the
material.
Material
bending
torsion
Shaft with shoulder
Shaft with semicircular notch
Shaft with retaining ring groove
S185-E335
S185- E335
S185-E335
1.5-2.0
1.5- 2.2
2.5- 3.0
1.3- 1.8
1.3- 1.8
2.5- 3.0
Key way in shaft
S185-E335
C45E+OT
50CrMo4+OT
1.9-1.9
1.9- 2.1
2.1- 2.3
1.5- 1.6
1.6- 1.7
1.7- 1.8
Woodruff key way in shaft
Spline shaft
S185-E335
S185- E335
2.0-3.0
-
2.0- 3.0
1.6- 1.8
Shaft interface to snug fit hub
S185- E335
2.0
1.5
Shaft or axle with t ransverse
through hole
S185- E335
1.4- 1.7
1.4- 1.8
S185- E335
1.3- 1.5
tensile loading
1.6- 1.8
.~ )
tl J!
~
I
\
stress
F
concentration in
not ched part
Stress concentration factor Pk
Notch shape
Flat bar with hole
Surface condition factor b, and size factor "2 for steel
t_ 0.91.0
1.6
t:--,. ~
. c:,b O8 t--,; ~::--, t:;.
~
0.1
" 0.6
:.::
0
K,...,
..... r--.
'i5
§ 0.5
~ 0.4
't:
iii
400
~ ::1.
.!:
-- -
4
10 ::, N
25 "'a::
t
-
Sc;-;:-r---e r1r
~
600
40 ~ ~
- 100 ~ .s:::
~
~
% "otu,·
.,
~
800
E
1000
O'>
~
::,
"O
~
., 0
1200
1
tensile stength Rmin N/mm - - -
1400
~
t~
..c:,
1.0
\
0.9
' tension, compression
I
~
~
t 0.8
2
., 0.1
N
·.;;
0.6
0
25
'
50
I
I
I I I
~
bending/torsion
I
I
I
I
I
15 100 125 150 mm 200
stock diameter d - - -
49
Physics: 2.6 Strength of M ateri als
Moments of area and Polar section moduli 1l
Bending and Buckling
Araamo,n-,tof
Axial section
i...tial
modulusW
Shape of the
cross-section
®I
n-d4
I =-64
ffi~t
®
n-d3
W =-32
n •(D" - d 4 )
64
I
Torsion
Polar section
modulus Wp
W=
n -d 3
WP= ---is
n -(04-d 4)
Wp =
32-D
n -(04 - d 4 )
16 - D
I = 0.05 • D4 - 0.083 d • D3
W= 0. 1 • D3-0.17 d - D2
Wp = 0.2 - D3-0.34 d-D2
I= 0.003 - (D + d)4
W = 0.012 . (D + d)3
Wp~0.2 - d 3
I= 0.003 - (D+ d)4
W = 0.012. (D + d)3
W0 = 0.024 - (D + d)3
@I
@
also applies for more keys
ti:·I
t4P
x~~
5 - ,J3-d4
Ix = I v = ~
5-s3
Wv = 24- ✓
3- 64
W0 = 0.123 - d3
w -h 3
I= - X
12
w -h 2
Wx = - 6-
W0 =~-w2-h
h -w 3
h -w2
Wv= - 6-
Values for,,
see t able below
Ix
B -H 3 - w-h3
12
Iv
H-B'-h- w3
12
..._
w
5. ,✓
3.da
5-s3
w, = - - ; j g " = ~
Iv = ~
x.Y..
Wp = 0.208 - h3
✓
2 -h3
W, = ~
5 - ,J3-s4
I =I =--,c
V
144
·ffl]
y
ha
W,=6
h4
lx = I , = 12
W, =
Wv
W0 = 0.188 • s3
5-d3
B-H3 - w - h 3
6 -H
Wo =
H-8 3 -h- w 3
6-8
t- (H+h)-(B+w)
2
B
11 2nd moments of inertia and axial section moduli fo r profiles see pages 146 to 151.
Auxliary value ~ for polar section moduli of rectangular cross-sections
h/w
,,
I
I
1
0.208
I
I
1.5
0.231
I
2
I
3
I
I
0.246
I
0.267
I
4
0.282
I
6
I
0.299
I 8 I 10 I ""
I 0.307 I 0.313 I 0.333
50
Physics: 2.6 Strength of Materials
Comparison of various cross-sectional shapes
u....
C.-Nction
Section modul or static moments for type of loading
Bending
Buckling
Torsion
mass density
w.
w,
w.
1...,
Standard
m'
designation
kg/m factor11
cm3
factor1I
cm3
factor1 I
cm3
fac:tor1I
cm3
factor1I
round bar
EN 10060100
61.7
1.00
98
1.00
98
1.00
491
1.00
196
1.00
square bar
EN 10059100
78.5
1.27
167
1.70
167
1.70
833
1.70
208
1.06
pipe
EN 10220 114.3 X 6.3
16.8
0.27
55
0.56
55
0.56
313
0.64
110
0.56
18.3
0.30
67.8
0.69
67.8
0.69
339
0.69
110
0.56
y
hollow
structural
section
EN 10210-2
100 X 100 X 6.3
16.1
0.26
59
0.60
38.6
0.39
116
0.24
77
0.39
y
hollow
structural
section
EN 10210-2
120 X 60 X 6.3
,
flat bar
EN 10058100 X 50
39.3
0.64
83
0.85
41.7
0.43
104
0.21
-
-
,,,
T-section
EN 10055 T100
16.4
0.27
24.6
0.25
17.7
0.18
88.3
0.18
-
-
U-Channel
section
EN 1026 U100
10.6
0.17
41.2
0.42
8.5
0.08
29.3
0.06
-
-
I-beam section
DIN 10251100
8.3
0. 13
34.2
0.35
4.9
0.05
12.2
0.02
-
-
I-beam section
DIN 1025IPB100
20.4
0.33
89.9
0.92
33.5
0.34
167
0.34
-
-
Shape
y
X
X
.
y
y
X
X
y
,$,
,e.
,a,
,,
r
y
y
,-[-,
y
·l·
·!·
y
y
11 Factor referenced t o round bar EN 10060-100 (cross-section in first row of table)
51
Phy sics: 2.7 The rm od y namics
Effects of changes in temperature
Temperature
T
373
K
273
0
t
+ 100 _ boiling point
oc
of water
0 __ melting point
of ice
Temperatures are measured in Keh/In (Kl. degrees Celsius
(Centigrade, °C) or degrees Fahrenheit (°F). The Kelvin scale
originates at the lowest p0ssible temperature, absolute zero;
t he origin of the Celsius scale is at the melting point of ice.
T temperature in K
t, D temperature in °C
(thermodynamic temperature)
tF temperature in °F
Example:
t=20°c; T= 1
T = t + 273 = (20 + 273) K = 293 K
_
_ absolute
273 zero
Temperature in
Kelvin
T = t + 273
Temperature in
degrees Fahrenheit
I
tF = 1.8 • t + 32
Linear expansion, Change in diameter
a1
coefficient of
linear expansion
!).t, Ml temperature change
Linear expansion
6./ linear expansion
!).d change in diameter
initial lengt h
d 1 initial d iameter
/1
,
Example:
Plate of unalloyed steel, /1 = 120 m m; a 1 = 0.000011 9 'C
M = 550°C; M = ?
A/ = a 1 -/1 -M
1
= 0.000 011 9,: • 120 mm• 550°C = 0.785 mm
Change in diameter
I
6.d = a 1 • d1 • M
For coefficients of linear expansion see
pages 11 6and 117
Change in volume
av
coefficient of
volumet ric expansion
I). V change in volume
V,
initial volume
6!, Mi temperature change
Example:
Gasoli ne, V, = 60 I; av= 0.001i ; M = 32°C; 6 V =?
1
ll>V = av -V, M = 0.001, : • 60 1- 32°C = 1.9 1
Change in volume
l 6.V=av•V1-M j
For solids
a v = 3-a1
For coefficient s of volumetric expansion see
page 117.
For volumet ric expansion of gases see page 42.
Shrinkage
S shrinkage allowance in %
/1
pattern length
Pattern length
workpiece length
I _ 1- 100%
, - 100% - S
Example:
Al casting,/= 680 mm; S = 1.2%; /1 =?
11
= /-100% = 680 m m -100%
100%-S
100% - 1.2%
For shrinkage allowances see page 163
= 688-2mm
Quantity of heat with changes in temperature
The specific heat c indicates how much heat is needed to Quantity of heat
warm up 1 kg of a substance by 1•c. The same quantity of
heat is released again during cooling.
O=c•m•M
spec. heat capacity
{).f, Mi temperature c hange
c
quantity of heat
m mass
Q
C
Example:
Steel shaft, m = 2 kg; c = 0.48 ~
;
kg -°C
M=800°C; 0 = 7
Q = c -m -M = 0.48 ~
• 2 kg • 800°C = 768kJ
kg-°C
I
1kJ = 1kW-h
3600
1kW • h = 3.6 MJ
For specific heat see
pages 116and 11 7.
52
Physics: 2.7 Thermodynamics
Heat for Melting, Vaporizing, Combustion
Heat of fusion. Heat of vaporization
Heat of vaporization
Heat energy is necessary to transform substances from Heat of fusion
a solid state to a liquid stat e or from a liquid state t o a
O=q-m
gaseous state. This is known as the heat of fusion or heat
of vaporization.
+100 t-He
=---=~-
.....-
'=l
0(
r
heat of fusion
heat of evaporation
specific heat of fusion
0
q
specific heat
of evaporation
m mass
Heat of vaporization
1
0 = ,. m
Example:
Copper, m = 6.5 kg; q = 213~; 0 = 7
kg
O = q · m = 213~ · 6.5kg = 1384.5 kJ ,,, 1.4 MJ
kg
quantity of heat a
For specific heat of
fusion and heat of
evaporation see
pages 116 and 117.
Heat flux
The heat flux <I> continually occurs w ithin a substance Heatflux with
w ith movement from higher to lower temperatures.
thermal conduction
The heat transmission coefficient k also compensates,
along with the thermal conductivity of a part, for t he heat
transmission resistance on the surfaces of the part.
s
<P heat flux
" thermal conductivity
k heat transmission
coefficient
M, Mi temperature difference
s
component thickness
A
area of the component
il-A-M
<1>= - - s
Heat flux with
heat transmission
Example:
Heat protection glass. k = 1.9 m2W ; A = 2.8rri2;
· "C
M = 32"C; <I> = ?
A
w
<l>=k • A• M = 1.9 rri2-"C • 2.8m2 • 32°C = 170W
For thermal conductivity values " see
pages 116 and 117.
For heat transmission
coefficients k see
below.
Heat of combustion
The net calorific value H,,., (H) of a subst ance refers
to the heat quantity released during the complet e
combustion of 1 kg or 1 m 3 of that substance.
0
heat of combustion
H net• H net calorific value
mass of solid and liquid fuels
m
V
volume of fuel gas
Heat of combustion of
solid and liquid sub-
Example:
I
MJ
Natural gas, V = 3.8 m3; H,,.,=35 mJ ; 0 = ?
stances
O = Hnet •m
Heat of combustion of
gases
O=Hnet•V
0 = /-(,et· V= 35 MJ -3.8m3 = 133MJ
m3
Heat transmission coefficients k
for construction materials and parts
Net calorific value H- IHI for fuels
0....
w
Solid
fuels
Liquid
fuels
0....
MJ/kg
MJ/kg
Gaseous
fuels
0.... Construction
MJ/m3 elements
mm
k~
wood
biomass (dry)
brown coal
coke
pit coal
15- 17
14-18
16- 20
30
30-34
alcohol
benzene
gasoline
diesel
fuel oil
27
40
43
41- 43
40-43
hydrogen
nat ural gas
acetylene
propane
butane
10
34- 36
57
93
123
50
12
365
125
80
5.8
1.3
1.1
3.2
0.39
outer door, steel
sash window
brick wall
intermediate floor
heat insulating board
s
53
Physics: 2.8 Electricity
Quantities and Units, Ohm's Law, Resistance
Electrical quantities and units
Unit
Quantity
Name
Symbol
Name
Symbol
electrical voltage
E
volt
V
electric current
I
ampere
A
electrical resistance
R
ohm
Q
electrical conductance
G
Siemens
electrical power
p
watt
s
w
H2 = ~
1A
I
1W = 1 V- 1A
I
I
I
Ohm's law
1'
0!'
V
l
RI
E
E voltage i n V
Electric current
I electric current in A
R resistance in Q
I
1 = 5_
R
I
Example:
I
R = 88 fl; E = 230V; / = ?
I = E._ = 230V = 2.6A
R aan
---
For ci rcuit symbols see
page 351.
- ---
Electrical resistance and conductance
{:m
~o
-~ 0
0.5
1
Resistance
R resistance in Q
G conductance in S
1.5
2 S 2.5
G
Conductance
R = 20fl; G = ?
1
G =..!_ = - - = 0.05S
R 20n
conductance u -
R = _!_
I
Example:
I
G = _!_
R
I
I
Electrical resistivity, electrical conductivity, conductor resistance
electrical resistivity in Q. mm2/m
electrical conductiv ity in m/(Q . mm2)
R resistance in Q
A wire cross section in m m 2
I
wire length in m
Example:
Electrical resistivity
(!
y
I
~
\
Copper wire, / = 100m;
n -mm2
A =1.5 mm2; /! = 0.0179 - - -; R = 1
m
• 100m
e •I 0.0179 n -mm'
m
1.19fi
R=- =
1.5mm2
A
1
e= -
I
-
r
I
Conductor resistance
I
For electrical resistivities, see pages 116 and 11 7.
e-1
R=A
I
Resistance and Temperature
Material
Tk value a in 1/K
aluminum
0.0040
lead
0.0039
gold
0.0037
copper
0.0039
silver
0.0038
tungst en
0.0044
tin
0.0045
zinc
0.0042
graphite
- 0.0013
constantan
± 0.00001
t,.R change in resistance in Q
R20 resistance at 20°c in Q
R, resistance at the temperature tin Q
a
temperature coefficient ( r. value) in 1/K
M temperature difference in K
Change in resistance
I
6.R = a • R20 • M
Resistance at
temperature t
Example:
R1 = R20 + 6.R
Resistance of Cu; Rio a 150 Q; t= 75°C; flt = 1
R1 = R20-(1 + a -M)
a =o.0039 1/ K; .i.t= 75°c - 20°c = 55°C " 55 K
flt =R2o• (l+ a- M)
= 150 Q - (1 +0.0039 1/K • 55 K) = 182.2 fi
_
_,
I
54
Physics: 2.8 Electricity
Current density, Resistor circuits
Current density in w ires
'Tffll--
Current density
current density in A/mm 2
electric current in A
A conductor cross section in mm2
Example:
J
I
._A
}6- --- B4
-
-~ 2
0
j o 1
2
3
4 mm2 6
A = 2.5mm2; I =4A;
I
I
P-
J = ~ = ~ = , .6 ~
A
conductor (cross-sectiooaO area A
2.5mm'
J = .!_
A
I
j
mm2
Voltage drop in wires
~~
f d/2
Ei l
>9
E, i
r
f d/2
Voltage drop
voltage drop in wire in V
voltage at t erminal in V
voltage across load in V
electric current in A
R1ine resistance for feed o r
return line in Q
Ed
E
Ee
I
I
Ed = 2 • I • R1ine
I
Voltage at load
I
~
Ec= E - Ed
I
Series resistor circuit
-
I
R, I
lk,
E,
Example:
-
~
R2I
f 2
II,,
R =R1 + R2 = 10f1+20f1 = 30fi
-
V l
~
R,
R 2I
l
Example:
R1 = 15!1; Rz=30!1; E = 12V;R = ?; / = ?;
1, = ?; ,, = ?
R = R1 -R2
15!1-30!1
R1 +R2 15n + 30n
-
10 n
1 =~ =~
= 12 A
R 10 n
E
E,
E1
12
11 = ~ =
V = 0.S A·
R1 15 !1
'
R = R1 + R2 + ...
I
Total voltage
E = E 1 + E2 + ...
I= I,= 12 = ...
I
R
total resist ance, equivalent resistance in Q
I
total current in A
E
total voltage in V
R,, R2 individual resistances in Q
1,. 12 partial current in A
E,. E2 voltage drop across R1 & R2 in V
'2
I
I
I
I
I
Voltage drops
1 = ~ = ~ = 0.4 A
R 30f1
E, =R, ./ = 10!1-0.4A = 4 V
E2= R,-1 = 20 !1-0.4A = av
Parallel resistor circuit
I
Total resistance
Total current
R1 = 10f!; R2 = 20!1; E = 12V;R =?; I =?;
E 1= ?; E2= 7
'
E
R
t otal resistance, equivalent resistance in Q
I
t otal current in A
E
t otal voltage in V
R,. R2 individual resistances in Q
1,. 1, partial current in A
E,, E, voltage drop across R1 & R2 in V
l 2 = E2 = 12V = 0.4A
R2 30!1
11 Use t his fo rmula if there are only two parallel
resisto rs in the circuit.
§_ = _&
E2 R2
I
Total resistance
1
1
1
- = - + - + ...
R R, R2
Rl) = R, ·R2
R1 + R2
Total voltage
I
I
E = E 1 = E2 = ...
I
Total current
I= 11 + / 2 + ...
I
Partial currents
I
!.J.. = R2
12
R,
I
55
Physics: 2.8 Electricity
Types of current
Direct current IDC; symbol-), DC voltage
t
..... L - - - - - - - - -
t---
t
-. ~--------
Direct current flows in one direction only and main- Electric current
tains a constant level of current. The voltage is also
constant.
I = constant
/
electric current in A
E
voltage in V
time ins
t---
Voltage
I
E = constant
Alternating current IACI; symbol -1. AC voltage
Cycle duration and Fraquancy
While the voltage is continuously changing in a sinu- Cycle duration
soidal pattern. the free electrons are also continuously alternating their direction of flow.
frequency in 1/s, Hz
period ins
angular frequency in 1/s
electric current in A
voltage in V
time ins
f
T
w
tt
tt
I
E
..... ...
Example:
Frequency 50 Hz; T = 7
1
T = ---, = 0.02 s
50,
rn
Angularfraquency
1t
-T
1 Hertz = 1 Hz = 1/s =
1 period per second
Maximum value and effective value of current and voltage
lmax maximum value of the electric current in A
leH effective value of the electric current in A
Emax maximum value of the voltage in V
Eett effective value of the voltage in V (voltage
that produces the same power as an identical
DC voltage across an ohmic resistor).
I
electric current in A
E
voltage in V
time ins
tt
..... ...
tt
Example:
Eett • 230 V; Emax = 7
En.ax =
Maximum value of the
electric current
lmax = fj_ • l eff
Maximum value of the
G:~.i,
E.,
Y2 · 230 V = 325 V
Three-phase current
120°
120°
t
t
.....
T (360°1
120°
Three-phase current is created from three
AC voltages each offset by 120°.
E
voltage in V
T
L1
period ins
phase 1
L2
phase 2
L3
phase 3
Eett
effective voltage between phase wire and
neutral wire = 230 V
Eett
effective voltage between two phase wires
= 400V
Maximum value of the
j
:~-V,
E.,
56
Physics: 2.8 Electricity
Electrical Work and Power, Transformers
Electrical work
W electrical work in kW - h
P electrical power in W
t time (power-on t ime) in h
-1 1:: IAii ilili ►
Electrical work
W= P·t
E><ample:
Hot plate. P = 1.8 kW; t = 3 h;
W = 7 in kW • h and MJ
1 kW • h = 3.6 MJ
NQ=
W - P - t = 1.8 kW - 3 h = 5.4 kW · h = 19.44 MJ
= 3600000 W - s
Electrical power with direct current and alternating or three-phase current with non-reactive load11
Direct or alternating current
-I
l
P
E
/
R
electr ical pow er in W
voltage (phase-to-phase voltage) in V
electric c urrent in A
resistance in Q
Power with direct
or alternating current
P= E -1
P =l 2 • R
1st e><ample:
l
Light bulb, E = 6V; 1= 5A;P = 7; R = ?
E
--
E2
P =-
P = E-1 = 6V - 5A = 30W
R
R
R =!i._= GV = 1.2 fi
/ 5A
Three-phase current
2ndeumple:
Annealing furnace, three-phase current.
E = 400V;P = 12 kW;/ = 7
Power with
P
12000W
1 =M- ✓
3 -400V = 173A
....!!..L
11 i.e. only w ith heating devices (ohm ic resistors)
Electrical power with alternating and three-phase current with reactive load component 12>
Alternating current
P
E
I
electrical power out put in W
voltage (phase-to-phase voltage) in V
electric current in A
cos,p power factor
EK8mple:
Three-phase current
Three-phase mot or, E = 400 V; I= 2 A;
COS<p = 0.85; p = ?
P = Y3 · E ·I· cos<p = Y3 ·400 V • 2 A· 0.85
= 1178W = 1.2kW
r,==1
Electric power output
Electric power output
with three-phase current
I
P= Y3·E• l • COS'{J
~
21 i.e. in electric motors and generators
Transformers
Input
side
(primary co il)
Output
side
(secondary
coil)
-- --/1
/2
mrn
N 1, N2 number of turns
E1• E2 voltages in V
/ 1,
Iz current level in A
E><ample:
N1 = 2875; N 2 = 100; E 1 = 230V; /1 = 0.25A; E2 = 7; /2 = 7
E = E1 -N2 = 230V -100 = BV
2
N1
2875
J1 -N1
N2
0.25A -2875
A
72
100
Electric current
I
Table of Contents
57
3 Technical drawing
3.1
it tH±IlJ
·~
3.2
te"1)erature ~
3.3
3.4
3.5
3.6
3.7
3.8
3.9
Basic geometric constructions
Lines and angles . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tangents, Circular arcs, Polygons . . . . . . . . . . . . .
Inscribed circles, Ellipses, Spirals . . . . . . . . . . . . .
Cycloids, Involute curves, Parabolas . . . . . . . . . .
58
59
60
61
Graphs
Cartesian coordinate system . . . . . . . . . . . . . . . . .
Graph types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
63
Drawing elements
Fonts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Preferred numbers, Radii, Scales . . . . . . . . . . . . .
Drawing layout . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Line types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
64
65
66
67
Representation
Projection methods . . . . . . . . . . . . . . . . . . . . . . . .
Views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sectional views . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hatching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
71
73
75
Entering dimensions
Dimensioning rules . . . . . . . . . . . . . . . . . . . . . . . .
Diameters, Radii, Spheres, Chamfers, Inclines,
Tapers, Arc dimensions . . . . . . . . . . . . . . . . . . . . .
Tolerance specifications . . . . . . . . . . . . . . . . . . . . .
Types of dimensioning . . . . . . . . . . . . . . . . . . . . .
Simplified presentation in drawings . . . . . . . . . .
76
78
80
81
83
Machine elements
Gear types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Roller bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Seals ..... .. .... .. .... ....................
Retaining rings, Springs . . . . . . . . . . . . . . . . . . . .
84
85
86
87
Workpiece elements
Bosses, Workpiece edges . . . . . . . . . . . . . . . . . . .
Thread runouts, Thread undercuts . . . . . . . . . . . .
Threads, Screw joints . . . . . . . . . . . . . . . . . . . . . . .
Center holes, Knurls, Undercuts . . . . . . . . . . . . . .
88
89
90
91
Welding and Soldering
Graphical symbols . . . . . . . . . . . . . . . . . . . . . . . . .
Dimensioning examples . . . . . . . . . . . . . . . . . . . .
93
95
Surfaces
Hardness specifications in drawings . . . . . . . . . .
Fo rm deviations, Roughness . . . . . . . . . . . . . . . .
Surface testing, Surface indications . . . . . . . . . . .
97
98
99
3.10 ISO Tolerances and Fits
Fundamentals ................. . ..... .. .... 102
Basic hole and basic shaft systems ........... 106
General tolerances ....... .. . .... ... ... ... .. 110
Roller bearing fits .. . ........... . ..... ...... 110
Fit recommendations . ..... .. .. .. ... ........ 111
Geometric tolerancing . . . . . . . . . . . . . . . . . . . . . . . 112
58
Technical drawing: 3.1 Basic geometric constructions
Line segments, Perpendiculars and Angles
Parallels to a line
Given: line segment AB and point Pon the desired parallel line g'
1. Arc with radius ,about A results in intersecting point C.
2. Arc with radius r about P.
3. Arc with radius r about C results in intersecting point D.
4. Connecting line segment PD is parallel line g' to AB.
A
B
(
Bisecting a line
Given: line segment AB
1. Arc 1 with radius r about A; r >
½AB.
2. Arc 2 with equal radius r about B.
3. The line connecting the intersecting points is the perpendicular
bisector or the bisector of line segment AB.
p
,
g
Dropping a perpendicular
Given: Straight line g and point P
4
1. Any arc 1 about P results in intersecting point A and B.
-----------6-
2. Arc 2 w ith radius r about A; r >
½AB.
3. Arc 3 with equal radius r about B (intersecting point C).
4. The line joining intersecting point C with P is the desired perpendicular.
Constructing a vertical line at point P
Given: Straight line g and point P
1. Arc 1 about P with any radius rresults in intersecting point A.
2. Arc 2 with same radius r about point A results in intersecting point B.
3. Arc 3 with equal radius r about B.
4. Construct a line from A to Band extend it (to intersecting point C).
5. Construct a line from point C to point P to obtain the vertical at P.
A
Bisecting an angle
3
Given: Angle a
1. Any arc 1 about S yields intersecting points A and B.
2. Arc 2 with radius ,about A; r>½ AB.
3. Arc 3 with equal radius r about B results in intersecting point C.
4. The line joining intersecting point C with S is the desired
bisected angle.
Dividing a line
2
3
4
5
Ak<::--,-,,~--,~--,~--,~----:lB
Given: Line AB should be divided into 5 equal parts.
1. Construct a ray from A at any desired angle.
2. Mark 5 equal lengths with a compass on the ray from A.
3. Construct a line from point 5' to B.
4. Construct parallels to 5' B through the other division points 1'- 4'.
Technical drawing: 3.1 Basic geometric constructions
59
Tangents, Circular arcs, Polygons
Tangent through point P on a cirde
Given: Circle and point P
1. Construct line segment MP and extend it.
2. Arc about P gives intersecting points A and B.
3. Arcs about A and B with the same radius yield intersecting points C
and D.
4. The line passing through C and Dis perpendicular to PM.
Tangent from a point P to a circle
Given: Circle and point P
1. Bisect MP. A is the midpoint.
2. Arc about A with radius r = AM yields intersecting point P. Tis the
tangent point.
3. Connect T and P.
4. MT is perpendicular to PT.
Rounding an angle (arc tangent to two straight lines)
Given: Angle ASB and radius r
1. Construct parallels to AS and BS of distance r. Their intersection M is
the desired center of the circular arc of radius r.
2. The intersection of the perpendiculars from M to the line segments
AS and BS are the transition points C and D for the arc.
Connecting two cirdes by arcs
Given: Circle 1 and circle 2; radii R; and R0
1. Circle about M 1 with radius R; + r 1.
2. Circle about M 2 with radius R; + r2 intersects with 1 to yield
intersecting point A.
3. Connecting M1 and M2 with A yields contact points Band C
for the inside radius R;.
4. Circle about M1 w ith radius R0 - r 1.
5. Circle about M 2 with radius R0 - r2 combined with step 4 results
in the intersecting point D.
6. D connected to M 1 and M 2 and extended gives the contact points E
and F for the outside radius R0 .
Circumscribed regular polygon (e.g. pentagonl
Given: Circle of diameter d
1. Divide AB into 5 equal parts (page 581.
2. An arc centered at A with radius r = AB yields points C and D.
3. Construct lines from C and D to 1, 3, etc. (all odd numbersl.
The intersecting points on the circle yield the desired vertices of the
pentagon.
For polygons with an even number of angles C and Dare connected
to 2, 4, 6 etc. (all even numbersl.
Circumscribed hexagon, dodecagon
A
Given: Circle of diameter d
1. Arc centered at A with radius r=
"t,
D
(
f
2. Arc with radius r about Band A.
3. Construct line segments connecting the intersecting points to yield
the hexagon.
B
For a dodecagon find intermediate points
including intersections at C and D.
60
Technical drawing: 3.1 Basic geometric constructions
Inscribed and circumscribed circles for triangles, Circle center point, Ellipse, Spiral
Circle inscribed in a triangle
Given: Triangle A, B, C
1. Bisect angle a .
2. Bisect angle {J (intersecting at point M).
3. Inscribed circle about M .
Circle circumscribing a triangle
Given: Triangle A, B, C
1. Construct the perpendicular bisector of line segment AB.
2. Construct a perpendicular bisector on line segment BC (intersecting
at point M ).
3. Circumscribed circle about M.
Finding the center of a circle
Given: Circle
1. Choose any straight line a that intersects the circle at A and B.
a
2. Straight line b (approximately perpendicular to straight line a) intersects circle at C and D.
3. Constru ct perpendicular bisectors on line segments AB and CO.
4. Intersecting point of t he perpendicular bisectors is the center M of
the circle.
Constructing an ellipse from two circles
Given: Axes AB and CD
1. Two circles about M with diameters AB and CD.
2. Construct several rays through M which intersect both circles
(E, F).
3. Construct parallels t o the two principle axes AB and CD through E
and F. Intersecting point s are points on the ellipse.
Constructing an ellipse in a parallelogram
Given: Parallelogram with axes AB and CD
1. A semi-circle with radius r- MC about A yields point E.
2. Subdividing AM (or BM) into halves, quarter~ nd eighths yields
points 1, 2 and 3. Construct parallels to axis CD through these points.
3. Dividing EA in halves, quarters and eighths yields points 1, 2 and 3
on the axis AE. Parallels to axis CD through those points give intersecting points Fon the circular arc.
D
4. Construct parallels t o AE through intersection _QQints F to the semi-cir•
cle axis, from there construct parallels to axis AB.
5. Parallel intersection points of matching numbers are points on the ellipse.
Spiral (approximate co nstruction using a compass)
Given: Rise a
1. Construct square ABCD with a/4.
2. A quarter circle of radius AD centered at A yields E.
3. A quarter circle of radius~ centered at B yields F.
4. A quarter circle of radius CF centered at C yields G.
5. A quarter circle of radius DG centered at D yields H.
6. A quarter circle of radius AH centered at A yields I (etc).
Technical drawing: 3.1 Basic geometric constructions
61
Cycloid, Involute, Parabola, Hyperbola, Helix
auxiliary
circle 5
intersection point of
auxiliary circle 5 with
parallel line 5
Cycloid
Given: Rolling circle of radius r
1. Subdivide the pitch circle into any number of equal sized parts, e.g. 12.
2. Divide the base line(= extent of the pitch circle = n - d) into equal parts,
in this case 12.
3. Vertical lines from segment poi nts 1- 12 on the base line to the extended vertical center line of the rolling circle yield the midpoints
M 1-M12-
4. Construct auxiliary circles about the midpoints M1- M12 with radius r.
horizontal
center line
5. The intersecting points of t hese auxiliary circles w ith the parallels
through the points on the rolling circle having the same numbers give
the points of the cycloid.
Involute
Given: Circle
1. Subdivide the circle into any desired number of equal sized parts,
e.g. 12.
2. Construct tangents to t he circle at each section.
3. Mark off the length of the developed circumference on each tangent
from its contact point.
4. The curve through t he endpoints forms the involute.
Parabola
Given: Orthogonal parabola axes and parabola point P
1. Parallel g to vertical axis through point P gives P'.
2. Divide distance OP' on the horizontal axis into any desired number of
parts (e.g. 5) and construct parallels to the vertical axis.
3. Subdivide distance PP' into the same number of segments and connect
to origin at 0.
4. Intersecting points of the lines w ith the matching number yield points
on the parabola.
Hyperbola
Given: Orthogonal asymptotes through Mand point Pon the hyperbola.
1. Construct lines g 1 and g2 parallel t o the asympto tes through point Pon
the hyperbola.
2. Const ruct any desired number of rays from M.
3. Construct l ines through the intersect ions of the rays w ith g 1 and g2
parallel to the asymptot es.
4. Intersecting points of the parallel lines (P 1, P2 ... ) are points on the
hyperbola.
•
Heliocoidal line <Helix)
Given: Circle of diameter d and pitch P
1. Divide semicircle into equal sect ions, e.g. 6.
2. Div ide the pit ch Pinto twice the number of equal segments, e.g. 12.
3. Extend the same number of horizontal and verti cal lines to intersection. The int ersecting points yield points on the heliocoidal line.
62
Technical drawing: 3.2 Graphs1l
Cartesian coordinate system
of DIN 46111973 03)
Coordinate axes
abscissa (horizontal axis; x -axis)
• ordinate (vertical axis; y-axis)
P1 (x4, y2)
ordinate
Values to be plotted
positive: from the origin towards the right, or up
• negative: from the origin towards the left, or down
Marking the positive axis direction with
arrow heads on the axes, o r
• arrows parallel to the axes
origin
Formula symbols are entered in italics on the
abscissa
• abscissa below the arrow point
• ordinate to the left next to the arrow point
or in front of the arrows parallel to t he axes.
Scales are normally linear, but sometimes they are divided logarithmically.
~NI~~~
formula
symbol
t
150
characteristic
Magnitudes of values. They are placed next to the scale
ticks. A ll negative values have a minus sign.
curve
100
-.,,
Value units are placed between the two last positive
numbers on the abscissa and ordinate or after the formula symbol.
units
-0.4 -0.3 -0.2 -0.1
-SO
Grid marks simplify plotting of the values.
£ -
magnitude of
/ ,oo
numeric value
Lines (curves) connect the values that have been plotted
on the graph.
-150
200 ~ - ~- - ~ - - ~- ~
N/mm1
150 l----+-- -+~ ,,,,,,,.:i:-=----1
t
100 l - - - +~ =--h--
-+---1
0.2
0.4 % 0.5
0.3
£-
Line widths. lines are drawn in the following proportion:
Gridlines: axes : curves~ 1 : 2 : 4.
Graph sections are constructed if values are not to be
plotted in each direction from the origin. The origin may
also be hidden.
Example (spring characteristic curve):
The following disk spring values are known:
t
"-
1400
N
1200
Spring displacementsin mm
0
0.3
0.6
1000
Spring force F
in N
0
600
1000 1300 1400
800
1.0
1.3
What is the spring force F with a spring displacement of s ~ 0.9 mm?
~
.e 600
"' 400
Solution:
The values are plotted on a graph and the points are
connected by a curve. A vertical line at s a 0.9 mm
intersect s the curve at point A.
C
~
200
0.2
0.4
0.6
0.8
10
1.2 mm 1.4
spring displacement s ~
With the help of a horizontal line through A, a spring
force of F ~ 1250 N is read from the ordinate.
11 Graphs are used to represent value-based relationships between changing variables.
63
Technica l drawing: 3.2 Graphs
Polar coordinate systems, Area graphs
Cartesian coordinate system (continued)
cf. DIN 461 (1973-03)
Graphs with multiple curves
~
~r--....
N/mm1
t
- "' \
R,
1200
1000
.c
f
800
600
400
200
When measured val ues are highly scattered, a different special
symbol is used for each curve, e.g : 0 , x, □
R.
1600
:--
'I.
\.'
Marking the curves
when the same type of line is used, by using the names or
formula symbols of the variables or by using d ifferent colors
for the curves
by different types of lines
O 100 200 300 400 °( 600
temperature - -
Polar coordinate system
cf. DIN 461 ( 1973-03)
Polar coordinate systems have a 360° division.
90°
Origin (pole). Intersection of horizontal and vertical axis.
oo
180°
(360°)
Angle layout. The angle 0° is assigned to the horizontal axis to
the right of the origin.
Angle position. Positive angles are plotted counter-clockw ise.
Radius. The radius corresponds to t he magnitude of the value t o
be plotted. Concentric circles may be drawn about the o rigin to
simplify plotting of the values.
210°
90°
oo
180°
(360°)
Example:
Using a measuring machine, the roundness of a turned bushing is checked to see if it lies w ithin the required tolerance.
The out-of-roundness found was probably caused by clamping t he bushing forcefully in the chuck.
210°
Area graphs
.!:4°fl
~.2
n,:=::
"'E
I! nnn n
2005
2006
2001
2008
Bar graphs
In bar graphs the quantities to be represented are drawn as horizontal or vertical columns of equal w idth.
Pie charts
Percent values are normally represented by pie charts. In t hese
the circumference of a circular area corresponds to 100%
'" 360°).
5%
5%
~
,.~
Central angle. The percentage xto be plotted determines the corresponding central angle:
360°-x%
100%
a= - - -
25%
:"
Exam ple:
What is the central angle for the percentage of lead in t he
alloy CuPb 15Sn87
Solution:
a= 360'- 15% = 54'
100%
64
Technical drawing: 3.3 Elements of drawing
Fonts
Lettering, fonts
cf. DIN EN ISO 3098-01 1998-04) and DIN EN ISO 3098·212000-11 )
The lettering of technical drawings can be done using type style A (close-spaced) or type style B. Both styles may be
drawn vertical (V) or slanted by 15° to the right (I = italics). To ensure good legibility, the distance between the characters should be two line widths. The distance may be reduced to one line w idth if certain characters are together,
e.g. LA, TV, Tr.
cf. DIN EN ISO 3098-0 ( 1998-04)
Dimensions
b 1 with diacritic11 characters
b:, without diacritic characters
b:, w ith upper case letters and
numbers
11 diacritic = used to further dif·
ferentiate, especially for letters
Character height h or height of upper
case letters (nominal size) in mm
3.5
2.5
1.8
7
5
Ratio of dimension to character height h
Type style
a
A
2
Uh
~h
14
~h
14
B
2
W h
~h
.2§.h
10
10
20
c,
"2
Ca
d
e
!!_h
14
.!Qh
14
4
Uh
4
Uh
1
Uh
6
Uh
5
Uh
_gh
10
7
W h
3
Wh
3
Wh
1
Wh
6
Wh
Wh
b:,
Greek alphabet
4
cf. DIN EN ISO 3098-3 12000-11 l
"
lambda
n Jt
pi
M µ
mu
p
p
rho
<I> 'I'
X X
phi
chi
theta
N
V
nu
l:
0
sigma
ljl
ljl
psi
iota
- ~
xi
T
T
tau
Q
OJ
omega
omicron
y u
A
a
alpha
z
t;
zeta
A
B
p
beta
H
l)
eta
r
y
gamma
e tt
"
b
delta
I
E
epsilon
K
E
14
cf. DIN EN ISO 3098·3 (1998-04)
b:,
b1
10
K
kappa
0
0
upsilon
Roman numerals
=3
XXX = 30
N =4
V - 5
VI = 6
XL = 40
L = 50
LX = 60
VII = 7
LXX = 70
VIII
C = 100
xx = 20
cc = 200
CCC = 300
CD = 400
D = 500
DC= 600
DCC = 700
DCCC= 800 • CM = 900
M = 1000
MM =2000
Examples: MDCLXXXVII= 1687
=1
X = 10
II
=2
III
MCMXCIX = 1999
=8
LXXX = 80
MMVIII = 2008
IX = 9
XC = 90
65
Technical drawing: 3.3 Elements of draw ing
Preferred numbers, Radii, Scales
Preferred numbers and series of preferred n umbers11
cf. DIN 323-1 (1974-081
RS
R 10
R 20
R 40
RS
R 10
R20
R40
1.00
1.00
1.00
1.00
4.00
4.00
4.00
4.00
1.06
4.25
1.12
1.12
4.50
4.50
5.00
5.00
5.60
5.60
6.30
6.30
7.10
7.10
8.00
8.00
9.00
9.00
10.00
10.00
1.18
1.25
1.25
1.25
1.40
1.40
4.75
5.00
1.32
5.30
1.50
1.60
1.60
1.60
6.00
1.60
6.30
6.30
1.70
1.80
1.80
2.00
2.00
2.24
2.24
6.70
1.90
2.00
7.50
8.00
2.12
8.50
2.36
2.50
2.50
2.50
9.50
2.50
10.00
2.65
2.80
Series
Multiplier
2.80
3.00
3.15
10.00
3. 15
3. 15
3.35
3.55
RS
q5 =
R 10
q 10 =
R 20
q20 =
Yio ~ 1.6
'°r,o ~ 1.25
)'10 ~ 1.12
20
3.55
40
R 40
3.75
q40 =
)'10 ~ 1.06
Radii
cf. DIN 250 (2002-041
0.2
1
1.2
10
1.6
12
100
110
125
140
2
2.5
25
28
0.3
0.4
0.5
0.6
0.8
3
4
5
6
8
16
18
20
22
160
180
200
Values shown in bold font in the table are preferred values.
32
36
40
45
50
Scale factors21
63
70
80
90
cf. DIN ISO 5455 ( 1979-121
Reduction factors
Actual size
1: 1
56
Enlargement factors
1:2
1:5
1 : 20
1: 200
1 : 2000
2: 1
5:1
1 : 50
1: 500
1 : 5000
20 : 1
50: 1
1 : 10
1 : 100
1 : 1000
1 : 10000
10: 1
1
> Pref erred numbers, e.g. for length dimensions and radii. Their usage prevents arbitrary graduations. In the series
of preferred numbers (base series R 5 to R 401, each number of the series is obtained by multiplying the previous
number by a constant multiplier for that series. Series 5 (R 51 is preferred over R 10, R 10 over R 20 and R 20 over
R 40. The numbers of each series can be mult iplied by 10, 100, 1000, etc. or divided by 10, 100, 1000, etc.
2> For special applicat ions the given enlargement and reduction factors can be expanded by multiplying by whole
multiples of 10.
66
Technical drawing: 3.3 Elements of draw ing
Drawing layout
Paper sizes (ISO)
cf. DIN EN ISO 5457 (1999-07) and DIN EN ISO 216 (2002-03)
AO
A1
A2
A3
A4
A5
A6
841 X 1189
594 X 841
420 X 594
297 X 420
210 X 297
148 X 210
105 X 148
821 X 1159
574 X 811
400 X 564
277 X 390
180 X 277
-
-
Format
Format
dimensions11in mm
Drawing area
dimensions in mm
11 The height: w idth aspect ratio of the drawing papers are 1 : (2 (= 1 : 1.414).
Folding for DIN A4 format
C:
....
·2:
oo I :!1
·rucn :;; I .E
E:!1 0 C I ti
"'
N
~2 1N I ~
r---;:i
~
190
'-
20
105
""
title block
l.,?---'"2nd fold
/ \
/
1_
v ....
2\
d
:"
"'
,_
2nd fold: Fold a triangle of 297 mm height
by 105 mm width towards the
left.
ve
0
N
2nd fold: Fold the remainder of the sheet
so that the edge of the 1st fold is
20 mm from the left edge of the
paper.
1st fold: Fold the left side (210 mm wide)
towards the right.
0
"'
1st fold: Fold right side ( 190 mm w ide)
toward the back.
A2 420 x 594
title block
,,
~
~
w(b
4th fo ld
I L
/)
cf. DIN 824 (1981-03)
A3 297 X 420
I ,, I
Cl
\
~ 1 ~ t f old ~
Trtle block
3rd fold: Fold the right side (192 mm wide)
towards the back.
4th fold: Fold the folded packet of 297 mm
height toward the back.
cf. DIN EN ISO 7200 (2004-05). Replacement for DIN 6771-1
The width of the title block is 180 mm. The sizes of the individual data fields (field widths and heights) are no longer
stipulated, in contrast to the previous standard. The table at the bottom of this page has examples of possible field sizes.
Example of a title block:
Technical reference
R-.dept.
AB 131
11
I Susan Miller
Approved by
Created by
12
1
John Smit h [ o
Kris tin Br own
13
Type of document
Assembly drawing
I John Davis
14
15
Document status
9
released
10
Titte, additional title
A225-03300-012 4
Circular
saw -----shaf1 / 3
2
°'""-'I
Release date L
IShHt
5
6
7 8
complete with bearing
A
2008-01-15 de
1/3
Drawing specific callouts, such as scale, projection symbol, tolerances and surface specifications should be indicated
on the drawing outside of the title block.
Data fields in the title block
Field name
Max. no. of
characters
1
2
3
Owner of the drawing
Title (drawing name)
Additional title
not specified
25
25
yes
yes
4
5
6
Drawing number
Change symbol (drawing version)
Issue date of the drawing
16
2
10
yes
-
yes
yes
-
7
4
4
30
-
yes
yes
9
Language identifier (de = German)
Page number and number of pages
Type of document
yes
-
10
9
60
10
11
12
Document status
Responsible department
Technical reference
20
10
20
-
yes
yes
yes
51
26
43
13
14
15
Drawing originator
Authorizing person
Classification/key words
20
20
not specified
yes
yes
-
44
FNlld
no.
8
Reid name
optional
required
-
-
yes
-
yes
Field size (mm)
width
height
69
60
60
i---I!..18
51
7
25
43
24
9
Lines in mechanical engin-ing drawings
No.
Name, reprnentation
01.1
Solid line, thin
d. DIN Iso 128-24 (1999-121
Examples of appllcation
dimension and extension lines
• origin circles and dimension line
terminators
• diagonal crosses to mark plane
surfaces
• framing details
projection and grid lines
deflection lines on rough and
machined parts
marking for repeated details (e.g.
root diameter of toothed gearl
leader and reference lines
root of thread
hatching
position direction of layers
(e.g. laminationl
• outline of hinged section
• short center lines
imaginary intersections from
penetrations
--------Free-hand line, thin 1l
• preferably hand-drawn representing border of partial or broken views
and sections, provided that the border is not a line of symmetry or a
center line
Break line, thin 11
preferably automated drawing representing border of partial or broken views and sections, provided that the border is not a line of symmetry or a center line
01.2
Solid line, thick
visible edges and outlines
crests of threads
limit of the usable thread length
cross-section arrow lines
surface structures
(e.g. knurlsl
02.1
Dashed line, thin
• hidden edges
02.2
Dashed line, thick
• identifies allowable areas for surface treatment (e.g. heat treatmentl
04.1
Dot-dash line
Uong dash), thin
center lines
04.2
Dot-dash line
Uong dashl, thick
marking areas of (delimited)
required surface treatment
(e.g. heat treatmentl
05.1
Two-dot dash-dot line
(long dash), thin
• main representations in graphs,
edges and flow charts
system lines (steel constructionl
• mold parting lines in views
• hidden contours
partial circle in gears
hole circle
lines of symmetry
• marking section planes
• outlines of adjacent parts
• contours of finished parts within
final position of movable parts
rough parts
centroidal axes
• framing special areas or fields
contours of the shape
projected tolerance zone
portions in front of the cutting plane
• outlines of alternative designs
11 Free-hand and break line types should not be used together in the same drawing.
cf. DIN EN ISO 128-20 (2002-12)
Lengths of line elements
Llneelement
Unetypeno.
Length
Uneelement
Unetypeno.
Length
02.1, 02.2, 04. 1,
04.2 and 05.1
3-d
04.1 and 05.1
24• d
gaps
short dashes
02.1 and 02.2
12 - d
Example: Une type 04.2
points
04.1, 04.2 and
05.1
< 0.5 • d
long dashes
bl ~1-
-
2~4~-d-
-
+-if-i--=~
68
Technical drawing: 3.3 El ements of drawing
Line types
Line thicknesses and line groups
cf. DIN ISO 128-24 (1999-12)
Line widths. Normally two line types are used in drawings. They are in a ratio of 1: 2.
Line groups. The line groups are ordered in a ratio of 1: f2 (.. 1: 1.4).
Selection. Line thicknesses and line groups are selected corresponding to the type and size of drawing, as well as to
the drawing scale and the requirements of microfilming and/or method of reproduction.
Associated line thicknesses (dimension in mm) for
Thick lines
Line group
Thin lines
Dimension and tolerance
callouts. graphical symbols
0.25
0.25
0.1 3
0.18
0.35
0.35
0.18
0.25
0.5
0.5
0.25
0.35
0.7
0.7
0.35
0.5
0.5
0.7
1.4
1.4
2
2
0.7
1.4
Examples of lines in technical drawings
cf. DIN ISO 128-24 (1999-12)
end position of the
moving part (05.1)
line of symmetry
(04.1)
dimension line
(01.1)
..
:
.----.
••
----
:
hidden
•
'•
identification of
section plane (04.2)
visible contours
(01.2)
extension _ _ __,
line (01.1)
A-A
hatching
line (01.1)
center line
(04.1)
r oot of
thread (01.1)
border
lines (01.1)
line of symmetry (04.1)
imaginar y
intersections
border line (01.1)
(01.1)
short center line (01.1)
surface structure
(knurl)
z
fully
hardened
(01.2)
hole circle
(041)
visible contours
(01.2)
contour (02.1)
des1gnat1on
of (heat) treatment !04.2)
edge in front of section plane (05.1)
69
Technical drawing: 3.4 Representations in drawings
General principles of presentation, Projection methods
General principles of presentation
cf. DIN ISO 128-30 (2002-05) and DIN ISO 5456-2 (1998-04)
Selection of the front view. The view that is selected for the front view is the one which provides the most information regarding shape and dimensions.
Other views. If other views are necessary for clear representation or for complete dimensioning of a workpiece, the
following should be observed:
• The selection of t he views should be limited to those most necessary.
• Additional views should contain as few hidden edges and contours as possible.
Position of other views. The position of other views is dependent upon the method of projection. For drawings based
on the first- and the third-angle projection methods (page 70) the symbol for the projection method must be given in
the title block.
Axonometric representation1>
cf. DIN ISO 5456-3 (1998-04)
Isometric projection
Diametric projection
z
X:Y:Z= 1:1:1
X : Y : Z = 0,5: 1 : 1
circle as an ellipse
X
X
Approximate construction of the ellipse:
1. Construct a rhombus tangential to the hole. Bisect the
sides of the rhombus to yield the intersecting points
M 1, M 2 and N.
2. Draw connecting lines from M 1 to 1 and from M 2 to 2
to yield the intersecting points 3 and 4.
3. Construct circular arcs with radius R about 1 and 2
and with radius r about 3 and 4.
Construction of ellipses:
1. Construct an auxiliary circle with radius r = d/2.
2. Subdivide height d into any desired number of equal
segments and construct grids (1to 3).
3. Subdivide the diameter of the auxiliary circle into the
same number of g rids.
4. Transfer the segment lengths a, b etc. from the auxiliary circle to the rhombus.
13
auxiliary circle
Cabinet projection
Cavalier projection
z
X : Y: Z = 0.5: 1 : 1
ellipse as
a circle
y
Ellipse construction ident ical to that on page 60 (ellipse
construction in a parallelogram).
Ellipse construction identical to that of the diametric projection (above).
11 Axonometric representations: simple, graphical representations.
70
Technical drawing: 3.4 Representations in drawings
· ·
h d
Pro1ect1on
met O s
cf DIN ISO 128 30 12002 051
dfld DIN ISO 5456 2 11998 041
Arrow projection method
Marking the direction of observation:
• with arrow lines and upper case letters
gJ f-s1 I
Marking the views:
• with upper case letters
Locations of the views:
• any location with respect to front view
Layout of upper case letters:
• above the views
• vertical in reading direction
• above or to the right of the arrow
lines
First-angle projection
Locations with respect to front view F:
T
top view
below F
LS
view from
right of F
the left side
RS
left of F
view from
the right side
B
bottom view
above F
R
rear view
left or right
of F
Symbol
Third-angle projection 11
Locations with respect to front view F:
f-s-1I
lJ
T
top view
above F
LS
view from
the left side
left of F
RS
view from
right of F
the right side
B
bottom view
below F
R
rear view
left or right
of F
Symbol
@El
Symbols for projection methods
Symbol 21for
first-angle projection
Symbol for firs1-angle projection
third-angle projection
l::
E3®
Germany and most
European countries
H
Application in
English speaking countries,
e.g. USA/Canada
3-d
h font height in mm (page 64)
H=2h
d = 0.1h
11 Second-angle projection is not provided.
21 The symbol for projection method is included in the drawing layout (page 66).
71
Technical drawing: 3.4 Representations in drawings
Views
<f 01N 1so 12e 30
and 34 12002 05>
Partial views
Application. Partial views are used to avoid unfavorable
projections or shortened representations.
Position. The partial view is shown in the direction of the
arrow or rotated. The angle of rotation must be given.
Boundary. This is identified w ith a break line.
Application. It is sufficient to represent just a portion of
the whole workpiece, for example if space is limited.
Marking. W ith two short parallel solid lines through the
line of symmetry on the outside of the v iew.
Application. If the representation is clear, a partial view is
sufficient instead of a full view.
Representation. The partial view (third-angle projection)
is connect ed with the main view by a t hin dot-dash line.
Adjacent parts
00
Application. Adjacent parts are drawn if it aids in understanding t he drawing.
Representation. This is done with thin two-dot dash-dot
lines. Sectioned adjacent parts are not hatched.
' - - - ~ housing
Simplified penetrations
sfje?lzz~1is ~~
Application. If the drawing remains clearly understandable, rounded penetrating lines may be replaced by
straight l ines.
Representation. Rounded penetrat ing lines are d rawn
with thick solid lines for grooves in shafts and penetrating holes whose diameters significantly differ.
sfj~lzzz¾E_lsfsfr :_1
•BD
Implied penetrating lines of imaginary intersections and
rounded edges are drawn with t hin solid l ines at the
location at which the (circumferential) ed ge would have
been with a sharp edged transition. The thin solid lines
do not contact the outline.
Broken views
Application. To save space only the important areas of
long workpieces need to be represented.
Representation. The boundary of the remaining parts is
shown by free-hand lines or break lines. The parts must
be drawn close t o each other.
72
Technical drawi ng: 3.4 Representatio ns in d rawings
Views
cf DIN ISO 128 30
111d 34 12002 051
Repeating geometrical elements
Applicat ion. For geometric elements which repeat regularly, t he individual element only needs to be drawn
once.
8,11110
!\j_\/-
~
,2
ti
;q
,.,,,...,
Representat ion. For geometric elements which are not
drawn,
• the positions of symmetrical geometric elements are
shown with t hin dot-dash lines.
• asymmetrical geometric elements of the area in which
t hey are found are d rawn with thin solid lines.
•I
l
The number of repeated elements must be given in the
dimensioning.
1
Parts at a larger scale (details!
z
Application. Partial areas of a workpiece which can not
be clearly represented may be drawn at a larger scale.
Z (10 , 1)
Ei U1 ti]
Representation. The partial area is framed w ith a t hin
solid line or encircled and marked w ith a capital letter.
The partial area is represented in an enlarged detail v iew
and is identified w ith the same capital letter. The enlarged scale is addit ionally given.
Minimal inclines
r n
I
~
i
Application. Minimal inclines on slopes, cones or pyram ids which cannot be shown clearly, do not have to be
drawn in the corresponding projection.
I
Represent ation. The edge representing the projection of
t he smaller d imension is drawn with a thick solid line.
i
Moving parts
,, ,
I I ---------
7
\
Application. Depicting alternative positions and limits of
movement of parts in assembly drawings.
->---=::-3-H-
i
r
T
Represent ation. Parts in alternate positions and limits of
movement are drawn wit h two-dot dash-dot lines.
l
Surface structures
~
Representation. Structures such as knurls and embossing are represented w ith t hick solid lines. Partial representation of the structure is preferable.
73
Technical drawing: 3.4 Representations in drawings
·
I ·
SeCtlOna VleWS
cf DIN ISO 12840
44 and 50 12002 051
Section types
view
full section
Section. The interior of a workpiece can be shown with
a section. The front part of the workpiece, which hides
the view to the interior, is perceived to be cut out.
-=~j
- -~
Q
In a section it is possible t o represent:
Q
• the cutting plane and additional workpiece outlines
lying behind the cutting plane or
-l
L
• only the cutting plane.
half section
part ial section
Full section. The full section shows the conceptualized
workpiece sectioned in a plane.
Half section. In a symmetrical workpiece one half is
represented as a view, the other half as a section.
Partial section. A partial section shows only part of the
workpiece in section.
Definitions
A
.
___,...---- section
line
cr oss-
Cutting plane. The cutting plane is the imaginary plane
w ith which the workpiece is sectioned. Complicated
workpieces can also be represented in two or more cutting planes.
Cross-section area. It is formed by the theoretical sectioning of t he workpiece. The cross-section area is
marked with hatch lines (see below and page 75).
Section line. It marks the position of t he cutting plane;
for two or more cutting planes it marks the cutting path.
T he section line is drawn with a thick dot-dash line.
---
A
8
___,
8-8
~m
For two or more cutting planes the path of t he section
line is emphasized o n the ends of the corresponding
plane using short thick solid lines.
Marking the section line. It is done w ith the same upper
case letters. Arrows drawn with thick solid lines indicate
the direction for viewing the cutting plane.
Marking the section. The sectional v iew is marked w ith
the same upper case reference letters as the section
lines.
---;
8
Hatching of sections
Hatching. The hatching is drawn with parallel solid lines,
preferably at an angle of 45° to the centerline or to the
main outlines. The hatching is interrupted for lettering.
Hatching is used for
• individual parts - all hatch lines for cross-section areas
should be in t he same direction and at the same spacing,
• parts adjacent to each other - hatch lines for t he different parts should be in different directio ns or at different spacing.
large cross-section areas - hatching preferably only
near boundaries or edges.
74
Technical drawing: 3.4 Representations in drawings
•
I •
SeCtlOOa VleWS
rf DIN ISO 128 40
c 4 and 5J ,2002 051
Special sections
II
II
{
rl
I
I
I
I
I
I
Profile sections. They may be
• drawn rotated in a view (revolved section).
The contour lines of the section are represented w ith
thin solid lines and are drawn w ithin the interior of the
part.
• taken out of a view (removed section).
The section must be connected w ith the view by a thin
dot-dash line.
Sections with intersecting planes. If two planes intersect. o ne cutting plane may be rotated in the projection
plane.
Details of rotated parts. Uniformly arranged details outside of the cross-section area, e.g. holes, may be rotated
in the cutting plane.
Outlines and edges. Contours and edges lying behind
the cutting plane are only drawn if they add clarity to the
drawing.
Parts that are not sectioned
Not sectioned in the lengthwise direction:
• parts that are not tiollow, e. g. screws, bolts, pins,
shafts
• areas of an individual part which should protrude from
the base body, e.g. ribs.
Notes on drawing
Tool edges
Circumferential edges. Edges exposed by sectioning
must be represented.
Hidden edges. In sections the hidden edges are not
represented.
Edges on the center line. If an edge falls on a centerline by sectioning, it is represented.
edge on the
t5 1K
Half-sections in symmetrical workpieces
Section halves of symmetrical workpieces are preferably
drawn in relation to the center line,
• below, w ith horizontal center lines
• to the right, for vertical center lines.
75
Technical drawing: 3.4 Representations in drawings
Hatching, Systems for entering dimensions
Hatching
cf. DIN ISO 128-50 (2002-05)
Section areas are generally marked with basic hatching w ithout consideration of the material.
Parts whose material should be emphasized can be identified using specific section lining.
Basic hatching (without considering the material)
Solids
~
Natural materials
- ----'··-··
~ ----·- · j
[]][IJ
wood
Metals
z-zegi
77,;~
~~~
carbon steel
~~;,·,
/// /// ///l
~ -:~/~!~
glass
~
...a
alloyed steel
~~~
..
_/ ·-/~
ceramic
Plastics
~
Ferro us
metals
cast iron
N on-ferrous
metals
r,-(ffffe701
~.£2.~
light alloys
~J
heavy m etals
9
~
J;
1- - -·1
. .
~
c
thermoplastics
~
- -J
oil
,~~
~.=<?_-=?.:"j
thermoset plastics
:l
~ -•
~
elastomers, rubber
Systems for entering dimensions
35 ! 0.02
- - -~
water
grease
t:: · ---:-~---:-. ~
.
.
~.-.=-::==::j
fuel
cf. DIN 406-10 (1992-12)
The dimensioning and tolerancing of workpieces can be
based on
• function,
• manufacturing or
• testi ng.
Several systems of dimensioning may be used within a
single drawing.
Dimensioning based on function
Characteristic. Selection, entry and tolerancing of the
dimensions is done according to design requirements.
Dimensioning based on fabrication
Characteristic. Dimensions which are necessary for
fabrication are calculated from functional dimensions.
+0.04
41 -0.01
Dimensioning based on testing
Characteristic. Dimensions and tolerances are entered
in the draw i ng according to the planned testing.
¢12 H8
76
Technical drawing: 3.5 Entering dimensions
Dimensioning drawings
Dimension lines, dimension line terminators, ext-ion lines, dimension numbers cf. DIN 406-11 (1992-12)
Dimension lines
ext ension Line dimension number
40/
dimension line
~
Design. Dimension lines are drawn as thin solid lines.
Entry. Dimension lines are used for:
length dimensions parallel to the length t o be dimensioned
angle and arc dimensions as a circular arc about the
center of the angle or arc.
dimension line termina t or
65
Limited space. If space is limited, dimension lines may be
• extended to the outside using extension lines
• entered within the workpiece
• drawn t o the edges of the part body.
20
Spacing. Dimension lines should have a minimum distance of
10 mm from the edge of bodies and
• 7 mm between each other.
Dimension Nne terminator
~
Extension lines
Dimension arrowheads. Generally arrowheads are
used t o delimit the boundaries of dimension lines.
• arrowhead length: 10 x dimension line width
• angle of lateral side: 15°
Dots. Used if space is limited.
• diameter: 5 x dimension line width
Design. Extension lines are drawn perpendicular to the
length to be dimensioned with thin solid lines.
Special features
• Symmetrical elements. Centerlines may be used as
extension lines w ithin symmetrical elements.
8
16
• Breaks in extension lines may be used e.g. for entering dimensions.
1 5
• Within a view the extension lines may be drawn to
spatially separate elements of the same o r similar
shape.
extension Line passing
through part
• Extension lines may not be extended from one view to
another view.
Dimension numbers
55
Entry. Dimension numbers are entered
• in standard lettering according to DIN EN ISO 3098
• with a minimum font size of 3.5 mm
• above the dimension line
• so that they are legible from below and from the right
• for multiple parallel dimension lines - separated from
each other.
Limited space. If there is limited space, the dimensioning numbers may be entered
• on a leader line
• over the extension of the dimension line.
Technical drawing: 3.5 Entering dimensions
77
Dimensioning drawings
Dimensioning rules, leader and reference lines, angle dimensions,
square and width across flats
cf. DIN 406-11 (1992- 121 and
DIN ISO 128-22 (1999- 111
Dimensioning rules
Entering dimensions
6
Each dimension is only entered once. If two elements
have identical dimensions but different shapes, they
must be dimensioned separately.
If multiple views are drawn, the dimensions should be
entered where the shape of the workpiece is best
recognized.
-+-
t t
N
+-- - --- "'
61
1.5
15
12
50
10
(15) 10
1 6
15
15
t:5
Symmetrical workpieces. The position of the center
line is not dimensioned.
Chained dimensions. Series of chained dimensions
should be avoided. If chained dimensions are required
for reasons related to manufacturing, one dimension of
the chain must be in parentheses.
Flat workpieces. For flat workpieces that are only drawn
in one view, the thickness dimension may be entered
with the reference letter t
in the view or
• near the view.
Leader and reference lines
Leader lines. Leader lines are drawn as thin solid lines.
They end
leader line
WAF24
reference line
¢4
leader line
w ith an arrowhead, if they point to solid body edges
or holes.
with a dot, if they point t o a surface.
w ithout marking, if they point to other lines.
Reference lines. Reference lines are d rawn in the reading direction w ith t hin solid lines. They may be connected t o leader lines.
Angular dimensions
Extension lines. The extension lines point toward the
vertex of the angle.
Dimension numbers. Normally these are entered tangentially to the dimensioning line so that their lower
edge points to the vertex of the angle if they are above
the horizontal center line and w ith their upper edge if
they are below it.
Square, width across flats
~ ffi
Square
Symbol. For square shaped elements the symbol is set
in front of the dimensioning number. The size of t he
symbol corresponds to the size of t he small letters.
Dimensioning. Square shapes should preferably be
dimensioned in the view in which their shape is recognizable. Only the length of one side of the square should
be entered.
~WAF11
~WAFH
~
Width across flats
Symbol. For widths across flats the upper case letters
WAF are placed in front of the dimensioning number, if
the width between flats cannot be dimensioned.
78
Technical drawing: 3.5 Entering dimensions
Dimensioning drawings
Diameters, radii, spheres, chamfers, inclines, tapers, arc dimensions
cf. DIN 406-11 (1992-121
Olarnet., raclus. sphere
Diameter
Symbol. For all diameters the symbol 0 is placed before the dimension number. Its overall height corresponds
to the height of the dimensioning number.
Limited space. In the case of limited space the dimension references the w orkpiece feature from the out side.
Radius
Symbol. For radii the lower case letter r is placed before
the dimensioning number.
Dimension lines. Dimension lines should be drawn
from the center of the radius or
• from the direction of the m idpoint.
(ff)
Sphere
Symbol. For spherical shape w orkpiece features the
capit al letter S is placed before the diameter or radius
sym bol.
Chamfers, countersinks
45° chamfers and countersinks of 90° can be simply
dimensioned by indicating t he angle and the chamfer
w idth. Both drawn and undrawn chamfers may be
dimensioned using an extension line.
2x45°
0.6x45°
~ 2 45°
X
0.6 x45°
Other chamfer angles. For chamfers w ith an angle deviati ng from 45° the
• angle and the chamfer w idth or
• the angle and the chamfer diameter
are t o be ent ered.
~
Inclines, tapers
cs
l:::::::..30%
Incline
Symbol. The symbol b.. is ent ered before the dimension numbers.
Orientation of the symbol. The symbol is oriented so that
its incline matches the incline of the workpiece. Preferably
the sym bol is connected to the inclined surface w ith a
reference line or a leader line.
Taper
Symbol. The sym bol C> is entered before the dimension numbers on a reference line.
Orientation of the symbol. The orientation of the symbol
m ust match the direction of the workpiece taper. The
reference line of the symbol is connected t o the outline
of the taper w ith a leader line.
Arc dimensions
Symbol. The symbol "
is entered before the dimension numbers. For manual drawing the arc may be
labeled w ith a sim ilar symbol over the dimension number.
Technical drawing: 3.5 Entering dimensions
79
Dimensioning drawings
Slots, threads, patterns
cf. DIN 406-11 (1992-12) and DIN ISO 6410-1 (1993-12)
Slota
10P9
~1
Slot depth. The slot depth is measured
N
0
,,...
"'
closed slot
open slot
h = 5+0.2
°'
z
from the slot side for closed slots
• from the opposing side for open slots.
♦
fT1
open slot
10N9 x 5+0.2
I
__!_ __ _ _
Simplified dimensioning. For slots represented only in
the top view, the slot depth is dimensioned
• with the letter h or
• in combination with the slot width.
With slots for retaining rings the slot depth may also be
entered in combination with the slot width.
~
36+0.3
Limit deviations for tolerance classes JS9, N9, P9 and
H11: page 109
Slot dimensions
for wedges see page 239
for fitted keys see page 240
for retaining rings see page 269
Threads
M16-RH
Code designation. Code designators are used for standard threads.
Left hand threads. left hand threads are marked with
LH. If both left hand and right hand threads are found on
a workpiece, the right hand threads get the addition RH.
:,::
-t
'°
i:._,__ -Pl==~----1
20
Multiple screw threads. For multiple screw threads the
pitch and the spacing are entered behind the nominal
diameter.
length specifications. These give the usable thread
length. The depth of the basic hole (page 211) is normally not dimensioned.
Chamfers. Chamfers on threads are only dimensioned if
their diameters do not correspond to the thread core or
the thread outside diameter.
Radial and linear patterns
10
20x16(=320)
(10)
16
Identical design elements. The following data is given
for spacing of identical design elements having the
same distance or angle between them
• the number of elements
• the distance between the e lements
• the overall length or overall angle (in parentheses).
12
8x 12(=96)
80
Technical drawing: 3.5 Entering dimensions
Dimensioning drawings
Tolerance specifications
cf. DIN 406-12 (1992-12!, DIN ISO 2768-1 (1991-06! and DIN ISO 2768-2 (1991-04)
Tolerance specifications using deviations
!
1
• 0.15
35 -0.10
I
I
I
Entry. The deviations are entered
~
~ 1 - - - r ' -~I :_•+
I 4o -0.11-oJ
• after the nominal size
• if there are two deviations, the upper deviation is
shown above the lower deviation
for equally large upper and lower deviations by a
± marl< before the number value, w hich is only entered
once
for angle dimensioning with units specified.
Tolerance specifications using tolerance classes
Entry. Tolerance classes are entered for
single nominal sizes: after the nominal size
• parts shown inserted: the tolerance class of the interior
dimension (hole! is before or over the tolerance class
of the outer dimension (shaft!.
Tolerance specifications for specific areas
Area of application. The area t o w hich the tolerance
applies is bounded by a thi n solid line.
Tolerance specifications using general tolerances
Application. General tolerances are used for
• linear and angular dimensions
• form and position.
They apply to dimensions without individual t olerance
entry.
DIN 509 - E 0.8 • 0.3
Drawing entry. The note for general tolerances (page
,....
"'
'&
~--e~l-ffi ~
bolts
'
40 ~
53
11 Ol can be located:
near the individual part drawings
• for title blocks according to DIN 6771 (retracted!:
in the title block.
10SPb 20
Entries. Given are:
ISO 2768-m
• the sheet number of the standard
• the tolerance class for linear and angular dimensions
• the tolerance class for form and positional tolerances,
as needed.
Technical drawing: 3.5 Entering dimensions
81
Dimensioning in drawings
Dimensions
cf. DIN 406-10 and - 11 (1992-12)
Types of dimensioning
10 60
basic dimension
5x45°
Basic Dimensions. The basic dimensions of a workpiece
are the
• total length
• total width
• total height.
Shape dimensions. Shape dimensions establish, e.g. the
dimensions of slots
• dimensions of shoulders.
Positional dimensions. These are used to specify the
location of
holes
slots
elongated holes, etc.
Special dimensions
Rough dimensions
Function. Rough dimensions might be used to g ive
information about, for example, the dimensions of cast
or forged workpieces before machining.
Labeling. Rough dimensions are put in brackets.
Auxiliary dimensions
Function. Auxiliary dimensions give additional information. They are not necessary to geometrically define the workpiece.
Labeling. Auxiliary dimensions are
put in parentheses
• entered without tolerances.
30
(35]
rough dimension
10
I: 25 .I 20
p
Dimensions not drawn to scale
Labeling. Dimensions not drawn to scale might be used
for drawing changes, for example, and they are marked
by underlining.
Prohibited are underlined dimensions in computer aided
(CAD) drawings.
Control dimensions
Function. It should be noted that these dimensions are
especially checked by the purchaser. If necessary a 100%
check will be performed.
Labeling. Control dimensions are set in frames with
rounded ends.
Theoretically precise dimensions
Function. These dimensions give the geometrically ideal
(theoretically precise) position of the shape of a design
feature.
Labeling. The dimensions are placed in a frame without
tolerance specifications and correspond with geometric
tolerancing.
82
Technical drawing: 3.5 Entering dimensions
Types of dimensioning
Parallel dimensioning, running dimensioning, coordinate dimensioning11 cf. DIN 406-1 1 ( 1992-121
Stack dimensioning
Dimension lines. Several dimension lines are entered
together for
• stacked linear dimensions
0
N
N
• concentric angular dimensions.
0
~
Running dimensioning
220 ,--,------,----t--190r
Origin. The dimensions are entered outwards from the
origin in each of the three possible directions. The origin
is indicated by a small circle.
11~~-t--+----+
Dimension lines. The following applies for the entries:
50
0-6-+"-+---+-+--+----'Sf-.-..
t:12
0
0
"'
• As a rule only one dimension line is used for each
direction.
If there is limited space two or more dimension lines
may be used. The dimension lines may also be shown
broken.
Dimensions
• must be provided with a minus sign if they are entered
from the origin in the opposite direction.
• may also be entered in the reading direction.
1 : : g +-0
.
-50
110
0
0
-50 _lli__j
Coordinate dimensioning
--¢
y
Item X
d
1
50 50 !2140
180 190 !2130
2
3 220 115 !2175
325 50
4
Cartesian coordinates (page 631
Coordinate values. These are
• entered in tables or
• entered near the coordinate points.
Point of origin. The point of origin
is entered with a small circle
• can lie at any location of the drawing.
Dimensions. These must be provided with a minus sign
if they are entered from the origin in the opposite direction to the positive direction.
t : 12
11
Item
1
2
3
4
r
,p
d
140 o• !2130
140 30° !2130
100 so• !2130
140 90° !2130
Polar coordinates (page 63)
Coordinate values. The coordinate values are entered in
tables.
Parallel dimensioning, running dimensioning and coordinate dimensioning may be combined with each other.
83
Technical drawing: 3.5 Entering dimensio ns
Simplified presentation in drawings
Simplified representation of holes
d. DIN 6780 (2000-10)
Hole baM, line widths for simpllfled representation
Full scale represen-I Full scale repretalion, full scale
sentation, simplidimensioning
tied dimensioning
I sentation,
Simplified represimplitied dimensioning
~ ~ rn
00 ag-m¢10x 14U
¢10x14U
¢10x14U
¢10x 14U
¢10x14U
Hole base
The shape of the hole base is given by a symbol
if necessary.
The symbol U for example means a flat hole
base (cylindrical end bore).
Line widths
For holes depicted in simplified form, the positions of holes should be drawn as:
• simply the intersecting axes in the top view
• the position of the holes in thick solid lines in
parallel axis representation.
Stepped holes, countersinks and chamfers, internal thraeds
¢ 11•6.SU
¢6.6
¢11•6.SU
¢6.6
dJ
~ ~ [TI
6
¢ 11•6.SU
¢6.6
¢ 11•6.SU
¢6.6
~~ ~
~ ~~
90°
¢ 12.4•90°
¢6.6
¢ 12.4x90°
¢6.6
6
M10
ffii8 ~ rn
M10•15/20
Stepped holes
For holes w ith two or more steps the dimensions
are w ritten under each other. Here the largest
diameter is written on the first line.
Countersinks and chamfers
For countersinks and hole chamfers the largest
countersink diameter and the countersink angle
are given.
M10x15/20
Internal threads
The thread length and the hole depth are separated by a slash. Holes without depth specificalion are drilled through .
Examples
¢12•90°
¢10H7
¢12•90°
¢10H7
M10-LHx12
M10-LHx12
¢8•0.3
¢8x90°
¢4.3
¢8•0.3
¢8x90°
¢4.3
ffi ~ rn
¢10H7
Hole 0 10H7
Through hole
Chamfer 1 x 45°
X
M10-LH
90°
• rn
~~~
-
.
Left hand thread M 10
Thread length 12 mm
Drilled through core hole
Cylindrical countersink 08
Bore depth 0.3 mm
Through hole 04.3 with
cone shaped counterbore 90°
Countersink diameter 0 B
84
Technical drawing: 3.6 Machine elements
Gear types
Representation of gears
Spur gear
cf. DIN ISO 2203 ( 1976-06)
Bevel gear
Worm gear
External helical gear
Internal spur gear
Rack and Pinion
Bevel gear set (shaft angle 90°)
Worm and worm gear
Sprockets
Positive drive belts
85
Technical drawing: 3.6 Machine elements
Roller bearings
Representation of roller bearings
simplif"ted
graphical
cl. DIN ISO 8826-1 (1990-121and DIN ISO 8826-2 (1995-101
Elements of a detailed simplified representation
Representation
explanation
[±] f;)
For general purposes a
roller bearing is represented as square o r rectangular with a free-standing upright cross.
a~
If necessary, the ro ller
bearing can be represented by its outli ne
and a free-standing
upright cross.
explanation, application
element
Long, straight line; for representing
the axis of the roller bearing elements for
bearings that cannot be adjusted.
,.,,--....._
Long, curved line; for representing the axis
of the roller bearing elements for bearings
that can be adjusted (self-aligning bearing).
Short straight line; used to represent the
position and number of rows of roller
bearing elements.
I
0
Circle; for the representation of roller bearing elements (balls, roller, needle rollers)
which are drawn perpendicular to their axis.
Examples of detailed simplified representation of roller bearings
Representation of single-row roller bearings
detailed
designation
graphical
simplified
Fl ~~
Fl g
f21 ~~
17 LJ
~ 1_m
~ ~
Radial-deep
groove ball
bearings,
cylindrical roller
bearings
Radial spherical
roller bearing
(barrel-shaped
bearing!
Angular-contact
ball bearing,
tapered roller
bearing
Needle bearing,
needle roller
assembly
Axial-deep grooved
ball bearing,
axial-roller bearing
Axial-spherical
roller bearing
Combined ball bearings
II ~
Combined
radial-needle
bearing w ith
angular-contact
ball bearing
~~
Combined
axial-ball bearing
w ith radial needle
bearin g
Representation of double row roller bearings
detailed
graphical
designation
simplified
Radial-deep
groove ball
bearings,
cylindrical roller
bearings
~ ~~
H ~~
~
II ~
~
I'+ +'I
n
m
-
Spherical roller
bearing, radialspherical
roller bearing
Angular-contact
ball bearings
Needle bearing,
needle roller
assembly
Axial-deep grooved
ball bearing,
dual action
Axial-deep grooved
ball bearing w ith
spherical seating,
dual action
Representation perpendicular to the rolling element axis
_
m
/ -~\
~
4-\ ·+-· t+
•
· ,. · _/
Roller bearing w ith
any desired type of
roller element
shape (balls,
rollers, needles)
86
Technical drawing: 3.6 Machine elements
Representation of seals and roller bearings
Simplified representation of seals
cf. DIN ISO 9222-1 11990-12) and DIN ISO 9222-2 (1991-03)
Representation
simplified
graphical
Elements of a detailed simplified representation
explanation
For general purposes a
seal is represented by a
square or rectangle and a
separate diagonal crossmark. The sealing direction can be given by an
arrow.
element
explanation, application
l ong line parallel to the sealing surface;
for the fixed (static) sealing element.
long diagonal line; for the dynamic sealing element; e.g. the sealing lip. The
sealing direction can be given by an
arrow.
/
Shon diagonal line; for dust l ip seal,
scraper rings.
/
Shon l ines pointing t o the middle of the
symbol; for the static pans of U-rings
und V-rings. packing.
If necessary, the seals can
be represented by the outline and a free-standing diagonal cross-mark.
Shon lines. which point to the middle of
the symbol; for the sealing lips of Urings und V-rings, packing.
T LJ
T and U; for non-contact seals.
Exampl• of detailed simpllfled repr-.itation of seals
Profile gaskets, packing sets, labyrinth seals
Shaft seals and piston rod seals
designation for
detailed
simplified
graphical
~ ;
~ ;
[Z] ~
rotation
linear
motion
Shaft seal
without dust
lip seal
Rod seal
without
stripper
Shaft seal
with dust lip
seal
Rod seal
with stripper
Shaft seal,
dual action
Rod seal,
dual
actio n
detailed
simplified
graphical
detailed
simplified
s ;I s ~
EJ ■ [2J ~
Q] ~ ~ .t...
Examples of simplified representation of seals and roller bearings
Deep grooved roller bearings and
radial shaft seal w ith dust lip seal'I
graphical
Dual row deep grooved roller bearings
and radial shaft seal 21
11 Top half: simplified representation; bottom half: graphical representation.
21 Top half: detailed simplified representation; bottom half: graphical representation.
Packing set21
87
Techn ical drawing: 3.6 Machine elements
Representation of retaining rings, Slots for retaining rings,
Springs, Splines and serrations
Representation of retaining rings and slots for retaining rings
Assembly dimension
Representation
f n
a
$ ~ I@
_
Retaining
rings for
shafts
(page 269)
""'
I
Retaining
rings for
holes
(page 269)
$!
,<t I
a --!..
mH13 I
~"O
f -....:_
I
Deviations
reference plane
for dimensioning11
a: roller bearing
width+ retaining
ring w idth
~ reference plane
for dimensioning11
I~
Deviations for d:,:
upper deviation: 0 (zerol
lower deviation: negative
Deviations f or a:
upper deviation: positive
lower deviation: O (zero)
Deviations for d:,:
upper deviation: positive
lower deviation: 0 (zero)
Deviations for a:
upper deviation: positive
lower deviation: O(zero)
H For functional reasons the reference plane for the dimensioning of slots is the locating face o f the part to be secured.
Representation of springs
Name
Cylindrical
helical compression
spring (round
w ire}
Cylindrical
helical tension spring
cf. DIN ISO 2162-1 (1994-08}
Reprnentation
sac:tion
view
Symbol
l·
tc
=
1F
~
-=""(£\
Disk spring assembly (disks
layered in the
same direction}
Symbol: l\_
Disk spring
assembly
(disks layered
in alternating
directions}
.IL...
~
{¼)
~.
J\.. •••
.
Representation
view
•.
Symbol
section
e e
T T
s m
f
i'
=~
~ ~
••=
~ @ ~·
.·. _
~ @
cf. DIN ISO 6413 (1990-03)
Hub
Shaft
Toothed shafts
or toothed
hubs with
involute
splines or
serrations.
Cylindrical
helical compression
spring (square
wire}
f§ I §
Representation of splines and serrations
Symbol: J l
Cylindrical
helical tension spring
1~
Disk spring
!simple}
Splines or
spline hubs
with straight
fl anks.
Name
Joint
.I\. • • •
.. . •
.
.
•
⇒ Splines ISO 14--6 x 26 n x 30: Spline profile with straight flanks according t o ISO 14, number of
splines N = 6, inner diameter d = 2617, outer diameter D = 30 (page 241)
Technical drawing: 3.7 Workpiece elements
Bosses on turned parts, Workpiece corners and edges
Bosses on turned parts
cf. DIN 67851 1991-11)
Largest diameter of the finished part in mm
Boss
Boss
d2max
dimensions
Example
--
--
¢05
·
dimen- upto 3 over3 over5 overs over 12 over 18 over 26 over40
sions
to 40
1060
to 12
to 5
10 8
to 18
1026
di.max
inmm
0.3
0.5
0.8
1.0
1.5
2.0
2.5
3.5
0.2
0.3
0.5
0.6
0.9
1.2
2.0
3.0
0.3
Drawing
entry
t· ·
lmax
~¢0.Sx0.3
inmm
Workpiece comers and edges
cf. DIN ISO 1371512000-12), replacement for DIN 6784
Workpiece edge/corner lies in reference to the ideal geometrical form
in area
inside
outside
Edge or
corner
material removal
burr
sharp edged
a
inner
edge
sharp edged
Dim. a (mm)
- 0.1; -0.3; -0.5; - 1.0; - 2.5
Symbol for
labeling workpiece
edges/comers
Symbol
element
field for entering
dimension
+
~
le: !
± 11
-0.05; -0.02; +0.02; +0.05
+0.1; + 0.3; +0.5; + 1.0; +2.5
Meaning for
Burr and material removal direction
outer edge
inner edge
Burr allowed,
material removal
not allowed
Transition allowed,
material removal not
allowed
Specification
allowed
for
Removal required, Removal required,
burr not
transition not
allowed
allowed
Example
Burr or transition
allowed
Meaning
Material removal or
t ransition allowed
11 only allowed with a dimension callout
outer edge
inner edge
Burr
Material
removal
•1
-,L
sJ
-ft J
1
Labeling of workpiece corners and edges
Examples
CoUective indications
L:.9.3
L:.95
~
Collective indications apply to all edges for which an
edge condition is not given.
Edges for which the collective indication does not
apply must be marked in the drawing.
The exceptions are placed after the collective indication
in parentheses or indicated by the base symbol.
L:.9.3
7
Collective indications which are
only valid for outside or inside
edges are given by the corresponding symbols.
lli
lli
m-ns:L .o.3
-0.1
L:.95
l=9.02
Outside edge without burr.
The allowable material removal
is between 0 and 0.3 mm.
Outside edge with allowable
burr of Oto 0.3 mm
(burr direction specified).
Inside edge with allowable
material rem oval between 0.1
and 0.5 mm (material removal
direction not specified).
Inside edge with allowable
material removal between 0 and
0.02 mm or allowable transition
up to 0.02 mm (sharp edged).
89
Technical drawing: 3.7 Workpiece elements
Thread runouts, Thread undercuts
Thread runouts for metric ISO threads
Pitch
External thread
11
ISO
standard
thread
p
d
0.2
0.25
0.3
0.35
Int ernal thread
~m;
~~~~1
M1
M 1.6
cf. DIN 76-1 (2004-06)
Thread runout 21
Pitch
11
ISO
standard
thread
max.
a1
max.
e1
p
d
0.5
0.6
0.75
0.9
0.6
0.75
0.9
1.05
1.3
1.5
1.8
2.1
1.25
1.5
1.75
1
1.2
1.35
1.5
1.8
2.3
2.6
2.8
3.4
2.1
2.25
2.4
3
3.8
X1
0.4
0.45
0.5
0.6
M2
M2.5
M3
0.7
0.75
0.8
1
M4
1.75
1.9
MS
2
M6
2.5
1.1
1.25
1.5
2
2.5
3
3.5
4
4.5
5
4
4.2
5.1
5.5
6
X1
81
max.
max.
M8
M10
M12
M 16
3.2
3.8
4.3
3.75
4.5
5.25
6
6.2
7.3
8.3
9.3
M20
M24
M30
M36
6.3
7.5
9
10
7.5
10.5
12
11.2
13.1
15.2
16.8
M42
M48
M56
M64
12.5
14
15
13.5
15
16.5
18
18.4
20.8
22.4
24
Pitch
11
ISO
standard
thread
p
d
0.2
0.25
0.3
0.35
_Ji_
91
z
/\. ,
A / ,3o min
0
Ct J ~l
Internal thread
form C and form D
X
it~
P1~1
~ 30° min.
5
11
9
e1
11 For fine threads the dimension of the thread runout is chosen according to the
pitch P.
21 As a rule; applies if no other entries are given.
If a shorter thread runout is necessary. this applies:
x2 ~ 0.5 • x 1; a, * 0.67 • a 1; e, ~ 0.625 · e1
If a longer thread runout is necessary, this applies:
B:,* 1.3-a1; 6J~ 1.6 - e1
Screw thread undercuts for metric ISO threads
External thread
form A and form B
Thread runout21
M1
M1 .6
cf. DIN 76-1 (2004-06)
External threads
Form A2I Form 9 31
dg
Y1
Y2
Y1
Y2
h13
min. max. min. max.
Internal threads
Form C21 Form 031
dg
Y1
{h
g,
Y2
H13 min. max. min. max.
0.1
0.12
0.16
0.16
d-0.3
d-0.4
d-0.5
d -0.6
0.45
0.55
0.6
0.7
0.7 0.25
0.9 0.25
1.05 0.3
1.2 0.4
0.5 d+0.1
0.6 d+0.1
0.75 d+0.1
0.9 d+0.2
0.8
1
1.2
1.4
1.2
1.4
1.6
1.9
0.5
0.6
0.75
0.9
0.9
1
1.25
1.4
0.4
0.45
0.5
0.6
M2
M2.5
M3
0.2
0.2
0.2
0.4
d-0.7
d-0.7
d - 0.8
d- 1
0.8
1
1.1
1.2
1.4 0.5
1.6 0.5
1.75 0.5
2.1 0.6
1
1.1
d + 0.2
d +0.2
1.25 d +0.3
1.5 d + 0.3
1.6
1.8
2
2.4
2.2
2.4
2.7
3.3
1
1.1
1.25
1.5
1.6
1.7
2
2.4
0.7
0.75
0.8
1
M4
MS
M6
0.4
0.4
0.4
0.6
d-1.1
d-1.2
d-1.3
d-1.6
1.5
1.6
1.7
2.1
2.45 0.8
2.6 0.9
2.8 0.9
3.5 1.1
1.75 d+0.3
1.9 d +0.3
d+0.3
2
2.5 d+0.5
2.8
3
3.2
4
3.8 1.75
4
1.9
4.2 2
5.2 2.5
2.75
2.9
3
3.7
1.25
1.5
1.75
2
M8
M10
M12
M16
0.6
0.8
1
d-2
d - 2.3
d- 2.6
d-3
2.7
3.2
3.9
4.5
4.4
5.2
6.1
7
1.5
1.8
2.1
2.5
3.2
3.8
4.3
5
d+0.5
d+0.5
d+0.5
d+0.5
5
6
7
8
6.7
7.8
9.1
10.3
4.9
5.6
6.4
7.3
2.5
3
3.5
4
M20
M24
M30
M36
1.2
1.6
1.6
2
d-3.6
d-4.4
d-5
d-5.7
5.6 8.7 3.2
6.7 10.5 3.7
7.7 12
4.7
9
14
5
6.3
7.5
9
10
d+ 0.5
d+ 0.5
d+ 0.5
d+0.5
10
12
14
16
13
6.3 9.3
15.2 7.5 10.7
17.7 9
12.7
20 10
14
4.5
5
5.5
6
M42
M48
M56
M64
2
2.5
3.2
3.2
d-6.4
d- 7
d-7.7
d-8.3
10.5
11.5
12.5
14
11
12.5
14
15
d+0.5
d+ 0.5
d+ 0.5
d+0.5
18
20
22
24
23
26
28
⇒
DIN 76-C: Screw thread undercut shape C
1
16
17.5
19
21
5.5
6.5
7.5
8
30
3.2
3.8
4.3
5
11
12.5
14
15
16
18.5
20
21
11 For fine thread screws the dimension of the thread undercut is chosen according
to the pitch P.
21 as a rule; always applies if no other entries are made
31 Only in cases where a shorter thread undercut is required.
90
Technical drawing: 3.7 Workpiece elements
Representation of threads and screw joints
~
rm 2J ~ ~
Representation of threads
cf. DIN ISO 6410-1 (1993-12)
Internal thread
'°
,
.§ ;7 ~ ~
~
e, accord. to DIN 76-1. Thread runout is normally not shown.
Bolt thread
Bolts in internal thread
Thread undercut
graphical
Pipe threads and pipe screw joints
symbolic
E3m{lt"□ ~
I
---i
Representation of screw joints
Hexagonal bolt and nut
e
detailed
sim plified
s
h1 bolt head hight
h1 nut height
h3 washer thickness
e diagonal between corners
s width across flats
d thread nominal 0
"'
h 1 ,. 0.1 • d
h1,. 0.8· d
h3'> 0.2• d
e ,. 2- d
s ,. 0.81 - e
e
Screw joint with
cap screw
Screw joint w ith
hexagonal screw
Screw joint with
countersunk head screw
Screw joint
with stud
91
Technical drawing: 3.7 Workpiece elements
Center holes, Knurls
Center holes
d . DIN 332-1 (1986-04)
Nominal sizes
Form
form 'R
_·
.rm
f
~ o
_
·
~o
-c:,'
'
cl-,
.,,
f m"'
a
t i
R
-0
A
form B
!m
l
-c:,'I
--- - ·
' ~
t
l
-c:,'I
f
~0~1~
B
-r¼
!f-~
formC
~·1~:l
-·-! f'/:.,...
~
N:t "tJ
'l::)
' ~,.>
f mm
~
1
1.25 1.6 2
2.5
2.12 2.65 3.35 4.25 5.3
d,
'l::)
0~
C
0~
NJ
fmin
1.9
2.3
2.9
3.7
4.6
5.8
7.4
9.2 11.4 14.7
3
4
5
6
7
9
11
14
tmin
1.9
2.3
2.9
3.7
4.6
5.9
7.4
9.2 11.5 14.8
a
3
4
5
6
7
9
11
14
tmin
2.2
2.7
3.4
4.3
5.4
6.8
8.6 10.8 12.9 16.4
a
3.5
4.5
5.5
6.6
8.3
10
12.7 15.6 20
b
0.3
0.4
0.5
0.6
0.8
0.9
1.2
d:3
3.15 4
5
6.3
8
10
12.5 16
=;,
18
22
22
25
1.4
1.6
18
22.4
tm in
1.9
2.3
2.9
3.7
4.6
5.9
7.4
3.5
4.5
5.5
6.6
8.3
10
12.7 15.6 20
25
b
0.4
0.6
0.7
0.9
0.9
1.1
1.7
3
d4
4.5
5.3
6.3
7.5
9
els
5
6
7.1
8.5
10
R:
B:
C:
9.2 11.5 14.8
1.7
2.3
11.2 14
18
22.4 28
12.5 16
20
25
31.5
curved bearing surface, w ithout protective countersink
straight bearing surface, without protective countersink
straight bearing surface, conical protective countersink
straight bearing surface, truncated conical protective counter
sink
d. DIN ISO 6411 (1997-1 11
A center hole is allowed
on the finished part
A center hole may not be present
on the finished part
+ -- -- jlSO 6411-A4/8.5
~ ISO 6411-A4/8.5
ISO 6411 - A4/8.5
B
1.6
18
a
Drawing callout for center holes
A center hole is
required on the finished part
5
6.3 8
10.6 13.2 17
a
A:
Form
3.15 4
6.7 8.5
< ISO 6411 - AA/8.5: center hole ISO 6411: a center hole is required on the finished part.
Form and dimensions of the center hole according to DIN 332: form A; d 1 = 4 mm; cl-, - 8.5 mm.
~'1
Knurls
"<5',"t:,r
~0
d, nominal diameter
di initial diameter
f spacing
Standard spacing values
t: 0.5; 0.6; 0.8; 1.0; 1.2; 1.6 mm
Drawing entry (example):
DIN 82-RGE 0.8
~
d. DIN 82 (1973-011
Letter
symbol
RAA
Representation
e
Name
Point
shape
Initial
diameter cl-,
Knurls with
axially parallel
grooves
-
d2 = d, - 0.5 · t
RBR
Right-hand
~ 3 0 ° knurl
-
cl-,= d 1 - 0.5 • t
RBL
~ 3 0 ° Left-hand knurl
-
cl-, = d 1- 0.5 · t
RGE
left-hand/righthand knurls
t - ~ 0
RGV
RKE
..,___
RKV
=;,
Ba
Axial and circumferential
knurl
raised
cl-, = d1- 0.67 . r
recessed
cl-, - d1 - 0.33 • t
raised
cl-, = d1- 0.67 • r
recessed
d2 = d1 - 0.33 • t
DIN 82-RGE 0.8: Left-hand/right-hand knurls. raised points, t = 0.8 mm
92
Technical drawing: 3.7 Wo rkpiece elements
Undercuts
Undercuts11
d. DIN 509 (2006-12)
form E
for cylindrical surface t o
be further machined
form F
for shoulders and cylindrical
surfaces t o be further machined
-- ~ f
i--.!--
t,
;, r l...;:1'·.l..:-1
.,,, I
60
z,. Z, = machining allowances
formG
fonnH
for small transition for planar and cylindrical surfaces
(for low loading)
to be further machined
~~z
:1. ~
;
1 "'{ ~~~
rlr 1A1-.
.,,,
-
..:-1
-
I
f
~_s-•
z
,,
[\:!', __x~.J"
0
0
I
~
-··
..:: '=i"'
--
"'T ./
- ·
I
..:-1.,,-f. ,.-f
Undercut DIN 509 - E 0.8 x 0.3: form E, radius r= 0.8 mm, undercut depth r, = 0.3 mm
=
Undercut dimensions and countersink dimensions
Form
r2I ± 0.1
r,
f
r,
Correlation to diameter d, 31
for workpieces w ith
g
Series Series + 0.1 +0.05 +0.2
1
2
0
0
0
E
and
F
1
H
increased
fatigue strength
Undercut
r x r1
E
Form
F
G
R0.2
0. 1
0.1
1
(0.9)
> 0 1.6-0 3
-
0.2 X 0.1
0.2
0
R0.4
-
0.2
0.1
2
(1 .1)
> 0 3-0 18
-
0.4 X 0.2
0.3
0
-
R0.6
0.2
0.1
2
(1 .4)
> 0 10-0 18
-
0.6 X 0.2
0.5 0.15
R0.6
0.3
0.2
2.5
(2.11
>0 18 -0 80
0.6 X 0.3
0.4
R0.8
-
0.3
0.2
2.5
(2.3)
> 0 18-0 80
-
0.8 X 0.3
0.6 0.05
-
R1
0.2
0.1
2.5
(1.8)
-
> 0 18-0 50
1.0 X 0.2
0.9
0.45
-
R1
0.4
0.3
4
(3.21
> 0 80
-
1.0 X 0.4
0.7
0
-
Rl.2
-
0.2
0.1
2.5
(21
-
>018-0 50
1.2 X 0.2
1.1
0.6
0.4
0.3
4
(3.41
> 0 80
-
1.2 X 0.4
0.9
0.1
0.3
0.2
4
(3.11
-
1.6 X 0.3
1.4
0.6
0.4
0.3
5
(4.8)
2.5 X 0.4
2.2
1.0
0.5
0 .3
7
(6.4)
-
>050-080
>080-0 125
> 0 125
4.0 X 0.5
3.6
2.1
-
R1.6
R2.5
R4
G
normal
loading
-
R1.2
'
Minimum d imension a for counter
sink on the opposing piece•I
R0.4
R0.8
R1.2
0
H
-
-
-
-
0.2
0 .2
(0.91
(1.11
> 0 3-0 18
0.4 X 0.2
-
-
0
0.3
0.05
(2.0)
(1.1)
> 0 18-0 80
-
-
0.8 X 0.3
-
-
-
0.35
0.3
0.05
(2.4)
(1.5)
-
> 0 18-0 50
1.2 X 0.3
-
-
-
0.65
41 Countersink dimension a on
11 All form s of undercut apply t o both shafts and holes.
opposing p iece
21 Undercuts with Series 1 radii are preferred.
31 The correlation to the diameter area does not apply with curved shoulders and
thin walled parts. For workpieces with differing diameters it may be advisable
to design all undercuts for all diameters in t he same form and size.
t~
A
'CINI
N
0-..,
-
·-+"<>!
.,1/, d1 = d, + a
y
Drawing entry for undercuts
Normally undercuts are represented in drawings as a simplified ent ry with the designator. However they can also be
complete ly drawn and dimensio ned.
Example: Shaft with undercut DIN 509 - Fl.2 x 0.2
Example: Hole with undercut- DIN 509 - E1.2 x 0.2
simplified entry
simplified entry
OIN 509-F 1.2 x 0.2
Fm
O" 509-ElM.2
~5+02
cof3f)mplete
entry
---n8•
complete entry
//
X
;,;
R1.2!0~1
<i',0
jjl/fe
"/////
--:
'
~
0
fm
y
1-
r/(~//
16
~~
2
93
Technical drawing: 3.8 Welding and soldering
Symbols for Welding and Soldering
Positioning of symbols for welding and soldering in drawings
cf. DIN EN 22553 (1997-03)
Basic terms
solid reference line
arrow line
weld symbol
joint
(e.g. butt joint)
'--.
tail
~/
/"'
I
dashed reference line
Reference line. This consists of the solid reference line
and the dashed reference line. The dashed reference line
runs parallel to the solid reference line and above or
below it. The dashed reference line is omitted for symmetrical welds.
Arrow line. It connects the solid reference l ine w ith
the joint.
Tail. Additional entries can be given here as needed for:
• method, process
• working position
• evaluation group
• additional material
Joint. Orientation of the parts to be joined to each other.
Weld information
Symbol. The symbol identifies the form of the weld. It is
preferably placed normal to the solid reference line, or if
necessary on the dashed reference line.
Arrangement of the weld symbol
position of the
weld symbol
position of the weld
(weld surface)
solid reference l ine
"arrow sideH
dashed reference line
"other side"
For welds represented in section or view, the position of
the symbol must agree with the weld cross section.
"other
side"
V
"arrow side"
VJ /..
VJ/ arrow line
)'\_""" ' ' " " "" " " " 1
17 "other side"
~ """"""-1
k '-..- arrow line
-
Arrow side. The arrow side is that side of the joint to
which the arrow line refers.
Other side. The other side of the joint that is opposite the
arrow side.
"arrow side"
cf. DIN EN 22553 (1997-03)
Supplemental and auxiliary symbols
I
Weld all around
F-
Field weld (weld is made on
the construction site)
Entry of the welding
process in the tail
Weld surface hollow (concave)
Weld surface flat (planar)
Weld surface curved (convex)
0...1
Weld surface notch free
Representation in drawings (basic symbolsl
Weld type/
symbol
graphical
1111111111111
Bun
weld
II
Representation
symbolic
It9 r,
cf. DIN EN 22553 (1997-03)
Weld type/
symbol
V groove
weld
V
graphical
Representation
symbolic
111111111,11,
, ~ r
94
Technical drawing: 3.8 Welding and soldering
Symbols for Welding and Soldering
Representation in drawings (basic symbolsl
Weld type/
symbol
Flare-V
groove
weld
.J\..
Plug
welding
n
Frontal
flush weld
Ill
Steepflanked weld
V.
Build-up
weld
rY"'\
Fold weld
~
~
Weld all
around
Rapresentation
graphical
cf. DIN EN 22553 ( 1997-03)
Weld type/
symbol
symbolic
I ~r
a,err . Bl ~ ~
B~~r
I ~r
8~ ~r r I ~ ~
uiu ~ [Q}r
I ~r
~,sr- I ~r
)))))))))))
~t9r
••
))))))))))))
Bevel
groove weld
V
Y-bun
weld
y
))))))))))))
U-groove
weld
))))))))))))
y
J-groove
weld
JI
3
~
Spot weld
~
3
0
...
~ ~
1/
□lQ~
1))1)))1)1)1)))
8feDt
BIEJt
§+;¥: I f
line weld
@:
~~
Field weld
with3mm
seam
thickness
))))))))))))
HY-weld
,,_
Fillet weld
graphical
~n
symbolic
Surface weld
-
~
-
95
Technical drawing: 3.8 Welding and soldering
Symbols for Welding and Soldering
Composite symbols for symmetrical welds1> !examples)
Weld type
Symbol
D(oublelV-weld
(X-weld)
Weld type
Representation
™
K
™
X
™
X
D(oublelbevel weld
D(ouble)Y-weld
cf. DIN EN 22553 (1997-03)
Symbol
™
X
™
D(oublelHY-weld
K
D(ouble)U-weld
11The symbols are loca-
ted symmetrical to the
reference line.
Example:
Application examples for auxiliary symbols
Weld type
Flat
reworked
V-weld
~
Flat
V-weld with
flat backing
run
g
w~
™1
Hollow fillet
weld.weld
transfer
unnotched
~
~ssss~sss~
8
l
v'
V
Meaning of the symbolic
symbolic
dimension entry
~1
EZZZ1~~
Butt weld, penetrating,
weld seam thickness s = 4 mm
t l00~cnl
~
~
~
~
rn
w~~~
cf. DIN EN 22553 (1997-03)
~ and dimensioning
graphical
"""'-1
11
V-weld
(penetrating
weldlwith
backing run
Represemation
1/2?~~
Weld type
weld
~
V
Symbol
Dimensioning examples
Flare-V
~
cf. DIN EN 22553 (1997-03)
Weld type
Y-weld
with
backing run
groove
symbolic
Representation
Convex
double
V-weld
I-weld
(non-penetratingl
graphical
Symbol
Flat
V-weld
I-weld
(penetrating)
Representation
~
111/IS0 5817-U
ISO 6941-PA/
EN 499-E 42 0 RR 12
~~ V/ ~""""""""""~
11 Supplementary requirements can be entered in a tail at the end of a reference line.
Butt weld, non-penetrating,
weld seam thickness s = 3 mm,
running over the entire
workpiece
Flare-V groove weld,
not completely melted down,
weld seam thickness s = 2 mm
V-weld (penetrating weld)
with backing run, fabricated by
manual arc welding (code 111
accord. to DIN EN ISO 4063),
required evaluation group C
accord. to ISO 5817; flat welding position PA accord. to ISO
6947; electrode E 42 0 RR 12
accord. to DIN EN 499
96
Technical drawing: 3.8 Welding and soldering
Symbols for Welding and Soldering,
Representation of adhesive, folded and pressed joints
Dimensioning examples (continued)
Weld type
Fillet weld
(contin•
uous)
k
~
~
g~
-~
Fillet weld
(interrupted)
Meaning of the symbolic
dimension entry
Representation and dlm-ioning
graphical
symbolic
~
I
0
Double
fillet weld
(interrupted,
staggered)
~
25 20
I
30
A
I
Lml
l,"'J
1m1j
a4" 3 x30 (10)
, a4V 3x30(10)
20
I
rnn1
Double fillet weld
(interrupted, symmetrical),
weld leg thickness a = 4 mm;
single weld length I = 30 mm,
weld spacing e= 10 mm,
w ithout end distance
z5 I\_ 2 X 20 7(30)
/ z5 V3x20L (30)
V
r /111
20 I 30 120 I 30 I 20
Symbolic representation of adhesive, folded and
pressed joints (examples)
Type of
joint
Weld type/
symbol
Meaning/
drawing entry
Type of
joint
20
Surface
seam11
--Adhesive
bondedseams
I• • I
i
i
~t
Folded
seam
5x20=
ET
I!
Fillet weld,
weld leg thickness z = 4 mm
(side length of the isosceles
triangle)
Fillet weld (interrupted),
weld leg thickness a= 5 mm;
2 single welds each w ith
I = 20 mm length;
weld spacing e = 10 mm,
end distance v = 30 mm
n•5r....2x20(10l
(10)
Double
fillet weld
(interrupted)
Fillet weld,
weld leg thickness a= 3 mm
(height of the isosceles triangle)
Double fillet weld
(interrupted, staggered),
weld leg thickness z = 5 mm;
single weld length/ = 20 mm,
weld spacing e = 30 mm,
end distance v = 25 mm
d . DIN EN ISO 15785 (2002-12)
Wald type/
symbol
Folded
seam
Meaning/
drawing entry
I
e I
·,r
6•1@ , -1
Er-1
¢5
Slant
/
seam 1'
//
I ~
I
11 The adhesive media is not shown for adhesive seams.
Pressed
seam
Pressed
seam
LS
t<4<a•
.,l
5x4Ll
I -$---~
97
Technical drawing: 3.9 Surfaces
Heat treated parts - Hardness specifications
Presentation and indication of heat treated parts on drawings
cf. DIN 6773 12001-04)
Heat treatment specifications
Term(s) for
material condition
Examples:
quenched and
tempered
hardened
hardened and
tempered
Measurable parameters of the material condition
hardness HRC
HV
value
HB
rockwell hardness
v ickers hardness
brinell hardness
M easuring points. Entering and dimensioning in the drawing with symbol (,!,).
hardness
indentalion
case hardening thickness
nitriding depth
effective hardening depth
Heat treatment diagram. Simplified, usually reduced scale representation of the
part near the title block.
carburizing depth
nitride white layer thickness
Minimum tensile strength or microstructure. If it is possible to test a part
treated in the same batch.
Eht
Nht
Rht
HTA
WL
annealed
nitrided
Possible additions
All entries are made with plus tolerances.
Identifying areas of the surface to undergo localized heat treatment
Area must be
heat treated.
Intermediate area may
not be heat
treated.
Area may be
heat treated.
Heat treatment specifications in drawings (examples)
Heat treatment of the entire part
Method
Quenching
and temper
ing,
Hardening,
Hardening
and
tempering
Nitriding,
Case
hardening
same requirements
~ ~ Rffil
---- 110 • 5
quenched and tempered
350 + 50 HB 2.5/187.5
hardened and tempered
58 + 4 HRC (j) 40 + 5 HRC
~ --i: __ __ __
case-hardened and tempered
© 60 + 4 HRC Ehl = 0.5 + 0.3
@ s52HRC
(~]) ~
-....;:: __
_
- - - surface hardened
620 + 120 HV 50
Rht 500 = 0.8 + 0.8
- - - hardened and entire
part tempered 60 + 3 HRC
~ d33
£{33
nitrided
;,900HV10
Nht = 0.3 + 0.1
Surfaced
hardening
Heat treatment
localized
different requirements
- -- surface hardened
and entire part tempered
@ s35 HRC
(!I s30 HRC
© 54 + 6 HRC
- ·case-hardened and
tempered 700 + 100 HV 10
Ehl ~ 1.2 + 0.5
EE}}
----- -- ·surface hardened
and tempered
61 + 4 HRC Rht 600 = 0.8 + 0.8
Hardening depths and tolerances in mm
Case-hardening depth Ehl
0.05+0.03
0.1+0.1
0.3+0.2
0.5+0.3
0.8+0.4
1.2+0.5
1.6+0.6
Nitriding depth Nht
0.05+0.02
0.1+0.05 0.15+0.02
0.2+0.1
0.25+0. 1
0.3+0.1
0.35+0.15
Induction hardening depth Rht
0.2+0.2
0.4+0.4
0.6+0.6
0.8+0.8
1.0+1.0
1.3+1.1
1.6+1.3
Laser/electr. beam hardening depth Rht
0.2+0.1
0.4+0.2
0.6+0.3
0.8+0.4
1.0+0.5
1.3+0.6
1.6+0.8
Control limit hardnesses at the specified hardening depths
Case-hardening depth Ehl
550 HV 1
Nitriding depth Nht
core hardness + 50 HV 0.5
Effective hardening depth Rht
0.8 . minimum surface hardness, calculated in HV
98
Technical drawing: 3.9 Surfaces
Form deviations and roughness parameters
Form deviations
d. DIN 4760 (1982-06}
Form deviations are deviations of the actual surface (surfaces ascertainable by measurement) from the
geometrically ideal surface, whose standard shape is defined by the drawing.
0agrNS of form deviation (Profile secExamples
tion repres. with vertical exaggeration)
1st degree: form deviation
~
~
.(.(/72'21
2nd degree: waviness
deviation in
straightness,
roundness
Deflection of the workpiece or the machine during fabrication of the part, malfunction or wear in the guides of the
machine tool.
waves
Vibrations of the machine, runout or shape deviation of a
m illing machine during fabrication of the part.
grooves
Geometry of the cuning tool, feed or depth of cut of the
tool during fabrication o f the part.
scoring,
scales,
bumps
Sequence of chip formation (e. g. tearing chip), surface
deformation due to blasting during fabrication of the part.
matrix
structure,
lanice structure
Crystallization cycles, matrix changes due to welding or hot
working, changes due to chemical effects, e.g. corrosion,
etching.
~
3rd degree: roughness
~
4th degree: roughness
~
5th and 6th degree: roughness
Cannot be represented
as a simple profile section
Possible causes
Surface texture profiles and parameters
d . DIN EN ISO 4287 11998-10) and DIN EN ISO 428811998-04)
Surface profile
Parameters
Explanations
Primary profile (act. profile, P profile)
Total height of
the profile Pr
The primary profile represents the foundation for calculating the parameters of the primary profile and forms the
basis for the waviness and roughness profiles.
The total height of the profile Pris the sum of the height of
the highest profile peak Zp and the depth of the lowest profile trough Zvwithin the evaluation length in-
Total height of
the profile Wt
The waviness profile is obtained by low-pass filtering, i.e. by
suppressing the short wavelength components of the profile.
'l ~~f
0:
t
Waviness profile (W-profile)
X
z~ ~= i
. ~:
Roughness profile (A-profile)
~
z ~:;-n .I, lr-:-:.-\
_Ii_
I,
--'-
z
I
·: I' JV r,
,.
°"
~
~
X~{~
Q:::
I,
" Rv = Zv 3
II
. ~...
..
..
n
X
I
•
n
~
w
•
VII,.-
V
In
II
•
material
ratio -:i
curve
u
50 ~
PRmr in °1.100
Z(x/ height of the profile at any position x; ordinate value
I n evaluation length
i,
sing le evaluation length
Total height of
the profile Rt
The roughness profile is obtained by high-pass filtering, i.e. by
suppressing the long wavelength components of the profile.
The total height of the profile Rt is the sum of the height of
the highest profile peak Zp and the depth of the lowest profile trough Zvwithin the evaluation length in-
Rp,Rv
Height of the highest profile peak Zp, depth of the lowest
profile trough Zv w ithin the sing le evaluation length t,.
Highest peak
of the profile
Rz11
The highest peak of the profile Rz is the sum of the height
of the highest profile peak Zp and the depth of the lowest
profile trough Zvwithin the single evaluation length i,.
Arithmetic
mean of the
profile ordinates Ra 11
The arithmetic m ean of the profile ordinates Ra is the
arithmetic mean of all o rd inate values Z(x/ within the single evaluation length i ,.
Material ratio
of the profile
Rmr
The material ratio of the profile expressed as a percentage,
Rmr, is the ratio of the sum of the contributing material
lengths at a specified section height to the t otal evaluation
length /0 •
Center line
Ix-axis} x
The center line (x-axis} xis the line corresponding to the
long wavelength profile component which is suppressed
by profile filtering.
x~l
In= 5-1,
'"' ~~~:h
~ "'
~
z
JL_JV
The total height of the profile Wt is the sum of the height of
the highest profile peak Zp and the depth of the lowest profile trough Zvwithin the evaluation length in.
1) For parameters defined over a single evaluation length, the arithmetic mean of 5 single
evaluation lengths to DIN EN ISO 4288 is used for determining t he parameters.
99
Technical drawing: 3.9 Surfaces
Surface testing, Surface indications
Measuring sections for roughness
d. DIN EN ISO 4288 (1998-041
Periodic
profiles
(e.g. turning
profiles>
Non-periodic
profiles
(e.g. grinding and
lapping profiles)
Non-periodic
profiles
(e.g. grinding and
lapping profiles>
Limit
Single/
wavetotal
length evaluation
length
Groove width
RSmmm
Rz
1-1m
Ra
1-1m
1-1m
mm
groove width
RSmmm
Rz
1-1m
Ra
1-1m
1-1m
> 0.01-0.04
upto 0.1
upto 0.02
0.08
mm
0.08/0.4
> 0.13-0.4
> 0.5- 10
>0.1-2
0.8
0.8/4
> 0.04- 0.13
> 0.1- 0.5
> 0.02- 0.1
0.25
0.25/1 .25
> 0.4-1.3
> 10- 50
> 2- 10
2.5
2.5/12.5
Periodic
Limit
Sing le /
wavetotal
profiles
length evaluation (e.g. turning
length
profiles)
I,, / 0
Indication of surface finish
Symbol
cf. DIN EN ISO 1302 (2002-061
Meaning
v
All manufacturing processes
are allowed.
.r
Material removal specified, e.g .
turning, milling.
r
Material removal not allowed
or the surface remains in delivered condition.
ef
Ir, ln
Additional marl<s
(
a surface parameter 0 with
numerical value in µm. transfer characteristic21/individual
evaluation length in mm
b secondary surface finish
requirement (as described
for a)
e~
All surfaces around the contour
must have the same surfacefinish.
C
manufacturing process
d symbol for the required
groove direction
(table page 100)
e machining deviation in mm
Examples
Symbol
~
~
✓ Rzmax 0.5
Meaning
material removing machi ning
not allowed
Rz = 10 µm (upper limit)
standard transfer
characteristic31
standard evaluation length4l
• 16% rule• 5>
Symbol
F
Machining can be done as
desired
• standard transfer
characteristic31
• Ra= 3.5 µm (upper limit)
• standard evaluation length 41
• 16% rule" 51
material removal machining
Rz = 0.5 µm (upper lim it)
• st andard transf er
characteristic3>
• standard evaluation length41
• "max. rule" 61
ground
sv{0.008-4/Ra 1.6
0.5 1.0.008-4/Ra 0.8
Meaning
material removal machining
Ra ~ 8 1-1m (upper limit>
• standard transfer
characteristic31
• standard evaluat ion length 41
• " 16% rule" 51
• applies all around the contour
• material removal machining
• manufacturing process
grinding
• Ra= 1.6 µm (upper limit)
• Ra= 0.8 µm (lower limit)
• for both Ra values:
• 16% rule" 51
• transfer characteristic
each 0.008 to 4 mm
• standard evaluation length 41
machining deviation 0.5 mm
• surface g rooves vertical
1l surface parameter, e.g. Rz, consists of the profile (here the roughness profile R) and the parameters (here: z).
21 transfer characteristic: wavelength range between the short wavelength filter .! and the long wavelengt h filter
5
"c • The wavelength of the long wavelength filter corresponds to the si ngle evaluation length I,. If no transfer char1
acteristic is ent ered, then the standard transfer characteristic applies3 .
31 standard transfer characteristic: the limit wavelength for measurement of the roughness parameters is dependent
upon the roughness profile and is taken from tables.
41 standard evaluation length In = 5 x single evaluation length I,.
51 "16o/o rule": only 16% of all measured values may exceed the chosen parameter.
61 "max. rule" ("highest value rule">: no measured value may exceed t he specified highest value.
100
Technical drawing: 3.9 Surfaces
Surface finish symbols
Indication of surface finish
cf. DIN EN ISO 1302 (2002-06)
Symbols for groove clrection
Representation
of groove
direction
~~&~g~g
~~ - - (8 ~ IL//:1
Symbol
Groove
direction
X
.L
parallel
to the
projection
plane
perpendicular to
the projection plane
crossed
in two
angular
directions
M
C
R
p
mult idirectional
approximately con-
approximately
radial to
the center
non-grooved
centric to
the center
surface, non·
directional or
t roughs
Sizes of the symbols
Letter height h in mm
2.5
3.5
5
7
10
14
20
d
0.25 0.35
0.5
0.7
1.0
1.4
2.0
H,
3.5
5
7
10
14
20
28
H2
8
11
15
21
30
42
60
Layout of symbols in drawings
Rz 12
Rz 10
Legibility
from below or from the right
Layout
directly on the surface o r with reference and
leader lines
Examples of drawing entries
Ra 6
A-A
II 0.05 A
~
101
Technical drawing: 3.9 Surfaces
Roughness of surfaces
Recommended assignment of roughness values to ISO tolerance specifications11
Nominal size
range
from-to
mm
Recommended
values of
ISO tolerance grade
Rzand Ra
5
6
7
8
9
10
11
2.5
1-6
0.4
2.5
6- 10
0.4
4
10- 18
0.8
4
18- 80
0.8
6.3
80- 250
0.8
6.3
250- 500
0.8
1
Achievable roughness of surfaces 1
4
0.8
4
0.8
4
0.8
6.3
0.8
10
1.6
10
1.6
6.3
0.8
6.3
0.8
6.3
0.8
10
1.6
16
1.6
16
1.6
6.3
1.6
10
1.6
10
1.6
16
3.2
25
3.2
25
3.2
10
1.6
16
3.2
16
3.2
16
3.2
25
3.2
40
6.3
16
3.2
25
6.3
25
6.3
40
6.3
40
6.3
63
12.5
25
6.3
40
12.5
40
12.5
63
12.5
63
12.5
100
25
IJm
Rz
Ra
Rz
Ra
Rz
Ra
Rz
Ra
Rz
Ra
Rz
Ra
Rz in µm for type of manufacturing Ra in µm for type of manufacturing
fine
normal
rough
fine
normal
rough
min.
from- to
min.
from-to
max.
max.
Manufacturing process
C>
C
Casting:
°§
Permanent mo ld casting
.E
~
"'
E
4
10
25
Die casting
Sintering:
~
Sand casting
S inter smooth
-
Calibrated smooth
Extrusion
Cl
C
Closed-die forming
0
Rod extrusion
Deep drawing sheet metal
.E
u.
Rolling:
Burnishing
Material
removal:
WireEDM
4
10
4
0.4
0.1
0.8
1.5
-
-
"
Diesinking
Cutting
Oxyacetylene cutting
operations: Laser cutting
II)
C
0
-~
:;;
Machining
operations:
Plasma cutting
-
Shearing
-
Water jet cutting
Drilling: Drilling in solid
4
16
0.1
6.3
0.4
Boring
Countersinking
0.
0
Cl
C
E:,
u
16
Routing
Turning: Longitudinal turning
Facing
Milling: Peripheral, face milling
Honing: Super finishing
Long-stroke honing
Lapping
Polishing
1
2.5
1.6
0.04
0.04
0.04
-
Grinding
0.1
10- 100
25- 160
63-250
2.5- 10
1.6- 7
25- 100
63-400
25- 100
4- 10
0.5- 6.3
2.8-10
5- 10
40- 100
10- 100
6- 280
10- 63
16- 100
40- 160
2.5- 25
10- 25
4-10
4- 63
10- 63
10- 63
0.1 - 1
1- 11
0.25- 1.6
0.04- 0.25
1.6-4
160
250
1000
-
-
1.6
1.6
0.05
0.8
0.2
0.2
0.4
0.4
0.006
0.006
0.006
0.8- 30
3.2-50
12.5-50
0.4- 1.6
0.3- 0.8
3.2- 12.5
2.5- 12.5
3.2-12.5
1-3.2
0.06- 1.6
0.4- 1
0.45
8- 16
1- 10
1- 10
1.6-12.5
6.3-25
6.3- 12.5
0.4- 3.2
1.6-6.3
0.8- 2
0.8-12.5
1.6-12.5
1.6- 12.5
0.02- 0.17
0.13-0.65
0.025- 0.2
-
0.005-0.035
0.012
0.2- 0.8
-
-
400
1000
400
16
10
16
31
1000
0.8
0.8
0.8
0.2
0.025
0.1
0.2
3.2
-
-
400
250
40
40
25
250
250
160
2.5
15
10
0.4
25
25
25
25
6.3
2
3.2
6.3
50
-
-
50
25
12.5
12.5
6.3
50
50
25
0.34
1.6
0.21
0.05
6.3
11 Roughness values, as long as they are not contained in DIN 4766-1 (cancelled) are according to specifications of the industry.
Read-out example:
reaming (for surface
characteristic Rz)
fine finishing
Rzm.,= 0.4
Rz:4
Rz =10
conventiotl finishing
rough finishing
Rz.,.,= 25
102
Technical drawing: 3.10 Tolerances and Fits
ISO system of limits and fits
Terms
d. DIN ISO 286-1 (1990-11)
Hole
N
GuH
GiH
ES
El
TH
shaft
N
Gus
G,s
es
ei
Ts
nominal size
hole max. dimension
hole min. dimension
hole upper deviation
hole lower deviation
hole tolerance
r - - nominal dimension
r - - nominal dimension
.l. ..i::::-- tolerance class
..L ..c:-- tolerance class
!1l20H1
!1l20s6
T"[__ tolerance grade
L _ fundamental deviation
Designation
Zero line
nominal dimension
shaft max. d imension
shaft min. dimension
shaft upper deviation
shaft lower deviation
shaft tolerance
T"[__
tolerance grade
L _ fundamental deviation
Designation
Explanation
Explanation
It represents the nominal dimension that is Fundament. A group of tolerances assigned to same
level of precision, e. g ITT.
referenced by the deviations and tolerances. tolerance
grade
Fundamental The fund. deviation determin. the position of Tolerance
deviation
the tolerance zone with resp. to the zero line. grade
Number of the fundamental tol. grade, e.g. 7
for the fundamental tolerance grade ITT.
Difference between the max. and the min. Tolerance
dimension or between the upper and lower class
deviation.
Name for a combination of a fundamental deviation and a tolerance grade, e.g.
H7.
Tolerance
Fundamental A tolerance assigned to a fundamental tole- Frt
tolerance
ranee grade, e.g. ITT and a nominal dimension
range, e.g. 30 to 50 mm.
Planned joining condition between hole
and shaft.
Limits, deviations and tolerances
d . DIN ISO 286-1 (1990-11)
Hole
Shaft
GuH= N+ ES
Gus =N+es
G1H = N+ El
G1s
= N + ei
TH = ES - El
Ts
= es- ei
Example: Shaft 0 20e8; GIs = ?; Ts = 7
For values for ei and es see page 107.
ei= - 73 µm =-0.073 mm; es=-40 µm =-0.040 mm
G,s = N + ei = 20 mm+ (- 0.073 mm)= 19.927 mm
Ts = es- ei =-40 µm- (-73 µm) =33 µm
Example: Hole 0 50 + 0.3/+ 0.1; GuH =?;TH = ?
GuH= N + ES = 50 mm + 0.3 mm = 50.30 mm
TH = ES - El = 0.3 mm - 0.1 mm = 0.2 mm
Frts
Clearance fit
Fcmax max. clearance
Fcmin min. clearance
d. DIN ISO 286-1 ( 1990-11)
Transition fit
Fcmax max. clearance
fimax max. interference
Fcmax = GuH - G1s
Example: Fit 030 H8/f7; Fcmax = ?; Fcm;n =?
For values for ES, El, es, ei see page 107.
GuH = N + ES= 30 mm+ 0.033 mm= 30.033 mm
GiH = N + El= 30 mm + 0 mm= 30.000 mm
I
Interference fit
Fimax max. interference
Fimin min. interierence
F1max = G1H - Gus
II
Fimin = GuH - G1s
GuH = N +ES = 30 mm+ (-0.020 mm) = 29.980 mm
G,H = N+ ES= 30 mm+ (- 0.041 mm) = 29.959 mm
Fcmax = GuH - G,s = 30.033 mm - 29.959 mm = 0.074 mm
Fcm;n = G1H - Gus = 30.000 mm - 29.980 mm = 0.02 mm
103
Technical draw ing: 3.10 Tolerances and Fits
ISO system of limits and fits
Fit systems
cf. DIN ISO 286-1 (1990-11)
Fit system: basic hole system (all hole dimensions have the funda mental deviation H)
Examples for nomina l dimension 25,
Fundamental deviations for shafts
tolerance g rade 7
-
l ""'
zc
j
H ..,._
Ill s t u v x y / zero line
de • •
c • • f g h js
"'
bl
I
a
-
C
clearance
fits
•
transition
fits
·~ .~
interference
f its
25n6
µm -
km n Pr · · · · · · z za
0
-
+40 -
• •zb
+
-
+20
+10
0
- 10
- 20 -30 -40 -
v,
C
~ 1ml
lisiffl
■
transition
fit
clearance
fit
interference
fit
Fit system: basic shaft system (all shaft dimensions have the fundamental d eviation h)
Examples for nomi nal d imension 25,
Fundamental allowances for holes
tolerance g rade 6
=A
Do□o
+
B (
DE
0
-
"
~
IIIJDDDDO Tuvxy /
F G H JS
Do
zero line
J K MN p R S
"'
C
□□□□ooz ZA
□zB
·~ -~
C
v,
-
transition
fits
clearance
fits
interference
fits
Dzc
0
+50 -
µm
- -
- 125F•I
+30
+20
+10 0
-10 -20 - 30
-40
-50 - clearance
1n
I IT2 1 1T3 I IT4 I IT5 I IT6 1 1n 1 1T0 I IT9 11no 11n1 11n2 11n3 I IT14 I 1T15 I IT16I IT171 1n0
Fundamental t olerances
mm
µm
0.8
1.2
2
3- 6
6- 10
1
1.5
1
1.2
1.5
10- 18
cf. DIN ISO 286-1 ( 1990-11)
Fundamental tolerance grade
up to3
40
60 0.1
0.6
1
18
25
30
48
75 0. 12 0.18 0.3
0.48
0.75
1.2
1.8
22
36
58
0.9
1.5
2.2
21
27
33
43
52
70
84
90 0.15 0.22 0.36 0.58
110 0.18 0.27 0.43 0.7
130 0.21 0.33 0.52 0.84
1. 1
1.3
1.8
2.1
2.7
3.3
16
25
39
46
54
100
120
2.5
30
35
40
62
74
1.6
19
22
1.9
3
3.5
4
3.9
4.6
10
14
5
6
8
12
4
6
9
5
6
8
9
11
13
15
18
7
11
13
15
18
25
14
2.5
3
4
1.5
2.5
2
2.5
4
1.5
2.5
3
4
4
2
2.5
3
4
5
6
3.5
5
8
8
10
12
4.5
6
7
8
10
12
16
20
23
29
32
46
250- 315
52
72
81
315- 400
7
9
13
18
25
36
57
400-500
500- 630
8
10
15
20
27
40
9
10
11
13
16
18
22
25
32
36
44
50
800- 1000 11
15
21
28
1000- 1250 13
18
24
40
47
55
18-30
30-50
50-80
80-120
120- 180
180-250
630- 800
(§1
interference
fit
transition
fit
fit
Fundamental tolerances
Nominal
dimension
range
over-to
mm
~
1250- 1600 15
21
29
33
39
1600- 2000 18
2000-2500 22
25
30
35
41
46
55
65
78
2500- 3150 26
36
50
68
96
0.14 0.25 0.4
1.4
115
160
185
160 0.25 0.39 0.62 1
190 0.3 0.46 0.74 1.2
220 0.35 0.54 0.87 1.4
1.6
250 0.4 0.63 1
290 0.46 0.72 1.15 1.85
2.9
4.6
7.2
130
210
320 0.52 0.81 1.3
2.1
3.2
5.2
8.1
89
140
230
360 0.57 0.89 1.4
2.3
3.6
5.7
8.9
63
70
97
110
155
175
250
4
4.4
6.3 9.7
7
11
80
125
200
280
320
400 0.63 0.97 1.55 2.5
1.1
1.75 2.8
440 0.7
500 0.8
1.25 2
3.2
5
8
12.5
56
90
140
230
360
560 0.9
1.4
2.3
3.6
5.6
9
14
66
78
105 165
260
420
4.2
125
195
310
500
660 1.05 1.65 2.6
780 1.25 1.95 3.1
5
6.6
7.8
10.5 16.5
12.5 19.5
92
150 230
370
440
600
700
920 1.5 2.3
1100 1.75 2.8
9.2
15
4.4
6
7
11
23
17.5 28
540
860 1350 2.1
5.4
8.6
13.5
21
63
11 0 175 280
135 210 330
87
100
140
3.3
3.7
2.2
2.5
5.4
6.3
33
The lim it deviat ions of t he tolerance grade for t he fundamental deviat ions h, js, H and JS can be derived from t he
fu ndamental tolerances: h: es: O; ei : - IT js: es = + IT/2; ei = - IT/2 H: ES = + IT; El = 0 JS: ES = + IT/2; El = - IT/2
104
Technical drawing: 3.10 Tolerances and fits
Fundamental deviations for shafts (selection)
Fundamental
deviations
Fundamental
t o lerance
grade
a
C
d
e
IT9
to
IT13
ITS
to
IT1 2
ITS
to
IT13
IT5
to
IT10
IT3
to
IT10
g
h
IT3
to
IT10
IT1
to
IT18
Table
applies to
all fundamental tolerance grades
Nominal
dimension
over- t o mm
Upper deviation es in µm
upto 3
- 270
3- 6
cf. DIN ISO 286-1 (1990-11)
m
k
ITS
to
ITS
ITT
n
p
s
IT3
IT3
IT3
to
to
to
IT3 to lT10
IT9
IT13
IT9
IT4
over
to
ITT all funda mental tolerance grades
ITT
Lower deviation ei in µm
- 60
- 20
- 14
-6
-2
0
-4
0
0
+2
+4
+6
+10
+14
- 70
- 30
- 20
- 10
-4
0
-4
+1
0
+4
+8
+12
+15
+19
+23
6 - 10
- 280
- 80
- 40
- 25
- 13
-5
0
-5
+1
0
+6
+10 +15
+19
10- 18
- 290
-95
-50
- 32
- 16
-6
0
-6
+1
0
+7
+12
+18
+23
+28
18-30
- 300
- 110
- 65
- 40
-20
-7
0
-8
+2
0
+8
+15 +22
+28
+35
30-40
-310
- 120
40-50
- 320
- 130
- 80
-50
-25
-9
0
- 10
+2
0
+9
+17 +26
+34
+43
50- 65
- 340
- 140
-150
- 60
-30
-10
0
- 12
+2
0
+11
+20 +32
+53
- 360
- 100
+41
65- 80
+43
+59
80-100
-380
- 170
+51
+71
100-120
-410
-180
120- 140
-460
- 200
- 120
0
+23 +37
+54
+79
+63
+92
+65
+100
+68
+108
180-200
-660
-240
+77
+122
200- 225
- 740
-260
225-250
-820
- 280
250- 280
-920
- 300
-1050
- 330
315-355
- 1200
-360
355-400
- 1350
-400
400-450
- 1500
-440
450-500
-1650
-480
-190
- 210
- 230
- 11 0
-125
- 135
-56
-62
- 68
- 17
-18
- 20
0
-21
- 26
0
- 28
0
- 32
+3
+4
+4
0
+13
- 230
0
- 18
+3
- 210
-15
0
- 15
-580
- 50
- 14
0
-520
-100
- 43
- 12
140- 160
- 170
- 85
- 36
160-180
280-315
- 145
- 72
0
0
+15
+17
+20
+27 +43
+ 31
+50
+34 +56
+4
0
+21
+37 +62
+5
0
+ 23
+40 +68
+80
+130
+84
+140
+94
+158
+98
+170
+108
+190
+1 14
+208
+126
+232
+132
+ 252
Calculation of limit deviations
Limit deviations for fundamental tolerance grades given in the table row "Table applies to" (above and page 105) can
be calculated using tables on this page and page 105 and the formulas below. The values necessary for the fundamental tolerances IT are found in the t able on page 103.
Formulas
for shaft deviations
ei= es- IT
es= ei + IT
Example 1: Shaft (outside dimension)
0 40g5; es=?; ei=?
Example 2: Hole (inside dimension)
0 100KG; ES = ?; El = ?
es (table above) = - 9 µm
ITS (table page 103) = 11 µm
ei = es- IT = - 9 µm - 11 µm = - 20 µm
ES (table page 105) = - 3 µm + t;.
(Value t;. for fundamental tolerance grade
ITS acc. to table, bottom of page 105: 7 µm)
ES= - 3 µm + 7 µm = 4 µm
ITS (table page 103) . 22 µm
El = ES - IT = 4 µm - 22 µm = -18 µm
for hole deviations
100
El = ES-IT
ES = El+ IT
IT
ei
(fundamental
tolerance
~ ~ - - - - ~ ~tolerance
n
_,,,, zero line
ES
tolerance
El
zone for hole
-
IT
lfundamental
tolerance
" tolerance
n
105
Technical drawing: 3.10 Tol erances and fits
lh'11•n
Fundamental deviations for holes (selection) 11
Fundamental
deviations
Fundamental
tolerance
grade
A
C
D
E
IT9
to
IT13
ITS
to
IT13
ITS
to
IT13
ITS
to
IT10
cf. DIN ISO 286-1 (1990-11)
H
J
K
M
N
IT3 IT3 IT1
to
to
to
IT10 IT10 IT18
ITS
to
ITS
IT3
to
IT10
IT3
to
IT10
IT3
to
IT11
F
G
Table
applies t o
all fundamental tolerance grades
Nominal
dimension
over-to; mm
Low er deviation El in µm
up to 3
+270
3-6
p
s
s
R
IT3 to IT10
to
ID
IT3 to ITS
ITS
P. R,
IT 8 to IT10
Upper deviation ES in µm
+60
+20
+ 14
+6
+2
0
+6
0
-2
-4
-6
- 10
+70
+30
+20
+10
+4
0 +10
- 1+6
-4 +6
-a +6
- 12
- 15
- 19
Q)
"O
- 14
6- 10
+280
+80
+40
+25
+ 13
+S
0 + 12
- 1 +6
-6+6 - 10 +6 ~
- 15
- 19
- 23
10- 18
+290
+95
+SO
+32
+ 16
+6
0 + 15
- 1 +6
-7+6 - 12 +6
- 18
-23
- 28
- 22
- 28
- 35
- 26
-34
-43
-41
-53
-43
-59
-51
- 71
-54
- 79
Cl
Q)
(.)
C:
18- 30
+300
+ 110
30- 40
+310
+ 120
40-50
+320
+130
50-65
+340
+ 140
+40 + 20
+65
+7
0 + 20
-2 +6
-a +6 -15 +6 ~
Q)
E
-9 + 6 - 17 +6 -
+80
+50 +25
+9
0 +24
- 2 +6
+ 100
+60
+ 10
0 +28
- 2+6 - 11 +t. - 20+6
c"'
Q)
65-80
+360
80- 100
+30
+ 150
+380
+410
+ 180
+460
+200
140- 160
+520
+210
160- 180
+580
+230
- 32
C:
+120
100- 120
"'
"O
.2 <l
+170
120- 140
E
+72
+36
+ 12
0 +34
- 3 +6 - 13 +t. - 23 +6
"':::, - 37
"'"'
C1>Q.
E .
.,o
"'~
-63
- 92
-65
- 100
-68
- 108
- 77
- 122
--ao
- 130
Q) t::
180-200
+660
+240
200- 225
+740
+260
225- 250
+820
+280
250- 280
+920
+300
280-315
+1050
+330
+ 145
+85 +43
+ 14
0 +41
- 3 +t. - 15 +t. - 27 +t.
-=~
- 43
cij co
"'t::
"'0
C:
-~
+ 170 + 100 +SO + 15
0 + 47
- 4+6 - 17 +t. -31 +6 ·;;
- 50
Q)
"O
~
Q)
C.
C.
+ 190 + 110 + 56
315- 355
+1200
+360
355- 400
+1350
+400
400- 450
+1500
+440
450-500
+1650
+480
+210
+125 +62
+ 17
+ 18
0 +55
0 +60
- 4+6 - 20+6 -34 +6 ~
- 4+ 6 - 21 +6 - 37 +6
+20
0 .+66
- 158
- 56
- 98
- 170
.E
- 108
- 190
- 114
- 208
- 126
- 232
- 132
- 252
315
to
400
400
to
500
"'
- 62
Q)
~
+135 +68
- 140
-94
£
:::,
+230
--a4
- 68
-5+6 - 23 +6 - 40+6
Values for a 11in pm
Nominal dimemion over-to in mm
Fundamental
tolerance
grade
3
to
6
6
to
10
10
to
18
18
to
30
30
to
50
50
to
80
80
to
120
120
to
180
180
to
250
250
to
315
1
1
1
1.5
1.5
2
2
5
2
3
2
3
4
3
4
3
4
4
1.5
2
3
4
4
1.5
1
4
5
5
6
6
7
5
7
5
7
3
4
3
7
5
9
6
11
7
9
9
11
13
13
15
17
20
21
23
ITS
6
3
6
7
7
ID
14
16
19
23
26
29
32
34
IT3
IT4
ITS
ITS
9
3
4
8
12
11 For examples of calculations see page 104.
106
Technica l d rawing: 3. 10 Tolerances and fits
ISO fits
Basic hole system
cf. DtN ISO 286-2 ( 1990-11 >
Limit deviations in µm for t olerance classesH
Nominal
d imension
range
over- to
mm
up to 3
3- 6
6-10
10- 14
14-18
18-24
24- 30
30- 40
40-50
50-65
65- 80
80- 100
100- 120
for shafts
for
hole
~
for
hole
Paired w ith an
H6 hole results in a
learance, t ransition, inte•fli•a
fit
h5
j5
k6
r6
n5
315- 355
355- 400
400- 450
450- 500
+18
0
-0
0
- 16
-34 -17 -11
+8 +12 + 18 +23
-3
+1 +7 +12
+34
+39
+23
+28
+37
+28
+21
0
-20 -7
0
-41 - 20 - 13
+9 +15 +21 +28
-4 +2
+8 +15
+41
+28
+35
+46
+34
+25
0
-25 - 9
0 +11 +18 +25 +33
-50 - 25 - 16 -5 +2
+9 +17
+60
+59
+34
+43
+80
+72
+30
0
- 30 - 10
0 +12 +2 1 +30 +39
-7 +2 +1 1 +20
-oO -29 -19
+35
0
0 +13 +25 +35 +45
-36 - 12
- 7 1 - 34 - 22 - 9 +3 +13 +23
0
-8
+5 +12 +20
- 3 +1 +12
+13
0
0
-9
+5 +15 +24
-4 +2 +15
+16
0
0
- 11
+6 +18 +28
-5 +2 +17
+19
0
0
- 13
+6 +21 43
-7
+2 +20
+41
+22
0
0
- 15
+6 +25 +38
-9
+3 +23
....!!!..
+10
0
+12
0
f7
k6
m6
n6
-+64
+68
+43
+88
+89
-+64
+81
+83
+83
+85
+88
+88
+7 +28 +46
- 11
+3 +Xl
+40
0
-43 - 14
0 +14 +28 +40 +52
-83 -39 -25 - 11 +3 +15 +27
0
-20
+7 +33 +51
-13
+4 +31
+100
+80
+104
+32
0
0
-23
+7 +36 +S1
- 16
+4 +34
+36
0
0
-25
+7 +40 +82
- 18
+4 +37
+40
0
0
-27
+7 +45 +87
-20 +5 +40
+73
+51
+78
+64
+88
+83
+90
+85
+109
+80
+84
+84
+117
+94
+121
+128
- 56 - 17
0 +16 +36 +52 +66
- 108 -49 -32 - 16 +4 +20 +34
+94
+130
+98
+88
+133
+108
+139
+114
+153
+128
+159
+132
+144
+108
+150
+114
+188
+128
+172
+132
-
+57
0
-62 -18
0 +18 +40 +57 +73
- 119 - 54 - 36 - 18 +4 +21 +37
+63
0
-o8 - 20
0 +20 +45 +63 +80
-1 31 -60 -40 - 20 +5 +23 +40
11 The tolerance classes in bold p rint correspond to row 1 in DIN 7157; their use is preferable.
+23
+48
+63
+1 13
+52
0
+19
+32
+78
+69
+93
+71
+101
+79
+117
+92
+125
+100
+133
+108
+151
+122
+159
+130
+189
+140
+190
+158
+202
+170
+228
+ 190
+244
+208
+X12
+232
+292
+252
+n
-50 - 15
0 +16 +33 +46 +60
- 96 -44 - 29 - 13 +4 +17 +31
+Xl
+82
+43
+88
+46
0
+20
+14
+41
+108
+n
+29
0
+18
+10
+23
+15
+28
+19
+93
+97
225-250
280-315
+31
+23
+11
0
180-200
250- 280
+15
0
+4 +6 +8 +10
-2
0
+2
+4
+6
+9 +12 +16
-2
+1
+4 + 8
+7 +10 +15 +19
-2
+1 +6 + 10
+3
-2
+4
-2
0
- 18
18
j6
0
-0
0
--8
0
-9
+14
+10
+20
+15
+25
+19
+25
0
..
h6
+6 +8
0
+4
+9 +13
+ 1 +8
+10 +18
+1 +10
160- 180
200-225
i1118rfeteuce
fit
transition
fit
g6
0
-4
0
-5
0
-0
120- 140
140- 160
clearance
fit
-0 -2
- 16
--8
-4
- 10
-22 - 12
- 13
-5
- 28 - 14
+6
0
+8
0
+9
0
±2
~
for shafts
Paired with an H7 hole
results in a
107
Technical drawing: 3. 10 Tolerances and fit s
ISO fits
Basic hole system
cf. DIN ISO 286-2(1990-11>
~.:.
Nominal
dimension
range
over- to
mm
upto 3
3-6
6-1 0
10 - 14
14 - 18
18- 24
24-30
30-40
40-50
50- 65
65-80
80- 100
100-120
for
hole
Limit deviations in µm for tolerance classes1>
for shafts
~
+14
0
+18
0
+22
0
+27
0
interference
flt
d9
e8
n
h9
-20
-45
- 30
-14
- 28
- 20
~
- 38
-40
- 76
-25
-47
-0
- 16
- 10
-22
- 13
- 28
0
-25
0
-30
0
-36
- 50
-93
- 32
-59
- 16
- 34
0
-43
-65
+33
0 - 117
-40
- 73
-20
-41
0
-52
-50
-a9
- 25
- 50
0
-62
~
+46 - 100
0 - 174 - 106
- 30
~
0
- 74
.+54 - 120
0 - 207
- 72
-126
- 36
- 71
0
--87
+63 - 145
0 - 245
--85
- 148
-43
0
--83 - 100
+39
0
-80
- 142
315- 355
355-400
400-450
450- 500
di)
+34
+18
+41
+23
+20
.a,
+116
+28
+80
+34
+fI7
+40
+33
+n
+74
+41
+81
+98
+80
+109
+70
+133
fff7
+148
+102
+178
+124
+'HNI
+14'
+170
+213
+190
+273
+210
+46
+28
+72
0
- 170 - 100
-285 - 172
-50
-96
0
- 11 5
+238
+330
+258
+368
+284
+396
+81
0
- 190
-320
- 110
- 191
-56
0
-108 - 130
+315
+431
a11
c1 1
d9
d11
h9
- 270
-330
- 270
-345
-280
-370
-60
- 120
- 70
- 145
--80
-170
- 20
-45
- 30
-40
-76
- 20
-80
- 30
- 105
-40
- 130
0
-25
0
-30
0
-36
0
-75
0
-90
+110
0
- 290
-400
-95
-205
-50
- 93
- 50
- 160
0
-43
0
- 110
+130
0
- 300
-430
- 110
-240
-65
- 117
-65
- 195
0
- 52
0
- 130
- 310
-470
- 320
-480
-340
-530
- 360
-550
- 380
- 120
-280
- 130
- 290
-140
- 330
- 150
-340
- 170
-390
- 180
-400
- 200
-450
-2 10
-460
-230
-480
- 240
-530
- 260
-550
-280
-570
-300
-620
-330
-650
- 360
-720
-400
- 760
-440
--840
-480
--880
--80
- 142
-80
- 240
0
-62
0
- 160
- 100
- 174
- 100
- 290
0
- 74
0
- 190
- 120
-207
- 120
-340
0
--87
0
-220
-145
- 245
- 145
- 395
0
-100
0
-250
- 170
- 285
- 170
-460
0
-115
0
- 290
- 190
-320
-190
-510
0
- 130
0
- 320
- 210
-350
- 125
-214
-62
- 119
0
-140
+97
0
-230 - 135
- 385 -232
-o8
- 131
0
- 155
+479
+380
+624
+435
- 210
-350
- 210
-570
0
- 140
0
-360
-230
- 385
-230
-630
0
0
- 155 -400
~
h11
0
~
+45
fff7
+64
+97
+64
+119
+80
+138
+97
+168
+122
+192
+148
+232
+178
+294
+210
+311
..i48
+3'13
+280
+160
0
+190
0
+220
0
+250
0
+373
+310
+457
+386
+497
+426
+556
+475
+806
+879
+590
+748
+880
+1187
+837
+480
+837
+740
+917
+540
+820
~o
-410
-630
-460
- 710
-520
-770
-580
--830
~o
+360
+290
0
-+320
0
+360 +525
+89
0
clearance
fit
+60
0
+75
0
+90
0
+308 +422
225-250
280-315
+32
♦-
180-200
250- 280
.... 8
+48
160-180
200-225
Paired wit h an H11 hole
results in a
resu lts in a
clearance
fit
120- 140
140-160
for shafts
for
hole
Paired with an H8 hole
+360
0
+400
0
-950
- 740
- 1030
--820
- 1110
-920
- 1240
- 1050
- 1370
-1200
- 1560
- 1350
- 17 10
- 1500
- 1900
- 1650
-2050
1> The tolerance classes in bold print correspond to row 1 i n DIN 7157; their use is preferable.
21 DIN 7157 recommends: nominal dimensions up to 24 mm: HB/x8; nominal dimensions over 24 mm: HB/u8.
108
Technica l d rawing: 3.10 Tolerances and fits
ISO fits
Basic shaft system
cf. DIN ISO 286-2 ( 1990-11 )
Limit deviations in µm for tolerance classes 1>
Nominal
dimension
range
over- to
mm
upto 3
3- 6
6-10
10 - 18
18 - 30
30 - 40
40 - 50
50-65
65-80
80- 100
100 - 120
for
shafts
for holes
clearance
fit
H6
transition lnliffleNIICI
fit
flt
-5
0
--6
0
--8
0
-9
+6
0
+8
0
+9
0
+11
0
+ 13
0
+2 - 2
--4 --8
+5 -1
-3 - 9
+5 -3
--4 -12
+6 --4
-5 - 15
+8 --4
-5 - 17
0
- 11
+16
0
0
- 13
~
0
--4
0
J6
M6
NII
....
for holes
for
shafts
Paired w it h an h5
shaft results in a
Pe
-e
~
Paired with an h6 shaft
results in a
clearance
fit
inlllrf9r'8ia
fit
transition
fit
F8
G7
H7
M7
N7
R7
f?i1
+12
+2
+16
+4
+20
+5
+24
+6
+28
+7
-2
0
+10 +4
0
--6 - 10 - 12
+12 +6 +3
0
-9 - 12
0
--6
0
+15 +8 +5
- 7 - 10 - 15
0
0
+18 +10
+6
0
--8 - 12 - 18
+21 +12
0
+6
0
- 9 - 15 -21
--4
- 14
--4
- 16
--4
- 19
-5
-23
-7
-28
-10
0
-13
+20
+6
+28
+10
+35
+13
+43
+16
+53
+20
-14
- 24
-15
- 27
- 17
-32
- 21
-39
-27
-48
0
-6
0
--8
0
-9
0
- 11
J7
K7
- 10
- 12
-5
-e
-13
-7
- 18
--8
-11
- 2A
-17
- 12
- 21
- 15
-28
- 18
-31
--4
+10
--6 - 20
- 12
--28
- 21
-37
0
- 16
0
--8
+64 +34 +25 +14 +7
0 - 11 - 18 - 25 - 33
+25 +9
+19
0
+13
-5
--6 - 24
- 14
-33
--a
-411
0
- 19
0
-9
+76 +40 +30 +18 +9
+30 +10
0 - 12 -21 - 30 - 39
0
- 15
+22
0
--6
+1 6
--6 -28
-11
-38
-30
-62
0
-22
+90 +47 +35 +22 +10
0 - 10
+36 +12
0 - 13 - 25 -35 --45
0
- 18
+25
0
+18
-7
--8
-33
- 20
-46
- 38
-e1
0
- 25
+106 +54 +40 +26 +12
0 - 12
+43 +14
0 - 14 - 28 --40 -52
0
- 20
+29
0
--8
+22
-7 -37
-22
-61
-41
-70
0
- 29
+122 +61 +46 +30 +13
0 - 14
0 - 16 - 33 --46 --60
+50 +15
0
- 23
+32
0
+25 -9
- 7 --41
-25
-{fl
-47
- 79
0
--32
+137 +69 +52 +36 +16
0 -14
+56 +17
0 - 16 -36 - 52 --66
0
- 25
+36
0
+29 -10
-7 --46
-28
-e2
-61
-{fl
0
- 36
+151 +75 +57 +39 +17
0 -16
+62 +18
0 - 18 --40 -57 - 73
0
- 27
+40
0
+33 - 10
- 7 - 50
-27
-e7
-65
-86
0
--40
+165 +83 +63 +43 +1 8
0 - 17
+68 +20
0 - 20 --45 --63 --80
-20
120-140
140 - 160
160- 180
180 - 200
200-225
225-250
250-280
280- 315
315 - 355
355- 400
400-450
450- 500
11 The tolerance classes in bold print correspond t o row 1 in DIN 7157; their use is preferable.
-20
- 11
- 23
- 13
- 28
- 18
-34
-20
-41
-25
-eo
-30
-4IO
-32
--62
-38
-34
-69
-42
- 72
-48
- 78
-58
-73 -e3
-41
-811
-78 -101
-48 - 77
-88 - 117
-eo -85
-80 - 125
-53 -83
-83 -133
-eo - 105
-108 -151
-G -113
- 109 - 159
-e7 - 123
- 113 - 189
-74 -138
- 128 - 190
-78 - 1150
-130 -202
-{fl -189
- 144 426
-83 - 187
- 150 - 2A4
- 103 -209
- 188 -272
- 109 - 229
- 1n - 292
109
Technical drawing: 3.10 Tolerances and fits
ISO fits
Basic shaft system
cf. DIN ISO 286-2 (1990-11)
Limit deviations i n µm for tolerance classes 11
Nomi nal
dimension
range
over-to
mm
bis 3
3- 6
6- 10
10- 18
18- 30
30-40
40- 50
50-65
65- 80
80- 100
100- 120
for
shafts
~
F8
H8 µ9/JS!!2l Ng3l
+ 120
+60
+ 145
+70
+170
+ 80
+205
+ 95
+240
+ 110
+280
+ 120
+290
+1 30
+330
+60
+20
+ 78
+30
+98
+40
+120
+50
+ 149
+65
+39
+14
+50
+ 20
+61
+ 25
+75
+32
+92
+40
+20
+06
+28
+ 10
+35
+13
+43
+ 16
+53
+20
+ 14
0
+ 18
0
+22
0
+27
0
+33
0
+ 12,5
- 12,5
+ 15
- 15
+ 18
- 18
+21,5
- 21,5
+26
- 26
-4
- 29
0
- 30
0
-36
0
- 43
0
- 52
- 6
- 31
-12
- 42
- 15
-51
- 18
-61
- 22
-74
+ 180
+80
+ 112
+50
+64
+25
+39
0
+31
- 31
0
- 62
- 26
- 88
0
-160
~ + 220 +134
+ 100
+60
+76
+30
+46
0
+37
- 37
0 - 32
- 74 -106
0
- 190
+260
+ 120
+159
+72
+90
+36
+54 +43,5
0 - 43,5
0 - 37
- 87 - 124
0
- 220
+305
+145
+185
+ 85
+ 106
+43
+63
0
+50
-50
0 - 43
-100 - 143
0
- 250
+ 355
+ 170
+ 215
+ 100
+ 122
+50
+72 +57,5
0 -57,5
0 -50
- 115 - 165
0
- 290
+400
+ 190
+240
+ 110
+ 137
+ 56
+81
0
+65
- 65
0 - 56
- 130 - 186
0
- 320
0 ~ +440
-140 +760 +210
+400
+840
0 +440 + 480
- 155 +880 + 230
+480
+265
+ 125
+ 151
+62
+89
0
+ 70
- 70
0 - 62
- 140 - 202
0
- 360
+290
+ 135
+ 165
+ 68
+97 +77,5
0 - 77,5
0 - 68
-155 -223
0
-400
0
- 25
0
- 30
0
- 36
0
-43
0
- 52
0
- 62
0
- 74
0
- 87
0
- 100
0
- 115
225-250
280-315
315-355
355-400
400-450
0
- 130
+340
+ 150
+ 390
+ 170
t---+ 400
+ 180
+ 450
+200
t---+460
+210
t---+480
+230
+530
+240
+ 550
+260
+ 570
+280
+ 620
+300
+650
+330
+720
-
-
450- 500
~
E9
180- 200
250- 280
transition fit
clearance fit
D10
160- 180
200-225
for
shafts
C11
120- 140
140- 160
fo r holes
Pairing with an h9 shaft
results in a
P9
0
- 60
0
- 75
0
- 90
0
- 110
0
- 130
for holes
Pairing with an
h 11 shaft results in a
clearance fit
A11
C11
D10
+330
+270
+345
+270
+ 370
+280
+400
+290
+430
+300
+470
+310
+480
+ 320
+530
+ 340
+550
+ 360
+600
+380
+630
+ 410
+ 710
+ 460
+ 770
+520
+820
+580
+950
+660
+ 1030
+740
+ 1110
+820
+ 1240
+920
+1370
+1050
+1560
+ 1200
+ 1710
+ 1350
+ 1900
+ 1500
+2050
+ 1650
+ 120
+60
+ 145
+70
+170
+80
+205
+95
+240
+ 110
+280
+ 120
+290
+130
+330
+140
+340
+ 150
+390
+ 170
+400
+ 180
+450
+200
+460
+2 10
+480
+ 230
+ 530
+240
+550
+260
+570
+280
+620
+300
+650
+330
+720
+360
+760
+400
+840
+440
+880
+480
+60 +60
0
+20
+78 +75
0
+30
+98 +90
+ 40
0
+ 120 + 110
0
+50
+ 149 + 130
0
+65
H11
+ 180 + 160
+80
0
+ 220 + 190
0
+ 100
+ 260 +220
+ 120
0
+305 +250
+145
0
+ 355 +290
+ 170
0
+400 +320
0
+ 190
+440 +360
+210
0
+480 +400
0
+230
1 > The tolerance classes in bold print correspond to row 1 in DIN 7157; their use is preferable.
2> The tolerance zones J9/JS9, J 10/JS10 etc. are all identical in size and are symm etrical to the zero line.
31 Tolerance class N9 may not be used for nominal dimensions s 1mm.
110
Technical drawing: 3.10 Tolerances and Fits
General tolerances, Roller bearing fits
General tolerances11 for linear and angular dimensions
cf. DIN ISO 2768-1 (1991-06)
Linear cirnensions
Tolerance
class
Limit deviations in mm for nominal dimension ranges
over3
t o6
over 6
to30
over 30
to 120
over 120
to400
± 0.05
± 0. 1
± 0.1
±0.2
±0.3
±0.5
± 0.5
±1
Rad,1 and chamfers
±0.15
± 0.3
± 0.8
± 1.5
± 0.2
± 0.5
± 1.2
± 2.5
0.5
to 3
f (fine)
m (medium)
C (coarse)
± 0.05
± 0.1
± 0.2
-
V (very coarse}
Tolerance
class
Limit deviations in mm for
nominal dimension ranges
f (fine)
m (medium)
C (coarse)
V (very coarse)
over3
to6
6
± 0.2
± 0.5
±1
±1
over 1000
to2000
over2000
to 4000
-
±0.3
±0.5
± 0.8
± 1.2
±2
±3
±4
±6
Angular dimensions
±2
±4
±8
Limit deviations in degrees and minutes
for nominal dimension ranges (shorter angle leg)
0.5
to 3
± 0.4
over 400
to 1000
over 10
to50
over 50
to 120
± 10
± 0° 30'
± 0' 20'
± 0° 10'
± 0° 5'
:t 1°30'
± 1'
± 2'
± o· 30·
± 1'
± 0° 15'
± 0' 10'
± 0' 20'
to 10
±2
± 3'
General tolerances11 for form and position
over 120
to400
± 0' 30'
400
cf. DIN ISO 2768-2 ( 199Hl4)
Tolerances in mm for
straightness and fla1ness
nominal dimension ranges in mm
Tolerance
class
upto
10
H
K
L
0.02
0.05
0.1
over
10
to
30
0.05
0.1
0.2
perpendicularity
symmetry
run
nominal dim. ranges in mm nominal dim. ranges in mm
(shorter angle leg)
(shorter feature)
over over over
over over over
over over over
100 300 1000 up to 100 300 1000 up to 100
300 1000
to
to
to
100
to
to
to
100
to
to
to
300 1000 3000
300 1000 3000
300 1000 3000
0.2
0.3
0.4
0.2
0.4
0.5
0.5
0.1
0.3
0.4
0.6
0.8
0.4
0.6
0.8
1
0.6
0.2
I 0.8 I 1
0.5
0.8
1.2
1.6
0.6
1
1.5
2
o.6 I 1 I 1.5 I 2
I I
over
30
to
100
0.1
0.2
0.4
I
11General tolerances apply to dimensions without individual tolerance entry. Drawing entry page 80.
Tolerances for the installation of roller bearings
cf. DIN 5425-1 (1984-11)
Radial bearing
lnner ring (shaft)
Load
case
circum-
•
•
ferential
7
Outer ring (housing)
Fundamental deviations
for shafts1l with
Fit
Load
transition
or
low
h, k
k,m
interference
medium
j,k,m
k,m, n, p
fit
required
high
m, n
n, p, r
clearance
fit
allowed
arbitrarily
large
ball bearing roller bearing
Load
case
•
•
corcum-
point load
ferential
j, h, g, f
Thrus1 bearing
Load type
.,
Bearing construction
Combined
radial/axial load
angular contact ball
bearing
spherical ro ller bearing
tapered roller bearing
Pure axial load
ball bearing
roller bearing
Fit
clearance
fit
allowed
transition
Load
Fundamental deviations
for housings11 with
ball bearing I roller bearing
arbit rarily
large
J,H,G,F
low
J
K
medium
K,M
M,N
high
-
N, P
or inter-
ference
fit
required
Shaft washer (shaft)
Housing plate (housing)
Fundamental deviat.
Fundamental deviations
for
shafts
1l
for housing 1l
Load case
Load case
circumfer.
point
j,k,m
H,J
load
load
point
circumfer.
j
K.M
load
load
-
h, j, k
-
H, G, E
1l Fundamental tolerance g rades: for shafts typically IT6, for bores typically IT7. If the smoothness and accuracy of
running must satisfy increased requirements, also smaller tolerance grades are specified.
111
Technical drawing: 3.10 To lerances and fits
Fit recommendations, possible fits
Fit recommendations11
cf. DIN 7157 (1966-01)
From row 1 j C11/h9, D10/h9, E9/h9, F8/h9, H8/f7, F8/h6, H7/f7, H8/h9, H7/h6, H7/n6, H7/r6, H8/x8 or u8
From row 2 j C11/h11, D10/hll, H8/d9, H8/e8, H7/g6, G7/h6, H11/h9, H7/j6, H7/k6, H7/s6
Possible frts (examples)
cf. DIN 7157 (1966-011
Basic hole2l
Characteristic/application examples
----
Clearance fits
0 IS;!
o llE
0 GjlEJ
0 11W
0 m]
loose running frt
H8/d9
H8/e8
o Aa"ll
HS/O
j6
Free running frt (Medium running fit): Sufficient clearance is
allowed for ease of assembly.
D10/h9
E9/h9
Close running fit: Clearance allows for parts to be easily assembled by hand while maintaining location accuracy.
~
0
00
0
F8/h9
0
(i.e. plain bearing of shaft)
t1E
H7/O
Sliding fit - free: Clearance allows accurate location and free
movement, including turning.
(i.e. piston valves in cylinders)
F8/h6
0
H7/g6
Sliding fit - constrained: Clearance allows better locational
accuracy while still allowing sliding or turning movement.
(i.e. transmission gear on shaft)
G7/h6
o !JE
H8/h9
Minimal clearance fit: Allows locational accuracy and hand
force assembly w ithout being a snug fit.
ml
H7/h6
Locational clearance fit: Allows snug fit of stationary parts that
may be assembled by hand force.
(i.e. punch in punch holder)
Transition fits
H7/j6
Locational t ransition fit - clearance: For accurate location allow ing more clearance than interference.
(i.e. gears on shafts)
H7/n6
Locational transition frt - interference: For accurate location
where interference is permissible.
(i.e. drill bushing in jigs)
---h6
H8/h9
o [;a;]
H7/h6
0 liE
(i.e. spacer sleeves)
h6
o Dm w
Clearance allows for loose fit of mating parts.
(i. e. spacer sleeves on shafts)
(i.e. collar on shaft)
g6
0 GIEi
Basic shaft21
h6
not specified
n6
0-
0-
o ia::i
0 a:!!
0 !!al
11
-
r6
-s6
Interference fits
H7/r6
Locational interference fit: For rigidity and alignment/accurate
location without special bore requirements.
H7/s6
Medium drive fit: For ordinary steel parts or shrink fits of light
sections. lightest fit possible for cast iron.
(i.e. bushings in housings)
(i.e. plain bearing bushings)
not specified
H8/u8
Force frt: For parts fitting that can withstand high mechanical
pressing force or shrink fitting.
(i.e. wheel on axle)
H8/x8
Extreme force fit: For parts that can only be assembled by stretching or shrinking.
(i.e. turbine blade on shaft)
Deviations from these fit recommendations should only be made in exceptional cases, e.g. installation of roller bearings.
21 The fits in bold p rint are tolerance combinations according to row 1. Their use is preferred.
112
Technical drawing: 3.10 Tolerances and fits
Geometric tolerancing
Tolerances of geometry, orientation, location and run-out
cf. DIN EN ISO 1101 (2006-02>
Structure of tolerance specifications
Datum
Toleranced element
• Identification ~ datum letterbox
datum letter
Datum element A
• ldentif,cation
feature control frame
Symbol o f ~
03 A / datum letter
tolerance value
tolerance type
datum line
datum base
toleranced
element
• Datum is the
datum line
with datum
,
arrow
• The tolerance applies to the
!En
mid~lane
axis
----~surface
s~
f
~
t=ti--fhne
Indications in drawings of datum specifications and toleranced elements
Datum
Simple datum
Common datum
Datum in feature Individual datum letter
control frame
Datum letters separated
with hyphens
M ultiple datum
(two or three elements>
Example
Order of datum letters
according to their importance
Examples
...~ ; ;;~;~;:+--+--+-<
!ll2Sh6
The axis of the hole
must run perpendicular
(tolerance value 0.04 mm>
to the datum surface.
The center plane of the slot
must run symmetrically
to the center plane of the
exterior surface (tolerance
value0.1 mm>.
The cylindrical surface
Ill 24g6 must run true to the
axis !ll20k6 and the flat
surface must be planar
(tolerance value 0.05 mm>.
Indication in drawings
Geometric
characteristic
symbols
The slot must lie symmetrical (tolerance value
0.06 mm> and parallel
(tolerance value 0.02 mm>
to the axis !ll 25h6.
cf. DIN ISO 1101 (1985-03>
Representation
in drawing
(examples>
Explanation
Tolerance zone
At all points across width b, the surface curve
must lie between two parallel lines spaced t =
0.1 mm apart
~~
The toleranced axis of the shaft must lie within a
cylinder with diameter t = 0.04 mm.
~
Geometric tolerances
Straightness
D
Flatness
The toleranced surface must be located between
two parallel planes spaced apart a distance of
t = 0.03 mm.
113
Techn ical drawing: 3.10 Tolerances and fits
Geometric dimensioning and tolerancing GD & T
Indications in drawings (continued)
Symbol and
toleranced
property
cf. DIN EN ISO 1101 (2006-02)
Explanation
Representation
in drawing
Tolerance zone
Tolerances of form (continued)
0
The cone"s circumferential line must lie between
two concentric circles spaced apart at a distance
of t= 0.08 mm in each point of the cone length I.
Circularity
~
!~
;,,...-
Cylindricity
The shell surface of the cylinder must lie between
two coaxial cylinders, which are spaced apart at
a radial distance of t = 0.1 mm.
Profile~
of
'"
line
The profile line must lie between two enveloping
lines, whose gap is bounded by circles of diameter t = 0.05 mm in each point of the workpiece
thickness b.
The centers of these circles lie on a geometrically
ideal line.
Qb
-
P
rofi
of
. le~
surface
8i
I
every cone
cross section
The surface of the sphere must lie between two
enveloping surfaces, whose gap t = 0.3 mm is
created by spheres. The centers of these
spheres lie on the geometri cally ideal surface.
Orientation tolerances
II
Parallelism
The hole's cent erline must lie between two
parallel planes spaced apart at a distance of
t = 0.01 mm. The planes are parallel to datum
line A and datum plane B and in line w ith the
defined direction (vertical in this case).
The ho le's centerlin e must lie within a cylinder
of diameter t = 0.03 mm. The centerline of t his
cylinder is parallel to datum line (axis) A.
Per-
The hole's centerline must lie within a cylinder
of diameter t = 0.1 mm that is perpendicular to
datum plane A.
penJ_ dicularity
L
Angu larity
The plane surface must lie between two planes
perpendicular to datum line A that are spaced
apart at a distance of r = 0.03 mm.
The hole's centerline must lie within a cylinder
of d iameter t = 0.1 mm. The centerline of the
cylinder is parallel to datum plane Band inclined
at a theoret ically exact angle of a = 45° wit h reference to datum plane A.
T-~
d a l ~ ~B
P
•• } ? n e
r -r ---,;
:.
~
The inclined plane must lie between two parallel
planes spaced at a distance of t = 0.15 mm that
are inclined at a theoretically exact angle of
a = 75° w ith reference to datum line A.
---
datum
line A
~
;.
'Z l.
45°
- -_:_:::-:~datum
lane A
IX
-r
tum
eA
114
Technical drawing: 3.10 Tolerances and fits
Geometric dimensioning and tolerancing GD & T
Indications in drawings (continued)
Symbol and
toleranced
property
Representation
in drawing
cf. DIN EN ISO 1101 (2006-02)
Explanation
Tolerance zone
Tolerances of location
The hole's centerline must lie within a cylinder
of diameter t = 0.05 mm. The cylinder's centerline
must coincide w ith the theoretically exact locat ion of the hole's centerline in regard to the
datum planes A, Band C.
Concentricity
-u
et
......_, Ci) ¢0.1 A
@
The surface must lie between two parallel
planes spaced apart at a distance of t = 0.1 mm
that are symmetrical to the theoretically exact
location of the toleranced surface in regard to
datum plane A and datum line B.
·:·
The center of the hole must lie in a circle of diameter t = 0. 1 mm that is concentric to the datum
point A in the cross section.
~ tum
point A
Coaxiality
The centerline of all diameters must lie w ithin a
cylinder of diameter t = 0.05 mm. The centerline
of this cylinder must coincide with the common
datum axis A-B.
Symmetry
The midplane of the slot must lie between two
parallel planes spaced apart at a distance of
t = 0.05 mm that are located symmetrical t o
datum plane A.
~
~
Runout tolerances
In every cross section. the circumferential line
must be perpendicular to the common datum line
A- B between two concentric circles in the same
plane having a radial distance of t = 0. 1 mm .
"'
•
Radial
circular
runout
In every cross section. the 120° circumferential
line must be perpendicular t o datum line A and
lie between two concentric circles in the same
plane that have a radial distance oft= 0. 1 mm.
I
In every diameter, the circumferential line must
lie in the plane surface between two circles that
have a radial distance of t - 0.04 mm. The centerline of each diameter must coincide with
datum line A.
Axial
circular
runout
The shell surface must lie between two coaxial
cylinders having a radial distance of t = 0.03 mm.
The centerlines of these cylinders must coincide
w ith the common datum line A- B.
Total
axial
runout
ffl
The plane surface must lie between two parallel
planes spaced apart at a distance of t - 0. 1 mm
that are perpendicular to datum line A.
r-~
datum
line A
every diameter
1
~"
Table of Contents
115
4 Materials science
Tungsten (W)
Zinc (Zn)
lin (Sn)
Unalloyed •
steels
523
::===s=:::::I
19.27
7.13
7.29
3390
419.5
231.9
Alloy
steels
Stainless
steels
4.1
Materials
Material characteristics of solids . . . . . . . . . . . . . 116
Material characteristics of liquids and gases . .. 117
Periodic table of the elements ............... 118
4.2
Designation system for steels
Definition and classification of steel ........... 120
Material codes, Designation ................. 121
4.3
Steel types, Overview .. .... ........ .. ... ... 126
Structural steels ........................... 128
Case hardened, quenched and tempered,
nitrided, free cutting steels ... ... ....... .. ... 132
Tool steels ... ... .. .. ..... .. .. ... .......... 135
Stainless steels, Spring steels ............ . ... 136
4.4
Finished steel products
Sheet, strip, pipes ........... . .............. 139
I 1&Mners I ~I_ C60E
_ __,
I3,CrM012II
Cf45
11:::=35=520==:::::
1 eowerva j I x12Cr13 I l.__3851
_1__,
~
~
- -. - -:-~-:-;1-~-:-~-~m-·-~-~-·-·_·_·_··_·_·_·_· _· _··_·_·_·_·_·_··_·_·_·_·_·_
· ·_·_·_
14_3~
45
Iron-Carbon phase diagram ................. 153
Processes ............. .. ..... ... . .... .... . 154
if
1J
1
' \
/M
i!PJ
.
4.6
Cast iron materials
Designation, Material codes ....... .. . ... .... 158
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Cast iron .. .... .. .............. . ... . ...... 160
Malleable cast iron, Cast steel ... ..... ..... ... 161
4.7
Foundry technology
Patterns, Pattern equipment ................. 162
Shrinkage allowances, Dimensional tolerances . 163
4.8
Light alloys, Overview of Al alloys ............ 164
Wrought aluminum alloys ..... . .. .. ......... 166
Aluminum casting alloys .. .. ... ....... .. .... 168
Aluminum profiles ......................... 169
Magnesium and titanium alloys ..... ..... .... 172
:'
...-- ,---- - -- - -- - -- - - - -- -- - - - - - - 1
4.9
Heavy non-ferrous metals, Overview . . . . . . . . . 173
Designation system . . . . . . . . . . . . . . . . . . . . . . . . 174
Copper alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
4.10 Other metallic materials
Composite materials, Ceramic materials
177
Sintered metals ....... ... .. ......... ....... 178
4.11 Plastics, Overview ...... .... .. .. .. .... ..... 179
Thermoplastics .. .... ...... ... .... . ..... .. . 182
Thermoset plastics, Elastomers ... ..... . ..... 184
Plastics processing ......................... 186
4.12 Material testing methods, Overview . . . . . . . . . . 188
Tensile testing ............................. 190
Hardness test .. . ... . ..... . .... ....... ..... 192
4.13 Corrosion, Corrosion protection . . . . . . . . . . . . . 196
4.14 Hazardous materials ....................... 197
116
Materials science: 4.1 Materials
Material characteristics of solids
Solid material
Density
Material
Melting
temp-
Boiling
Latent
tempheat of
erature
erature
fusion
at 1.013 bar at 1.013 bar at 1.013 bar
Thermal
conductivity
at 20°C
specific
heat
at 0-100' C
Specific
electrical
resistivity
at 20'C
kJ/ (kg · K) Q. mm2/m
C
{}20
kg/dm 3
q
'C
"
;_
'C
kJ/kg
W/(m-K)
Aluminum (Al)
Antimony (Sb)
Asbestos
2.7
6.69
2.1- 2.8
659
630.5
~ 1300
2467
1637
356
163
204
22
-
-
Beryllium (Be)
Bismuth (Bi)
Cadmium (Cd)
1.85
9.8
8.64
1280
271
321
~ 3000
-
Carbide (K 20)
Carbon (diamond)
Cast iron
14.8
3.51
7.25
Chromium (Cr)
Cobalt (Co)
Coke
7.2
8.9
1.6 - 1.9
Concrete
Constantan
Copper (Cu)
1.8- 2.2
8.89
8.96
Cork
Corund um (Al203)
CuAI alloys
0.1- 0.3
3.9-4.0
7.4 - 7.7
-
-
-
2050
1040
2700
2300
CuSn alloys
CuZn alloys
Foam rubber
7.4- 8.9
900
8.4- 8.7 900- 1000
0.06- 0.25
-
-
Glass (quartz glass)
Gold (Au)
Graphite (C)
2.4-2.7
19.3
2.26
520- 55011
1064
~ 3550
G reases
Ice
Iodine (I)
0.92-0.94
0.92
5.0
30- 175
0
113.6
Iridium (Ir)
Iron oxide (rust)
Iron. pure (Fe)
22.4
5.1
7.87
Lead (Pb)
Magnesium (Mg)
Magnesium alloy
{}
"
Mean
Coefficient
of Nnear
expansion
0- lOO'C
a,
1/'Cor 1/K
0.028
0.39
0.0000238
0.0000108
-
0.94
0.21
0.81
-
-
165
8.1
91
1.02
0.12
0.23
0.04
1.25
0.077
0.0000123
0.0000125
0.00003
0.6- 1.6
0.000005
0.000001 18
0.0000105
0.13
0.062
0.0000084
0.0000127
1560
765
59
54
~ 4000
> 2000
~ 3550
1150- 1200
2500
-
81.4
125
58
0.80
0.52
0.50
69
69.1
0.18
0.46
0.43
0.83
~ 1
23
384
0.88
0.41
0.39
0.49
0.0179
0.00001
0.0000152
0.0000168
0.04- 0.06
12 - 23
61
1.7-2.1
0.96
0.44
-
0.0000065
0.0000195
46
105
0.04- 0.06
0.38
0.39
0.02- 0.03
0.05- 0.07
0.0000175
0.0000185
-
-
-
0.8-1.0
3 10
168
0.83
0.13
0.71
101s
0.022
0.000009
0.0000142
0.0000078
0.2 1
2.3
0.44
2.09
0.23
59
0.58 (pwdr)
81
0.13
0.67
0.47
-
-
0.13
0.000012
0.13
1.04
0.208
0.044
1903
1493
2642
2880
134
268
-
-
1260
1083
~ 2400
-
~ 2595
213
2300
2300
167
-
-
-
-
-
-
-
-
2707
67
~ 4800
~ 300
-
100
183
332
62
2443
1570
1536
>4350
135
-
-
3070
276
11.3
1.74
~ 1.8
327.4
650
~ 630
1751
11 20
1500
24.3
195
-
34.7
172
46-139
-
-
0.000029
0.000 026
0.0000245
Manganese (Mn)
Molybdenum (Mo)
Nickel (Ni)
7.43
10.22
8.91
1244
2620
1455
2095
4800
2730
251
287
306
21
145
59
0.48
0.26
0.45
0.39
0.054
0.095
0.000023
0.0000052
0.000013
Niobium (Nb)
Phosph., yellow (P)
Pit coal
8.55
1.82
1.35
2468
44
~4800
280
288
21
53
0.217
0.0000071
1200
1769
4300
113
1.09
0.13
1.3
Porcelain
Quartz, flint (Si0 2)
Selenium. red (Se)
2.3 - 2.5
2.1- 2.5
4.4
-
0.45
70
0.17
-
-
2.3
21 .5
1.05
-
0.24
Plaster
Platinum (Pt)
Polystyrene
-
0.273
0.80
1.02
1.63)
9.9
0.2
83
91)
407
Silicon (Si)
Silicon carbide (SiC)
Silver (Ag)
-
-
~ 1600
-
1480
220
2230
688
83
2.33
1423
2355
1658
2.4 dilsintegrates inlto C and Si abo[ve 3000' C
10.5
961.5
2180
105
21 cross grain
31 at 800°C
H transformation temperature
-
-
0.000051
-
-
0.053
0.0000065
-
0.098
1010
0.000009
0.00007
1.23)
0.8
0.33
1012
0.000004
0.000008
0.75
1.051)
0.23
2.3 • 109
-
0.0000042
-
-
0.015
0.0000193
117
Materials science: 4.1 Materials
Material characteristics of solid, liquid and gaseous materials
Solid materials (continuedl
.
Melting
Boiling
Latent
t emptempheat of
erature
erature
fusion
at 1.013 bar at 1.013 bar at 1.013 bar
/)
/J
q
(l
kg/dm3
·c
·c
kJ/kg
Density
Material
~
97.8
~ 1500
~ 1500
890
2500
Thermalconductivity
at 20°C
Mean
specific
heat
at 0-100°C
Spec:if"oc
electrical
resistivity
at 20°c
C
(l,O
1.3
0.49
0.51
0.04
0.14- 0.18
0.7
).
W/(m-KI
113
205
kJ/(kg • K) Q-mm2/m
Coefficient
of linear
expansion
o-100°c
a,
or 1/K
,re
Sodium (Na)
Steel, unalloyed
Steel, alloyed
0.97
7.85
7.9
-
-
126
48- 58
14
Sulfur (SI
Tantalum (Tai
Tin (Snl
2.07
16.6
7.29
113
2996
231.9
344.6
5400
2687
49
172
59
0.2
54
65.7
0.70
0.14
0.24
-
Titanium (Ti)
Tungsten (W)
Uranium (U)
4.5
19.27
19.1
1670
3390
1133
3280
5500
~ 3800
88
54
356
15.5
130
28
0.47
0.13
0.12
0.42
0.055
0.0000082
0.0000045
-
Vanadium (VI
Wood (air driedl
Zinc (Zn)
6.12
0.20-0.72
7.13
1890
~ 3380
343
31.4
0.06-0.17
113
0.50
2.1-2.9
0.4
0.2
-
Latent
heat of
vaporization21
r
kJ/kg
Thermal•
conductivity
at20°C
Specific
heat
-
-
-
419.5
907
101
0.000071
0.0000119
0.0000161
-
0. 124
0. 114
0.0000065
0.000023
~ 0.000042
0.06
0.000029
Liquid materials
Density
Material
at 20°c
(l
kg/dm3
Freezing
Boiling
Ignition or melting
temp- temperatemperature
ture
erature
at 1.013 bar at 1.013 bar
I)
/J
/J
·c
·c
·c
at 20·c
).
C
W/(m - KI
kJ/(kg • Kl
Coefficient
of volume
expansion
av
1/°C o r 1/K
Alcohol 95 %
Diesel f uel
Ethyl ether (C 2H5l20
0.81
0.81- 0.85
0.71
520
220
170
- 114
- 30
- 116
78
150- 360
35
854
628
377
0.17
0.15
0.13
2.43
2.05
2.28
0.0011
0.00096
0.0016
Fuel oil EL
Gasoli ne
Machine oil
~ 0.83
0.72-0.75
0.91
220
220
400
-10
-30 - - 50
- 20
> 175
25-210
> 300
628
419
-
0.14
0.13
0.13
2.07
2.02
2.09
0.00096
0.0011
0.00093
Mercury (Hg)
Petroleum
Water, distilled
13.5
0.76- 0.86
1.0031
-
-39
-70
0
357
> 150
100
285
314
2256
10
0.13
0.60
0.14
2.16
4. 18
0.00018
0.001
0.000 18
11 above 1000 °C
21 at boiling temperature and 0.013 bar
Specific
heat
at 20°C and 1,013 bar
c,,31
I c;,•>
kJ/(kg • Kl
550
-
3> at 4 °C
Gaseous materials
Material
Density Specific
Melting
Bolling
at 0°C and gravity11 temperature temperature
1.013 bar
at 1.013 bar
at 1.013 bar
I)
/J
(l
eleL
3
·c
·c
kg/m
).
Coefficient
of thermal
conductivity21
W/(m -K)
)./).A
Thermal
at 20°C
Acetylene (C2H2I
Air
Ammonia (NH3)
1.17
1.293
0.77
0.905
1.0
0.596
-84
- 220
- 78
- 82
- 191
-33
0.021
0.026
0.024
0.81
1.00
0.92
1.64
1.005
2.06
Butane (C4H1ol
Carbon diox. (C021
Carbon monox. (COi
2.70
1.98
1.25
2.088
1.531
0.967
- 135
- 57 51
- 205
- 0.5
- 78
- 190
0.0,6
0.0,6
0.025
0.62
0.62
0.96
-
-
0.82
1.05
0.63
0.75
Freon (CF2Cl2I
Hydrogen (H2I
Methane (CH4)
5.51
0.09
0.72
4.261
0.07
0.557
- 140
- 259
- 183
- 30
- 253
- 162
0.010
0.180
0.033
0.39
6.92
1.27
-
-
14.24
2.19
10.10
1.68
Nitrogen (N2I
Oxygen (021
Propane (C3Hal
1.25
1.43
2.00
0.967
1.106
1.547
-2 10
- 219
- 190
-196
- 183
- 43
0.026
0.026
0.0,8
1.00
1.00
0.69
1.04
0.91
0.74
0.65
-
-
1.33
0.716
1.56
n Specific g ravity= density of a gas e divided by the density of air (lA•
21 Coefficient of thermal conductivity = the thermal conductivity). of a gas divided by the thermal conductivity ).A of air.
4 > at constant volume
51 at 5.3 bar
3> at constant pressure
Peri! od
1
2
3
4
5
Main groups
IA
I
1H
IIA
Hydrogen
Relative atomic mass
1.008
3 Li
4 Be
Lithium
Beryllium
6.941
9.012
11 Na
12 Mg
Radioactive elements
in red, e.g. 222
Synthetic elements
in parentheses, e. g. (261)
24.305
19 K
Potassium
39.102
Calcium
37 Rb
Rubi•
dium
I Ill B
20 Ca
40.078
38 Sr
Ill A
IVA
VA
VIA
VIIA
black print
brown print
blue print
7N
80
9 F
e > 5 kg/dm3
58
ec
Boron
Cerbon Nitrogen Oxygen Fluorine
10.811
12.011
14 Si
13 Al
A luminum
Silicon
14.007
15 P
Phosphorus
30.974
15.999
18 S
Sulfur
32.088
34 Se
18.998
11 Cl
Chlorine
35.453
....
NfD11 _
...s::
a,
...CDa,
33 As
35 Br • Kr
Arsenic Seleni- Bromine
Kl'tPIOII
um
78.960 79.904 auoo
vi
53 I
M X.
::J
Iodine
x.non
52 Te
Telluri-
Strontium
en
(")
iii'
(")
!11
...!"-
s::
a,
co
...cij'
55 Cs
Cesium
132.905
7
solid:
liquid:
gaseous:
Transition elements
85.468
6
Letter symbols
01)
Element name; state at
273 K (0°C) and 1.013 bar:
11 Light metals Q s 5 kg/dm 3; Heavy non-ferrous metals
Sodium Magnesium
22.989
......
Main groups
Atomic number----+
(• proton number)
Sodium
vi
87 Fr
Francium
223
Nonmetals
Metalloids
Light metals11
Actinides
89- 103
119
M ateria ls science: 4.1 M aterials
Chemicals used in metal technology, molecular groups, pH value
Important chemicals used in metal technology
Technical
designation
Chemical
designation
Formula
Properties
U se
Solvent for paint,
acetylene and plast ics
Acetone
Acetone
(propanone)
(CH3),CO
Colorless, combustible, lightly
volatile liquid
Acetylene
Acetylene,
Ethane
C2H2
Highly reactive, colorless
gas, highly explosive
Fuel for welding,
source mat erial for plastics
Aqueous
cleaner
Vario us
surfactants
Various water soluble
substances
Solvent, cleaning agent;
emulsifying and thickening
agent
Carbonic acid
Carbon dioxide
-COO--OSO:r
-SO:r
CO2
Carbon
tetrachloride
Cleaning
agent
Carbon
tetrachloride
Organic
solvent
cc1.
CnH2n+2
Colorless, sometimes light ly
combustible liquids
Solvent for fats and oils,
cleaning agent
Copper v itrio l
Copper sulfate
CuSO 4
Blue, water soluble crystal,
moderately toxic
Electroplating baths, pest
control, for scribing
Corundum
A luminum oxide A l2O3
Very hard colorless crystal,
melting point 2050 •c
Ethyl alcohol
Ethyl alcohol,
denatured
C2HsOH
Colorless, lightly combustible
liquid, boiling point 78 °C
Hydrochloric
acid
Hydrochloric
acid
Nitric acid
HCI
Colorless, pungent smelling,
strong acid
Grinding and polishing agent,
oxide ceramic materials
Solvent, cleaning agent,
for heating purposes, fuel additive
Etching and pickling of metals,
manufacture of chemicals
HNO3
Very strong acid, d issolves metals (except precious metals)
Soda
Sodium
carbonate
Na2CO 3
Colorless crystal, slig htly water
soluble, basic
Spirits of
ammonia
NH4OH
Colorless, pungent smelling
liquid, weak lye
Sulfuric acid
Ammonium
hydroxide
Sulfuric acid
H2 so.
Colorless, oily, odorless
liquid, st rong acid
Etching and pickling of metals,
manufacture of chemicals
Degreasing and cleaning
bat hs, wat er softening
Cleaning agent (fat solvent),
neutralization of acids
Pickling of metals, electroplating
baths, storage batteries
Table salt
Sodium chloride
NaCl
Colorless, crystalline salt,
slightly water soluble
Condiment, for freezing m ixtures,
for chlorine extraction
Nitric acid
Water soluble, non-eombustible Shielding gas for MAG
gas, solidifies at - 78 •c
welding, dry ice
as refrigerant
Colorless, non-combustible
Solvent for fats, o ils and
paint
liquid, harmful to health
Frequently occurring molecular groups
Molecular group
Designation Formula
Example
Description
Desig nation
Formula
Carbide
=C
Carbon compounds; to some extent very hard
Silicon carbide
SiC
Carbonate
= CO3
Compounds of carbonic acid, addition of heat
yields CO 2
Calcium carbonate
CaCO3
Chloride
- Cl
Salts of the hydrochloric acids; usu. dissolve readily in water
Sodium chloride
NaCl
Hydroxide
- OH
Calcium hydroxide
Ca(OH),
Nitrate
- NO3
Hydroxides are produced from metal oxides and water;
behave as basics
Salts of t he nitric acids; usu. dissolve readily in water
Potassium nitrat e
KNO3
Nitride
=N
Nitrogen compounds; some of them are very hard
Silicone nitride
SiN
Oxide
=0
Oxygen compounds; most commonly occurring
molecular group on earth
A luminum oxide
A l2O3
Sulfate
= SO4
Salts of the sulfuric acids; usu. dissolve readily in water
Copper sulfate
CuSO4
Sulfide
=S
Sulfur compounds; important ores, chip breaker
in free cutting steels
lron(II) sulfide
FeS
pH valua
Type of aqueous
solution
<
pH value
0
Concentration
Winmoln
1()0
increasingly acidic
I
neu•
I
tral
increasingly basic
11
12
>
1
2
3
4
5
6
7
8
9
10
13
14
10-1
10-2
10""3
1o-4
10-S
10--0
10-7
10--0
10-9
10-10 10- 11 10-12 10-13 10-1•
120
Materials science: 4.2 Steels, Designation system
Definition and classification of steel
c1
°
I
10020
N EN
12000 071
A lloy w ith iron as t he main component and a carbon content under 2.0%.
Steel
I
Microstructure
The microstructural components, e. g. f errite, pearlite, carbides, and the crystalline
structure, e. g. fine g rain, coarse grain, bands, determine the steel properties, e. g.
strength, toughness, workability, machinability, weldability.
I
Infl uenced by
I
I
Steel manufacture
I
I
I
Composition
Degree of pu rity
Deoxidat ion
- carbon content
- a lloying elements
- non-metallic
i nclusions
- phosphorus and
sulfur content
rim med,
semi-killed or
killed
cast
I
I
I Classification11 I
I
Unalloyed steels
I
I
Classificatio n
I
I
I
Quality st eels
>-
No alloyi ng element
reached t he limit value
according to
table 1
IHigh-grade steels
High-grade steels differ from quality steels d ue t o:
- more careful production
- higher degree of purity
I
Alloy steels
- at least o ne alloying
element reaches the
limit value according to
tabl e 1
- st eel types not
conforming to t he
definition for stainless
steels
I
Stainless steels21
- chrome content
at least 10.5 %
- carbon content
maximum 1.2 %
Classification by main
charact eristics int o
Subsequent processing
For exam ple:
Forming: rolling, st amping,
drawing, bending etc.
Heat treatment: quenching and t ernpering, surface hardening etc.
Annealing: normalizi ng,
spheroidizing, full annealing etc.
Joining: weld ing, brazing etc.
Coating: galvanizing etc.
- improved deox idation
- more exact composition
>-
- improved hardenability
L..l
Table 1: Umit values for
unalloyed steels
%
ea.
ment
Al
0.30
Bi
Co
0.30
0.06 Ti
0.05
Cu
0.40 Ni
0.30
V
0.10
Cr
0.30 Pb
0.40
w
0.30
Ea.
%
Element
o/o
Mn
1.65
Se
0.10
0.10 Mo
0.08
Si
0.60
ment
Nb
M ain grades
I
Unalloyed quality steels
Alloy quality steels
Steel group (excerpt)
Example
Steel group (excerpt)
Example
Unalloyed structural st eels
S235JR
Rail steels
R0900Mn
Unalloyed st eels for
quenching & t empering
C45
Magnetic steel sheet
and strip
M 390-50E
Free cutting steels
10S20
M icroalloyed steels w ith
high y ield strengths
H400M
Weldable unalloyed
fine-grain steels
S275N
Phosphorus alloyed steels
w ith hig h yield st rengths
H180P
Unalloyed press. vessel steels P235GH
I
Unalloyed high-grade steels
Alloy high-grade steels
Steel group (excerpt)
Example
Steel group (excerpt)
Example
Unalloyed steels for quenching
and tempering
C45E
Alloy steels for quenching
and t empering
42CrMo4
- corrosion-resistant
steels (pages 136, 137)
Unalloyed case hard. steels
C15E
Case hardening alloy steels
16MnCr5
- heat resist ant steels
Unalloyed tool steels
C45U
Nitriding steels
34CrAINi7
- h igh-temperature
st eels
Unalloyed steels for flame
and induction hardening
C60E
A lloy t ool steels
X40Cr1 4
High-speed steels
HS6-5-2-5
1
1 The main grade " Basic st eels" was omitted. All previous basic steels are produced as q uality steels.
21 The stain less st eels have t heir own gro up. They are alloy steels, so t hey are not classified as quality or high-grade
steels.
Materials science: 4.2 Steels, Designation system
121
Designation of steels using material numbers
Material numbers
cf. DIN EN 10027-2 (1992-09), replaces DIN 1700711
Steel designations (page 122) or material numbers are used to identify and differentiate steels.
Material number
(with additional symbol +N)
Designation
Designation of
steel (examples):
42CrMo4+N
1.7225+N
or
The material numbers consist of a 6-character number (five numeric characters and a decimal point). They are bet ter suited for data processing than designations.
I Material number I
I I
Example:
11
I II
I _
I
_i
I- J12 J2s _+N..i
I
I I
M aterial main group
1 - Steel
1 1
Steel group
number
I
Supplemental symbol
If the material number is insufficient
to clearly describe the steel, the supplemental symbol of the designation is
added (page 125).
Steel type number
I
Each steel w ithin a steel group receives
its own type number.
I
I
Unalloyed steels
Alloy steels
I
I
Steel
group
number
St eel groups21
01, 91
General structural steels, Rm < 500 N/mm2
02, 92
Other structural steels not specified for
heat treatment with
Rm < 500 N/mm2
Steel
g roup
number
Steel g roups
Quality steels
Quality steels
03, 93
04, 94
05, 95
08, 98
Steels w ith special physical
properties
09, 99
Steels for various areas of application
20- 28
Alloy tool st eels
Steels w ith 0.12% s C < 0.25% or
400 N/mm2 s Rm < 500 N/mm2
32
High-speed steels with cobalt
33
High-speed steels w ithout cobalt
Steels w ith 0.25% s C < 0.55% or
500 N/mm2 s Rm < 700 N/mm2
35
Roller bearing steels
36, 37
Steels w ith special magnetic
properties
38. 39
Steels w ith special physical
properties
40-45
Stainless steels
Steels with C < 0.12% or
Rm < 400 N/mm2
06, 96
Steels with C " 0.55% or
Rm " 700 N/mm2
07, 97
Steels with high phosphorus and
sulfur content
High-grade st eels
High-grade steels
Nickel alloys, chemical resistant,
high-temperature
10
Steels w ith special physical
properties
11
Structural, machine and vessel st eels
with C <0.5%
12
Machine steels with C "0.5%
13
Structural, machine and vessel steels
with special requirements
85
Nitriding steels
15- 18
Unalloyed tool steels
87-89
High-strength weldable steels
47, 48
Heat resistant steels
49
High-temperature materials
50-84
Structural, machine and vessel
steels with various alloy
combinations
11 The material numbers remained unchanged with t he conversion from DIN 17007 t o DIN EN 10027-2.
2 1 C carbon, Rm tensi le strength
Values for t ensile st rength Rm and for carbon content Care mean values.
122
Materials science: 4.2 Steels, Designation system
Designation system for steels
cf DIN EN 10J27 1 12005 101
Designation by application
The codes for steels are composed of main and supplemental symbols. Main symbols reflect the application or
chemical composition. Supplemental symbols depend on t o the steel or product group.
Example: Pinion shaft
~ - -t£-f l
·•·
Main
Suppl. ! J I I I I
sy~bol sy~bol
Unalloyed structural steel
I S355JR+AR
I Designation I I Steel group
I DIN EN 10027-1 I I DIN EN 10025-2
MIIJMP ijl JI ,
I 42CrMo4+N I
I
I Hot-rolled round steel bar I
Designation
according to the
chemical composition (page 124)
I
I
I
DIN EN 10060
Main symbols for the designation by application
Main symbol11
Application
Main symbol11
Application
Steels for steel construction
s
23521
Prestressing steels
y
1n031
Steels for m achine construction
E
36021
Flat rolled products for cold w orking
D
)(5241
Slllels for pressure 11811881 construction
p
2&521
Rail steels
R
26051
Steels for pipes and tubes
L
38021
Flat products of high-strength steels
H
C4008I
Concrete reinforcing steels
B
50021
Magnetic steel, sheet and strip
M
400-5011
Packaging steel, sheet and strip
T
s5502
To identify cat llNI, the main symbol is p,-ied by the letter G.
1
11 The main symbol is composed of the code letter and
a number and may include an additional letter.
21 Yield strength Re for the smallest product thickness
31 Nominal value for minimum tensile strength Rm
4 1 As-rolled condition C, D, X followed by two symbols
61 As-rolled
condition C, D, X and m inimum yield
strength Re or as-rolled condition CT, DT, XT and
minimum tensile strength Rm
71 Maxim um magnetic hysteresis loss in W/kg x 100
and nominal thickness x 100 separated by a hyphen
51 Minimum hardness in accordance with Brinell HBW
Steels for steel construction
Designation example:
I
I= : :. : ion I
S 235 JR+N
IT--,strength R. for
I
IYield
smallest product thickness
ISupplemental symbols I
Product group (selection)
Standard
Supplemental symbols
Hot-rolled unalloyed
structural steels
DINEN
10025-2
Notch impact energy in J at •c I C special cold workability
JR I 27 I 20 ° I J2 I 27 1-20· +AR delivered in as-rolled condition
Jo I 21 I o • I K2 I 40 1-20• 1 +N normalized
Normalized/normalizing rolled,
grain-refined structural steels
suit able for welding
DINEN
10025-3
N
Thermomechanically rolled struc- DINEN
tural steels suitable for welding
10025-4
M
normalized or normalizing rolled, notch impact energy values
at -2o· c.
NL like N, but notch impact energy values at -50°C
thermomechanically rolled, notch impact energy values
at - 2o•c
ML like M, but with notch impact energy values at -so•c
Hot-rolled structural steels w ith
higher yield strength in the
quenched and tempered state
DIN EN
10025-6
Q quenched and tempered, notch impact energy values at - 20 •c
QL quenched and tempered, notch impact energy values at -40"C
QL1 quenched and tempered, notch impact energy values at -60°C
Steels for bright
steel products
DINEN
10277-1, 2
C special cold workability
+PL polished
+C drawn
+SH peeled
+SL ground
Hot-rolled hollow sections of
unalloyed structural steels and
grain-refined structural st eels
DINEN
10210-1
JR, JO, J2 and K2 as w ith DIN EN 10025-2
N, NL as with DIN EN 10025-3
H hollow section
-
S235JR+N: Steel-construction steel Re= 235 N/mm2, notch impact energy 27 J at -20 °C, normalized l+N)
123
Materials science: 4.2 Steels, Designation system
Designation system for steels
cf DIN EN 10027 1 12005 101
StNls for machine construction
Designatio n example:
E355 +AR
IT,-
I
l=
i~~ructioo l
Yield strength for the
smallest product thickness
I
I
I
Supplemental symbols
I
Product group (selection)
Standard
Supplemental symbols
Hot-rolled unalloyed
structural steels
DIN EN
10025-2
Steels for bright
steel products
DIN EN
10277-1, 2
GC
+AR
GC
+C
+SH
Pipes and tubes, seamless,
cold-drawn
DIN EN
10305-1
+A annealed
+N normalized
Seamless tubes made of
unalloyed and alloyed steel
DIN EN
10297-1
J2 notch impact energy values at -20 •c
K2 notch impact energy values at - 40 •c
+AR delivered in as-rolled condition +N normalized +OT quenched
and tempered
special cold workability
delivered in as-rolled condition +N normalized
special cold workability
drawn
+PL polished
peeled
+SL ground
bright-drawn/hard +LC brigth-drawn/soft
+C
+SR bright-drawn and stress relieved
=> E355+AR: machine construction steel, yield strength Re= 355 N/mm2, delivered in as-ro lled condition (+AR)
Rat products for cold wortcing
Designation example:
Code letter for
flat product
for cold working
DC04-A-m
TTT-,-
Code letter for rolling condition
I
X rolling condition not specified
C cold-rolled 0 hot-rolled
Product group (selection)
Cold-rolled flat products
made of soft steels
for cold working
Continuously hot-dip finished
strip and sheet made of soft
steels for cold working
I
Code number for the
type of steel, main
I
properties pege 141
Supplemental symbols
(product-group specific
definition)
I
II
Standard
Supplemental symbols
OINEN
10130
Surface type and finish
A Faults not affecting workability and adhesion of surface coating
are permissible.
B The better face must be flawless to the extent that the look of
quality lacquer finish or coating is not affected.
g smooth
m dull
r rough
b particularly smooth
DIN EN
10327
D hot-dip coating
Coating (followed by coating mass in g/m2 , e.g. Z140)
+AS aluminum-silicon alloy
+AZ aluminum-zinc alloy
+Z zinc
+ZA zinc-aluminum alloy +ZF zinc-iron alloy
Coating finish:
N typical zinc flower with +Z
M small zinc flower with +Z
R typical finish with +ZF
Type of surface:
B improved finish
A typical finish
C best finish
=> DC04-A-m: Flat product for cold working (D>, cold-rolled (C), steel type 04 (page 141), surface type A,
surface finish dull (m)
Rat products made of high-strength steels for cold wortcing
Designation example:
~TT~
Code letter for flat
product of highstrength steel for cold
Code letter for rolling condition
X rolling condition not specified
C cold-rolled
D hot-rolled
wor1<ing
.,,_,., Yl8KI strengm
R,, • 300 N/mm2
T500 minimum tensile mength
Rm • 500 N/mm2
I
Supplemental
symbols
(product groupspecific definition)
Product group (selection)
Standard
Supplemental symbols
Cold-rolled strip and sheet
made of micro-alloy steels
DINEN
10268
B bake-hardening steel Y high-strength 1-F steel I isotropic steel
P phosphor-alloy steel LA low-alloy/micro-alloy steel
Surface type and finish
for rolling width< 600 mm as with DIN EN 10139
for rolling width >: 600 mm as with DIN EN 10130
=> HCT500-B-g: Cold-rolled flat product made of high-strength steel (H). cold-rolled (C), minimum tensile strength
Rm = 500 N/mm2 (T500), surface type B, smooth surface (g)
124
M at erials science: 4.2 Steels, Designatio n syst em
Designation system for steels
ct DIN EN 100n 1 I200s 101
Designation by chemical composition
T he m ai n sy mbols reflect the chemical compositio n and are creat ed on the basis o f four d ifferent designation
groups. The supplemental symbols depend on t he steel group o r p rod uct group.
Example: Pinion shaft
Main
Suppl.
symbol symbol
42CrMo4+N
Hot -ro lled ro und steel bar
Designatio n
Steel gro up
DIN EN 10027-1
DIN EN 10083-1
Designatio n
according t o the
applicatio n
(pag e 122)
DIN EN 10060
Designation groups. examples and application of the main symbols11
UnlllloY9(l stNls
manganese content < 1 %
except
free.cutting steels
Aloy . - - . frN.
cutllng stNls
unalloyed steels with a
manganese content > 1 %
Aloy stNls
average content of
individual alloying element
above 5 %
42CrMo4
X12CrNl18-8
C15E
Applcatlon eamples:
unalloyed case-hardening
steels,
unalloyed q uenched and
tempered steels,
unalloyed tool steels
Applcatlon ex.nples:
Appllcation examples:
free-cutting steels.
StaiolNI stNII
~rdening alloy steels. corrosion-resistant.
heat-resistant. hightemperature steels
quenched and tempered
alloy steels,
Tool ,.,,.,.
tool alloy steels,
cold work steels
hot work steels
spring steels
Content of alloying elements
in percent in the following
order W-Mo-V-Co
10 - 10 % tungsten (WI
4 - 4 %molybdenum(Mol
3 - 3% vanadium (V)
10 - 10% cobalt (Co)
11 To ident ify cast st eel, the main symbol is preceded by the letter G; to ident ify powder metallurgical st eel, the
main sy mbol is preced ed by the letters PM.
Unalloyed steels with a manganese content < 1 %, except free-cutting steals
C15 E+S+BC
Designation example:
.-----------,J
Main symbols
Supplemental symbols
C code letter (carbon steel)
15 code number for the carbon content
C........,, • 15(100 .. 0.15%
Refer to such aspects as special applications,
control of the sulphur content, special cold
workability, heat t reatment states. The definition
of t he supplemental symbols varies accord ing
to t he steel group (page 125).
=> C45E+S+BC: quenched and tempered unalloyed steel, C content 0.45% . prescribed max. sulphur content (El. treated
for shearability (+S), blasted (+BC) (supplemental symbols on page 125, quenched & tempered steels)
Alloy steels, frff-cuttlng steels, unaloyed steels with a manganese content > 1 %
Designation example·
18CrNiMo7-6 +TH+BC
I
Main symbols
18 code number for the carbon content
~ • 18/100 ,. 0.18%
Cr, NI, Mo alloying e'-ts
(in the order of lheir mass portion)
NI Alloy contents
Cr.-.,, • 7/4 ,. 1.75%
Ni.-.,, • 6/4 ,. 1.5%
Mo • low content
-
~
Supplemental symbols
Factors for alloy contents
lf
Alloying elements
Factor
Cr, Co, Mn, Ni, Si, W
4
Al, Be, Cu, Mo, Nb,
Pb, Ta, 1i, V, Zr
10
C,Ce, N, P, S
100
B
1000
Refer to such aspects as special applications, heat t reatment states, quenching
stress, surface finish, degree
of deformation. The definition
of the supplemental symbols
varies according to the steel
group (page 125).
17CrNiMo6-4+TH+BC: Case-hardening alloy steel, C content 0.17% (17), Cr content of 1.5% (6), Ni cont ent
1.0 % (4), low M o content. treated for quenching stress (+T H) and blasted (+BC)
(supplemental symbo ls on page 125, case-hardening steels)
125
Materials science: 4.2 Steels, Designation system
Designation system for steels
Steel group/
product group (selection)
, f DIN EN 10027 1 12005 101
Standard
Supplamental symbols
DINEN
10084
prescribed maximum sulphur oontent
E
R prescribed sulphur content range
+H normal hardenability +HH restricted hardness tolerance, upper range
+HL restricted hardness tolerance. lower range
Treatment conditions:
+S treated for shearability
+A soft-annealed
+FP treated for ferrite-pearlite microstructure and quenching stress
+TH treated for quenching stress
+U untreated
Surface finish:
+BC blasted
+HW hot worked
+Pl pickled
Hot-worked quenched
and tempered steels
DIN EN
10083-1
10083-2
E, R as with care-hardening steels as per DIN EN 10084 (above)
Treatment conditions
+A soft-annealed +H normal hardenability +N normalized
+HL restricted hardness tolerance. lower range
+HH restricted hardness tolerance, upper range
+QT quenched and tempered +S treated for shearability +U untreated
Surface finish:
+BC blasted
+HW hot-worked
+P pickled
+RM hot-worked and pre-machined
Hot-worked freecutting steels
DIN EN
10087
Under normal conditions, no supplemental symbols provided (in
special cases for direct quenching types: +OT quenched and tempered)
t
Hot-worked casehardening steels
11,
'
DINEN
Bright steel products made of
case-hardening steel, quenched & 10277-1
tempered steel, free-cutting steel 10277,3..5
+C cold-drawn
+SL ground
Seamless steel tubes made of
case-hardening steels and
quenched & tempered steels
+AR as rolled
+N normalized
+A soft-annealed
+FP treated for ferrite-pearlite microstructure and quenching stress
+OT quenched & tempered
+TH treated for quenching stress
DINEN
10297-1
+SH peeled
+PL polished
=
16MnCr5+A: Case-hardening alloy steel, C oontent 0.16% (16), Mn content 1.25% (51, low Cr content, soft-annealed (+A)
Alloy steels, the content of et least one alloying element is above 5% (without high-speed steels)
Designation example:
X4CrNi18-12 +20
w
Main symbols
X code letter for the designation group
4 code number for medium carbon content
~ m • 4/100 • 0.04%
Cr, Ni main alloying elements (Cr > Nil
18-12 alloy contents in %
chromium • 18%, nickel • 12%
I
Supplemental symbols
Specification of heat treatment conditions, the
rolling condition, the type of execution, the
surface finish.
The definition of the supplemental symbols
varies according to the product group.
I
I
Steel group/
product group (selection)
Hot-rolled corrosion-resistant
sheets and strips
Cold-rolled corrosion-resistant
sheets and strips
=
I
Standard
DINEN
10088-2
DINEN
10088-2
Supplemental symbols (selection)
Treatment condition
Type of execution/surface finish
+A annealed
+OT quenched &
tempered
+OT650 quenched &
tempered to
Rm = 650 N/mm2
+AT solution annealed
+P precipitation
hardened
+P1300
precipitation
hardened to
Rm= 1300 N/mm2
+SR stress relieved
annealed
+ 1 hot-rolled products
1U not heat-treated, not descaled
1C heat treated, not descaled
1E heat treated, mechanically descaled
1D heat treated, pickled, smooth
1G ground
+2 cold-rolled products
2C, E, D, Gas with hot-ro lled products
2B like D but cold-rolled in addition
2R bright-annealed
20 hardened and tempered, scale-free
2H strain-hardened (with different
hardness stages), bright surface
X2CrNi18-9+AT+2D: Alloy steel, C content 0.02% 12), Cr content 18%, Ni content 9%, solution annealed (+AT),
cold-rolled (+21, hot-treated, pickled, smooth surface (DI
126
Materials science: 4.3 Steels, Steel types
Subgroups,
delivery conditions
Unalloyed structural steels, hot-rolled
Steels for steel
and machine
construction
DIN EN
100 25•2
Steels for
machine
construction
page 130
good machinability
weldable, except for S185
cold and hot workable
Welded constructio ns in steel
and machine construction,
simple machine parts
machinable
not weldable
cold and hot workable
Machine parts w ithout heat
treatment, e.g. by hardening,
quenching and tempering
Fine-grain steels suitable for welding
page 131
DIN EN
weldable
Weldments with high toughNormalized
10025-3
hot workable
ness, resistance to brittle
t - - - - - - - + - - - - - + - - - - - - - - - - - - - < fracture and aging stability
Thermomechan DIN EN
weldab le
in machine and steel construcically ro lled
10025-4
not hot workable
tion
Quenched and tempered structural steels with high yield strength
DIN EN
10025-6
Alloy steels
weldable
hot workable
Case hardened steels
Unalloyed
steels
DIN EN
10084
Alloy steels
page 132
in spheroidized condition
good machinability
hot workable
after surface carburization
surface hardenable
Small parts with wearresistant surface
Dynamically stressed
parts with wear-resistant
surface
Quenched and tempered steels
Unalloyed
quality steels
Unalloyed highgrade st eels
Alloy steels
DIN EN
l0083•2
DIN EN
10083-3
page 133
in spheroidized condition
good machinability
hot workable
hardenable (uncertain
results with unalloyed
quality steels)
Parts with high strength,
which are not hardened
Parts with high strength and
good toughness
Highly stressed parts with
good toughness
Steels for flame and induction hardening
Unalloyed
steels
Alloy st eel s
DIN EN
10083-2,
DIN EN
10083-3
page 134
in spheroidized condition
Parts with low core strength
good machinability
but hardening of specific areas
hot workable
directly hardenable; possible f-------------+---+---+--f-----1
to harden individual workLarger parts with high core
piece areas, e.g. tooth faces strength and hardening of spe- •
quenching and tempering of cific areas
workpieces before hardening
Nitriding steels
Alloy steels
page 134
DIN EN
10085
• in spheroidized condition
good machinability
• hardenable by nitride forming
elements, lowest quenching
distortion
• quenching and tempering of
workpieces before nitriding
Parts with increased fatigue
strength, parts subject to wear,
Parts subjected to temperatures up to 500 ·c
Spring steels
Unalloyed and
alloy steels
11 Product forms:
page 131
High-strength weldments in
machine and steel constructions
page 138
DIN EN
10270
DIN EN
10089
cold or hot workable
high elastic formability
high fatigue strength
S sheets, strips
W wires
Leaf springs, helical springs,
disc springs, torsion bars
B bars, e.g. flat, square and round bars
P profiles, e. g. channels, angles, tees
127
Materials science: 4.3 Steels, Steel types
Free cutting steels
page 134
Non-heattreatable st~els
DIN EN
10087
Free cutting
case hardened
steels
DIN EN
10087
Free cutting
quenched and
tempered steels
DIN EN
10087
Mass produced turned parts
w ith low strength requirements
optimal machinability
(short chipping)
Like unalloyed case hardened
non-weldable
might not respond uniformly steels;
better machinability
to heat treatment with case
hardening or quench
Like unalloyed quenched and
and tempering
tempered steels; better
machinability, less fatigue
strength
Tool steels
page 135
DINEN
ISO 4957
in spheroidized condition
good machinability
non-cutting cold and hotworkable
full hardening up to max.
10 mm d iameter
Low st ressed tools for cutting
and non-cutting forming at
operating temperatures up to
200 °c
Cold work
steels,
alloy
DIN EN
ISO 4957
in spheroidized condition
machinable
hot workable
larger case hardening depth,
higher strength. more wearresistant than unalloyed cold
work steels
Highly stressed tools for cutting and non-cutting forming
at operating temperatures
over 2oo• c
Hot work
steels
DIN EN
ISO 4957
in spheroidized condition
machinable
hot w orkable
hardens over the entire
cross section
Tools for non-cutting
form ing at operating
temperatures over 200 ' C
High-speed
st eels
DIN EN
ISO 4957
in spheroidized condition
machinable
hot w orkable
hardens over the
entire cross section
Cutting materials for cutting
tools, operating temperatures
up t o 600 °C,
highly stressed forming tools
Cold work
steels,
unalloyed
Corrosion resistant steels
pages 136, 137
Ferritic
st eels
DINEN
10088-2,
DINEN
10088-3
machinable
good cold-workable
weldable
heat treatment does not
increase strength
Low st ressed rust-free parts;
parts w ith high resistance t o
chlorine induced stress,
corrosion cracking
Austenitic
steels
DIN EN
10088-2,
DIN EN
10088-3
machinable
very good cold workabil ity
weldable
no increase in strength
through heat treatment
Non-rusting parts with high
corrosion resistance,
widest application range of all
stainless steels
Martensitic
steels
DIN EN
10088-2,
DIN EN
10088-3
machinable
in spheroidized condition
cold-workable
with low carbon content
weldable
heat treatable
Highly stressed non-rusting
parts, w hich can also be
quenched and tempered
11 Product forms:
. .
.
s sheets, strip
W wires
B bars, e.g. flat, square and round bars
P profiles, e.g. channels, angles, tees
..
..
128
Materials science: 4.3 Steels, Steel types
Selecting structural steels by application
I
I
I
I
Unalloyed steels
I
I
Heat treatment, e.g. hardening o r
quenching and t empering not intended
Heat treatment intended
(page 129)
I
I
I
Selection by
application
Main characteristics are determined by
I
Example: unalloyed structural steels
(page 130)
Composit ion
• manganese (Mn)
• carbon (C)
• silicon (Si) • copper (Cu)
maximum values in%
Minimum
requirements
Type of steel,
designation
• strength
S185
not specified
• strength
• toughness
E295, E335,
E360
not specified
C
• strength
• toughness
• weldability
• strength
I Mn I Si I Cu
S235JR
0.17
1.40
-
S275JR
0.21
1.50
-
S355JR
0.24
1.60
0.55
S235J0
0.17
1.40
-
S275J0
0.18
1.50
-
I
I
Purity grade
phosphorus (P)
sulphur (S)
nitrogen (N)
maximum values in%
Deoxidation
I s I N
p
DO11
-
not specified
0.045
0.045
0 .014
FN
0.35
0.035
0.035
0.012
FN
0.55
0.030
0.030
0.01 2
FN
0.55
0.030
0.030
• higher toughness
• weldability
• strength
S355J0
0.20
1.60
0.55
S450J021
0.20
1.70
0.55
S235J2
0.17
1.40
-
S275J2
0,18
1,50
-
S355J2
0.20
1.60
0.55
S355K2
0.20
1.60
0.55
0.012
FN
0.025
FF
0.55
0.025
0.025
0.012
FF
0.55
0.025
0.025
-
FF
• highest toughness
• weldability
I
More steel groups, e.g.
I
I
• cold-rolled flat products
o f high-strengt h steels
• flat products for cold working
I
I
• pressure vessel steels
• packaging steel sheet and strip
• steels for pipes and tubes
I
• concrete reinforcing steels
• prestressing steels
magnet ic steel sheet
I
I
I
Required properties are not achieved
I
For selection according to chemical composition, see page 129
I
I
11 DO type of deoxidation: FN semi-killed steel; FF killed steel with nitrogen binding elements
21 Additional alloying elements: niobium 0.06 % max.; vanadium 0. 15 % max.; titanium 0.06% max.
I
129
Materials science: 4.3 Steels, Steel types
Selecting structural steels by chemical composition
I
T
I
Unalloyed steels
I
Heat t reatment provided,
e.g. hardening or quench and t empering
Salection according to carbon content
• heat
treatment
or
I
I
Steel group
I
I
Main properties are determined by
I
Minimum
requirements
page 128
no
Composition
Purity grade
• carbon (Cl • manganese (Mn) • phosphorus (Pl
• silicon (Si)
• sulfur (S)
• ot her alloying elements (L)
Designation
I
I
Cin% Mn in % Si in %
Cl0
Case hardened
..--steels31
C15
Quenched and
tempered steels
Case hardened
• heat
steels
treatment
with proven
Quenched and
values
tempered steels
0. 10
0.45
0. 15
0.45
C35
0.35
0.65
C60
0.60
0.75
-
ClOE
0. 10
0.45
C15E
0. 15
0.45
C35E
0.35
0.65
C60E
0.60
0.75
-
-
DO
FN
>--
0.045
-
FN
0.045
FN
>--
0.63
FN
-
-
0.40
FN
- -
0.035
FN
>--
0.035
FN
0.63
I
FN
Further requirements
11 L
Maximum percentage (Cr + Mo+ Ni)
21 DO Type of deoxidation: FN semi-killed cast
31 The steels C10 and C15 are no longer included in t he standard
0021
L11in% Pmax in % Smax in%
0.40
Deoxidation
I
I--
Alloy steels
case hardened steels DIN EN 10084. However, t hey are still
available from specialty dealers.
Effect of alloying elements (selection)
Properties influenced
by alloying elements
Tensile strengt h
A lloying elements
Ni
Al
w
• •
-
• • • • • •
Cr
Cold workability
• ••
•-
Machinability
-
Yield strength
0
Impact toughness
0
Wear-resistance
0
Hot workability
High-temperature strength
Corrosion resistance
Hardening temperature
Hardenability, temperability
Nitridability
increase
0
-
Co
•- • •
•
• • •
•0
0
0
-
0
0
0
0
-
-
Mo
Si
Mn
• • ••
•
•
•
0
0
0
0
0
0
0
0
0
0
•- • •- •- •- -• •
•
• • - • •
• • • • • •
• ••
• •- • -- • - •
•
•
• •0
0 decrea se
0
0
- no significa nt effect
Example: Gears, case hardened, rough parts drop forged, reliable heat treat ment is required
Wanted: Suit able steels
Solution: Heat t reat ment (case hardening) provided - case hardened st eel, C s 0.2 %
The properties of unalloyed q uality and high-grade steels are insufficient - alloy steels
Increase of hot workability: Mn, V; increase of hardenability: Cr, Ni
Steel selectio n: 16MnCr5, 20M nCr5, 15NiCr13 (page 132)
s
-
0
-
p
•
•
0
0
-
0
0
0
•- •
-
0
-
-
0
0
0
0
Weldability
•
0
-
V
130
Materials science: 4.3 Steels, Steel types
Unalloyed structural steels
Unalloyed structural steels, hot-rolled
Notch
i mpact
energy
Steel type
I
Material
DesignationI number
001>
I
·c
at
d. DIN EN 10025-2 (2005-04), replaces DIN EN 10025
ElongaYield strength Re
tion
in N/mm2 for
product t hickness in mm at frac- Properties,
ture
application
A3l
,. 16 > 16 > 40 > 63
,; 40 s63 s80
%
Tensile
strength
I I I
R m2l
N/mm2
KV
J
"
'
Structural and machine construction steels
S185
1.0035
-
-
-
290- 510
185
175
175
175
18
S235JR
S235J0
S235J2
1.0038
1.0114
1.0117
FN
FN
FF
20
0
- 20
27
360- 510
235
225
215
215
26
S275JR
S275J0
S275J2
1.0044
1.0143
1.0145
FN
FN
FF
20
0
- 20
27
410- 560
275
265
255
245
23
S355JR
S355J0
S355J2
1.0045
1.0553
1.0577
FN
FN
FF
20
0
- 20
27
470-630
355
345
335
325
22
S355K2
S450J0
1.0596
1.0590
FF
FF
-20
0
40
27
470- 630
550- 720
355
450
345
430
335
410
325
390
22
17
470- 610
295
285
275
265
20
Non-weldable, simple
steel constructions
Basic machine parts,
weldments in steel and
machine construction;
levers, bolts, axles,
shafts
Highly stressed weld ments in steel, crane
and bridge construction
Steels for machine construction
FN
-
-
1.0060
FN
-
-
570- 710
335
325
315
305
16
1.0070
FN
-
-
670-830
360
355
345
335
11
E295
1.0050
E335
E360
1> DO Type of deoxidation:
Axles, shafts,
bolts
Wear parts;
pinion gears, worms,
spindles
FF killed cast st eel.
- manufacturer's option;
FN semi-killed cast steel;
21 Values apply to product thicknesses from 3 mm to 100 mm.
3 > Values apply to product thicknesses from 3 mm to 40 mm and longitudinal test pieces with
Lo =5.65 . fs;, (page 190)
The steel types listed in the table are unalloyed quality steels acc. to DIN EN 10020 (page 120)
Tadmic:al properties
-
-
Waldability
Hot workability
Steels of grade groups JR - JO - J2- K2 are weldable
using all processes.
Increased strength and product thickness also increase
the risk of cold cracks.
Steels S185, E295, E335 and E360 are not weldable,
because the chemical composition is not specified.
The steels are hot workable. Only products which are
ordered and delivered in normalized (+N) or normalizing
rolled (+N) condition must meet the requirements of the
above table. The treatment condition must be specified
at the time of ordering.
Example: S235J0+N or 1.0114+N
Cold workability
The additional C or GC symbol is appended to the designation of a steel type suitable for cold working (edge folding, roll forming, cold-drawing), and these types are also assigned their own material number.
Staal types for cold working
Material
Designation number
Suitable fo r 1>
F
S235JRC
S235J0C
S235J2C
1.0122
1.0115
1.0119
E295GC
1.0533
H Forming process:
R
Material
Designation number
C
. . .
- - .
F edge fo lding:
Suitable for 11
F
S275JRC
S275J0C
S275J2C
1.0128
1.0140
1.0142
E335GC
1.0543
R roll fo rm ing:
R
Material
Designation number
C
. ..
.
-
-
C cold drawing:
S355J0C
S355J2C
S355K2C
1.0554
1.0579
1.0594
E360GC
1.0633
• well-suited
Suitable for 11
F
R
C
-
-
.
...
- unsuitable
131
M aterials science: 4.3 Steels, Steel types
Weldable fine-grain and quenched & tempered structural steels
Weldable fine-grained structural steels (selection)
I
i
Steel type
Material
Designation number
DC1I
I
Notch impact
energy Kv11 in J at
temperatures in •c
Tensile
s1rength
Rm
N/mm 2
I 0 1-20
+20
cf. DIN EN 10025-3 and DIN EN 10025-4 (2005-04).
replaces DIN EN 10113
Yield strength R0
Elongain N/mm2 for
tion
nomi nal thicknesses at frac- Properties,
inmm
ture
application
A
s 16I> 16 °I>40
%
s 40
< 63
Unaloyed quality steels
S275N
S275M
1.0490
1.8818
N
M
55
S355N
S355M
1.0545
1.8823
N
M
55
47
47
370- 510
370- 530
275
40
470- 630
355
345
335
22
40
265
255
24
Aloy high-grade steels
High toughness,
brittle fracture and
aging resis1ant;
weldments in machin
ery, crane and bridge
construction, automo-
S420N
S420M
1.8902
1.8825
N
M
55
47
40
520- 680
420
400
390
19
S460N
S460M
1.8901
1.8827
N
M
55
47
40
550- 720
540- 720
460
440
430
17
11 DC Delivery condition:
N normalized/normalizing rolled
21 Values apply to V-notch longitudinal test pieces.
t ive manufacturing,
conveyors
M thermomechanically rolled
Assignment of steels: DIN EN 10025-3 -> S275N, S355N, S420N, S460N
DIN EN 10025-4 -> S275M, S355M, S420M, S460M
Technical properties
Weldability
The steels are weldable. Increased strengt h
and product thickness also increase the
risk of cold cracks.
Hot workability
Cold workability
Only steels S275N, S355N,
S420N and S480N are hot
workable.
Cold-bending or edge folding is guarant eed for nominal thicknesses up to
16 mm, if cold-workability is specified
in the order.
Cluenched and tempered struc. steels with higher yield strength (selection) cf. DIN EN 10025-6 (2005-02),
replaces DIN EN 10137-2
Steel type
Designation 11
Material
number
S4600
S460QL
Notch impact energy
KV inJat
temperatures in °c
0
- 20
-40
1.8908
1.8906
40
50
30
40
30
S500O
S500QL
1.8924
1.8909
40
50
30
40
30
S620O
S620QL
1.8914
1.8927
40
50
30
40
30
S890Q
S890QL
1.8940
1.8983
40
50
30
40
30
S960O
S960QL
1.8941
1.8933
40
50
30
40
11 Q quenched and tempered;
impact values to - 40 °C
-
30
Ten.s ile
strength
Rm
N/mm2
550-720
Elonga·
Yield strength R0
t ion
in N/mm2 for
nominal thicknesses at frac· Properties,
inmm
application
ture
A
> 50 > 100
>3
%
s 50
s 100 s 150
460
440
400
17
High toughness, high
590- 770
500
480
440
17
700- 890
620
580
560
15
940-1 100
890
830
-
11
980- 1150
960
-
-
10
resistance to brittle
fracture and aging
stability;
highly stressed weldments in machinery.
crane and bridge
construction, auto-
motive manufacturing, conveyors
QL quenched and tempered, guaranteed minimum values for notched bar
Technical properties
Weldability
Hot workability
Cold workability
The steels are not weldable w ithout limitations.
Professional planning of the welding parameters
is required. Increased s1rength and product thick-
The steels are hot workable up
to the temperature limit for
stress relief annealing.
Cold-bending or edge folding
ness also increase the risk of cold cracks.
is guaranteed for nominal
thicknesses up to 16 mm, if
cold-workability is specified
in the order.
132
Materials science: 4.3 Steels, Steel types
Case hardened steels, unalloyed and alloy
Case hardened steels (selection)
Steel type
Designation 1>
Material
number
Hardness HB in
delivery condition21
+A
I
cf. DIN EN 10084 (2008-061
Core properties after
case hardening3I
+FP
Tensile
strength
Rm
N/mm 2
Hardening
Yield
Elong. method Properties,
41
applications
strengt h at fracture
A
Re
N/mm2
%
D is
Unalloyed case hardened steels
C10E
C10R
1.1121
1.1207
131
90- 125
49- 640
295
16
C15E
C15R
1.1141
1.1140
143
103- 140
590- 780
355
-
Alloy case hardened steels
..
..
1.7016
1.7014
174
-
700-900
450
11
28Cr4
28CrS4
1.7030
1.7036
217
156- 207
"' 700
-
-
16MnCr5
16MnCrS5
1.7131
1.7139
207
140- 187
780- 1080
780-1080
590
590
10
10
..
.
16NiCr4
16NiCrS4
1.5714
1.5715
217
156- 207
"'900
-
-
-
18CrMo4
18CrMoS4
1.7243
1.7244
207
140- 187
"900
-
-
0
20MoCr3
20MoCrS3
1.7320
1.7319
217
145- 185
a, 900
-
-
20MoCr4
20MoCrS4
1.7321
1.7323
207
140- 187
880-1180
590
10
17CrNi6-6
22CrMoS3-3
1.5918
1.7333
229
217
156- 207
152- 201
;o 1100
-
-
-
15NiCr13
10NiCr5-4
1.5752
1.5805
229
192
166- 207
137 - 187
920- 1230
a, 900
785
10
-
-
-
20NiCrMo2-2
20NiCrMoS2-2
1.6523
1.6526
212
149 - 194
780- 1080
590
10
17NiCrMo6-4
17NiCrMoS6-4
20NiCrMoS6-4
1.6566
1.6569
1.6571
229
149 - 201
149-201
154- 207
a, 1000
;o ,000
a, 1100
-
-
20MnCr5
20MnCrS5
1.7 147
1.7149
217
152- 201
980- 1270
685
8
18NiCr5-4
14NiCrMo13-4
18CrNiMo7-6
1.5810
1.6657
1.6587
223
241
229
156- 207
166- 217
159- 207
;o 1100
1030-1390
1060- 1320
785
-
10
8
stress;
levers, pegs, bolts,
rollers, spindles, pressed
and stamped parts
..
17Cr3
17CrS3
-
Small parts with average
0
.
.
0
.
.
-
-
..
..
..
.
.
..
0
-
Parts subject to
alternating stresses,
e.g. in gearbox;
gears, bevel and ring
gears, driving pinions,
shafts, propellershafts
.
Parts subject to highly
alternating stresses,
e.g . in gearbox;
gears, bevel and
ring gears,
driving pinion.
shafts, propellershafts
Parts subject to larger
dimensions;
pinion shafts, gears,
ring gears
11 Steel types with added sulfur, e. g. 16MnCrS5, have an improved machinabilit y.
21 Delivery condition: +A spheroidized; +FP treated for ferrite-pearlite microstructure and hardness range
3> Strength values are valid for test pieces with 30 mm nominal diameter.
4> Hardening methods:
D Direct hardening: The workpieces are quenched directly from the carburizing temperature.
S Simple hardening: After carburizing the workpieces are usually left to coo l at room temperature. For hardening they are reheated.
• well-suited o conditionally suitable - unsuitable
For heat treatment of case hardened steels, see page 155
133
Materials science: 4.3 Steels, Steel ty pes
Quenched and tempered steels, unalloyed and alloy
Quenched and tempered steels (selection)
Steel type
Designation
cf. DIN EN 10083-2 and DIN EN 10083-3
Strength values for rolled diamet er d in mm
Material
number
Tensile strength
Rm in N/mm2
Tll
> 16
,.40
I
>40
s 100
Yield strength Elongation at
Properties.
R0 in N/mm2
fracture
applications
EL i n%
> 161 > 40
> 161 >40
s 40 s 100 s 40 s 100
cf. DIN EN 10083-2 (2006-10)
Unalloyed quenched and tempered staels2l
C22E
C35
1.11 51
1.0501
+N
410
410
210
210
25
+QT
470- 620
-
290
-
22
25
-
+N
520
520
270
270
19
19
C35E
1.1181
+OT
600- 750
550-700
380
320
19
20
C45
1.0503
+N
580
580
305
305
16
16
C45E
1.1191
+OT
650- 800
630- 780
430
370
16
17
C55
1.0535
+N
640
640
330
330
12
12
C55E
1.1203
+QT
750- 900
700- 850
490
420
14
15
C60
1.0601
+N
670
670
340
340
11
11
C60E
1.1221
+OT
800- 950
750- 900
520
450
13
14
28Mn6
1.1170
+N
600
600
310
310
18
18
+OT
700- 850
650- 800
490
440
15
16
600-750
650- 800
450
550
350
400
15
14
17
15
Parts subject to lower
stresses and small
quench and tempering d iameters;
screws, bolts, axles,
shafts, gears
cf. DIN EN 10083-3 (2007-01)
Alloy quenched and tempered staels
38Cr2
46Cr2
1.7003
1.7006
+OT
700- 850
800- 950
34Cr4
37Cr4
1.7033
1.7034
+OT
800- 950
850- 1000
700- 850
750- 900
590
630
460
510
14
13
15
14
25CrMo4
25CrMoS4
1.7218
1.7213
+OT
800-950
700-850
600
450
14
15
41Cr4
41CrS4
1.7035
1.7039
+OT
900-1 100
800-950
660
560
12
14
34CrMo4
34CrMoS4
1.7220
1.7226
+OT
900- 1100
800-950
650
550
12
14
42CrMo4
42CrMoS4
1.7225
1.7227
+OT
1000- 1200
900- 1100
750
650
11
12
50CrMo4
51CrV4
1.7228
1.8159
+OT
1000- 1200
900-1100
780
800
700
10
12
30NiCrMo16-6
34CrNiMo6
1.6747
1.6582
+OT
1080- 1230
1100- 1300
1080- 1230
1000-1200
880
900
880
900
10
10
11
36NiCrMo16
30CrNiMo8
1.6773
1.6580
+OT
1250- 1450
1100- 1300
1050
900
9
10
20M nB5
30MnB5
1.5530
1.5531
+OT
750- 900
800- 950
-
600
650
-
15
13
-
27MnCrB5-2
39M nCrB6-2
1.7182
1.7189
+OT
900- 1150
1050- 1250
800- 1000
1000- 1200
750
850
700
800
14
12
15
12
Parts subject to higher stresses and larger
quenched and tempered d iameters;
drive shafts, worms,
gears
Parts subject to high
stresses and larger
quenched and ternpered diamet ers;
shafts. gears, larger
forged parts
Parts subject to highest stresses and large
quenched and ternpered diameters
-
11 T treat ment condition: +N normalized; +OT quenched and tempered
For unalloyed quenched and tempered steels t he treatment conditions +N and +OT also apply to t he quality and
high-grade st eels, for example for C45 and C45E.
21 Unalloyed quenched and tempered steels C35, C45, C55 and C60 are quality steels, steels C22E, C35E, C45E, C55E
and C60E are produced as high-grade steels.
For heat treatment of quenched and tempered steels, see page 156
134
Materials science: 4.3 Steels, Steel t ypes
Nitriding steels, Steels for flame and induction hardening, Free cutting steels
Nitriding steels (selection)
Steel type
cf. DIN EN 10085 (2001-07>. replaces DIN 17211
Designat ion
Material
number
Spheroidized
hardness
HB
Tensile
strength 11
Yield
Elongation
strength 11 at fracture11 Properties.
EL
applications
Re
%
N/mm2
31CrMo12
3 1CrMoV9
1.8515
1.8519
248
248
980-1180
1000- 1200
785
800
11
10
Wear parts up to 250 mm thickness
Wear parts up to 100 mm thickness
34CrAIMo5-10
40CrAIMo7-10
1.8507
1.8509
248
248
800-1000
900- 1100
600
720
14
13
Wear parts up to 80 mm t hickness
High-temperature wear parts up to 500°C
34CrAINi7-10
1.8550
248
850- 1050
650
12
Large parts; piston rods, spindles
Rm
N/mm2
11 Strength values: The values for tensile strength Rm, yield strength Re and elongation at fracture EL apply to material thicknesses from 40 to 100 mm in the quenched and tempered condition.
For heat t reatment of nitriding steels, see page 157
cf. DIN EN 1008311
Steels for flame and induction hardening (selectio n)
Steel type
Designation
Material
number
Spheroidized
hardness
HB
Tensile
strengt h 21
C45E 11
C60E11
1.1191
1.1221
207
241
37Cr4
46Cr2
1.7034
1.7006
255
+OT
850- 1000
800- 950
41Cr4
42CrMo4
1.7035
1.7225
255
+OT
900- 1100
1000- 1200
Yield strength Re
Elonin N/mm2 for nominal gation at
Properties,
thicknesses in mm
fracture
applicatio ns
EL
s 16
> 16
> 40
%
s 40 s 100
T21
+OT
650- 800
800-950
490
580
430
520
370
450
16
13
750
650
630
550
510
400
14
13
800
900
660
750
560
650
12
11
Rm
N/mm2
Wear parts with high
core strength and good
toughness; crank shafts
drive shafts, cam shafts,
worms, gears
11 The previous standard DIN 17212 was w ithdrawn without replacement. For flame and induction hardenable steels,
see quenched and tempered steels DIN EN 10083-3 (page 133). For unalloyed high-quality st eels acc. to DIN EN
10083-2, hardness results are only assured if the steels are ordered with austenite g rain sizes 5.
21 T treatment condition: +OT quenched and tempered
For heat t reatment of steels for flame and induction hardening, see page 156
Free cutting steels (selection)
Steel type
Designation 11
Material
number
T21
cf. DIN EN 10087 (1999-01)
For product thicknesses from 16 to 40 mm
Tensile
Yield
Elongation Properties,
strength
strength at fracture applications
Hardness
HB
Rm
Re
N/mm2
N/mm2
EL
%
'
11 SM n30
11 SMnPb30
1.0715
1.0718
+U
112- 169
380- 570
-
-
• Steels unsuitable for heat
treatment
11 SMn37
11SMnPb37
1.0736
1.0737
+U
112- 169
380- 570
-
-
Small parts subject t o low
stress; levers, pegs
10S20
10SPb20
1.0721
1.0722
+U
107- 156
360- 530
-
-
• Case hardened steels
15SMn13
1.0725
+U
128- 178
430-600
-
35S20
1.0726
+U
154- 201
520- 680
-
35SPb20
1.0756
+OT
-
600- 750
380
16
44SMn28
1.0762
+U
187- 238
630- 800
-
-
44SMnPb28
1.0763
+OT
-
700- 850
420
16
46S20
1.0727
+U
175- 225
590- 760
-
-
46SPb20
1.0757
+OT
-
650- 800
430
13
Wear-resistant small parts;
shafts, bolts, pins
• Quenched and tempered
steels
Larger parts subject to higher
stress;
spindles, shafts, gears
11 Steel types w ith lead additives, e.g. 11SMnPb30, have better machinability.
21 T t reat ment condition: +U untreated; +OT quenched and tempered
All free cutting steels are unalloyed qual ity steels. It is not possible to guarantee a uniform response to case
For heat treatment of free cutting steels, see page 157
hardening or quench and tempering.
Material s science: 4.3 Steels, Steel types
135
Cold work steels, Hot work steels, High-speed steels
Tool steels (selection)
Steel type
Designation
Material
number
!
cf. DIN EN ISO 4957 (2001-02), replaces DIN 17350
Tempering
Hardness Hardening
HB11
t emperature QM21 temperat. Application examples, properties
max.
·c
·c
Cold work steels, unalloyed
C45U
1.1730
190
800- 830
0
180- 300
Non-hardened mounted parts for tools,
screwdrivers, chisels, knives
C70U
1.1520
190
790- 820
0
180- 300
Centering pins, small dies, vise jaws, trim•
ming press
C80U
1.1525
190
780- 810
w
180- 300
Dies with flat cavities, chisels,
cold extruding dies, knives
C105U
1.1545
213
770- 800
w
180-300
Simple cutting tools, coining dies,
scribers, piercing plugs, twist drills
Cold work steels, alloy
21MnCr5
1.2162
215
810-840
0
150- 180
Complex case hardened press forms for
plastics; easily polished
60WCrV8
1.2550
230
880- 930
0
180- 300
Cutters for steel sheet from 6 to 15 mm, cold
punching dies, chisels, center punches
90MnCrV8
1.2842
220
790- 820
0
150- 250
Cutting dies, stamps, plastic stamping
molds, reamers, measuring tools
102Cr6
1.2067
230
820- 850
0
100- 180
Drills, milling cutters, reamers, small cutting
d ies, turning centers for lathes
X38CrMo16
1.2316
250
1000- 1040
0
650- 700
Too ls for processing chemically aggressive
t hermoplastics
40CrMnNiMo8-6-4
1.2738
235
840- 870
0
180- 220
Plastic molds of all types
45NiCrMo16
1.2767
260
840- 870
O,A
160- 250
Bending and embossing tools, shearing
blades for thick material
X153CrMoV12
1.2379
250
1020- 1050
O.A
180-250
Cutting tools sensitive to breaking, milling
cutters, broaching tools, shearing blades
X210CrW12
1.2436
255
950- 980
O,A
180 - 250
High-performance cutting t ools,
broaching t ools, stamping tools
55NiCrMoV7
1.2714
250
840- 870
0
400-650
Plastic molds, small and medium sized dies,
hot shearing blades
X37CrMoV5-1
1.2343
235
1020- 1050
O,A
550- 650
Die casting molds for light alloys,
extrusio n tools
32CrMoV12-28
1.2365
230
1020-1050
O,A
500- 670
Die casting molds for heavy non-ferrous
metals, extrusion tools for all metals
X38CrMoV5-3
1.2367
235
1030- 1080
O,A
600- 700
High-quality dies. highly stressed
tools for manufacture of screws
HS6-5-2C
1.3343
250
1190-1230
O,A
540- 560
Twist drills, reamers, m illing cutters, thread
cutters, circular saw blades
HS6-5-2-5
1.3243
270
1210- 1250
O,A
550-570
Highly stressed twist drills, milling cutters.
roughing tools with high toughness
HSl0-4-3-10
1.3207
270
1210- 1250
O,A
550- 570
Lathe tools for automatic machining,
high cutting capacity
HS2-9-2
1.3348
250
1190- 1230
O, A
540- 580
Milling cutters, twist drills and thread cutters. high
cutting hardness, high-temp. strength, toughness
Hot work steels
High-speed steels
21 QM Quenching medium; W water; 0 oil; A air
11 Delivery condition: annealed
For designations of tool steels, see page 125; for heat treatment of tool steels. see page 155
136
M aterials science: 4.3 Steels, Steel types
Stainless steels
Corrosion-resistant steels (selection)
cf. DIN EN 10088-2 and 10088-3 (2005-091
Steel type
D11
oc21 Thickness
Material
Designation
number
I
X2CrNi1 8-9
X2CrNiN19-11
X2CrNi 18-10
X5CrNi18-10
X8CrNiS18-9
X6CrNili18-10
X4CrNi18-12
X5CrNiMo17-12-2
X6CrNiMoTI17-12-2
X2CrNiMo18-14-3
X2CrNiMoN17-13-3
X2CrNiMoN17-13-5
Xl NiCrMoCu25-20-5
11
1.4310
1.4307
1.4306
1.4311
1.4301
1.4305
1.4541
1.4303
1.4401
1.4571
1.4435
1.4429
1.4439
1.4539
..
..
.. .
.
.. .
..
. ..
.. .
..
Tensile
strength
Rm
Yield
strength
Rpo,2
Elongation at
fracture
N/mm2
N/mm 2
EL
8
600- 950
250
40
-
s 40
500- 750
195
40
C
p
s 8
s 75
520- 700
500-650
220
200
45
sis
Austenitic steels
X 10Cr Ni18-8
d
mm
C
s
Properties,
applications
%
-
s 160
500- 700
175
45
C
p
s 8
s 75
520- 700
500- 700
220
200
45
-
s 160
460- 680
180
45
C
p
8
s 75
"
550- 750
540-750
290
270
40
-
s 160
550-760
270
40
C
p
s 8
s 75
540- 750
230
210
45
Springs for temperatures
up to 300°C, automotive
manufacturino
Household containers,
chemical and food industry
Equipment and parts
exposed to organic and
fruit acids
Equipment for the dairy
and brewery industry,
pressure vessels
Deep-drawn parts in t he
food industry, easily polished
-
s 160
500- 700
190
45
p
s 75
500- 700
190
35
-
s 160
500-750
190
35
C
p
s 8
s 75
520- 720
500- 700
220
200
40
-
s 160
500-700
190
40
C
s
8
500- 650
220
45
-
s 160
500- 700
190
45
Chemical industry;
bolts, nuts
C
p
s 8
s 75
530- 680
520- 670
240
220
40
45
Parts in the paint, oil and
t extile industry
..
.
.. .. .
. "
..
.. .
"
.
..
.
s 160
500- 700
200
40
C
p
s 8
s 75
540- 690
520- 670
240
220
40
-
s 160
500- 700
200
40
C
p
s
8
75
550- 700
520-670
240
220
40
45
-
s 160
500- 700
200
40
C
p
s 8
s 75
580- 780
300
280
35
40
-
s 160
580- 800
280
35
C
p
s
8
75
580- 780
290
270
35
40
-
s 160
580- 800
280
35
C
p
s 8
s 75
530- 730
520- 720
240
220
35
-
s 160
700- 800
200
35
D Delivery forms: S sheet, strip; B bars, profile
P hot-rolled sheet
21 DC Delivery condit ion: C cold-rolled strip;
Parts in t he food and dairy
industry
Consumer goods used in
the household, parts in the
photo industry
Parts in the textile,
synthetic resin and rubber
industry
Parts w ith improved
chemical resistance for the
pulp industry
Pressure vessels with
increased chemical resistance
Resistant to chlorine
and higher temperatu res; chemical industry
Resistant to phosphoric,
sulfuric and hydrochlo ric
acids;
chemical industry
137
Mat eria ls science: 4.3 Stee ls, Stee l types
Stainless steels
Corrosion-resistant steels (continued)
d . DIN EN 10088-2 and 10088-3 (2005-09}
Steel type
o»
M aterial
number
Designation
!
.
.
..
.. .
.. .
.
.
..
1.4003
X2CrNi12
X6Cr 13
1.4000
X6Cr1 7
1.4016
X2CrTi12
1.4512
X6CrMo17-1
Yield
strength
Rpo.2
N/mm2
8
25
450- 650
280
250
20
18
slB
Ferritic steels
1.4113
X3Crli17
1.4510
X2CrMoli18-2
1.4521
C
p
s
s
Elongationat
fracture
Tensile
strength
Rm
N/mm2
oc2I Thickness
d
mm
EL
%
-
s 100
450- 600
260
20
C
p
s
s
8
25
400- 600
240
220
19
25
-
s
400- 630
230
20
C
p
8
s 25
450- 600
260
240
20
20
s
Properties,
applications
Automotive and container
manufacturing, conveyors
Resistant to water and
steam; household
equipm ent, fittings
Good cold workability.
able to be polished;
flatware, bumpers
-
s 100
400- 630
240
C
s
8
450-650
280
23
Catalytic converters
C
s
8
450 - 630
260
18
-
s 100
440-660
280
18
Automotive manufacl uring; trim, hub caps
C
s
8
450- 600
260
20
Welded parts in
food industry
C
s
s
8
12
420-640
420- 620
300
280
20
Bolts. nuts,
heat ers
p
11 D Delivery forms: S sheet, strip; B bars, profile
21 M F Mill finish: C cold-rolled strip; P hot-rolled sheet
Martensitic steels
Steel type
011
Designation
Mat.
no.
s
X 12Cr13
X20Cr13
X30Cr13
X46Cr13
oc2I
1.4006
1.402 1
1.4028
1.4034
X39CrMo17-1 1.4122
X3CrNiMo13-4 1.4313
B
..
.
..
.. .
.
..
.. ..
.
C
p
Thickness
d
mm
s
s
ElongaYield
tional
strength
Properties,
fracture
applications
Rpo,2
EL
2
N/mm
%
H3I
Tensile
strength
Rm
N/mm2
8
75
A
QT650
s 600
650-850
450
-
20
12
Resistant to water
and steam, food industry
-
s 160
QT650
650- 850
450
15
C
p
s
s
8
75
A
QT750
s 700
750- 950
550
15
10
-
s 160
QT800
800- 950
600
12
C
p
s
8
s 75
A
QT800
s 740
800-1000
600
15
10
-
s 160
QT850
850- 1000
650
10
C
s
8
s 160
A
QTBOO
s 780
850-1000
245
650
12
10
Hardenable; table knives
and machine knives
8
60
A
QT900
s 900
900- 1100
280
800
12
11
Shafts, spind les,
armat ures up to 600°C
75
QT900
900- 11 00
800
11
s 1100
320
800
-
s 160
A
QT900
High t oughness;
pumps, turbine wheels,
reactor construction
-
C
s
s
p
s
-
-
900- 11 00
12
Axles, shafts,
pump parts,
propellers
Bolts, nut s, springs,
piston rods
11 D Delivery forms: S sheet, strip; B bars, profi le
21 DC Delivery cond ition: C cold-rolled strip; P hot-rolled sheet
31 H Heat treatment condition: A solution annealed; QT750 quenched and tempered to minimum tensile strength
Rm • 750 N/mm2
~
138
Materials science: 4.3 Steels, Steel types
Spring steel
Steel wire for springs, patented drawn
Wire
type
SL
SM
cf. DIN EN 10270-1 (2001-12), replaces DIN 17223
Minimum tensile strength Rm in N/mm2 for the nominal diameter din mm
0.5
0.8
1.0
8.0
10.0
15.0
-
-
1720 1600
1.5
1510 1460 1410
2.0
2.5
3.0
1370 1320
3.4
4.0
1290 1260
4.5
1210 1120
1060
-
-
2200 2050
1980
1850
1740
1690
1630
1590
1500 1460
1400
1310 1240
1110
1020
1530
5.0
6.0
20.0
SH
2480 2310
2330 2090
1970
1900
1840
1790 1740
1690
1660
1590
1490
1410
1270
1160
OM
2200
2050
1980
1740
1690
1630
1590
1500
1460
1400
1310
1240
1110
1020
DH
2480
2310
2230 2090
1790 1740 1690
1660
1590 1490 1410 1270
1160
1850
1970 1900 1840
1530
W,re diameter din mm (selection)
all
types,
except
SL11
0.30 - 0.32 - 0.34 - 0.36 - 0.38 - 0.40 - 0.43 - 0.48 - 0.50 - 0.53 - 0.56 - 0.60 - 0.63 - 0.65 - 0.70 0.75 - 0.80 - 0.90 - 1.00 - 1.10 - 1.20 - 1.25 - 1.30 - 1.40 - 1.50 - 1.60 - 1.70 - 1.80 - 1.90 - 2.00 2.10 - 2.25 - 2.40 - 2.50 - 2.60 - 2.80 - 3.00 - 3.20 - 3.40 - 3.60 - 3.80 - 4.00 - 4.25 - 4.50 - 4.75 5.00 - 5.30 - 5.60 - 6.00 - 6.30 - 6.50 - 7.00 - 7.50 - 8.00 - 8.50 - 9.00 - 9.50 - 10.00
11 Wire type SL is only supplied in diameters d = 1 t o 10 mm.
Operating conditions, applications
Wire
type
Suitable for springs with:
Applications
SL
Low static loading
SM
Moderate static or, less often, dynamic loading
SH
High static or low dynamic loading
OM
Moderate dynamic loading
DH
High static or average dynamic loading
Tension springs,
compression springs,
torsion springs in equipment and
machine construction,
wire type DH is also suitable
for shaped springs.
Wire coatings, delivery forms
Designation
Wire
surfaces
Letter
symbol
Wire
surfaces
Delivery forms
ph
phosphatize
z
w ith zinc coating
cu
copper coated
ZA
w ith zinc/aluminum coating
⇒
Spring wire EN 10270-1 DM 3,4 ph: Spring type OM, d = 3,4 mm, phosphatized surface (ph)
Hot-rolled steels for quenched and tempered springs
Steel type
Designation
Hotrolled
Spheroidized
+A
Material
number Hardness Hardness
HB
HB
• in coils or on spools
• straightened rods in bundles
cf. DIN EN 10089 (2003-04), replaces DIN 17221
In quenched and temrered
condition (+OT) 1
Tensile
Yield Elongation Properties, applications
strength
strength at fracture
EL
Rm
Roo.2
N/mm2
N/mm2
%
38Si7
1.5023
240
217
1300- 1600
1150
8
46Si7
1.5024
270
248
1400-1700
1250
7
Leaf springs, helical springs
55Cr3
1.7176
> 310
248
1400-1 700
1250
3
Larger tension and compression springs
54SiCr6
1.7102
310
248
1450- 1750
1300
6
Spring wire
61SiCr7
1.7108
310
248
1550- 1850
1400
5.5
Leaf springs, helical springs
51CrV4
1.8159
> 310
248
1400- 1700
1200
6
Highly stressed springs
Spring screw locks
Explanation 11 Strength values apply to test pieces with d = 10 mm diameter.
⇒
Round bar EN 10089 - 20 x 8000 - 51CrV4+A: Bar diameter d = 20 mm, bar length/ = 8000 mm,
steel type 51CrV4, delivery condition spheroidized (+A)
Wire diameter d in mm (selection)
Delivery forms
5.0 - 5.5 - 6.0 - 6.5 - 7.0- 7.5 - 8.0 -8.5 - 9.0-9.5 - 10.0-10.5 -11.011.5 - 12.0 - 19.0 - 19.5 - 20.0 - 21.0 - 22.0 - 23.0 - 27.0 - 28.0 - 29.0 - 30.0
• directional rods
• wire coils
139
M ateri als science: 4.4 Steels, Finish ed products
Sheet and strip metal - Classification, overview
I
Delivery form
Type
Commercial formats
: Classification according to
I
.
Sheet
L7
Usually rectangular plates in
small format: wx I= 1000 x 2000 mm
med. format: wx I= 1250 x 2500 mm
large format: WX /= 1500 x 3000 mm
Sheet t hicknesses: s = 0, 14- 250 mm
Fabrication method
-
Process
Remarks
Hotrolled
Sheet t hicknesses up to approx.
250 m m, surfaces in ro lled condition
or pickled
Coldro lled
Sheet thicknesses up to approx.
10 mm, smooth surfaces,
tight process tolerances
Strip
lb
Rolled (coils) continuous strip
Strip t hickness s = 0, 14- approx.
10mm
Strip w idth w up to 2000 mm
Coil diameter up to 2400 mm
• for feed stock at automat ic
manufact uring plants or sheet
metal blanks for secondary
processing
Cold-rolled
w ith surface
fi nishing
Sheet metal types - Overview (selection)
Main characteristics
• higher corrosion resistance,
e.g. from galvanizing, organic
coating
• for decorative purposes, e.g. with
plastic coat ing
better workability, e.g. by textured
surfaces
.
Designation, steel types
Standard
Cold-rolled sheet and strip
• cold workable
(deep drawing)
• weldable
surface
paintable
Flat rolled products fro m soft steels
DIN EN 10130
Cold strip from soft steels
DIN EN 10207
Flat products with high yield strengt hs
DIN EN 10268
Flat products for enameling
DIN EN 10209
Cold-rolled sheft and strip with sur f - finishing
higher corrosion
resistance
. possibly better
workability
Hot-dip finished sheet and strip
DIN EN 10327
Zinc electroplated flat products
from steel fo r cold working
DIN EN 10152
Organically coat ed flat products
from steel
DIN EN 10169-1
Cold-rolled sheets and strip for packaging
• corrosion resistant
Black plate for manuf acture of tinplate
DIN EN 10205
• cold workable
• weldable
Packaging sheet metal from electrolytically
t inned o r chromed steel
DIN EN 10202
Delivery form 11
Sh
I St Ithickness range
. ..
.. ..
..
..
..
..
..
-
0.35-3 mm
s10mm
s3mm
s 3mm
s3 mm
0.35-3mm
5J mm
0.14- 0.49 mm
0.14- 0.49 mm
Hot-rolled sheet and strip
Same properties
as the
corresponding
steel groups
(pages 126, 127)
Sheet and strip from unalloyed and alloy steels,
e.g. struct ural steels as per DIN EN 10025,
fine-grain structural steels as per DIN EN 10113,
DIN EN 10051
case hardened steels as per DIN EN 10084,
quenched and tempered steels as per DIN EN
10083, stainless steels as per DIN EN 10088
• high
y ield strengt h
Sheet met al from structural steels wi th higher
yield strength, quenched and tempered
DIN EN 10025-6
• cold
workability
Flat products of steel with high
yield strength
DIN EN 10149-1
11 Delivery fo rms:
Sh sheet; St st rip
..
...
sheet up to
25 mm thickness,
strip up to
10 mm thickness
3- 150 mm
sheet upto
20 mm thickness
140
Materials science: 4.4 Steels, Finished products
Cold-rolled sheet and strip for cold working
Cold-rolled strip and sheet from soft steels
Steel type
Material
number
Designation
Type of
surface
A
cf. DIN EN 10130 (2007-021
Tensile
strength
Rm
N/mm2
Elongation
at fracture
Yield
strength
Re
N/mm 2
270- 410
140
280
28
EL
%
Lack
of flowlines11
Properties,
Application
-
DC01
1.0330
DC03
1.0347
A
B
270- 370
140
240
34
6 months
DC04
1.0338
A
B
270-350
140
210
38
6 months
DC05
1.0312
A
B
270- 330
140
180
40
6 months
DC06
1.0873
A
B
270-350
120
180
38
unlimited
time
Delivery forms
(standard
values)
Sheet thicknesses: 0.25 - 0.35 - 0.4 - 0.5 - 0.6 - 0.7 - 0.8 - 0.9 - 1.0 - 1.2 - 1.5 - 2.0 - 2.5 - 3.0 mm
Metal sheet d imensions: 1000 x 2000 mm, 1250 x 2500 mm, 1500 x 3000 mm, 2000 x 6000 mm
strip (coils) up to approx. 2000 mm wide
Explanation
hi In subsequent non-cutting processes, e.g. deep drawing, no flow lines appear within the given time
period. The time period begins at the agreed upon delivery date.
B
Type of surface
Designation
3 months
Cold workable, e.g. by
deep drawing, weldable,
surface paintable;
worked sheet parts
in automotive,
general machi ne and
equipment manufacturing, in the construction
industry
Surface finish
Description of t he surface
Designation
Finish
Average roughness Ra
A
Defects, e.g. pores, scoring, may not influence the workability and the adhesion of surface coatings.
b
g
very smooth
smooth
Ra s 0.4 µm
Ra s 0.9 µm
B
One side of the sheet must be free of defects
so that its surface finish w ill not influence
quality painting.
m
r
matt
rough
0.6 µm < Ra s 1.9 µm
Ra > 1.6µm
=>
Sheet EN 10130- DC06 - B - g: Sheet metal from DC06 material, surface type B, smooth surface
Cold-rolled strip and sheet
of high yield steels (selection)
Steel type
cf. DIN EN 10268 (2006-10)
Designation
Material
number
Tensile
strength
Rm
N/mm2
Yield
strength
Re
N/mm2
Elongation
at fracture Properties,
Application
EL
%
HC180Y
HC220Y
HC260Y
1.0922
1.0925
1.0928
340- 400
350- 420
380- 440
180- 230
220- 270
260-320
36
34
32
Cold workability at high mechanical strength,
sophisticated deep-drawn parts
HC180B
HC220B
HC300B
1.0395
1.0396
1.0444
300- 360
320- 400
400- 480
180- 230
220- 270
300- 360
34
32
26
Good cold workability, increase of the yield strength
through heat treatment after the shaping process;
exterior parts of the vehicle body
HC180P
HC260P
HC300P
1.0342
1.0417
1.0448
280- 360
360- 440
400- 480
180- 230
280-320
300- 360
34
29
26
Good cold workability, high impact resistance and
fatigue strength;
parts of the body skin, deep-drawn parts
HC260LA
HC380LA
HC420LA
1.0480
1.0550
1.0556
350-430
440- 560
470-590
260-330
380- 480
420-520
26
19
17
Good weldability and limited cold workability,
good impact resistance and fatigue strength;
reinforcing parts of the vehicle body
Forms of
delivery,
surface
finishes
Forms of delivery see DIN EN 10130 (table on top)
Surface finishes: The products are available with the surface finish types A and Bin accordance with
DIN EN 10130. For LA types, e. g. HC380LA, only surface finish type A is available.
For rolling width > 600 mm, the surface finishes also comply with DIN EN 10130.
=>
Sheet metal EN 10628- HC380LA-A- m: Sheet metal of material HC380LA, surface finish A, matt (ml
141
M aterials science: 4.4 Steels, Finished product s
Cold-rolled and hot-rolled sheet
Hot-dip galvanized strip and sheet
from soft steels for cold working
Steel type
Designation
Material
number
DX510+2
DX510+2F
1.0226+2
1.0226+2F
DX520+2
DX52D+2F
.
Guarantee
for strength
values 11
cf. DIN EN 10327 (2004-09)
replaces DIN EN 10142
Tensile
strength
Yield
strength
Elongation
at fract ure
Rm
Re
EL
Lack
of flow
lines2>
Cold working
grade
N/mm2
N/mm 2
%
8 days
270-500
-
22
1 month
machine seamed
q uality
1.0350+2
1.0350+2F
8 days
270- 420
140- 300
26
1 month
drawing grade
DX53D+2
DX53D+2F
1.0355+2
1.0355+2F
6 months
270- 380
140- 260
30
6 mont hs
deep drawing grade
DX54D+2
DX54D+2F
1.0306+2
1.0306+2F
6 months
260- 350
120- 220
6months
extra deep
drawing g rade
DX56D+2
DX56D+2F
1.0322+2
1.0322+2F
6 months
270- 350
120- 180
6months
special deep
drawing grade
Del ivery forms
(standard
values)
Sheet thicknesses: 0.25 - 0.35 - 0.4 - 0.5 - 0.6 - 0.7 - 0.8 - 0.9 - 1.0 - 1.2 - 1.5 - 2.0 - 2.5 - 3.0 mm
Metal sheet d imensions: 1000 x 2000 mm, 1250 x 2500 mm, 1500 x 3000 mm, 2000 x 6000 mm
strip (coils) up to approx. 2000 mm w ide
Explanation
1> Values
36
34
39
37
for tensile strength Rm, yield strength Re and elongation at fracture EL are only
guaranteed w ithin the given ti me period. The t ime period begins at the agreed upon delivery date.
2> In subsequent working, e.g . deep d rawing, no flow lines appear within a given period. The time
period begins at the agreed upon delivery date.
Composition, properties and structures of the coating
Designat ion
+2
+2F
Composition, properties
Designation
Coatings of pure zinc, shiny flowe r patterned surface, protect ion against atmospheric corrosion
Abrasion resistant coating of a zinc-iron
alloy, uniform matt gray surface, corrosion
resist ant like +2
N
M
R
Structure
Zinc flowers in different sizes
Small zinc flowers, often not v isible.
Uniform matt g ray surface
(texture information only combined w ith
coating +ZF)
Type of surface
Designation
Meaning
A
B
C
No surface defects are allowed, e.g. dots, stripes
Improved surface compared to A
Best surface, high-quality painting must be assured on one side of t he sheet
=
Sheet EN 10142 - DX53D+ZF100-R-B: Sheet of DX53D material, coating of
iron-zinc alloy with 100 g/m2, uniform matt gray (A) and improved (B) surface
Hot-rolled sheet and strip
cf. DIN EN 10051 (1997-11)
Hot-ro lled sheet and strip according to DIN EN 10051 are manufactured
from steels of various material g roups, for example:
Steel group, designation
Materials
Delivery forms
(standard values)
=
Standard
Page
Structural steels
Case hardened steels
Quenched and tempered steels
DIN EN 10025
DIN EN 10084
DIN EN 10083
130
132
133
Weldable fine-g rain steels
Heat-treatable structural steels, high y ield strength
DIN EN 10113
DIN EN 10137
13 1
131
Stainless steels
Pressure vessel steels
DIN EN 10088
DIN EN 10028
136
Properties and
applications of the
steels are given on
the pages for the
individual steel.
-
Sheet thicknesses: 0.5-1.0 - 1.5 - 2.0 - 2.5-3.0 - 3.5 - 4.0 - 4.5 - 5.0 - 6.0 - 8.0 - 10.0 - 12.0 - 15.0 18.0 - 20.0 - 25.0 mm. Sheet and strip dimensions see DIN EN 10142.
Sheet EN 10051 - 2,0 x 1200 x 2500: Sheet thickness 2,0 mm, sheet dimensions 1200 x 2500 mm
Steel EN 10083-1 - 34Cr4: Carbon quenched and tempered steel 34Cr4
142
Materials science: 4.4 Steels, Finished products
~fll"'lllt:INIIII ,._..., lll~J•IINH
1:..1~----... •111 ...,, f!.J~•11111iT
Seamless tube for machine construction (selection)
d
s
outside diameter
wall thickness
dxs
m' linear mass density
W, axial section
,.
modulus
axial geometrical
moment of inertia
·e
-
' -~
X
s
w.
dxs
cm2
m'
kg/m
cm3
cm4
26.9 X 2.3
26.9 X 2.6
26.9 X 3.2
1.78
1.98
2.38
1.40
1.55
1.87
1.01
1.10
1.27
1.36
1.48
1.70
35 X 2.6
35 X 4.0
35 X 6.3
2.65
3.90
5.68
2.08
3.06
4.46
2.00
2.72
3.50
40 x4
40 X 5
40 x8
4.52
5.50
8.04
3.55
4.32
6.31
44.5 X 4
44.5 X 5
44.5 X 8
5.09
6.20
9.17
51 X 5
51 x8
51 X 10
7.23
10.81
12.88
s cross-sectional area
d
Material,
annealing
condition
cf. DIN EN 10297-1 (2003-06}
,.
s
,.
w.
cm2
m'
kg/m
cm3
cm•
54 X 5.0
54 X 8.0
54x 10.0
7.70
11.56
13.82
6.04
9.07
10.85
8.64
11.67
13.03
23.34
3 1.50
35.18
3.50
4.76
6.13
60.3 x8
60.3x 10
60.3 X 12.5
13.14
15.80
18.77
10.31
12.40
14.73
15.25
17.23
19.00
45.99
51.95
57.28
3.71
4.30
5.47
7.42
8.59
10.94
70x 8
70 X 12.5
70 X 16
15.58
22.58
27.14
12.23
17.73
21.30
21.75 76.12
27.92 97.73
30.75 107.6
4.00
4.87
7.20
4.74
5.53
7.20
10.54
12.29
16.01
82.5 X 8
82.5 X 12.5
82.5 X 20
18.72
27.49
39.27
14.70
21.58
30.83
31.85 131.4
42.12 173.7
51.24 21 1.4
5.68
8.49
10.11
7.58
10.13
11.25
19.34
25.84
28.68
88.9 X 10
88.9 X 16
88.9 X 20
24.79
36.64
43.29
19.46
28.76
33.98
44.09 196.0
57.40 255.2
62.66 278.6
Annealing condition11
Steel group
Steel type, examples
Machine construction unalloyed
steels
alloy
E235, E275, E315
E355K2, E420J2
+AR or +N
+N
unalloyed C22E, C45E, C60E
alloy 41Cr4, 42CrMo4
+N o r +OT
+OT
Quenched and
tempered steels
Case hard. steel, unall., alloy
C10E, C15E, 16MnCr5
+A or+N
Properties and applications of steels, see pages 126 and 127.
Precision steel tube, cold-drawn seamless (selection)
d
s
s
cf. DIN EN 10305-1 (2003-02}
dxs
cm3
,.
cm4
0.22
0.31
0.39
0.06
0.07
0.09
0.03
0.04
0.04
0.35
0.49
0.63
0.27
0.38
0.49
0.09
0.12
0.14
15x 2
15 X 2.5
15 X 3
0.82
0.98
1.13
0.64
0.77
0.89
20 X 2.5
20 X 4
20x 5
1.37
2.01
2.36
25 X 2.5
25 X 5
25 X 6
30x 3
30x 5
30 X 6
dxs
outside diameter
wall thickness
s
cm2
m'
kg/m
10 X 1
10 X 1.5
10 X 2
0.28
0.40
0.50
12 X 1
12 X 1.5
12 X 2
w.
s
,.
w.
cm2
m'
kg/m
cm3
cm4
35 X 3
35 X 5
35 x8
3.02
4.71
5.53
2.37
3.70
4.34
2.23
3.11
2.53
3.89
5.45
3.79
0.05
0.07
0.08
40 x4
40 X 5
40 x8
4.52
5.50
8.04
3.55
4.32
6.31
3.71
4.30
5.47
7.42
8.59
10.94
0.24
0.27
0.29
0.18
0.20
0.22
50 X 5
50 x8
50 X 10
7.07
10.56
12.57
5.55
8.29
9.87
7.25
9.65
10.68
18. 11
24.12
26.70
1.08
1.58
1.85
0.54
0.68
0.74
0.54
0.68
0.74
60 X 5
60 X 8
60 X 10
8.64
13.07
15.71
6.78
10.26
12.33
10.98
15.07
17.02
32.94
45.22
51 .05
1.77
3.14
3.58
1.39
2.46
2.81
0.91
1.34
1.42
1.13
1.67
1.78
70 X 5
70 X 10
70 X 12
10.21
18.85
21.87
8.01
14.80
17.17
15.50
24.91
27.39
54.24
87. 18
95.88
2.54
3.93
4.52
1.99
3.08
3.55
1.56
2.13
2.31
2.35
3.19
3.46
80 X 8
80 X 10
80 X 16
18.10
21.99
32.17
14.21
17.26
25.25
29.68
34.36
43.75
118.7
137.4
175.0
cross-sectional area
m' linear mass density
W, axial section
modul us
axial geometrical
moment of inertia
,.
I
"j
~
X 1-.
'I"
\
L...
~
X
d
Materials,
surface,
annealing
condition
Steel group
Surfaces
Unalloyed structural
steels, free cutting
steels, quenched and
tempered steels
Tubes w ith smooth interior
and exterior surfaces,
surface roughness
Ras0,4µm
Annealing condition 11
+C or
+A or +N
Properties and applications of steels, see pages 126 and 127.
Explanation
11 +A spheroidized;
+C cold-rolled;
+AR condition after hot working;
+N
no rmalized;
+QT quenched and tempered
Materials science: 4.4 St eels, Finished products
143
Hot-rolled steel profiles
Cross-section
~
~':"~:'.'
r{-,~~
Designation,
dimensions
Round steel bar
d= 8-200
Square steel bar
8=8- 120
Standard.
page
DINEN
10060
page 144
DIN EN
10059
page 144
~
~
g3
g3
g
13
~
Flat steel bar
b xs= 10x5 to 150x60
Square
tube
8= 40- 400
Rectangular
tubes
axb=
50 X 25 to 500 X 300
DINEN
10058
page 144
DINEN
10210-2
page 151
DIN EN
10210-2
page 151
Circular tube
Dxs =
21.3 X 2.3 to 1219 X 25
Equal leg
t ee
b = h = 30- 140
Steel channel
h = 30- 400
DINEN
10210-1
DINEN
10055
page 146
DIN
1026-1
page 146
1> according to EURONORM 53-62: IPB = HE to B, IPBI
Designation,
Cross-section
TI
g
~
TI
dimensions
Z profile steel
h = 30- 200
Equal leg
steel angle
a= 20- 250
Unequal leg
steel angle
ax b =
30x20 t o 200x 150
Narrow I -beam
I series
:0
TI
Wide I -beam
IPB series11
JD
DIN
1027
DIN EN
10056-1
page 148
DIN EN
10056-1
page 147
DIN
1025-1
h = 80- 160
Medium width I-beam
IPE series
TI
Standard,
page
h= 80- 600
h= 100- 1000
Wide I -beam
light duty
IPBI series1>
DIN
1025-5
page 149
DIN
1025-2
page 150
DIN
1025-3
page 149
h = 100- 1000
Wide I -beam
reinforced design
IPBv series•>
h = 100- 1000
= HE to A, IPBv = HE to M
DIN
1025-4
page 150
144
M aterials science: 4.4 Steels, Finished products
Steel bar, hot-rolled
Hot-rolled round steel bar
g
Diameter d
i nmm
Diameter d
inmm
cf. DIN EN 10060 (2004-021, replaces for DIN 1013-1
Unalloyed structural steel according to DIN EN 10025 or quenched and
tempered steel according to DIN EN 10083
Material:
Type of delivery: Manufactured lengths (Ml "' 3 m < 13 m, normal lengths (Fl s 13 m ± 100 mm,
precision lengths (El < 6 m ± 25 mm,"' 6 m < 13 m ± 50 mm
10 -1 2 - 13-14 - 15 - 16 - 18 - 19 - 20 - 22 - 24 - 25 - 26 - 27-28 - 30 - 32 - 35 - 36-38 - 40 42 - 45 - 48 - 50 - 52- 55 - 60 -63 - 65 - 70 - 73 - 75 - 80 - 85 - 90 - 95 - 100 - 105 - 110 - 11 5 120 - 125 - 130 - 135 - 140 - 145 - 150-155 - 160 - 165 -170 -175 - 180 - 190- 200 - 220 - 250
limit
deviations
inmm
Diamet er d
inmm
limit
deviations
inmm
Diameter d
inmm
Limit
deviat ions
inmm
Diameter d
inmm
lim it
deviations
inmm
220
± 3.0
250
±4.0
10- 15
± 0.4
36-50
± 0.8
105- 120
± 1.5
16-25
±0.5
52-80
± 1.0
125-160
± 2.0
26- 35
±0.6
85- 100
± 1.3
165- 200
± 2.5
=
Round bar EN 10060- 40 x 6000 F steel EN 10025-S235JR: Hot-rolled round steel bar,
d = 40 mm, normal length 6000 mm, made of S235JR
Hot-rolled square steel bar
~
Lengt h of side a
inmm
cf. DIN EN 10059 (2004-021, replaces DIN 10 14-1
Unalloyed struct ural steel according to DIN EN 10025
M aterial:
Type of delivery: Manufactured lengths (Ml "' 3 m < 13 m, normal lengths (Fl" 13 m ± 100 mm,
precision lengths IE)< 6 m ± 25 mm,"' 6 m < 13 m ± 50 mm
8 - 10 - 12 - 13 - 14- 15- 16 - 18 - 20 - 22 - 24 - 25 - 26 - 28 - 30 - 32 - 35 - 40 - 45 - 50 - 55 60 - 65 - 70- 75 - 80 - 90 - 100 - 110 - 120- 130- 140 - 150
lim it
limit
lim it
limit
Length of side a
Length of side a
Length ofside a
Length of side a
deviations
deviations
deviations
deviations
inmm
inmm
inmm
inmm
inmm
inmm
in m m
inmm
8-14
± 0.4
26- 35
±0.6
55- 90
± 1.0
110- 120
± 1.5
15-25
±0.5
40- 50
± 0.8
100
" 1.3
130- 150
± 1.8
=
Square bar EN 10059 - 60 x 6000 F steel EN 10025--S235JR: Hot-rolled square steel bar,
a = 2.36 in, norm al length 6000 mm, made of S235JR
Hot-rolled flat steel bar
B
Material:
cf. DIN EN 10058 (2004-021, replaces DIN 1017-1
Unalloyed structu ral steel according to DIN EN 10025
Type of delivery: Manufactured lengths (Ml"' 3 m < 13 m , normal lengths (Fl s 13 m ± 100 mm,
precision lengt h (El< 6 m ± 25 mm, "' 6 m < 13 m ± 50 mm
Nominal width w
inmm
10 - 12 - 15 - 16 - 20 - 25 - 30 - 35 - 40 - 45 - 50 - 60 - 70 - 80 - 90 - 100 - 120 - 150
Nominal thickness s in mm
5 - 6 - 8- 10-12 - 15 - 20 - 25 - 30 - 35 - 40 - 50 - 60 - 80
Allowable deviations to nominal width w
Nominal w idt h w
Limit deviations
Nominal w idth w
inmm
inmm
inmm
Limit deviations
inmm
Nominal w idth w
inmm
Limit deviations
inmm
10 - 40
± 0.75
85- 100
± 1.5
45- 80
± 1.0
120
±2.0
150
± 2.5
Limit deviatio ns
inmm
Nominal thickness s in mm
limit deviations
inmm
Nominal t hicknesssin mm
Limit deviat ions
inmm
±0.5
25-40
± 1.0
50- 80
± 1.5
Allowable deviations to nominal thickness s
Nominal t hickness sin mm
5-20
=
Flat steel bar EN 10058 - 20 x 5 x 6000 F steel EN 10025--S235JR: Hot-rolled flat steel bar,
b = 20 mm, s = 5 mm, normal length 6000 mm, made of S235JR
145
Materials science: 4.4 Steels, Finished products
Steel bars, bright
Common dimensions of bright steel bars (selection)
Designation
Nominal dimensions
Flat steel bar
Width w, height h in mm
w
h
w
h
w
h
w
h
18
20
22
25
45
50
56
63
2-32
2-32
3-32
3-40
70
80
90
100
4-40
5- 25
5-25
5-25
w
h
w
h
5
6
8
10
2-3
2- 4
2- 6
2- 8
12
14
15
16
2 -1 0
2- 10
2- 12
2 -1 2
2 - 12
2- 16
2 - 12
2 -20
28
32
36
40
2 - 20
2-25
2-20
2 -32
B3
Nominal thicknesses h in mm: 2 - 2.5 - 3 - 4 - 5 - 6 - 8 - 10 -12 - 15 - 16 - 20 - 25 - 30- 32 - 35 - 40
Square steel bar
Side length a in mm
g
4
4.5
5
6
7
8
9
10
11
12
13
14
2
2.5
3
3.2
3.5
4
4.5
5
5.5
6
7
8
9
10
11
12
13
14
15
16
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
16
18
20
22
25
28
36
40
45
50
63
70
80
100
41
46
50
55
60
65
70
75
80
85
90
95
100
58
60
63
65
70
75
90
100
110
120
125
130
140
150
Side lengt h s in mm
Hexagonal bar steel
g
17
19
21
22
24
27
30
32
36
38
Diameter d in mm
round steel bar
@
27
28
29
30
32
34
35
36
38
40
42
45
48
50
52
55
80
85
160
180
200
I 1 mm to 13 mm I > 13 mm to 25 mm > 25 mm to 50 m m
polished round steel bar
0.5mm
1 mm
5mm
common diameter gradation I
I
common delivered diameters
cf. DIN EN 10278 (1999-12)
Delivery conditions
~
I
Finished conditio n I
Code
+C
cold drawn
I
I
+SH
peeled
l
I
+SL
ground
l +PL
I polished
Round bright steel bar, d 20 mm,
= Tolerance class h9, mill length 6000 mm, free cutting steel 44SMn28, cold drawn, surface
quality class 3
Round EN 10278 - 20 h9 x mill length 6000 EN 10277-3 - 44SMn28+C- Class 3:
=
cf. DIN EN 10277-1 to -5 (1999-10)
Material groups and assigned delivery conditions
Delivery conditions 11
Material groups
.. ...
+SH
Steels for general engineering use
Free cutting steels
Free cutting case hardened steels
Free cutting quenched and temp. steels
Unalloyed case hardened steels
Case hardened alloy steels
Unalloyed quenched and tempered steels
Quenched and tempered alloy steels
+C
+C+QT +QT+C +A +SH
+A+C +FP +SH +FP +C
..• .. . . . .
. . .. .. .. .. . .
11 Explanation pages 124 and 125
cf. DIN EN 10278 (1999-12)
Length types and length limit deviations
Length type
Length in mm
Manufactured length 3000-9000
Lim it deviations in mm
Order information
± 500
length
Mill length
3000- 6000
0/+200
e.g. mill lengt h 6000
Precision length
up to 9000
by agreement, but min.± 5
length and limit deviation
146
Materials science: 4.4 Steels, Finished product s
Structural Tee, Steel channel
Equal leg Tee, hot-rolled
cf. DIN EN 10055 (1995-12)
s
b
k
X,:::
I
w,
.!!J.
X-=-I7:tx
-l~
Q_ .
4 r-
·
'
-e:1~
Material:
'"'
'--.. ~
; ;.1
~ ~
"'
Designation
Unalloyed structural steel DIN EN 10025, e.g. S235JA
Delivery type: Lengths to order w ith a usual limit deviation of
± 100 mm or a reduced lim it deviation ± 50 mm,
± 25 mm, ± 10 m m
I
--of
r= s
s
e,
r, =~
I
2
For the bending axis
y-y
Tracing d imension
accord. to DIN 997
x-x
m'
kg/m
ly
Wy
cm
I,
cm4
W,
cm2
cm3
cm4
cm3
w,
mm
W:1
mm
2.26
2.97
3.77
1.77
2.33
2.96
0.85
0.99
1.1 2
1.72
3.10
5.28
0.80
1.23
1.84
5.66
7.94
10.6
13.6
20.9
29.6
39.9
4.44
6.23
8.23
10.7
16.4
23.2
31.3
1.39
1.66
1.94
2.22
2.74
3.28
3.80
12.1
23.8
44.4
73.7
179
366
660
3.36
5.48
8.79
12.8
24.6
42.0
64.7
0.87
1.04
2.58
6.06
12.2
22.1
37.0
88.3
179
330
0.58
0.90
1.29
2.42
4.07
6.32
9.25
17.7
29.7
47.2
17
19
21
30
34
38
45
60
70
80
17
19
22
30
35
40
45
60
70
75
30
35
40
50
60
70
80
100
120
140
b= h
30
35
40
50
60
70
80
100
120
140
=
Tee profile EN 10055- TSO- S235JA: Struct ural steel tee, h = 50 mm, from S235JA
T
S=t
4
4.5
5
6
7
8
9
11
13
15
I
I
Distance
of the
xaxis
Dimensions
inmm
w axial section modulus
m' linear mass density
cross-sectional area
second moment of inertia
Steel channel, hot-rolled
- "'
~
x-
.P.
I
u
30x 15
30
40 x20
40
50 x25
50
60
80
100
120
160
200
260
300
350
400
=
m' linear mass density
Unalloyed structural steel DIN EN 10025, e.g. S235J0
: - -~ x
Delivery type: M anufaciured lengths 3 m to 15 m; normal lengths up to 15 m
± 50 mm; slope angle at h :,; 300 mm: 8 %; h > 300 mm: 5 %
~
I
,tt
b
15
33
20
35
25
38
30
45
50
55
65
75
90
100
100
110
s
4
5
5
5
5
5
6
6
6
7
7.5
8.5
10
10
14
14
r, = t
-
Dimensions
inmm
h
30
30
40
40
50
50
60
80
100
120
160
200
260
300
350
400
w axial section modulus
cross-sectional area
second moment of inertia
Material:
.J.___
Designation
6.4
8.4
11
11
13
17
21
;--.,,..s•;.--♦1
rr,.., d,
ey
w,...,_
4.3
4.3
6.4
cf. DIN 1026-1 (2000-03)
s
~~
..._I
,,:::
d,
mm
s
t
4 .5
7
5.5
7
6
7
6
8
8.5
9
10.5
11.5
14
16
17.5
18
h,
12
10
18
11
25
20
35
46
64
82
115
151
200
232
276
324
cm2
2.21
5.44
3.66
6.2 1
4.92
7.12
I
I
Distance
to the
yaxis
m'
8y
kg/m
cm
1.74
4.27
2 .87
4.87
3.86
5.59
6.46 5.07
11.0
8 .64
13.5 10.6
17.0 13.4
24.0
18.8
32.2 25.3
48.3 37.9
58.8 46.2
77.3 60.6
91.5 71.8
0.52
1.3 1
0.67
1.33
0.81
1.37
0.91
1.45
1.55
1.60
1.84
2.01
2.36
2.70
2.40
2.65
r2 "'.!.
I
2
I
r3 :,; 0,3 • t
For the bending axis
,.
x- x
cm 4
2.53
6.39
7.58
14. 1
16.8
26.4
31 .6
106
206
364
925
1 910
4 820
8 030
12840
20 350
y-y
w,
cm3
Iv
cm4
w.
cm¥,
1.69
0.38
0.39
4.26
5.33
2.68
3.97
1.14
0.86
7.05
6.68
3.08
6.73
2.49
1.48
10.6
9.12
3.75
10.5
4.51
2.16
26.5
19.4
6.36
41.2
29.3
8.49
60.7
43.2
11.1
116
85.3
18.3
191
148
27.0
371
317
47.7
535
495
67.8
734
570
75.0
1020
846
102
Channel DIN 1026 - U100 - S235JO: Steel channel, h = 100 mm, from S235J0
I
Tracing
dimensions
DIN 997
d,
w,
mm mm
10
20
11
20
16
20
18
25
30
30
35
40
4.3
8.4
6.4
8.4
8.4
11
8.4
13
13
17
21
23
50
55
58
60
25
28
28
28
147
M at erials science: 4.4 Steels, Finished product s
Steel angle
Unequal leg steel angle, hot-rolled (selection)
-
f
i'
)TTr
[
-~
~
( ·R --\ .;, .
-~
.._ t
l
Desig nation
L
w axial sectio n modulus
m' linear mass density
s cross-sectional area
i---
. G
,.
cf. DtN EN 10056-111998-10)
b
Dimensions
inmm
a
b
t
s
second moment of inertia
Material:
Unalloyed structural steel DIN EN 10025-2, e. g. S235J0
Delivery type: From 30 x 20 x 3 t o 200 x 150 x 15, in manufactured lengths
,. 6 m < 12 m, normal lengths a, 6 m < 12 m ± 100 mm
I
r 1 "" t
I
I
Distances
to axes
m'
kg/m
ex
ey
cm2
cm
cm
I
r2 " ' l
2
For the bending axis
Tracing dimension
x-x
accord. to DIN 997
fx
cm•
y- y
Wx
cm3
w.
w,
cm•
cm'!i
mm mm mm mm
lv
W2
-
30 X 20 X 3 30
30 X 20 X 4 30
40 X 20 X 4 40
40 X 25 X 4 40
20
20
3
4
1.43
1.86
1.12
1.46
0.99
1.03
0.50
0.54
1.25
1.59
0.62
0.81
0.44
0.55
0.29
0.38
17
17
-
20
25
4
4
2.26
2.46
1.77
1.93
1.47
1.36
3.59
3.89
1.42
1.47
0.60
1. 16
0.39
0.69
22
22
-
45 X 30 X 4 45
50 X 30 X 5 50
60 X 30 X 5 60
60 X 40 X 5 60
60 X 40 X 6 60
65 X 50 X 5 65
70 X 50x 6 70
30
30
4
5
2.87
3.78
2.25
2.96
1.48
1.73
0.48
0.62
0.74
0.74
5.78
9.36
1.91
2.86
2.05
2.51
0.91
1.11
30
40
40
50
50
5
5
6
5
6
3.36
3.76
4.46
4.35
5.41
2.17
1.96
2.00
1.99
2.23
0.68
0.97
1.01
1.25
1.25
15.6
17.2
20.1
23.2
33.4
4.07
4.25
5.03
5.14
7.01
50
50
6
8
5.65
7.39
2.44
2.52
1.21
1.29
40.5
52.0
8.01
10.4
2.63
6.11
7.12
11.9
14.2
14.4
18.4
1.14
2.02
2.38
3.19
3.78
75 X 50x 6
75x 50x 8
4.28
4.79
5.68
5.54
6.89
7.19
9.41
25
30
35
35
35
35
40
3.81
4.95
40
40
80 X 40x 6 80 40
80 X 40x 8 80 40
80 X 60 x 7 80 60
100 X 50x 6 100 50
100 X 50 X 8 100 50
6
8
7
6.89
9.01
9.38
5.41
7.07
7.36
2.85
2.94
2.51
0.88
0.96
1.52
44.9
57.6
59.0
8.73
11.4
10.7
7.59
9.61
28.4
2.44
3.16
6.34
45
45
45
6
8
8.71
11.4
6.84
8.97
3.51
3.60
1.05
1.13
89.9
116
13.8
18.2
15.4
19.7
3.89
5.08
65 X 7 100 65 7
65 X 8 100 65 8
65x 10 100 65 10
75x 8 100 75 8
75x 10 100 75 10
75x 12 100 75 12
11.2
12.7
15.6
13.5
16.6
19.7
8.77
9.94
12.3
10.6
13.0
15.4
3.23
3.27
3.36
3.10
3.19
3.27
12.2
15.0
17.8
3.83
3.92
4.00
16.6
18.9
23.2
19.3
23.8
28.0
27.6
34.1
40.4
7.53
8.54
10.5
11.4
14.0
16.5
15.5
19.1
22.7
15.5
19.1
22.7
113
127
154
133
162
189
226
276
323
37.6
42.2
51.0
64.1
77.6
90.2
80 x 8 120 80 8
80 X 10 120 80 10
80 x 12 120 80 12
75 X 8 125 75 8
75 X 10 125 75 10
75 X 12 125 75 12
1.51
1.55
1.63
1.87
1.95
2.03
1.87
1.95
2.03
55
55
55
55
55
12.2
15.0
17.8
4.14
4.23
4.31
1.68
1.76
1.84
247
302
354
29.6
36.5
43.2
13.2
16.2
19.1
11.6
14.3
16.9
15.5
19.1
19.6
21.7
25.7
3 1.7
12.2
15.0
4.78
4.88
1.34
1.42
291
356
33.4
41.3
80.8
98.1
114
67.6
82.1
95.5
45.2
54.7
8.75
10.8
50
50
15.4
17.0
20.2
24.8
5.26
5.30
5.40
5.52
1.57
1.61
1.69
1.81
455
501
588
713
46.7
51.6
61.3
75.2
77.9
85.6
99.6
119
60
60
60
60
12
15
10
12
27.5
33.9
24.2
28.7
21.6
26.6
19.0
22.5
5.08
5.21
4.81
4.89
171
205
199
233
29.2
43.0
23.0
33.8
6.93
7.16
627
761
553
651
1220
1758
63.3
77.7
54.2
64.4
200x 100x10 200 100 10
200 X 100 X 15 200 100 15
2.12
2.23
2.34
2.42
2.01
2.22
13.1
14.5
17.1
21.0
24.8
30.4
25.9
30.7
93.2
137
210
299
26.3
38.5
100 X
100 X
100 X
100 X
100 X
100x
120 X
120 X
120 X
125 X
125 X
125 X
75
75
135 X 65 X 8 135
135x 65 X 10 135
150x 75 X 9 150
150 x 75 X 10 150
150x 75 X 12 150
150x 75x 15 150
65 8
65 10
75 9
75 10
75 12
75 15
150 X 90 X 12 150 90
150 X 90 X 15 150 90
150 X 100 X 10 150 100
150 X 100 X 12 150 100
=>
-
-
-
55
55
55
-
50
50
50
80
80
80
50
50
50
-
60
60
60
60
65
65
LEN 10056-1 -65 x 50 x 5 - S235J0: Unequal leg steel angle, a = 65 mm, b = 50 mm,
t = 5 mm, from S235J0
-
-
105
105
105
105
105
105
105
105
W:i
12
12
12
15
17
17
17
22
d,
8.4
8.4
11
11
13
13
30
30
17
17
17
21
21
30
30
21
23
22
22
35
23
23
23
30
30
25
25
35
35
35
40
40
40
25
25
25
25
25
25
45
45
45
40
40
40
25
25
25
22
35
35
40
40
40
40
50
50
55
55
150 55
150 55
25
25
25
25
25
28
28
28
28
28
28
28
28
28
28
148
Materials science: 4.4 Stee ls, Finished prod uct s
Steel angle
Equal leg steel angle. hot-rolled (selectio n)
- - ""
t
s
I
I
-~
--l-x
"':i' x~p ·-
~~r ·~A! A f), j
I
~
W2 >.._
a
Designation
cross-sectional area
second moment of inertia
M aterial:
~
~
cf. DIN EN 10056-1 (1998-101
.... f
I
Dimensions
inmm
Unalloyed structural steel DIN EN 10025-2, e.g. S235JO
Delivery type: From 20 x 20 x 3 to 200 x 250 x 35, in manufactured lengths
" 6 m < 12 m, normal lengths .. 6 m < 12 m ± 100 mm
I
r1 "" t
I
I
s
m'
a
t
cm2
kg/m
20 X 20 X 3
25 X 25 X 3
25 X 25 X 4
20
25
25
3
3
4
1.12
1.42
1.85
0.882
1.1 2
1.45
0.598
0.723
0.762
0.39
0.80
1.02
30 X 30 X 3
30 X 30 X 4
35 X 35 X 4
30
30
35
40
40
45
50
50
50
60
60
60
1.74
2.27
2.67
3.08
3.79
3.90
3.89
4.80
5.69
5.82
6.91
9.03
8.70
8.13
9.40
1.36
1.78
2.09
2.42
2.97
3.06
3.06
3.77
4.47
0.835
0.878
1.00
40x
40 X
45x
50 X
50x
50x
60x
60x
60x
65x
70x
70x
3
4
4
4
5
4.5
4
5
6
5
6
8
7
6
7
6
8
8
10
7
8
75x 75 X 6
75x 75 X 8
80x 80 X 8
80x 80 X 10
90x 90 X 7
90x 90 X 8
65
70
70
75
75
80
80
90
90
90x 90 X 9
90 X 90 X 10
100 X 100 X 8
100 X 100 X 10
100 X 100 X 12
120x 120x 10
90
90
100
120x 120x 12
130x 130x 12
150x 150x 10
120
130
150
150x 150x 12
150x 150x 15
160x 160x 15
150
150
160
180
200
200
200
250
180 X 180 X 18
200 X 200 X 16
200 X 200 X 20
200 X 200 X 24
250 X 250 X 28
=>
100
100
120
'2
"'.!.
2
Distances For t he bending axis
to
x-xand y - y
axes
e
I• = Iv
W. = Wv
cm
cm•
cm3
L
40 X 4
40 X 5
45 X 4.5
50 X 4
50 X 5
50 X 6
60x 5
60 X 6
60 X 8
65 X 7
70 X 6
70 X 7
w axial section modulus
m' linear mass density
I
Tracing dimension
accord . to DIN 997
w,
W2
mm
mm
0.28
0.45
0.59
12
15
15
1.40
1.80
2.95
0.65
0.85
1.18
17
17
18
4.57
5.42
7.09
1.12
1.16
1.25
1.36
1.40
1.45
1.64
1.69
1.77
4.47
5.43
7.14
8.97
11.0
12.8
19.4
22.8
29.2
1.55
1.91
2.20
2.46
3.05
3.61
4.45
5.29
6.89
22
22
25
30
30
30
35
35
35
-
6.83
6.38
7.38
1.85
1.93
1.97
33.4
36.9
42.3
7.18
7.27
8.41
35
40
40
8.73
11.4
12.3
15.1
12.2
13.9
6.85
8.99
9.63
11.9
9.61
10.9
2.05
2.14
2.26
2.34
2.45
2.50
45.8
59.1
72.2
87.5
92.6
104
8.41
11.0
12.6
15.4
14.1
16.1
40
40
45
45
50
50
9
10
8
10
12
10
15.5
17.1
15.5
19.2
22.7
23.2
12.2
13.4
12.2
116
127
145
177
207
313
17.9
19.8
19.9
15.0
17.8
18.2
2.54
2.58
2.74
2.82
2.90
3.31
50
50
55
55
55
50
12
12
10
12
15
15
27.5
30.0
29.3
21.6
23.6
23.0
3.40
3.64
4.03
368
472
624
18
16
20
34.8
43.0
46. 1
61.9
61.8
76.3
27.3
33.8
36.2
48.6
48.5
59.9
4.12
4.25
4.49
5.10
5.52
5.68
24
28
90.6
133
71.1
104
5.84
7.24
737
898
1100
1870
2340
2850
3330
7700
24.6
29. 1
36.0
42.7
50.4
56.9
67.7
83.5
95.6
145
162
199
235
433
-
-
-
-
-
d,
mm
4.3
6.4
6.5
8.4
8.4
11
11
11
13
13
13
13
17
17
17
21
21
21
23
23
23
23
25
25
50
50
60
60
60
60
80
80
90
105
25
25
25
25
25
25
25
25
28
105
105
11 5
28
28
28
65
65
65
70
75
135
150
150
150
150
28
28
28
LEN 10056-1 - 70 x 70 x 7 - S235JO: Equal leg steel angle, a = 70 mm, t = 7 mm,
from S235JO
-
-
28
28
149
M aterials science: 4.4 Steels, Finished products
Medium width and wide I-beams
Medium w idth I-beams (IPE), hot-rolled (selection)
~
d,
~
+---,._
d . DIN 1025-5 (1994-031
s
cross-sectional area
w axial section modulus
I
second moment of inertia
m· linear mass density
;
-·- -!..
<:
x-
-
-- ---
--x
j,
I
Mat erial:
Unalloyed st ruct ural steel DIN EN 10025-2, e.g. S235JR
Delivery type:
St andard lengths, 8 m to 16 m ct 50 mm with h < 300 mm,
8 m to 18m ± 50mmwit h h2,300 mm
w-'
Designation
For the bending axis
y- y
x-x
Dimensions in mm
s
IPE
h
100
120
140
160
180
200
240
270
300
360
400
500
600
100
120
140
160
180
200
240
270
300
360
400
500
600
=
b
55
64
73
82
91
100
120
135
150
170
180
200
220
s
4.1
4.4
4.7
5.0
5.3
5.6
6.2
6.6
7.1
8.0
8.6
10.2
12.0
t
r
5.7
6.3
6.9
7.4
8.0
8.5
9.8
10.2
10.7
12.7
13.5
16.0
19.0
7
7
7
9
9
12
15
15
15
18
21
21
24
cm2
10.3
13.2
16.4
20.1
23.9
28.5
39.1
45.9
53.8
72.7
84.5
116
156
m'
I,
w.
kg/m
cm4
cm3
8. 1
171
34.2
10.4
318
53.0
12.9
541
77.3
15.8
869
109
18.8
1320
146
22.4
1940
194
30.7
3890
324
36.1
5790
429
42.2
557
8360
57.1 16270
904
66.3 23130 1160
90.7 48200 1930
122
92080 3070
ly
cm4
15.9
27.7
44.9
68.3
101
142
284
420
604
1040
1320
2140
3390
s
~
- "'£
s
-c
X -
-·-
·
;,
I
I
Material:
X
m' linear mass density
Unalloyed structural steel DIN EN 10025-2, e.g. S235JR
Delivery t ype: St andard lengths, 8 m to 16 m ct 50 mm with h < 300 mm
-1
" "'' lw,I .1
I
b
d . DIN 1025-2 ( 1994-31
w axial section modulus
cross-sectional area
second mo ment of inertia
I
~ -~
IPBI
5.8
8.7
12.3
16.7
22.2
28.5
47.3
62.2
80.5
123
146
214
308
I -profile DIN 1025 - S235JR - IPE 300: Medium width I-beams with parallel flange surfaces,
h = 300 mm, from S235JR
Wide I-beams light duty IIPEII, hot-rolled (selection)
Designation
~~
cm
Tracing dimension
accord. to DIN 997
w,
d,
mm
mm
30
8.4
36
8.4
40
11
44
13
50
13
56
13
17
68
72
21
80
23
90
25
96
28
110
28
120
28
I
I
r "' 3 • s
For the bending axis
Dimensions in mm
s
x- x
W,
cm•
349
606
1030
1670
2510
3690
cm~
21.2
25.3
31.4
38.8
45.3
53.8
m'
kg/m
16.7
19.9
24.7
30.4
35.5
42.3
12
13
15.5
76.8
97.3
124.0
60.3
76.4
97.6
19
23
25
28
159.0
198.0
226.0
286.0
125.0
155.0
178.0
224.0
Ix
Tracing dimension
accord. to DIN 997
y-y
Iv
~~
72.8
106
155
220
294
389
cm4
134
231
389
616
925
1340
cm
26.8
38.5
55.6
76.9
103
134
7760
13670
22930
675
1010
1480
2770
4760
6990
23 1
340
466
-
45070
86970
141200
303400
2310
3550
4790
7680
8560
10370
11 270
12640
57 1
691
751
843
-
b
100
120
140
160
180
200
s
5
5
5.5
6
6
6.5
t
cm2
100
120
140
160
180
200
h
96
114
133
152
171
190
8
8
8.5
9
9.5
10
240
280
320
230
270
3 10
240
280
300
7.5
8
9
400
500
600
800
390
490
590
790
300
300
300
300
11
12
13
15
=
I-profile DIN 1025 - S235JR - IPBI 320: Wide I-beams light duty from S235JR
Designation according to EURONORM 53-62: HE 320 A
w,
56
W2
~
66
-
-
76
86
100
110
-
-
-
-
d,
13
17
21
23
25
25
94
110
120
35
45
45
25
25
28
120
120
120
130
45
45
45
40
28
28
28
28
-
-
150
Mat erials science: 4.4 St eels, Finished products
Wide I-beams
Wide I-beams (IPB), hot-rolled (selection)
w,
I >;- I
-4 ~
.c::
-
X-
·-
second moment of inertia
--1
.!. "'2
240
280
320
h
100
120
140
160
180
200
240
280
320
400
400
500
600
500
600
800
200
800
w axial selection modulus
m' linear mass density
unalloyed structural steel DIN EN 10025-2, e.g . S235JR
t
l"'i
Delivery type: standard lengths, 8 m to 16 m :1: 50 mm at h < 300 mm,
8mto 18m :1: 50 mmat h ;o 300mm
I
r1 "'2 • s
Dimensions in mm
IPB
100
120
140
160
180
=:,
cross-sectional area
Material:
b
Designation
s
I
· -X
--A- /
I
cf. DIN 1025-2 (1995-11}
s
6
6.5
7
8
8.5
9
10
10.5
11.5
13.5
14.5
15.5
17.5
b
100
120
140
160
180
200
240
280
300
300
300
300
300
s
t
10
11
12
13
14
15
17
18
20.5
24
28
30
33
cm2
26.0
34.0
43.0
54.3
65.3
78.1
106
131
161
198
239
270
334
I
For the bending axis
y- y
Ix
Wx
ly
w.
4
3
4
cm
cm
cm
cm 3
450
89.9
167
33.5
864
144
318
52.9
1510
78.5
216
550
2490
3 11
889 111
426
1360 151
3830
5700
570
2000 200
11260
938
3920 327
19270
1380
6590 471
1930
9240 616
30820
57680
2880 10820 721
107200
4290 12620 842
171000
5700 13530 902
359100
8980 14900 994
x- x
m'
kg/m
20.4
26.7
33.7
42.6
51.2
61.3
83.2
103
127
155
187
212
262
I -profile DIN 1025 - S235JR -IPB 240: Wide I-beam with parallel flange faces, h = 240 mm, made of S235JR,
designation according to EURONORM 53-62: HE 240 B
Wide I-beams, reinforced version UPBvl hot-rolled (selection)
~
~-·
......
·- · ~-
' '
!...
.c::
X-
·
r~
-1
. , .-. 1
,.__ ..,, lw,111
b
I
I I
s
cross-secti onal area
w axial selection modulus
second moment of inertia
m' linear mass density
unalloyed structural steel DIN EN 10025-2, e.g. S235JR
Delivery type: standard lenglhs, 8 m to 16 m :1: 50 mm at h < 300 mm,
8 m to 16 m ± 50 mm at h ;o 300 mm
I
=:,
I
'"' s
Dimensions in mm
s
IPBv
100
120
140
160
180
200
240
280
320
400
500
600
800
h
120
140
160
180
200
220
270
310
359
432
524
620
814
b
106
126
146
166
186
206
248
288
309
307
306
305
303
s
12
12.5
13
14
14.5
15
18
18.5
21
21
21
21
21
cf. DIN 1025-4 (1994-03)
I
Material:
- -- x
. _;,
,
Designation
Tracing dimension
according to DIN 997
w,
W2
d,
w.i
mm mm mm mm
56
13
66
17
76
21
86
23
25
100
110
25
96
35
25
110
25
45
120
45
28
120
45
28
120
45
28
120
45
28
130
40
28
t
20
21
22
23
24
25
32
33
40
40
40
40
40
cm 2
53.2
66.4
80.5
97.1
11 3
131
200
240
312
319
344
364
404
m'
kq/m
41.8
52.1
63.2
76.2
88.9
103
157
189
245
250
270
285
317
For the bending axis
x- x
y- y
w,
Ix
Wx
ly
cm4
cm 3
cm4
cm3
1140
190
75.3
399
2020
283
703 112
3290
411
1140 157
5100
1760 212
568
748
7480
2580 277
10640
967
3650 354
24290
1800
8150 657
39550
2550 13160 914
68 130
3800 19710 1280
104100
4820 19340 1260
161900
6180 19150 1250
237400
7660 18280 1240
442600 10870 18630 1230
Tracing dimension
according
to DIN 997 in mm
w,
w,
d,
W2
13
60
17
68
76
21
23
86
100
25
110
25
- 100 35 25
- 116 45 25
- 126 47 28
- 126 47 28
- 130 45 28
- 130 45 28
- 132 42 28
I-profile DIN 1025 - S235JR -IPBv 400: Wide I -beam, reinforced version, made of S235JR, designation
according to EURONORM 53-62: HE 400 M
151
Materials science: 4.4 Steels, Finished products
Tubes
'
,p
,p
'i'
,,. .
- ·-·+I ·- "'
x-
·-X
~
-
i
';'
,,.
x-
-
"'a
Material:
i
-+ ·.2 i
- x
"'
Unalloyed structural steel DIN EN 10025
Delivery type: DIN EN 10210-2
manufactured lengths 4 m to 16 m, profile
dimensions ax a = 20 x 20 to 400 x 400
DIN EN 10219-2
manufactured lengths 4 m to 16 m, profile
dimensions ax a = 20 x 20 to 400 x 400
DIN EN 10210 and DIN EN 10219 also contain circular tubes,
along w ith square and rectangular tubes.
b >...
Hot worked square and rectangular tubes
Nominal
dimension
axa
ax b
mm
40 X 40
50x 50
60x 60
50 X 30
60 x40
80 x40
100 X 50
=
Linear
mass den•
Wall
thickness
sity
m'
s
kg/m
mm
3.41
3.0
4.0
4.39
2.5
3.68
3.0
4.35
3.0
5.29
6.90
4.0
5.0
8.42
3.0
3.41
4.0
4.39
3.0
4.35
4.0
5.64
4.0
6.90
8.42
5.0
6.0
9.87
4.0
8.78
5.0
10.8
cf. DIN EN 10210-2 (1997-11)
Area moments and section moduli
Cross
section
s
cm 2
4.34
5.59
4.68
5.54
6.74
8.79
10.7
4.34
5.59
5.54
7.19
8.79
10.7
12.6
11.2
13.7
for the bending axes
y- y
w.
Iv
Wv
cm3
cm4
cm 3
I,
cm4
9.78
11.8
17.5
20.2
36.2
45.4
53.3
13.6
16.5
26.5
32.8
68.2
80.3
90.5
140
167
4.89
5.91
6.99
8.08
12.1
15.1
17.8
5.43
6.60
8.82
10.9
17.1
20. 1
22.6
27.9
33.3
9.78
11.8
17.5
20.2
36.2
45.4
53.3
5.94
7.08
13.9
17.0
22.2
25.7
28.5
46.2
54.3
4.89
5.91
6.99
8.08
12.1
15.1
17.8
3.96
4.72
6.95
8.52
11.1
12.9
14.2
18.5
21.7
Ip
w,
cm 4
cm3
15.7
19.5
27.5
32.1
56.9
72.5
86.4
13.5
16.6
29.2
36.7
55.2
65.1
73.4
113
135
7.10
8.54
10.2
11.8
17.7
22.0
25.7
6.51
1 .11
11.2
13.7
18.9
21.9
24.2
31.4
36.9
Tube DIN EN 10210 - 60 x 60 x 5 - S355JO: Square tube, a = 60 mm, s = 5 mm,
made of S355JO
Cold worked, welded, square and rectangular tubes
Nominal
Linear
dimension
mass denWall
axa
sity
thickness
ax b
m'
s
mm
kg/m
mm
2.0
1.68
2.03
30x 30
2.5
3.0
2.36
2.0
2.31
2.82
2.5
40 X 40
3.30
3.0
4.0
4.20
3.0
7.07
80 X 80
4.0
9.22
5.0
11.3
2.0
1.68
40x 20
2.5
2.03
3.0
2.36
4.25
3.0
4.0
5.45
60 X 40
5.0
6.56
3.0
5.19
4.0
6.71
80 x40
8.13
5.0
6.13
3.0
100 X 40
4.0
7.97
5.0
9.70
=
for torsion
x- x
Cross
section
s
cm 2
2.14
2.59
3.01
2.94
3.59
4.21
5.35
9.01
11.7
14.4
2.14
2.59
3.01
5.41
6.95
8.36
6.61
8.55
10.4
7.81
10.1
12.4
cf. DIN EN 10219-2 (1997-11)
Area moments and section moduli
for torsion
for the bending axes
y-y
x- x
Ip
w,
I,
w.
Iv
cm"3
cm 4
cm 3
cm4
cm4
cm 3
4.54
2.75
1.81
2.72
1.81
2.72
3.20
3.16
2.10
3.16
2.10
5.40
3.50
2.34
3.50
2.34
6. 15
3.58
6.94
3.47
6.94
3.47
11.3
5.23
13.6
6.21
4.11
8.22
4.11
8.22
9.32
4.66
9.32
4.66
15.8
7.07
11 .1
5.54
19.4
8.48
11.1
5.54
87.8
22.0
140
33.0
87.8
22.0
27.8
180
4 1.8
111
27.8
111
49.7
131
32.9
218
131
32.9
1.34
3.45
2.36
1.34
4.05
2.02
2.72
1.54
1.54
4.06
4.69
2.35
4.57
3.00
2.60
1.68
1.68
5.21
11.2
25.4
8.46
13.4
6.72
29.3
36.7
13.7
3 1.0
10.3
16.3
8.14
42.8
15.6
18.4
9.21
11 .8
35.3
8.78
43.9
15.3
52.3
13.1
17.6
55.2
18.8
16.2
21.5
10.7
64.8
12.3
65.0
21.7
75.1
18.8
24.6
59.0
19.4
21.7
10.8
92.3
18.5
74.5
24.0
116
23.1
26.7
13.3
27.1
30.8
15.4
87.9
27.9
136
w.
Tube DIN EN 10219 - 60 x 40 x 4- S355JO: Rectangular tube, a ~ 60 mm, b = 40 mm,
s = 4 mm, made of S355JO
152
Materials science: 4.4 Steels, Finished products
Linear mass density and area mass density
Linear mass density1l (Table values f or steel w ith density e = 7.85 kg/dm3)
d diameter
m' linear mass density
a length of side
SW w idths across flats
Round steel bar
Steel wire
d
mm
m'
kg/1000 m
d
mm
m'
kg/1000 m
d
mm
m'
kg/ 1000 m
d
mm
m'
kg/m
d
mm
m'
kg/m
d
mm
m'
kg/m
0.10
0.062
0.55
1.87
1.1
7.46
3
0.055
18
2.00
60
22.2
0.16
0.158
0.60
2.22
1.2
8.88
4
0.099
20
2.47
70
30.2
0.20
0.247
0.65
2.60
1.3
10.4
5
0.154
25
3.85
80
39.5
0.25
0.385
0.70
3.02
1.4
12.1
6
0.222
30
5.55
100
61.7
0.30
0.555
0.75
3.47
1.5
13.9
8
0.395
35
7.55
120
88.8
0.35
0.755
0.80
3.95
1.6
15.8
10
0.617
40
9.86
140
121
139
0.40
0.986
0.85
4.45
1.7
17.8
12
0.888
45
12.5
150
0.45
1.25
0.90
4.99
1.8
20.0
15
1.39
50
15.4
160
158
0 .50
1.54
1.0
6. 17
2.0
24.7
16
1.58
55
18.7
200
247
m'
kg/m
SW
mm
m'
kg/m
Rat steel bar
Hexagonal steel bar
a
mm
m'
kg/m
a
mm
m'
kg/m
6
0.283
20
3. 14
40
12.6
6
0.245
20
2.72
40
10.9
8
0.502
22
3.80
50
19.6
8
0.435
22
3.29
50
17.0
10
0.785
25
4.91
60
28.3
10
0.680
25
4.25
60
24.5
12
1.13
28
6. 15
70
38.5
12
0.979
28
5.33
70
33.3
a
mm
m'
kg/m
SW
mm
m'
kg/m
SW
mm
14
1.54
30
7.07
80
50.2
14
1.33
30
6.12
80
43.5
16
2.01
32
8.04
90
63.6
16
1.74
32
6.96
90
55.1
18
2.54
35
9.62
100
78.5
18
2.20
35
8.33
100
68.0
Linear mass density of special profiles
Profile
Page
Profile
Tee
EN 10055
146
Tubes
EN 10210-2
Page
Angles, equal legs
EN 10056-1
148
Tubes
EN 10219-2
151
Angles, unequal legs
EN 10056-1
147
A luminum round bars
DIN 1798
169
151
St eel channel
DIN1026-1
146
Aluminum square bars
DIN 1796
169
1-beams lPE
DIN 1025-5
149
Aluminum flat bars
DIN 1769
170
1-beams lPB
DIN 1025-2
149
Aluminum round t ube
DIN 1795
171
I-beams, narrow
DIN 1025-1
150
Aluminum channel
DIN 9713
171
Area mass density11 (Table values for steel w ith density e a 7.85 kg/dm3l
Sheet
s sheet thickness
m" area mass density
s
mm
s
mm
m"
kg/m 2
m"
kg/m 2
s
mm
m"
kg/m 2
s
mm
m"
kg/m 2
s
mm
m"
kg/m 2
s
mm
m"
kg/m 2
78.5
0.35
2.75
0.70
5.50
1.2
9.42
3.0
23.6
4.75
37.3
10.0
0.40
3.14
0.80
6.28
1.5
11.8
3.5
27.5
5.0
39.3
12.0
94.2
0.50
3.93
0.90
7.07
2.0
15.7
4.0
31.4
6.0
47.1
14.0
110
0.60
4.71
1.0
7.85
2.5
19.6
4.5
35.3
8.0
62.8
15.0
118
11 Table values can be calculated for a different material by taking a ratio of its density to the density of steel
(7,85 kg/dm3) .
Example: Sheet metal w ith S = 4.0 mm of AIMg3Mn (density 2.66 kg/dm3). From the table: m" = 31.4 kg/m2 for steel.
AIMg3Mn: m" = 31.4 kg/m2 , 2.66 kg/dm 3n .B5 kg/dm3 = 10.64 kg/m2
153
Materials science: 4.5 Heat treatment
Iron-Carbon phase diagram
.,
3 11001-- - - - - + - - - --
'-t-'-- - - - -+-- - - - - - + - - + - - - - - + - - - - - -+-- - - - - i
l!?
8.
E 1000 >-- - - - - + - - --+- - - + , - - - - - ~ - - - - - + - - ~ - - - - + - - - - - ~ - - - - - <
s
ledeburite + cementite
(+ graphiteI11
K
fe rrite
hypereutectoid 2.06
4.3
carbo n content
~
6.67
~
eutectoid
eutectic m ixture
steel
cast iron
11 For iron types with a C content over 2.06% (cast ironl and additional Si content, a porti on of the unalloyed pre-
cipitates in the form of graphite.
Microstructures of unalloyed steel
Heat treatment of steel
Carbon content and crystalline structure
Etchant: 3% nitric acid /alcohol solution
M agnification approx. 500 : 1
1100
"C
1000
_.,t
900
:
''
3 800
-.,A.,•
0.1%C
ferrite
l'=
.,
C.
E 700
t emperature range:
~
0.45%C
ferrite + peat1ite
l
I
temperature
ranges:
600
stress relief anneal
recrystallization anneal
I
ferrite + pearlite
pearlite pearlite + cementite
500
0
0.2
0.4
0.6
0.8
carbon content
1.0
1.2 % 1.4
1.3 % C
pear1ite + grain
boundary cementite
154
M at erials science: 4.5 Heat treatment
Normalizing
Heat and hold at annealing temperature
- structural transf ormation (aust enite)
Contro lled cooling to room temperature
- fine-grained normal structure
To normalize coarse grain structures
in rolled, cast, welded and forged
products
Spt.roidizing
Heat t o annealing temperature, hold at tem- To improve co ld workability, machinperature o r cycle anneal
ability and hardenability;
- spheroidizing of the cementite
can be used f or all steels
Cool down to room temperat ure
Stress relief anneal
Heat and hold at annealing temperature
(below structure t ransition)
- stress relief by plastic
deformation of the workpieces
Cool down to room temperature
To reduce internal stresses in welded,
cast and f orged parts;
can be used for all steels
Heat and hold at hardening temperature
For parts subject to wear stress, e.g.
t ools, springs, g uideways, press
forms;
steels suitable fo r heat treat ment w ith
C > 0,3%, e.g.
C70U, 102Cr6, C45E, HS6-5-2C,
X38CrMoV5-3
Hardening
- structural t ransfo rmatio n {au stenite)
~
"
i
!
I,£._
_ _......'..__
_,__
Quench in o il, wat er, air
- brittle hard, fine structure (martensite)
Temper - transfo rmation of martensite,
hig her toughness, working hardness
time ~
Quenching and tempering
~
"
i
! _ _ _ __ _ _ __
time ~
Heat and hold at hardening temperature
- stru ctural transformation (austenite)
Quench i n o il, water, air
- hard, brittle, fine-g rain structure (martensite), for larger sized parts fine
core struct ure (bainit e)
Temper at higher t emperatures than for
hardening
- martensite reduction, fi ne structure, high
strength w ith good toug hness
Usually used for dynamically loaded
workpieces w ith high strengt h and
good toughness, e.g. shafts, gears,
screws;
q uenched and t empered steels,
see page 133,
nitriding st eels, see page 134,
steels fo r flam e and ind uction
hardening, see page 134,
steels fo r heat-treatable springs,
see page 138
Carburize machined workpieces on the
surface layer
Cool to room temperature
- normal structure (ferrite, pearlite,
carbides)
Harden (for procedure see hardening)
- surface hardening: heat t o surface
hardening temperature
core hardening: heat to hardening
t emperature of the core area
For workpieces w ith wear-resist ant
surfaces, high fatigue strength and
good core strength, e.g. gears, shafts,
bolts;
surface hardening: high wear-resistance, low core strength
core hardening: high core strength,
hard brittle surface;
case hardened st eels, see page 133,
free cutting st eels, see page 134
Anneal usually finish-m achined workpieces
in nitrogen-producing at mospheres
- f ormation of hard, wear-resistant and
temperature-resistant nitrides
For workpieces w ith wear-resistant
surfaces, high fatigue strength and
good temperature-resistance, e.g.
valves, piston rods, spindles;
nitriding st eels, see page 134
Case hardening
~
"
~
~
~
! - ---~~-time
~
Nitriding
ib
time ~
Cool in still air o r in
nitrogen stream
11 For annealing and tempering t em peratures, quenching media and attainable hardness values, see pages 155 to 157.
155
M aterials science: 4.5 Heat t reatment
Tool steels, Case hardened steels
Heat treatment of unalloyed cold work steels
Steel type
cf. DIN EN ISO 4957 (2001-02)
Surface hardness
in HRC ~
after
Full
Case
after
Cooling
harden. harden. hard- tempering2> at
medium
depthII up to 0 ening 100 200 300
mm
mm
Spheroidizing
Hardening
TemperaHot
Tempe- Hardness
working
ture
rature
HB
temperature
Designation
Mat erial
number
C45U
C70U
1.1730
1.1520
1000- 800
C80U
C90U
C105U
1.1525
1.1535
1.1545
·c
·c
max.
·c
680- 710
207
183
800- 820
790- 810
1050- 800
1050- 800 680- 710
1000-800
192
207
212
780- 800
770- 790
770- 790
·c ·c ·c
water
3.5
3.0
15
10
58
64
58
63
54
60
48
53
water
3.0
10
64
64
65
64
64
64
60
61
62
54
54
56
1> For diam eters of 30 mm.
2> The t empering temperatu re is set according t o the application and t he desired working hardness. The steels are
normally delivered spheroidized.
Heat treatment of alloy cold work steels,
hot work steels and high-speed steels
Steel type
cf. DIN EN ISO 4957 (2001-02)
Hardening
Surface hardness in HRC N
tempe·
cooling
after
after tempering2> at
rature11
medium harden- 200 300 400 500 550
ing
Designation
Hot
Material working
number temperature
Spheroidizing
tempe- Hardn.
rature
HB
·c
max.
105V
X153CrMoV12
1.2834
1.2379
1050-850
710- 750
800- 850
212
255
780-800
1010- 1030
X210CrW12
90MnCrV8
102Cr6
1.2436
1.2842
1.2067
1050- 850
800- 840
680- 720
710- 750
255
229
223
60WCrV8
X37CrMoV!>-1
1.2550
1.2343
1050-850
1100- 900
7 10-750
750- 800
HS6-!>-2C
HSl Q--4-3-10
HS2-9-1-8
1.3343
1.3207
1.3247
1100- 900
770-840
·c
·c ·c ·c ·c ·c
·c
water
68
air
63
64
61
56
59
48
58
40
58
36
56
96- 980
780- 800
830 - 850
oil
64
65
65
62
62
62
60
56
57
58
50
50
56
42
43
52
40
40
229
229
900-920
1010-1030
oil
62
53
60
52
58
52
53
53
48
54
46
52
269
302
277
1200- 1220
oil,
1220- 1240
hot
1180- 1200 bat h, air
64
66
66
62
61
62
62
61
62
62
62
61
65
66
68
65
67
69
1> The austenitizing time is the ho lding time at hardening temperature, which is approx. 25 min for cold work steels
and approx. 3 m in. for high-speed steels. Heating is performed in stages.
2> High-speed steels are tempered at least twice at 540- 570 °C. Holding time at t his t emperature is at least 60 m in.
Heat treatment of case hardened steels
Steel type1I
cf. DIN EN 10084 (2008-06)
Hardening
End quench test
Designation
Hardness HRC at distance of:
Material Carburi2ing Core harden. Surf. harden. Temper- QuenchTemp.
ing
ing
number temperature temperature temperature
medium
max.21 3mm 5mm 7mm
'C
•c
·c
C10E
C15E
1.1121
1.1141
17Cr3
16MnCr5
1.7016
1.7131
20MnCr5
20MoCr4
1.7147
1.7321
17CrNi6-6
t 5NiCr 13
1.5918
1.5752
830- 870
840- 880
20NiCrMo2-2
18CrNiMo7-6
1.6523
1.6587
860- 900
830- 870
·c
·c
860- 900
880- 980
-
-
-
-
-
-
880
870
47
47
44
46
40
44
33
41
870
910
49
49
49
47
48
44
46
41
870
880
47
48
47
48
46
48
45
47
920
860
49
48
48
48
45
48
42
48
water
880- 920
780- 820
150- 200
oil
11 The same values apply t o steels with controlled sulfur content, e.g. C10R. 20MnCrS5.
2> For steels with normal hardenability (+H) at a distance of 1.5 mm from t he end f ace.
-
156
Materials science: 4.5 Heat treatment
Quenched and tempered steels
Heat treatment of unalloyed quenched and tempered steels
Steel types2'
cf. DIN EN 10083-2 (2006-10) 11
End quench test
Quenching and tempering
Hardness HRC at
hardening depth in mm31 Hardening 41 Quenching medium Tempering51
1
3
5
·c
·c
Normalizing
Designation
Material
number
·c
·c
C22E
1.1151
880- 940
-
-
-
-
860- 900
water
550- 660
C35E 11
C40E
C45E 11
1.1181
1.1186
1.1191
860- 920
850- 910
840- 900
870
870
850
48- 58
51- 60
55- 62
33- 55
35- 59
37- 61
22- 49
25- 53
28- 57
840-880
830- 870
820- 860
water or o il
550- 660
C50E 11
C55E 11
C60E
1.1206
1.1203
1.1221
830-890
825-885
820-880
850
830
830
56- 63
58- 65
60- 67
44- 61
47-63
50- 65
31-58
33- 60
35- 62
810- 850
810-850
810- 850
oil or water
550- 660
28Mn6
1.1170
850- 890
850
45- 54
42- 53
37- 51
840- 880
water or oil
540- 680
Heat treatment of quenched and tempered alloy steels (selection)
Steel types2l
Designation
Surface
Material hardness61
number
HRC
38Cr2
46Cr211
1.7003
1.7006
54
34Cr4
37Cr4 11
41Cr411
1.7033
1.7034
1.7035
51
53
25CrMo4
34CrMo4
42CrMo411
1.7218
1.7220
1.7225
53
50CrMo411
51CrV4
39NiCrMo3
1.7228
1.8159
1.6510
58
34CrNiMo6 1.6582
30CrNiMo8 1.6580
36NiCrMo16 1.6773
-
38Mn85
1.5532
33MnCr85-2 1.7185
-
cf. DIN EN 10083-3 (2007-011 11
End quench test
Quenching and t empering
Hardness HRC at
3
hardening depth in mm l Hardening4l Quenching medium Tempering 51
1.5
5
15
•c
·c
·c
51 - 59
54-63
37- 54
40-59
- 35
22-39
830- 870
820-860
oil or water
oil or water
850
49- 57
51 - 59
53- 61
45- 56
48- 58
50- 60
27- 44
31-48
32- 52
830- 870
825-865
820- 860
water or oil
oil or water
oil or water
540- 680
850
44-52
49- 57
53- 61
40- 51
48- 57
52- 61
27- 41
34- 52
37- 58
840- 900
830- 890
820- 880
water or oil
oil or water
o il or water
540- 680
-
850
58- 65
57-65
52- 60
57- 64
56-64
50- 59
48- 62
48- 62
43- 56
820- 870
820- 870
820- 850
oil
oil
oil or water
540-680
-
850
50- 58
48- 56
50- 57
50- 58
48- 56
48- 56
48- 57
46- 55
47- 55
830- 860
830-860
865-885
oil or water
o il or wat er
air or oil
540-660
540- 660
550- 650
-
850
52- 60
50- 59
31 - 47
840- 880
water/oil
400- 600
-
880
48-57
47-57
41-54
860-900
oil
400- 600
850
-
-
540- 680
11 DIN 17212 "Steels for flame and induction hardening" was withdrawn w ithout replacement. More information about
steels fo r flame and induct ion hardening on page 133 and 134 in the section "Quenched and tempered steels".
21 Identical values apply to the hig h-grade steels C35 t o C60 and steels with controlled sulphur content, such as C35R.
31 Hardenability requirements: +H normal hardenability
41 The lower temperature range applies to quenching in wat er, the higher range to quenching in oil.
51 The tempering time is 60 minutes minimum.
61 Minimum surface hardness of the steel after flame or induction hardening.
Hardenability and hardening depth of quenched and tempered steels (scatter bands)
t 10
u
:22Z C35E
>--
60
60 1~
~ so
.s oI\/,
t
4
~ 30
20
v,
~
..c
10
so
>- _
\ !½::>:;,: ._ 5 10 15 20 25 30
SSS
40
200
7
r,,- 77
~~~
5
:222 51CrV4+HH
~
so
~ ~ ?>.
~ )(
10
60
~ s2;, ,._
30
0
:222 37Cr4 + HH
37Cr4+ HL
10 15 20 25 30 35
hardening dept h - -
40
30
200
/
V',,
SSS 51CrV4+HL
V/ ¾
//, ½ V/,,
--::. ~I'\_'\
"""
/V'
v.,; RS<:
-...::.: 0-.'\
""
:so
I~
5 10 15 20 25 30 35 40 45
so
157
Materials science: 4.5 Heat treatment
Nitriding steels, Free cutting steels, Aluminum alloys
Heat treatment of nitriding steels
Steel type
Designation
Material
number
24CrMo13-6
31CrMo12
32CrAIMo7- 10
31CrMoV9
33CrMoV12-9
34CrAINi7-10
41CrAIMo7-10
40CrMoV13-9
34CrAIMo5-10
1.8516
1.8515
1.8505
1.8519
1.8522
1.8550
1.8509
1.8523
1.8507
cf. DIN EN 10085 (2001-0H
Heat treatment before nitrid ing
Quenching and tempering
Spheroid.
Hardening
Tempering
temperature
Tempera- Quenching temperature3l4l
ture21
medium
'C
'C
'C
650-700
650- 700
650- 750
680 - 720
680- 720
650- 700
650-750
680- 720
650-750
870- 970
870- 930
870- 930
870-930
870- 970
870- 930
870-930
870- 970
870- 930
Nitriding treatment11
Gas
nitriding
Nitrocarburizing
Hardness51
'C
'C
HV1
-
800
-
oil or
water
800
580- 700
500- 600
570- 650
950
950
950
1l The nitriding t ime is a function of the desired nitriding hardness depth.
21 Austenitizing time at least 0.5 hours.
31 Tempering time at least 1 ho ur.
41 The tempering temperature should not be less than 50°C above the nitriding temperature.
51 Hardness of the nitrided surface.
Heat treatment of free cutting steels
cf. DIN EN 10087 ( 1999-01)
Free cutting case hardened steels
Steel type
Designation
Material
number
Carburizing
temperature
'C
10S20
10SPb20
15SMn13
1.0721
1.0722
1.0725
880-980
Core hardening Surface harden.
temperature
temperature
'C
'C
880-920
780-820
Quenching
medium 11
Quench. and
t emp. tempera!.
'C
Quenching
medium11
Tempering
temperature2l
'C
water, oil,
emulsion
150- 200
Free cutting quenched and tempered steels
Steel type
Designation
M aterial
number
Hardness
temperature
'C
1.0726
35S20
860- 890
water
35SPb20
1.0756
or oil
36SMn14
1.0764
850- 880
36SMnPb14
1.0765
540- 680
38SMn28
1.0760
850- 880
38SMnPb28
1.0761
oil or
44SMn28
1.0762
water
44SMnPb28
1.0763
840-870
1.0757
46S20
1l The choice of quenching medium depends on the shape of the workpiece.
31 Values apply to diameters 10 < d " 16.
Quenched and tempered 3l
N/mm 2
N/mm2
Rm
A
%
430
630- 780
15
Re
14
460
460
700- 850
480
15
16
490
12
21 Tempering time at least 1 hour.
Hardening of aluminum alloys
Alloy EN AWDesignation
Mat erial
number
AICu4MgSi
AICu4SiMg
AIMgSi
Al MgSi1MgMn
Al Zn4,5Mg1
Al Zn5,5MgCu
Al Si7Mgll
2017
2014
6060
6082
7020
7075
420001)
Solution
Artificial aging
Type of age annealing temperature holding
time
hardening21 temperature
h
'C
'C
T4
T6
T4
T6
T6
T6
T6
5- 8
500
525
Natural
aging time
days
100-300
8 - 24
5-8
470
525
ll Aluminum casting alloy EN AC-Al Si7Mg or EN AC 42000.
21 T4 solution annealed and naturally aged; T6 solution annealed and artificially aged.
-
-
4
Age hardened
Rm
N/mm2
A
%
390
420
130
280
210
545
250
12
8
15
6
12
8
1
158
Material science 4.6 Cast iron
Designation system for cast iron materials
Designations and material numbers
cf. DIN EN 1560 (1997-08)
Cast iron materials are referenced either with a designation or a material number.
Example:
Cast iron with flake graphite, tensile strength Rm = 300 N/mm2
Designation
EN-GJL-300
Material number
EN-JL1050
Mftwialdeeignations
Material designations have up to six characters without spaces,
beginning with EN (European standard) and GJ (cast iron; I iron)
Designation example:
EN
EN
EN
EN
EN
EN
EN
350
HB155
350-22U
450-6
360-12
HV600(XCr14)
XNiCuCr15-6-2
GJ
GJ
GJ
GJ
GJ
GJ
GJ
W
Cast iron with flake graphite
Cast iron with flake graphite
Cast iron with spheroidal graphite (ductile Iron)
Malleable cast iron - blackheart
Malleable cast iron - whiteheart
Wear-resistant cast iron
Austenitic cast iron
T
I
Mechanical properties or
chemical composition
(numbers/leners)
A austenite
=
Mechanic&I properties
F ferrite
P peartite
M martensite
L ledeburite
0 quenched
T quenched and
tempered
B not
decarburized
W decarburized
350
minimum tensile strength Rm in N/mm2
350-22 additional elongation at fracture EL in%
S
Test specimen cast separately
u
cast-on
C
taken from the casting
Addltional
requirements
D rough
casting
H heat treated
casting
W weldable
z additional
requirements
HB155 max. hardness
Chemical composition
Data are based on steel designations,
see page 125
Mat.-ial numbers
Material numbers have seven characters without spaces,
beginning with EN (European standard) and J (iron; I iron)
Designation examples:
EN
EN
EN
J
J
J
0 4
0 2
, 3
7
2
0
Cast iron with flake graphite and hardness as characteristic spheroidal
g raphite casting with cast-on test specimen, characteristic Rm
Malleable cast iron w ithout special requirements, characteristic Rm
Material
characteristic number
tensile
strength
2 hardness
3 chemical
com position
Every cast iron material
is assigned a two-digit
number.
A higher number indicates a higher strength.
IJ .. u
Material~
(number)
O no special requirements
1 separately cast test specimen
2 cast-on test specimen
3 test specimen taken from the casting
4 toughness at room temperature
5 toughness at low temperature
6 specified weldability
7 rough casting
8 heat treated casting
9 additional requirements
Type
M aterial science 4.6 Cast iron
159
Classification of Cast Iron Materials
.
Examples/
Standard
material number
Tensile
strength
Rm
Properties
N/mm 2
•
Application examples
Cast iron
w ith flake
graphite (gray
iron )
with spheroidal
graphite
DINEN
1561
DINEN
1563
EN-GJL-150
iGG-15)11
EN-JL1020
100
to
450
Very good castability,
For complex workpi eces
good compression strength, w ith many contours;
very versatile in its applica·
damping capacity,
emergency running
tions.
properties, and good
corrosion resistance
Machine frames,
gear housings
EN-GJS-400
(GGG-40)1>
EN-J S1030
350
to
900
Very good castability,
high strength even with
dynamic loading,
surface hardenable
Wear stressed
workpieces;
clutch parts, fittings,
engine/motor construction
with vermicular
graphite
ISO
1611 2
ISO
16112/JV/300
300
to
500
Very good castability, high
strength without expensive
alloying additions
Aut omotive parts,
engine/motor construction,
gear housings
bainitic
cast iron
DINEN
1564
EN-GJ S-800-8
EN-J S1100
800
to
1400
Heat treatment and controlled cooling produce bainite and austenite for high
strength and good tough-
Highly stressed parts, e.g.
wheel hubs, gear rings, ADI
castings2>
wear-resistant
DIN EN
12513
EN-GJN-HV350
EN-J N2019
> 1000
Wear-resistant due to
martensite and carbides,
also alloyed with Cr and Ni
ness
castings,
white cast iron
Wear-resistant cast iron,
e.g. dressing rolls,
dredging shovels,
impellers for pumps
Malleable cast iron
decarburized
(whiteheart)
DIN EN
1562
EN-GJMW-350
(GTW-35)11
EN-JM1010
270
to
570
Decarburization of the surface by tempering. High
strength and t oughness,
ductile
True to shape, thin-walled,
impact-loaded parts;
levers, brake drums
not
decarburized
iblackheart)
DIN EN
1562
EN-GJMB-450
(GTS-45)1>
EN-JM1 140
300
to
800
Cluster graphite in entire
cross-section due t o malleablizing. High strength
and toughness in larger
wall thickness
True t o shape, thick walled,
impact stressed parts;
levers, universal joint yokes
for general
use
DIN EN
1029331
GE240
1.0446
380
to
600
Unalloyed and low alloy
cast steel for general use
Minimum mechanical values
from - 10°C t o 300°C
w ith improved
weldability
DINEN
10293"1
G20Mn5
1.6220
430
to
650
Lower carbon content with
Welded assembly construction,
fine-grain structural steels with
larger wall thickness
quenched and
t empered
cast st eel
DIN EN
1029351
G30CrMoV6-4
1.7725
500
to
1250
Fine quenched and t ernpered structure w ith high
toughness
Chains.
plating
for pressure
DIN EN
10213
GP280GH
1.0625
420
to
960
Types with high strength
and toughness at low and
high temperatures
Pressure vessels for hot or
cold media, high temperal ure resistant and tough at
low temperatures; rustproof
stainless
DINEN
10283
GX6CrNi26-7
1.4347
450
to
1100
Resistant to chemical attack
and corrosion
Pump impellers in acids,
duplex steel
heat -resistant
DIN EN
10295
GX25CrNiSi18-9
1.4825
400 !0
550
Resistant to scaling gases
Turbine parts,
furnace grates
c-stee1
vessels
manganese and m icroalloy
2> ADI - Austempered Ductile Iron
11 previous designation
31 Replaces DIN 1681 4) Replaces DIN 17182 5> Replaces DIN 17205
160
Material science: 4.6 Cast iron
Cast iron with flake graphite, Cast iron with spheroidal graphite
Cast iron with flake graphite (gray iron)
cf. DIN EN 156111997-081
Tensile strength ~ as identifying ch..-ristic
Type
Designation
Material
number
Hardness HB as identifying characteristic
Wall
thickness
Tensile st rength
mm
N/mm2
Type
Rm
Designation
Material
number
Wall
thickness
Brinell
hardness
mm
HB30
EN-GJL-100
EN-GJL-150
EN-JL1010
EN-JL1020
5- 40
2.5- 300
100- 200
150- 250
EN-GJL-HB155
EN-GJL-HB175
EN-JL2010
EN-JL2020
40- 80
40- 80
max. 155
100- 175
EN-GJL-200
EN-GJL-250
EN-JL1030
EN-JL1040
2.5- 300
5 - 300
200- 300
250- 350
EN-GJL-HB195
EN-GJL-HB215
EN-JL2030
EN-JL2040
40-80
40- 80
120- 195
145- 215
EN-GJL-300
EN-GJL-350
EN-JL1050
EN-JL1060
10- 300
10 - 300
300-400
350-450
EN-GJL-HB235
EN-GJL-HB255
EN-JL2050
EN-JL2060
40- 80
40-80
165- 235
185- 255
=
=
EN-GJL-100: Cast iron with flake graphite (gray
iron), minimum tensile strength Rm = 100 N/mm2
EN-GJL-HB215: Cast iron w ith flake g raphite (g ray
iron), maximum Brinell hardness= 215 HB
Properties
Good castability and machinability, vibration damping, corrosion resistance, high compression strength,
good sliding properties.
Application examples
Machine frames, bearing housings, plain bearings, pressure-resistant parts, turbine housings.
Hardness as characteristic property provides information on the machinability.
Cast iron with spheroidal (nodular) graphite
cf. DIN EN 1563 12005-10)
Tensile strength ~ as identifying characteristic
Type
Designation
Material
number
Tensile
strength
Yield
strength
Rm
Roo.2
Elongation
EL
Properties,
application examples
N/mm2
N/mm 2
%
EN-GJ S-350-22-LT1l
EN-GJS-350-22-RT2l
EN-GJS-350-22
EN-JS1015
EN-JS1014
EN-JS1010
350
350
350
220
220
220
22
22
22
EN-GJS-400-18-LT1l
EN-GJS-400-18-RT2l
EN-GJS-400-18
EN-GJS-400-15
EN-JS1025
EN-JS1024
EN-JS1020
EN-JS1030
400
400
400
400
250
250
250
250
18
18
18
15
EN-GJ S-450-10
EN-GJS-500-7
EN-GJ S-600-3
EN-JS1040
EN-JS1050
EN-JS1060
450
500
600
310
320
370
10
7
3
Good machinability,
average wear resistance;
fittings, press frames
EN-JS1070
700
420
EN-JS1080
800
480
EN-JS1090
900
600
21 RT for room temperature
1l LT for low temperatures
2
2
2
Good surface hardness;
gears, st eering and clutch parts,
chains
EN-GJS-700-2
EN-GJ S-800-2
EN-GJS-900-2
=
Good machinability,
low wear resistance;
housings
EN-GJS-400-18: Cast iron with spheroidal (nodular) graphite, minimum tensile strength Rm = 400 N/mm 2;
elongation at fracture EL = 18%
HardMSS HB as identifying characteristic
Type
Designation
Material
number
Tensile
strength
Yield
strength
Rm
N/mm2
Rpo.2
N/mm2
Brinell
hardness
HB
EN-GJS-HB130
EN-GJS-HB150
EN-GJS-HB155
EN-JS2010
EN-JS2020
EN-JS2030
350
400
400
220
250
250
< 160
130- 175
135- 180
EN-GJ S-HB185
EN-GJS-HB200
EN-GJ S-HB230
EN-JS2040
EN-JS2050
EN-JS2060
450
500
600
310
320
370
160- 210
170 - 230
190- 270
EN-GJS-HB265
EN-GJS-HB300
EN-GJS-HB330
EN-JS2070
EN-JS2080
EN-JS2090
700
800
900
420
480
600
225- 305
245- 335
270- 360
=
Properties,
application examples
By specifying hardness values the purchaser can better adapt process parameters to machining of the cast parts.
Applicati ons as above.
EN-GJS-HB130: Cast iron w ith spheroidal (nodular) graphite, Brinell hardness HB 130, maximum hardness
161
Material science: 4.6 Cast iron
Malleable cast iron, Cast steel
Malleable cast iron11
Type
Designat ion
Material
I number
cf. DIN EN 1562 (2006-081
Tensile
strength
Rm
N/mm2
Yield
Elongation Brinell
strength at fracture hardness Properties,
EL
application examples
Rpo.2
HB
N/mm 2
%
Decarburizing annealed malleable cast iron lwhiteheart malleable cast iron)
-
EN-JM1010
EN-JM1030
EN-JM1040
EN-JM1050
350
400
450
550
220
260
340
4
5
7
4
230
220
250
250
All types have good castability and
good machinability.
Workpieces with low wall thickness,
e. g. levers, chain links
EN-GJMW-360-12 EN-JM1020
360
190
12
200
Especially well suited for welding.
EN-GJMW-350-4
EN-GJMW-400-5
EN-GJMW-450-7
EN-GJMW-550-4
-
EN-GJMW-350-4: Whiteheart malleable cast iron, Rm= 350 N/mm2, EL= 4 %
Non-decarburizing annealed malleable iron lblackheart malleable caat ironl
EN-GJMB-300-6
EN-JM1110
300
-
6
- 150
EN-GJMB-350-10
EN-GJMB-450-6
EN-GJMB-500-5
EN-GJMB-550-4
EN-JM1 130
EN-JM1140
EN-JM1150
EN-JM11 60
350
450
500
550
200
270
300
340
10
6
5
4
-150
150-200
165- 215
180- 230
EN-GJMB-600-3
EN-GJMB-650-2
EN-GJMB-700-2
EN-GJMB-800-1
EN-JM1170
EN-JM1180
EN-JM1190
EN-JM1200
600
650
700
800
390
430
530
600
3
2
2
1
195-245
210- 260
240- 290
270- 320
-
High pressure tightness
All types have good castability and
good machinability.
Workpieces with high wall thickness,
e. g. housings, universal joint yokes
pistons
EN-GJMB-350-10: Non-decarburizing annealed malleable cast iron, Rm= 350 N/mm2, EL= 10%
11 Previous designations: page 159
cf. DIN EN 10293 (2005-06111
Cast steel for general applications (selection)
Tensile
strength
Type
Yield Elongation
strength
Notch
impact
energy
K.,
Properties,
application examples
Designation
Material
number
Rm
N/mm 2
Rpo.2
N/mm2
EL
%
J
GE20021
GE24021
GE30021
1.0420
1.0445
1,0558
380-530
450- 600
600- 750
200
240
300
25
22
15
27
31
27
For workpieces with average
dynamic loading;
w heel spiders, levers
G17Mn531
G20Mn521
GX4CrNiMo16-5-131
G28Mn621
G10MnMoV6-331
G34CrMo4 31
1.1131
1.6220
1.4405
450- 600
480- 620
760- 960
240
300
540
24
20
15
70
60
60
Improved weldability;
composite welded structures
1.1165
1.5410
1.7230
520- 670
600- 750
620- 770
260
500
480
18
18
10
27
60
35
For workpieces with high dynamic
loading;
shafts
G32NiCrMo8-5-4 31
GX23CrMoV12-131
1.6570
1.4931
850- 1000
740- 880
700
540
16
15
50
27
For corrosion-protected workpieces
wit h high dynamic loading
11 DIN 17182 "Steel cast types with improved weldability and t oughness• was wi thdrawn without replacement.
31 quenched and tempered
21 normalized
Cast steel for pressure vessels (selection)
Type
Designation
Material
number
cf. DIN EN 10213 (2004-031
Tensile
Yield
Elongation
Notch
strength'' strength 11 at fracture impact
Properties,
energy
K., application examples
EL
Rm
Rpo.2
N/mm2
%
J
N/mm2
GP240GH
G17CrMo5-5
1.0619
1.7357
420
490
240
315
22
20
27
27
GX8CrNi12
GX4CrNiMo16-5-1
1.4107
1.4405
540
760
355
540
18
15
45
60
11 Values for a wall thickness up to 40 mm
For high and low temperatures, e.g.
steam turbines, super heated steam
armatures, also corrosion resistant
162
Material science: 4.7 Foundry technology
Patterns, Pattern equipment and core boxes
1
DIN
7~~~51
9
5~
Materials and grades
Materials
Characteristics
Wood
Plastic
Metal
Plywood. particle board or
sandwich board, hard and
soft wood
Epoxy resins o r
polyurethane with
fillers
Cu, Sn, Zn alloys
Al alloys
Cast iron or steel
Recurring individual pieces
and smaller lots, low precision requirements;
normally hand molding
Jobbing work and volume
M_
oderate to la_r~e volumes
production with higher preci- ~.:i~i~~~::i~~•soon
machine molding
sion requirements;
hand and machine molding
Max. production run
for molding
approx. 750
approx. 10000
approx. 150000
Quality classes''
w121, W2, H3
P1 2 ', P2
M1 21, M2
Surface quality
Sand paper
60- 80 grit
Ra = 12.5 µm
Ra = 3.2- 6.3 µm
Type of material
Application
11 Classification system for the manufacture and use of patterns, pattern equipment and core boxes, according to
their application, quality and service life: W wood; P plastic; M metal
21
best grade
Mold draft for sand casting
Mold draft Tin mm
Small draft surfaces
Large draft surfaces
Height h
mm
Hand molding
Molding sand Molding sand
clay bonded
chem. bonded
Machine
molding
Hand molding
Molding sand
Molding sand
clay bonded
chem. bonded
Machine
molding
-30
1.0
1.0
1.0
1.5
1.0
1.0
> 30- 80
2.0
2.0
2.0
2.5
2.0
2.0
> 80-180
3.0
2.5
2.5
3.0
3.0
3.0
> 180-250
3.5
3.0
3.0
4.0
4.0
4.0
> 250- 1000
+ 1.0 mm each 250 mm
> 1000- 4000
+ 2.0 mm each 1 000 m m
Paint and color codes on patterns
Surf- or partial surt-
Basic color for areas that
should remain unmachined
on the casting
Cast steel
blue
Nodul•
cast
iron
Gray
purple
red
cast
iron
Malleable
Iron
gray
Areas to be machined on the
casting
Locations of loose parts
and their attachments
Locations of
chill plates
Core marks
Risers
framed in black
Haavy
metal
Light
castings
alloy
castings
yellow
green
163
Material science: 4.7 Foundry t echnology
Shrinkage allowances, Dimensional tolerances, Molding and casting methods
Shrinkage allowances
cf. DIN EN 12890 (2000--061
Shrinkage
Cast iron
~
Other casting materials
-.....1n %
-
In %
w ith flake graphite
1.0
Cast steel
w ith spheroidal graphite, annealed
0.5
A ustenitic manganese cast steel
2.3
w it h spheroidal graphite, not annealed
1.2
A l, Mg, CuZn alloys
1.2
austenitic
2.5
CuSnZn, Zn alloys
1.3
m alleable cast iron, decarburizing anneal
1.6
0.5
CuSn alloys
1.5
malleable cast iron, no decarburizing anneal
2.0
Cu
1.9
Dimensional tolerances and machining allowances, RMA
-
Examples of toleranca specifications in a drawing:
1. ISO 8062..c:T12-RMA6 (HI
Tolerance g rade 12, material allowance 6 mm
cf. DIN ISO 8062 (1998-08)
R
rough cast ing - nominal dimension
d imension after finishing
casting tolerance grade
t otal casting to lerance
RMA material allowance for machining
F
CT
T
2. Indiv idual tolerances and machining allowances are given
directly after a dimension.
I
I
R = F + 2 • RMA + T/2
CastingtolerNominal
d imensions
in mm
Total cast ing tolerance T in mm
for casting tolerance grade CT
2
1
3
4
5
6
7
~
8
9
10
11
12
13
14
15
16
- 10
0.09 0.13 0.18 0.26 0.36 0.52 0.74
1.0
1.5
2.0
2.8
4.2
-
> 10- 16
0.10 0.14 0.20 0.28 0.38 0.54 0.78
1.1
1.6
2.2
3.0
4.4
-
-
-
-
> 16-25
0.11 0.15 0.22 0.30 0.42 0.58 0.82
1.2
1.7
2.4
3.2
4.6
6
8
10
12
> 25- 40
0.12 0.17 0.24 0.32 0.46 0.64 0.9
1.3
1.8
2.6
3.6
5
7
9
11
14
> 40-63
0.13 0.18 0.26 0.36 0.50 0.70 1.0
1.4
2.0
2.8
4.0
5.6
8
10
12
16
> 63- 100
0.14 0.20 0.28 0.40 0.56 0.78 1.1
1.6
2.2
3.2
4.4
6
9
11
14
18
> 100- 160
0.15 0.22 0.30 0.44 0.62 0.88 1.2
1.8
2.5
3.6
5
7
10
12
16
20
> 160- 250
-
0.24 0.34 0.50 0.70
1.0
2.0
2.8
4.0
5.6
8
11
14
18
22
> 250-400
-
-
0.40 0.56 0.78
1.1
1.6
2.2
3.2
4.4
6.2
9
12
16
20
25
0.64 0.90
1.2
1.8
2.6
3.6
5
7
10
14
18
22
28
-
-
-
1.4
2.0
2.8
4
6
8
11
16
20
25
32
> 400-630
> 630- 1000
1.0
1.4
Molding and casting methods
Method
Application
Advantages and
Hand
molding
large castings,
small lots
all sizes, expensive,
low dimensional
disadvantages
Relative dimen• Achievable
Casting material sional accuracy11 roughness Ra
in mm/mm
intJm
GJL, GJS, GS,
GJM, AI and
Cu alloys
0.00- 0.10
40- 320
Machine
molding
small to medium
dimensionally accurate, GJL, GJS, GS,
sized parts, volume good surface
GJM. A l alloys
0.00- 0.06
20- 160
Vacuum
molding
medium to large
parts, volumes
dimensionally accurate, GJL, GJS, GS,
GJM, Al and
good surface,
Cu alloys
high investment cost s
0.00- 0.08
40- 160
Shell
molding
small parts,
large volumes
dimensio nally accurate, GJL, GS,
A l and Cu alloys
high mold costs
0.00-0.06
20- 160
Investment
casting
small parts,
large volumes
complex parts,
high mold costs
GS,AI alloys
0.00- 0.04
10- 80
Die casting
small to medium
sized parts,
large volumes
dimensionally accurate
even w ith t hin walls,
fine-grain structure,
high investment costs
hot chamber:
Zn, Pb, Sn, Mg
cold chamber:
Cu,AI
0.00- 0.04
10- 40
accuracy
' ' The ra tio of largest relative deviatio n to the nominal dimension is called t he relative dimensional accuracy.
164
Material science: 4.8 Light alloys
Aluminum, Aluminum alloys - Overview
Alloy
group
Material
number
Main characteristics
Main areas of application
Product shapes11
s
I
Pure aluminum
Al
(Al content
> 99.00%)
AIMg
I
I
T
page 166
AW-1000 • very good cold workability
to
weldable and brazable
AW-1990
difficult for cutting machining
(Series1000) corrosio n resistant
anodized for decorative
purposes
Containers, conduits and
equipment for the food and
chemical industry, electrical
conductors, reflectors, trims,
license plates in automotive
. ..
manufacturing
Aluminum, wrought aluminum alloys, non-heat treatable (selection)
AIMn
B
AW-3000 • cold workable
to
• weldable and solderable
AW-3990 • good machinability in
(Series 3000) work-hardened condition
Compared to Series 1000:
higher strength
• improved lye resistiv ity
AW-5000 • good cold workability with high
work hardening
to
AW-5990
limited weldability
(Series 5000) good machinability in work-hardened condition and with higher
alloy contents
• weather and saltwater resistant
page 166
Roofing, siding, and supporting
structures in the construction
industry, parts for radiators and air
conditioning units in automotive
manufacturing,
d rink and food cans
in the packaging industry
.. .
Lightweight material for superstructures of commercial vehicles,
tank and silo trucks,
metal signs, traffic sign,
rolling shutters and doors,
windows, doors, hardware in the
•
..
construction industry, machine
frames. parts in the construction of
jigs and fixtures and mold making
AIMgMn
• good cold workability with high
work hardening
good weldability
good cutting machinability
saltwater resistant
. ..
Aluminum, wrought aluminum alloys, heat treatable (selection)
AIMgSi
AW-6000
to
AW-6990
(Series 6000)
A ICuMg
AW-2000
to
AW-2990
(Series 2000)
AIZnMgCu
1)
21
AW-7000
to
AW-7990
(Series 7000)
good cold and hot workability
corrosion resistant
good weldability
good cutting machinability in
heat treated condition
high-strength values
good high-temperature strength
limited corrosion resistance
limited weldability
• good cutting machinability in
heat treated condition
.,1
·"
. ,1
Lightweight material in automotive
and aircraft construction;
with Pb, Sn or Bi additions:
very good cutting machinable free
cutting alloys
. ,1
. ,1
.,1
highest strength of all Al alloys
High-strength lightweight material
best corrosion resistance
in aircraft industry, machine con-
in artificially aged condition
limited weldability
good cutting machinability in
heat treated condition
struction, tools and molds for plastic molding, screws, extruded parts
Product forms: S sheet; B bars; T t ubes
Free machining alloys are only delivered as bars or tubes.
page 167
Load-bearing structures in the
construction industry,
windows, doors,
machine beds,
hydraulic and pneumat ic parts;
with Pb, Sn or Bi additions:
very good cutting machinable free
cutting alloys
. . .
165
Material science: 4.8 Light alloys
Aluminum, wrought aluminum alloys: Designations and material numbers
Designations for aluminum and wrought aluminum alloys
cf. DIN EN 573-2 (1994-12)
The designations apply to wrought products, e.g. sheet, bars, tubes, w ires and for wrought parts.
Designation examples:
EN AW · Al 99,98
EN AW· Al Mo1SiCu • H111
I
--r-
I
T
Chemical composition, purity
EN European standard
AW A luminum wrought products
A l 99.98
Mg1SiCu
--
pure aluminum, degree of purity 99,98% A l
1% Mg, low percentage of Si and Cu
cf. DIN EN 515 (1993-12)
Material condition (excerpt)
Condition
Meaning of the
material conditions
Symbol Meaning of the symbol
manufacl ured
condition
F
Wrought products are manufactured without specifying mechanical
limits, e.g. tensile strength, yield strength, elongation at fracture
Wrought products
w ithout secondary
operations
spheroidized
0
01
02
Spheroidizing can be replaced by hot working
Solution annealed, cooled slowly to room temperature
Thermomechanically formed, highest workability
To restore worka
bility after cold
working
Work
hardened
H12
to
H18
Work hardened with the following hardness grades:
H12
H14
H16
H18
4/• hard
3'4 hard
¼hard
½ hard
Hl 11
Hl12
Annealed w ith subsequent slight work hardening
Slight work hardening
To assure guaranteed mechanical
values,
e.g. tensile strength
y ield strength
Tl
T2
T3
Solution annealed, stress relieved and naturally age hardened, not redressed
Quenched like Tl, cold worked and naturally aged
Solution heat treated, cold worked and naturally age hardened
Heat
treated
T3510
T3511
Solution annealed, stress relieved and naturally aged
Like T3510, redressed to hold the limit deviations
T4
T4510
Solution annealed, naturally age hardened
Solution annealed, stress relieved and nat urally age hardened, not redressed
T6
T6510
Sol ution annealed, artificially aged
Solution annealed, stress relieved and artificially aged, not red ressed
TB
T9
To increase in tensile strength, yield
strength and hardness, reduction of
the cold workability
Solution annealed, cold worked, artificially aged
Solution annealed, artificially aged, cold worked
Material numbers for aluminum and wrought aluminum alloys
cf. DIN EN 573-1 (1994-12)
Material numbers apply to wrought products, e.g. sheet, bars, tubes, wires and for w rought parts.
Designation examples:
ENAW - 1050A
~-515~T
I
EN European standard
AW A luminum wrought products
I
I
I
Indicates that count ry-specific limits deviat e
from the ori ginal alloy.
I
I
I
Alloy modifications
Alloy groups
Number
Group
Number
Group
1
2
pure Al
AICu
5
6
AIMg
AIMgSi
3
4
AIMn
AISi
7
8
AIZn
other
0
1-9
--
Original alloy
A lloys that deviate
from the original alloy
Type number
Within an alloy group, e.g.
AIMgSi, each type is assigned
its own number.
166
Material science: 4.8 Light alloys
Aluminum, wrought aluminum alloys
Aluminum and wrought aluminum alloys,
cf. DIN EN 485-2 (2004-09),
DIN EN 754-2, 755-2 (2008-06)
non-heat treatable (selection)
Designation
(materialnumber)ll
A l 99.5
( 1050A)
Delivery
forms21
R
.
Al Mn1Cu
(3003)
s
trim
., 95
95- 130
130- 165
" 35
" 35
" 110
25
25
6
Equipment manufact uring,
extruded parts,
vehicle superstructures,
0, H111
0.5- 1.4
1.5-2.9
3.0-5.9
90- 130
90- 130
90- 130
"35
" 35
" 35
19
21
24
p
z
z
F, H112
0, H111
H14
s 200
s 80
s 40
., 95
95- 130
130-165
"35
., 35
" 110
25
25
6
w
0, H111
0.5- 1.4
1.5- 2.9
3.0- 5.9
95- 135
95- 135
95- 135
" 35
"35
"35
17
20
23
p
z
z
F, H112
0, H111
H14
s 200
s 80
s 40
" 100
100- 145
" 140
"40
a, 40
" 110
18
18
6
w
0 , H111
0.5-1.49
1.5-2.9
3.0- 5.9
100- 145
100-145
100- 145
" 35
" 35
" 35
19
20
22
p
z
z
F, H112
0, H111
H14
s 200
s 80
s 30
" 160
150- 200
200-240
" 60
" 60
" 160
16
17
5
w
0, H111
0.5- 1.4
1.5- 2.9
3.0-5.9
160-200
160- 200
160-200
" 60
"60
" 60
14
16
18
p
z
z
F, H112
0, H111
H14
s 150
s 80
s 25
" 180
180-250
240-290
,,so
a,80
., 180
14
16
4
.
•
w
0, H11 1
0.5- 1.4
1.5- 2.9
3.0- 5.9
190-240
190-240
190- 240
ae 80
a,80
" 80
14
16
18
-
F, H112
0, H11 1
H14
s 200
s 80
s 40
"250
250-320
270-350
., 110
a, 110
., 180
14
16
8
Optical equipment,
packaging
.
p
z
z
-
p
s 200
., 200
200- 275
,,95
a. 85
10
18
Container construction,
-
.
F, H112
0, H111
w
0 , H111
0.5- 1.4
1.5-2.9
3.0 - 5.9
215- 275
215-275
215- 275
a, 85
a, 85
;,, 85
13
15
17
tank and silo trucks
p
z
z
F, H111
0, H111
H1 2
s 200
s 80
s 30
., 270
270- 350
"280
" 110
" 110
a. 200
12
16
6
Mold making and
construction of jigs and fixtures, machine frames
-
.
-
.
-
.
t
-
Al Mg2Mn0.3
(5251)
.
-
-
.
.
-
Al Mg4.5Mn0.7
(5083)
Rm
N/mm 2
Yield Elong. at
strength fracture Applications,
EL
Examples
Rpo.2
N/mm2
%
22
26
29
.
.
Al Mg3Mn
(5454)
Tensile
strength
" 20
" 20
" 20
-
AIMg1
(5005)
AIMg5
(5019)
Thickness/
diameter
mm
"70
-
AIMg3
(5754)
condition41
Equipment manufacturing,
pressure vessels,
signs,
packaging,
.
'
Material
25
25
6
-
AIMnl
(3103)
DC3
.
-
.
-
-
F, H112
0, H111
H14
s 200
s80
s 40
" 60
60-95
100- 135
w
0, H111
0,5- 1,4
1,5- 2,9
3,0- 5,9
65-95
65-95
65-95
p
z
z
F, H112
0, H111
H14
s 200
"60
s 10
w
p
z
z
" 20
-
heat exchangers
Roofing,
facades,
load-bearing structures
in metal working
Roofing,
facades,
w indows, doo rs,
hardware
Equipment and devices for
the food industry
Equipment manufacturing,
aircraft industry,
body parts,
mold making
including pressure vessels,
conduits,
11 For simplification all designations and material numbers are written witho ut the addition "EN AW-".
21 Delivery forms: R round bar; S sheet, strip
31 DC Delivery condition: p extruded; z drawn; w
•> Material condition, see page 165
cold-rolled
167
Material science: 4.8 Light alloys
Wrought aluminum alloys
Wrought aluminum alloys,
cf. DIN EN 485-2 (2004-091,
DIN EN 754-2, 755-2 (2008-061
heat treatable (selection)
Delivery
forms21
Designation
(materialnumberl1I
<•
Al Cu4PbMgMn
(20071
AICu4PbMg
(20301
Al MgSiPb
(60121
AI Cu4SiMg
(2014)
Al Cu4Mg1
(20241
AI MgSi
(60601
Al Si1MgMn
(60821
Rm
Yield Elong. at
strength fracture Application,
EL
Examples
Roo.2
N/mm2
%
.
-
p
z
z
T4. T4510
T3
T3
s 80
,. 30
30- 80
"370
" 370
" 340
" 250
" 240
" 220
8
7
6
-
p
z
z
T4, T4510
T3
T3
s 80
,;30
30- 80
" 370
"370
" 340
" 250
"240
" 220
8
7
6
-
p
z
z
TS, T6510
T3
TS
s 150
s 80
"'80
" 310
" 200
"310
" 260
" 100
"260
8
10
8
p
z
z
0, H111
T3
T4
"'200
,; 80
s80
s 250
" 380
"380
s 135
" 290
"220
12
8
12
w
0
0.5- 1.4
1.5- 2.9
3.0- 5.9
"' 220
s 220
,. 220
,; 140
s 140
s 140
12
13
16
p
z
z
0, H111
T3
T6
,.200
10- 80
,.so
,. 250
" 425
" 425
s 150
"290
"'315
12
9
5
s 220
s 220
,;220
s 140
s 140
,; 140
12
13
13
.
.
.
-
-
.
.
-
-
.
.
.
.
.
-
A l Zn5.5MgCu
(70751
Tensile
strength
s
Al Zn5Mg3Cu
(70221
Thickness/
diameter
mm
R
AI Zn4.5Mg1
(70201
Material
DC 3 condition41
.
-
N/mm2
Free cutting alloys.
also good machinability
at high machining
o utputs, e. g. fo r
turned parts, milled parts
Parts in hydraulic,
pneumatic,
automotive and aircraft
manufacturing,
load-bearing structures in
metal manufacturing
Parts in automotive and
aircraft manufacturing,
load-bearing structures in
metal working
w
0
0.5-1.4
1.5-2.9
3.0- 5.9
-
p
z
z
T4
T4
TS
s 150
s 80
s 80
s 120
., 130
" 215
,. 60
., 65
" 160
16
15
12
W indows, doors, vehicle
superstructures, machine
beds, optical equipment
-
p
z
z
0, H111
T4
T6
s 200
s 80
,;80
s 160
"205
" 310
s 110
" 110
2: 255
14
14
10
w
0
0.5- 1.4
1.5-2.9
3.0 - 5.9
s 150
s 150
"' 150
s 85
s 85
s 85
14
16
18
Hardware, parts in mold
making and manufacturing
of jigs and fixtures,
machine beds, equipment
in the food industry
p
z
TS
TS
s 50
s 80
., 350
a, 350
" 290
a, 280
10
10
w
0
0.5 - 1.4
1.5- 2.9
3.0- 5.9
"' 220
"' 220
s 220
,; 140
"' 140
s 140
12
13
15
p
z
TS, T6510
TS
s80
,;80
,: 490
a,460
,: 420
"380
7
8
w
TS
3.0- 12
12.5-24
25- 50
2: 450
., 450
.,450
" 370
., 370
2: 370
8
8
7
p
z
z
0, H111
TS
T73
,. 200
,. 80
s 80
s 275
" 540
., 455
s 165
., 485
., 385
10
7
10
w
0
0.4-0.75
0.8-1.45
1.5-2.9
"275
" 275
" 275
" 145
" 145
" 145
10
10
10
.
-
.
-
.
-
.
Parts in automotive and aircraft manufacturing,
machine beds,
superstructures of rail cars
Parts in hydraulic,
pneumatic and aircraft
manufacturing,
screws
Parts in automotive
and aircraft manufacturing,
mold making and
manufacturing of jigs and
fixtures, screws
11 For simplificat ion all designations and material numbers are written without the addition "EN AW-•.
21 Delivery forms: R round bar; S
sheet, st rip
DC Delivery condition: p extr uded; z drawn; w cold-rolled
41 Material condition, see page 165
31
168
Material science: 4.8 Light alloys
Aluminum casting alloys
Designation of aluminum castings
cf. DIN EN 1780-1 ... 3 (2003-01), DIN EN 1706 (1998-06)
Aluminum castings are identified by designations or material numbers.
Designation
examples:
Designation
EN AC - Al Mg5KF
Material number
EN AC - 51300KF
--T
-r
I
EN
AC
I
I
K - casting method
European standard
Aluminum casting
F - material condition
(table below)
I
K - casting met hod
F - material condition
(table below)
I
I
I
I
Qiernical composition
Alloy groups
Type number
Example
Alloy percentage
No.
Group
No.
Group
A1Mg5
AISi6Cu
5%Mg
6% Si, additions of Cu
21
41
AICu
AISiMgli
46
47
AISi9Cu
AISi(Cu)
AICu4Mgli
4% Cu, additions of
Mg and Ti
42
44
AISi7Mg
AISi
51
71
AIMg
AIZnMg
Casting method
Material condition
Letter
Letter
Casting method
F
s
K
D
L
Sand casting
Permanent mold
casting
Die casting
Investment casting
Within one alloy g roup each
type has its own number.
Meaning
0
Casting condition, without subsequent processing
Spheroidized
T1
T4
Controlled cooling after pouring, naturally aged
Solution annealed and naturally aged
TS
T6
Contro lled cooling after pouring, artificially aged
Solution annealed and artificially aged
Aluminum casting alloys
cf. DIN EN 1706 (1998-06)
Strength values in casting condition (F)
Designation
(materialnumber)11
c21
HB
s
AC-A1Mg3
(AC-51000)
K
AC-AIMg5
(AC-51300)
K
AC-AIMg5(Si)
(AC-51400)
K
AC-AISi12
(AC-44100)
AC-AISi7Mg
(AC-42000)
AC-AISi12(Cu)
(AC-47000)
AC-AICu4Ti
(AC-21100)
Hardn. Tensile
M31 strength strength
s
s
s
K
L
s
K
L
s
K
s
K
Rm
Yield
Elongatio n
at fracture
Rpo.2
EL
N/mm 2
N/mm2
Properties•>
%
C
p
M
Application
Corrosion resistant,
F
F
50
50
140
150
70
70
3
5
-
-
• polishable,
F
F
55
60
160
180
90
100
3
4
-
-
•
F
F
60
65
160
180
100
110
3
3
-
-
•
F
F
F
50
55
60
150
170
160
70
80
80
4
5
1
• •
0
T6
T6
T6
75
90
75
220
260
240
180
220
190
2
1
1
0
•
0
F
F
50
55
150
170
80
90
1
2
• •
-
T6
T6
95
95
300
330
200
220
3
7
-
ibration and high temp.
• vresistance;
simple castings
anodized for decorative
purposes; fittings,
household appliances,
ship building,
chemical i ndustry
Resistant to weather
influences, for complex,
thin-walled and pressuret ight parts;
pump and motor housings,
cylinder heads, parts in aircraft manufact uring
Highest strength values.
-
11 For simplification all designations and material numbers are written without "EN".
e.g. AC-AIMg3 instead of EN AC-AIMg3 or AC-51000 instead of EN AC-51000.
31 M material condition (table above)
21 C casting method (table above)
41 C castability, P pressure tig htness, M machinability; • very good, o good, - conditionally good
169
Material science: 4.8 Light alloys
Aluminum profiles - Overview, Round bars, Flat bars
Aluminum sections, Overview
Fabrication,
dimensions
Illustration
Standard
Illustration
Round bars
Standard
seamless extruded
d= 20- 250 mm
DINEN
755-7
cold-drawn seamless
d = 3- 270mm
DINEN
754-7
extruded
a = 15- l OOmm
DINEN
754-4
extruded seamless
a = 15- 250 mm
b = 10- 100 mm
DIN EN
755-7
cold-drawn seamless
a = 15- 250mm
b= 10-100 mm
DIN EN
754-7
sharp corners or
round corners
h = 10- 200 mm
DIN
177111
sharp corners or
round corners
h = 15- 100 mm
DIN
9714 11
Round tubes
OJ
DJ
extruded
d = 3 - 100mm
DIN EN
755-3
drawn
d=8- 320mm
DIN EN
754-3
extruded
S= 10-220 mm
DIN EN
755-4
d rawn
s = 3- 100 mm
DIN EN
754-4
a[
Square tubes
Square bars
DI]
Rat bars
Rat tubes
634
extruded
W= 10-600mm
s=2-240 mm
DINEN
755-4
drawn
w=5-200mm
s = 2-60 mm
DINEN
754-4
,~1~1
Sheet and strip
L profiles
~
rolled
S= 0.4-15 mm
□
DINEN
485
Channels
Tees
□
sharp corners or
round corners
h= 10- 160mm
TI
DIN
971311
11 Standards were withdrawn without replacement.
cf. DIN EN 754-3, 754-4 (1996--011, DIN 179811, DIN 179611
Round bars, Rat bars, drawn
s
Fabrication,
dimensions
s
cross•sectional area
m' linear mass
density
W axial section modulus
I axial moment
of inertia
"'·
tfl
"'·
xm,._,+·
a
d,a
mm
I x= Iv
cm4
Wx= Wv
cm 3
kg/m
0
□
0
□
0
□
0
□
10
12
16
0.79
1.13
2.01
1.00
1.44
2.56
0.21
0.31
0.54
0.27
0.39
0.69
0.10
0.17
0.40
0.17
0.29
0.68
0.05
0.10
0.32
0.08
0.17
0.55
20
25
30
3.14
4.91
7.07
4.00
6.25
9.00
0.85
1.33
1.91
1.08
1.69
2.43
0.79
1.53
2.65
1.33
2.60
4.50
0.79
1.77
3.98
1.33
3.26
6.75
35
40
45
9.62
12.57
15.90
12.25
16.00
20.25
2.60
3.40
4.30
3.31
4.32
5.47
4.21
6.28
8.95
7.15
10.68
15.19
7.37
12.57
20.13
12.51
21.33
34.17
50
55
60
19.64
23.76
28.27
25.00
30.25
36.00
5.30
6.42
7.63
6.75
8.17
9.72
12.28
16.33
21.21
20.83
27.73
36.00
30.69
44.98
63.62
52.08
76.26
108.00
Materials
!
m'
cm2
Wrought aluminum alloys, see pages 166 and 167.
11 DIN 1796 und DIN 1798 were replaced by DIN EN 754-3 or DIN EN 754-4. The
DIN EN standards contain no dimensions. However, dealers continue to offer DIN
1798 and DIN 1796 round and square bars.
O round bars; □ square bars
170
Material science: 4.8 Light alloys
Flat bars from aluminum alloys
cf. DIN EN 754-5 (1996-01), replaces DIN 176911
Rat bars, drawn (selection)
s cross-sectional area
wxh
s
m'
e,.
e.,
Wx
Ix
Wv
Iv
m' linear mass
density
e distance to edge
W axial section modulus
I axial moment
of inertia
mm
cm2
kg/m
cm
cm
cm 3
cm4
cm 3
cm4
10 X3
10 X 6
10 X8
0.30
0.60
0.80
0.08
0.16
0.22
0.15
0.3
0.4
0.5
0.5
0.5
0.0,5
0.060
0.106
0.0007
0.0,8
0.042
0.033
0.100
0.133
0.0,6
0.050
0.066
15 X3
15 X 5
15X 8
0.45
0.75
1.20
0.12
0.24
0.32
0.15
0.25
0.4
0.75
0.75
0.75
0.022
0.090
0.230
0.003
0.027
0.064
0. 112
0.225
0.300
0.084
0.168
0.225
20 X 5
20 X 8
20 X 10
1.00
1.60
2.00
0.27
0.43
0.54
0.25
0.4
0.5
1.0
1.0
1.0
0.083
0.213
0.333
0.020
0.085
0.166
0.333
0.533
0.666
0.333
0.533
0.666
2Qx 15
25x 5
25 X 8
3.00
1.25
2.00
0.8 1
0.34
0.54
0.75
0.25
0.4
1.0
1.25
1.25
0.750
0.104
0.266
0.562
0.026
0.106
1.000
0.520
0.833
1.000
0.651
1.041
25 X 10
25 X 15
25 X 20
2.50
3.75
5.00
0.67
1.01
1.35
0.5
0.75
1.0
1.25
1.25
1.25
0.416
0.937
1.666
0.208
0.703
1.666
1.041
1.562
2.083
1.302
1.953
2.604
30 X 10
30 X 15
3Q X 20
3.00
4.50
6.00
0.81
1.22
1.62
0.5
0.75
1.0
1.5
1.5
1.5
0.500
1.125
2.000
0.250
0.843
2.000
1.500
2.250
3.000
2.250
3.375
4.500
40 X 10
4Q X 15
4Q X 20
4.00
6.00
8.00
1.08
1.62
2.16
0.5
0.75
1.0
2.0
2.0
2.0
0.666
1.500
2.666
0.333
1.125
2.666
2.666
4.000
5.333
5.333
8.000
10.666
40 X 25
40 X3Q
40 X35
10.00
12.00
14.00
2.70
3.24
3.78
1.25
1.5
1.75
2.0
2.0
2.0
4.166
6.000
8. 166
5.208
9.000
14.29 1
6.666
8.000
9.333
13.333
16.000
18.666
50 X 10
50 X 15
50 X 20
5.00
7.50
10.00
1.35
2.03
2.70
0.5
0.75
1.0
2.5
2.5
2.5
0.833
1.875
3.333
0.416
1.406
3.333
4.166
6.250
8.333
10.416
15.625
20.833
50 X 25
50 X30
50 X 35
12.50
15.00
17.50
3.37
4.05
4.73
1.25
1.5
1.75
2.5
2.5
2.5
5.208
7.500
10.208
6.510
11.250
17.864
10.416
12.500
14.583
26.041
31.250
36.458
50 X40
60 X 1Q
60 X 15
20.00
6.00
9.00
5.40
1.62
2.43
2.0
0.5
0.75
2.5
3.0
3.0
13.333
1.000
2.250
26.666
0.500
1.687
16.666
6.000
9.000
4 1.668
18.000
27.000
60 x 20
60 X25
60 X 30
12.00
15.00
18.00
3.24
4.05
4.86
1.0
1.25
1.5
3.0
3.0
3.0
4.000
6.250
9.000
4.000
7.812
13.500
12.000
15.000
18.000
36.000
45.000
54.000
60 X 35
60X 4Q
so x 10
21.00
24.00
8.00
5.67
6.48
2.16
1.75
2.0
0.5
3.0
3.0
4.0
12.250
16.000
1.333
21.437
32.000
0.666
21 .000
24.000
10.666
63.000
72.000
42.666
Box 15
80 X 20
80 X 25
12.00
16.00
20.00
3.24
4.52
5.40
0.75
1.0
1.25
4.0
4.0
4.0
3.000
5.433
8.333
2.250
5.333
10.416
16.000
21.333
26.666
64.000
85.333
106.66
8Q X 3Q
80 X 35
8Q X 40
24.00
28.00
32.00
6.48
7.56
8.64
1.5
1.75
2.0
4.0
4.0
4.0
12.000
16.333
21.333
18.000
28.583
42.666
32.000
37.333
42.666
128.00
149.33
170.66
100 X 20
100 X30
100 X40
20.00
30.00
40.00
5.40
8.10
10.8
1.0
1.5
2.0
5.0
5.0
5.0
6.666
15.000
26.666
3.666
22.500
53.333
33.333
50.000
66.666
166.66
250.00
333.33
~1
(
"'·
,.., ,.. !
x_ '""" .....
...
!
,tJ.
""'
~
"'
Edge radii r
h
mm
mm
,; 10
0.6
> 10-30
1.0
> 30- 60
2.0
fmax
Material Wrought aluminum alloys, see pages 166 and 167.
11 DIN EN 754-5 cont ains no dimensions. Specialized dealers still offer flat bars in dimen-
sions according to DIN 1769.
171
M at erial science: 4.8 Light alloys
Round tubes, Channels from aluminum alloys
cf. DIN EN 754-7 (1998-101. replaces DIN 179511
Round tubes, cold-drawn seamless (selection)
outside diameter
wall thickness
d
s
s
cross-sectional
area
m' linear mass
density •
W axial section
modulus
I axial moment
of inertia
x.$.\_ -+ -
X
'
-
.!.. _
d
cm3
Ix
cm•
s
cm2
m'
kg/m
dxs
mm
mm
cm2
m'
kg/m
Wx
cm3
Ix
cm•
10 X 1
1o x 1.5
,o x 2
0.281
0.401
0.503
0.076
0.108
0.136
0.058
0.075
0.085
0.029
0.037
0.043
35 x 3
35 X 5
35 X 10
3.016
4.712
7.854
0.814
1.272
2.121
2.225
3.114
4.067
3.894
5.449
7.118
12 X 1
12 X 1.5
12 X 2
0.346
0.495
0.628
0.093
0.134
0.170
0.088
0.116
0.136
0.053
0.070
0.082
40 x 3
40 X 5
4Q X 10
3.487
5.498
9.425
0.942
1.484
2.545
3.003
4.295
5.890
6.007
8.590
11.781
16 X 1
16 X 2
16 X 3
0.471
0.880
1.225
0.127
0.238
0.331
0.133
0.220
0.273
0.133
0.220
0.273
50 x3
50 X 5
50 X 10
4.430
7.069
12.566
1. 196
1.909
3.393
4.912
7.245
10.681
12.281
18.113
26.704
20 X 1.5
20 X 3
20 X 5
0.872
1.602
2.356
0.235
0.433
0.636
0.375
0.597
0.736
0.375
0.597
0.736
55 X 3
55 X 5
55 X 10
4.901
7.854
14.137
1.323
2.1 10
3.817
6.044
9.014
13.655
16.201
24.789
37.552
25 X 2
25 X 3
25 X 5
1.445
2.073
3.142
0.390
0.560
0.848
0.770
1.022
1.335
0.963
1.278
1.669
60 X 5
60 X 10
6Q X 16
8.639
15.708
22.117
2.333
4.241
4.890
10.979
17.017
20.200
32.938
51.051
60.600
30 X 2
3Q X 4
30 X 6
1.759
3.267
4.524
0.475
0.882
1.220
1.155
1.884
2.307
1.733
2.826
3.461
70 X 5
70 X 10
70 X 16
10.210
18.850
27.143
2.757
5.089
7.331
15.498 54.242
24.908 87.179
30.750 107.62
Material
e.g. aluminum alloys. non-heat t reatable, see page 166
aluminum alloys, heat-treatable. see page 167
s
dxs
Wx
11 DIN EN 754-7 contains no dimensions. Specialized dealers still offer round tubes in dimensio ns accord ing to DIN 1795.
Extruded channel sections (selectio n)
cf. DIN 9713 (1981-09)11
hxwxs x t
s
mm
cm2
m'
kg/m
Bx
cm
cm
Wx
cm3
Ix
cm4
cm 3
ly
cm4
2ox2ox3x3
3Qx30 x 3x3
35x 35x3x3
1.62
2.52
2.97
0.437
0.687
0.802
1.00
1.50
1.75
0.780
1.10
1.28
0.945
2.43
3.44
0.945
3.64
6.02
0.805
2.06
2.91
0.628
2.29
3.73
modulus
axial moment
of inertia
4o x 15 x 3x3
40 X 20 X 3X 3
4Qx3Qx3x3
1.92
2.25
2.85
0.518
0.608
0.770
2.0
2.0
2.0
0.431
0.610
3.62
2.04
2.59
7.24
4.07
5.17
2.49
0.810
1.30
2.49
0.349
0.795
2.52
e/ i' ~l
4Q X 30X4 X 4
4Q X 4QX 4 X4
4ox4ox5x5
3.71
4.51
5.57
1.00
1.22
1.50
2.0
2.0
2.0
1.05
1.49
1.52
4.49
5.80
6.80
8.97
11.6
13.6
3.03
4.80
5.64
3.17
7.12
8.59
5o x 3o x3x3
5QX30X4X4
50 x 4ox5x5
3.15
4.91
6.07
0.851
1.33
1.64
2.5
2.5
2.5
0.929
1.38
1.42
4.88
7.83
9.32
12.2
19.6
23.3
2.91
5.65
6.54
2.70
7.80
9.26
60 X 30 X 4 X 4
60X4Q X 4X4
60X40X5 X 5
4.51
5.31
6.57
1.22
1.43
1.77
3.0
3.0
3.0
0.896
1.29
1.33
7.90
10.1
12.0
23.7
30.3
36.0
4.12
6.35
7.47
3.69
8.20
9.94
"' w
8QX 4Q X 6 x 6
80 X 45 x 6 x8
100 X 40 X 6 X 6
8.95
11.2
10.1
2.42
3.02
2.74
4.0
4.0
5.0
1.22
1.57
1.11
20.6
27.1
28.3
82.4
108
142
10.6
13.9
12.5
20.6
21.8
13.8
Rounded edges ,, and ,,
100 X 50 X 6 X 9
120 X 55 X 7 X 9
140 X 60 X 4 X 6
14.1
17.2
12.35
3.80
4.64
3.35
5.0
6.0
7.0
1.72
1.74
1.83
43.4
61.9
56.4
217
295
350
19.9
28.2
24.7
34.3
49.1
45.2
w w idth
h
height
s
cross-sectional
area
m ' linear mass
density
w axial section
I
-
I
s
X
.:
+
t
y
-
x -<::
o/
I
t
r,
'2
mm
mm
mm
3. 4
2.5
0.4
5, 6
4
0.6
8, 9
6
0.6
Mat erials
6v
Wv
AIMgSi0.5; AIMgSi1; AIZn4.5Mg1
11 DIN 9713 was wit hdrawn w ithout replacement. Specialized dealers still offer channels
according to this standard .
172
M ateri al science: 4.8 Light alloys
Magnesium alloys, Titanium, Titanium alloys
Wrought magnesium alloys (select ion)
Designation
Materialnumber
Delivery
form"
B
M gMn2
MgAl3Zn
3.3520
3.5312
MgAl6Zn
3.5612
MgAl8Zn
3.5812
T
M 2I
Bardiameter
mm
F20
F24
,;80
s 80
200
240
F27
" 80
270
195
10
Higher strength, limited weldability; lightweight material
F29
F31
,; 80
,; 80
290
310
205
215
10
6
in automotive, machine and
aircraft manufacturing
D
...
...
.• •
cf. DIN 9715 (1982-08)
Yield
Elong. at
Tensile
strength strenglh fracture Properties.
EL
application
Rm
Rpo.2
N/mm2 N/mm2
%
145
155
Corrosion resistant,
15
10
weldable, cold wori<able;
cladding, containers
11 Delivery forms: B bars, e.g . round bars; T tubes; D stamped part
21 M material condition F20 - Rm = 10 • 20 = 200 N/mm 2
Magnesium casting alloys (selection)
Designation 11
Mat eMaterial- M2I rial- Hardness
11
condiHB
nu mber
t ion3I
MCMgAl8Zn1 MC21110
.
MCMgAl9Zn1
MC21120
MCMgAl6Mn
MCMgAl7Mn
MCMgAl4Si
MC21230
MC21240
MC21320
cf. DIN EN 1753 ( 1997-08)
Tensile
strengt h
Elong. at
fracture
N/mm 2
Yield
strength
Rpo.2
N/mm2
Rm
EL
Properties,
application
%
s
F
T6
50- 65
50- 65
160
240
90
90
2
8
K
K
D
F
T4
F
50- 65
50- 65
60- 85
160
160
200- 250
90
90
140- 160
2
8
,. 7
s
F
T6
55- 70
60- 90
160
240
90
150
6
2
High-strength,
good slid ing properties,
weldable;
K
K
D
F
T6
F
55- 70
60- 90
65- 85
160
240
200- 260
110
150
140- 170
2
2
1- 6
automotive and aircraft
manufacturing,
armatures
D
D
D
F
F
F
55- 70
60- 75
55- 80
190- 250
200- 260
200- 250
120- 150
130- 160
120- 150
4 - 14
3 - 10
3 - 12
Fatigue resistant, dynamically loadable, high tem-
Very good castability,
dynamically loadable,
w eldable;
gear and motor
housings
perature resistant, gear
and motor housings
11 For simplification, designations and material numbers are written without the "EN-" prefix,
e. g. MCMgAIBZn1 instead of EN-MCMgAl8Zn 1.
21 M casting method: S sand casting; K permanent mold casting; D die casting
31 Material condition, see designation of aluminu m casting alloys, page 168
Titanium, titanium alloys (selection)
Designation
Material-
Delivery
form 1l
number
s
Ti l
Ti2
Ti3
3.7025
3.7035
3.7055
Ti1Pd
Ti2Pd
3.7225
3.7235
TiAl6V6Sn2
3.7175
TiAl6V4
3.7165
TiAl4Mo4Sn2
3.7185
B
T
cf. DIN 17860 (1990-11)
Sheet
Hardthickness
ness
s
HB
mm
Tensilestrengt h
Rm
N/mm2
Yield
Elong. at
strength fracture Properties,
EL
application
Rpo,2
N/mm2
%
• • •
0.4- 35
...
120
150
170
290- 410
390- 540
460- 590
180
250
320
30
22
18
0.4 - 35
...
120
150
290- 410
390- 540
180
250
30
22
<6
6- 50
320
320
;,, 1070
"' 1000
1000
950
10
8
in machine construction,
e lectrical engineering,
precision engineering,
• • •
<6
6 - 100
310
310
;,, 920
a. 900
870
830
8
8
6 - 65
350
a. 1050
1050
9
optics and medical technology, chemical indust ry, food indust ry, aircraft manufacturing
...
11 Delivery forms: S sheet and strip; B bars, e.g . round bars; T tubes
Weldable, solderable,
g lueable, machinable,
cold and hot workable,
fatigue resistant,
corrosion resistant;
weight saving designs
Material science: 4.9 Heavy non-ferrous metals
173
Overview of the heavy non-ferrous metals
Heavy non-ferrous metals have a density I!> 5 kg/ dm3 . However. in t echnical literature e., 4.5 kg/dm 3 is also used
as limit for non.ferrous m etals.
Construct ion materials in m achine and plant construct ion: copper, tin, zinc, nickel, lead and their alloys
• Met als used for alloys: chromium , vanadium, cobalt lfor effects of alloying metals, see page 129)
• Precious metals: gold, silver, platinum
Pure metals: Homogeneous structure; low strengths, lesser importance as a construction material; usually used
based o n materi al typical properties, e.g. good electri cal conductivity.
Heavy non-ferrous m etal alloys: Im proved properties compared to base metals, such as higher strength, higher hardness, better m achinability and corrosion resistance, construct ion m at erials for various application. Classified according to manufacture into wrought alloys and casting alloys.
Overview of common heavy non-ferrous metals and alloys
Metal, alloy
group
Main characteristics
Application examples
Copper (Cu)
High electrical conductiv ity and thermal conductivity, inhibits bacteria, viruses and molds, corrosion resistant, good appearance, easily recyclable
Pipes in heating and plumbing eq uipment,
cooling and heating coils, electrical wiring,
electrical parts, cookware, building facades
CuZn
(brass)
Wear-resistant, corrosion-resistant, good hot
and co ld workability, good machinability, polishable, shiny golden, medium strengths
• Wrought alloys: deep-drawn parts, screws,
sp rings, pipes, instrument parts
• Casting alloys: armature housings,
plain bearings, precision mechanical parts
CuZnPb
Very good machinability, lim ited cold workability, Automatic screw machine parts, precision
very good hot workability
mechanical parts, fittings, hot-pressed parts
CuZn
mult i-alloy
Good hot workability, hig h strengths,
wear-resistant, weather-resistant
A rmat ure housings, plain bearings, flanges,
valve parts, water housings
CuSn
(bronze)
Very corrosion-resistant, good sliding properties,
good wear-resistance, strengt h result ing from
cold working is highly variable
• Wrought alloys: hardware, screws,
springs, metal hoses
• Casting alloys: spi nd le nuts,
w o rm gears, solid plain bearings
CuAI
High strength and toughness, very corrosion
resistant, salt water resistant, heat resistant,
highly cavitat ion resistant
Cu Ni(Zn)
Extremely corrosion resistant, silvery
appearance, good machinability, polishable,
cold workable
Wrought alloys: highly stressed lock
nuts, ratchet wheels
Casting alloys: armatures in the chemical
industry, pump bodies, propellers
Coins, electrical resist ors,
heat exchangers, pumps, valves in
salt water cooling systems, ship building
Zinc (Zn)
Resistant t o atmospheric corrosion
Corrosion protect io n of steel parts
Znli
Good workability, joinable by soft soldering
Roofi ng, gutters, downspout s
ZnAICu
Very good castability
Thin walled, fi nely articulated die castings
Tin (Sn)
Good chemical resistance, non-toxic
Coating of steel sheet
SnPb
Low viscosity
Soft solder
SnSb
Good d ry running properties
Small, dimensionally precise die castings,
plain bearings wit h average loading
Nickel (Ni)
Corrosion resist ant, high temperature resistant
Corrosion protection layer on steel parts
NiCu
Extremely corrosion resistant and high t emp. resist. Equipment. condensers, heat exchangers
NiCr
Extremely corrosion resistant and very high temper- Chemical installat ions, heating t ubes,
ature resistant and non scaling, e.g. age hardenable boiler internals in power plants, gas turbines
Lead (Pb)
Shields against x-ray and gamma rays, corrosion Shielding, cable sheathing,
resistant, toxic
tubes fo r chemical equipment
PbSn
Low viscosity, soft, good dry running properties
Soft solder, sliding sheat hs
PbSbSn
Low viscosity, corrosion resistant, good running
and slid ing properties (low friction)
plain bearings, small, dimensionally precise die
castings such as pendulums, parts for measuring
equipment. meters
174
Material science: 4.9 Heavy non-ferrous metals
Designation of heavy non-ferrous metals
Designation system (excerpt )
cf. DIN 1700 (1954-07)11
Example:
NiCu30Fe F45
GD-Sn80Sb
Manufacture, application
E
G
GC
GD
GK
GZ
L
s
i
,--i-,
Electrical material
Sand casting
Continuous casting
Die casting
Permanent mold casting
Centrifugal casting
Solder
Weld ing filler alloys
Chemical composition
Example
Comment
NiCu30Fe Ni-Cu alloy,
30% Cu, t race iron
SnB0Sb
Sn-Sb alloy, 80% Sn,
approx. 20 % Sb
11 The standard has been w ithdraw n. However the material designations are
still used in individual standards.
Designation system for copper alloys
Examples:
CuZn31Si
CuZn38Pb2
CuSTPb2
Special properties
F45 minimum tensile strength
Rm= 10 • 45 N/mm2
=450 N/mm2
a
age hardened
annealed
g
h
hard
ka
naturally aged
ku
cold worked
partially age hardened
ta
wa artificially aged
WU
hot worked
2h
drawn hard
cf. DIN EN 1982 (2008-08) and 1173 (2008-08)
-R620
Casting method
-T -~
GS Sand casting
GM Permanent mold casting
GZ Centrifugal casting GC Continuous casting
GP Die casting
L
Chemical composition
Example
Meaning
CuZn31Si
Cu alloy, 31% Zn, t race Si
CuZn38Pb2
Cu alloy 38% Zn, 2% Pb
CuSn 11Pb2
Cu alloy 11 % Sn, 2% Pb
Product form
C
B
Material in the form of castings
Material in ingot form
Wrought alloys (without code letter)
Material condition (selection)
Example
M eaning
Example
A007
D
Elongation at fracture EL = 7%
Drawn, without specified
mechanical properties
Y450
M
H160
Vickers hardness HV = 160
R620
Meaning
Yield strength R0 = 450 N/mm2
Manufactured condition, without specified
mechanical properties
Minimum tensile strength Rm= 620 N/mm'
Material numbers for copper and copper alloys
Example:
cf. DIN EN 1412 (1995-12)
CW024A
~
--T
~ 1
I
C Cast material
B Material in ingots
W Wrought material
Number between 000 and 999 without
specified meaning (sequent ial number)
I
Code letters for material groups
Lener
Material group
Lener
AorB
Copper
H
Copper-nickel alloys
Coro
Copper alloys, percentage of the
alloying element < 5%
E or F
Copper alloys, percentage of the
alloying elements" 5%
Copper-aluminum alloys
J
K
Lor M
Nor P
R ors
Copper-zinc alloys
Copper-tin alloys
Copper-zinc binary alloys
Copper-zinc-lead alloys
Copper-zinc mult i-alloys
G
Material group
Material numbers for castings of zinc alloys
cf. DIN EN 12844 (1999-01)
Z P 041 0
Example:
1z
Zinc alloy
rr l
I
IP Cast ing
I
AI content
04 " 4% aluminum
I
I
Cu content
1 " 1 % copper
Content of the next higher
alloying element
0 = next higher alloying
element < 1%
Material science: 4.9 Heavy non-f errous metals
175
Copper alloys
Wrought copper alloys
Designation,
Material
number11
Bars
c•I
031
mm
Tensile
Yield
Elong. at
Hardness strength strength fracture Properties,
HB
EL
application examples
R,,,
"i,0.2
N/mm2 N/mm2
%
Copper-zinc alloys
CuZn28
(CW504LI
CuZn37
(CW508L)
CuZn40
(CW509l)
cf. DIN EN 12163 (1998-04)
R310
R460
4-80
4- 10
-
310
460
120
420
H085
H145
4- 80
4- 10
85- 115
2: 145
-
-
R310
R440
2- 80
2- 10
-
310
440
120
400
30
H070
H140
4- 80
4- 10
70- 100
2: 140
-
-
-
-
R340
HOBO
2- 80
-
340
260
25
-
-
2: 80
-
27
-
Copper-zinc alloys (multi-alloys)
CuZn31Si
(CW708RI
CuZn38Mn1AI
(CW716R)
CuZn40Mn2Fe1
(CW723R)
5-40
5- 14
-
460
530
250
330
22
12
H115
H140
5-40
5- 14
115-145
2: 140
-
-
-
R490
R550
5- 40
5-14
-
490
550
210
280
18
10
H120
H150
5- 40
5-14
120- 150
2: 150
-
-
-
R460
R540
5- 40
5- 14
-
460
540
270
320
20
8
H110
H150
5-40
5-14
110-140
2: 150
-
-
-
160
450
20
CuZn36Pb3
(CW603N)
40- 80
2- 4
90
150
340
550
CuZn38Pb2
(CW608N)
R360
R550
40-80
2- 6
90
150
360
550
150
420
25
CuZn40Pb2
(CW617NI
R360
R550
40- 80
2- 4
90
150
360
550
150
420
20
R340
R550
2- 60
2-6
-
-
340
550
230
500
45
H085
H180
2-60
2-6
85-115
2: 180
-
-
R390
R620
2- 60
2- 6
-
-
390
620
260
550
H090
H185
2- 60
2- 6
90- 120
2: 185
-
-
R390
R620
2- 60
2- 6
-
390
620
260
550
H090
H185
2- 60
2- 6
90- 120
2: 185
-
-
-
Copper-tin alloys
CuSn8P
(CW459K)
Very good hot workability,
machinable; rivets, screws
Good cold workability; hot workable,
machinable, good sliding properties;
sliding parts, bearing bushings,
guides
Good hot workability, cold
workable, machinable, sliding
properties, weather resistant;
sliding elements, guides
Good hot workability, cold workable,
machinable, average strength,
weather resistant;
equipment manufacturing,
architecture
cf. DIN EN 12164 (2000-09)
R340
R550
CuSn8
(CW453K)
Very good cold workability, good
hot workability, machinable,
very easily polished; deep-drawn
parts, screws, springs, press rollers
cf. DIN EN 12163 (1998-04)
R460
R530
Copper-zinc-lead alloys
CuSn6
(CW452K)
Very good cold workability, good
hot workability, machinable,
very easily polished;
instrument parts, bushings
Excellent machinability, limited cold
workability; automatic lathe parts
Excellent machinability, good cold and
hot workability; screw machine parts
Excellent machinability, good hot
workability; stamping blanks, gears
cf. DIN EN 12 163 ( 1998-04)
-
-
-
45
45
-
High chemical resistance,
good strength;
springs, metal hoses, pipes and
bushings for suspension bodies
High chemical resistance,
high-strength, good sliding
properties; plain bearings, rolled bearing bushings, contact springs
Excellent sliding properties, high
wear-resistance, endurance strength;
highly stressed plain bearings in automotive and machine manufacturing
11 Materi al numbers according to DIN EN 1412, see page 174.
2 1 C Material condition according to DIN EN 1173, see page 174. In manufactured condition Mall alloys can be deliv-
ered up to diameter D = 80 mm.
3 1 O Diameter for round bars, width across flats for square bars and hexagonal bars, thickness for flat bars.
176
Material science: 4.9 Heavy non-ferrous metals
Copper and refined zinc alloys
Designation,
Material
Bars
c21
number11
031
mm
Tensile
Yield
Hardness strength strength
HB
R,,,
1\,0.2
CuAl10Fe3Mn2
(CW306GI
CuAl10Ni5Fe4
(CW307G)
EL
"'
590
690
330
510
12
6
Corrosion-resistant, wear-resistant,
resistant; screws, shafts, gears, worm
gears, valve seats
nonscaling, fatigue resistant, high tern-
CuNi18Zn20
(CW409J)
cf. DIN EN 12163 ( 1998-041
fatigue-resist ant, high-temperature
H140
H170
10- 80
10- 50
140- 180
"' 170
-
-
-
A680
A740
10- 80
-
680
740
480
530
10
8
H170
H200
10- 80
170-210
"' 200
-
-
-
perature resistant; capacitor bases,
-
-
control parts for hydraulics
-
Copper-nickel-zinc alloys
CuNi12Zn24
(CW430JI
Properties,
application examples
N/mm2
-
10- 80
10-50
fracture
N/mm2
Copper-aluminum alloys
A590
A690
Elong. at
Corrosion resistant, wear-resistant,
cf. DIN EN 12 163 (1998-041
A380
A640
2-50
2-4
-
380
640
270
550
38
H090
H190
2- 50
2- 4
90- 130
"' 190
-
-
-
A400
A650
2- 50
2- 4
-
-
400
650
280
580
35
H100
H200
2- 50
2- 4
100- 140
"' 200
-
-
-
-
Extremely good cold workability,
machinable, easily polished;
deep-drawn parts, flatware, applied
arts, architecture, spring contacts
Good cold workability, machinable,
non-tarnishing, easily polished;
membranes, spring contacts,
flatware
11 Material numbers according to DIN EN 1412, see page 174. 21C Material condition according to DIN EN 1173, see page 174
31 D Diameter for round bars, width across flats for flat bars and hexagonal bars, thickness for flat bars.
Cast copper alloys
cf. DIN EN 1982 (1998-12)
Tensile
Designation,
Material numberII
strength
R,,,
N/mm2
Eking. at
Yield strength
fracture
'\,o..z
A
N/mm2
Hardness Properties, application
HB
%
CuZn15As-C
(CC760S)
160
70
20
45
Excellent soft and hard solderability,
salt water resistant; flanges
CuZn32Pb2-C
(CC750S)
180
70
12
45
CuZn25Al5Mn4Fe-C
(CC762S)
750
450
8
180
Very high strength and hardness,
good machinability; plain bearings
CuSn12-C
(CC483K)
260
140
7
80
High wear-resistance;
spindle nuts, worm gears
CuSn11Pb2-C
(CC482K)
240
130
5
80
Wear-resistant, good dry running
properties; plain bearings
CuAl10Fe2-C
(CC331G)
500
180
18
100
Mechanically stressed parts;
levers, housings, bevel gears
CuAl10Ni3Fe2-C
(CC332G)
500
180
18
130
Corrosion stressed parts;
ar matures, propellers
CuAl10Fe5Ni5-C
(CC333G)
600
250
13
140
Strength and corrosion
stressed parts; pumps
Good machinability, resistant to industrial water up to 90°C; armatures
1) Material numbers according to DIN EN 1412, see page 174. More cast Cu alloys for plain bearings, see page 261.
Strength values apply t o separately sand-cast test specimens.
High-grade cast zinc alloys
cf. DIN EN 12844 (1999-011
ZP3(ZP0400)
ZP5 (ZP0410)
280
330
200
250
10
5
83
92
Very good castability; preferred alloys
for die castings
ZP2 (ZP0430)
ZP8 (ZP0810)
335
370
270
220
5
8
102
100
Good castability; very good
machinability, universally applicable
ZP12 (ZPl 110)
ZP27 (ZP2720I
400
425
300
300
5
2.5
100
120
Injection, blow, and deep-draw molds
for plastics, sheet metal working tools
177
Material science: 4.10 Other materials
Composite materials, Ceramic materials
Composite materials
Composite
material
Base
material'l
Tensile Elong. at Modulus
Fiber Density strength teer
of
elasticity
content
-
Service
tempe-
Application examples
EA
E
%
N/mm2
upto "C
365
3.5
-
-
Shafts, joints, connecting bars,
ship hulls, rotor blades
1.5
130
3.5
10800
50
Containers, tanks, pipes,
dome lights, body parts
35
1.4
1so2I
531
5000
190
Large-area, stiff housing parts,
power plugs
PC
30
1.42
9021
3_531
6000
145
Housings for printers, computers,
televisions
PPS
30
1.56
140
3.5
11200
260
Lamp sockets and coils
in electrical equipment
PAI
30
1.56
205
7
11700
280
Bearings, valve seat rings,
seals, piston rings
PEEK
30
1.44
155
2.2
10300
315
light construction materials in
aerospace applications, metal
substitute
CFRP
PPS
30
1.45
190
2.5
17 150
260
Like FRP-PPS
(Carbon
fiber
reinforced
plastic)
PAI
30
1.42
205
6
11 700
180
Like FRP-PAI
PEEK
30
1.44
210
1.3
13000
315
Like FRP-PEEK
{!
oa
%
g/cm3
N/mm2
EP
60
-
UP
35
PASS
FRP
(Fiberglass
reinforced
plastic)
1l EP epoxide
PPS polyphenylene sulfide
UP unsaturated polyester
PAI polyamideimide
21 ay yield stress
31 ts elongation at yield stress
PASS polyamide 66, semi-crystalline
PEEK polyetheretherketone
PC polycarbonate
Ceramic materials
Rexiwal Modulus Coefficient
of
of linear
Material
Density strength
elasticity expansion Properties, application examples
E
a
Oesignation
g/cm3
C130
2.5
160
100000
0.000005
Hard, wear-resistant, chemical and heat resistant,
high insulating resistance;
insulators, catalytic converters, refractory housings
C799
3.7
300
300000
0.000007
Hard, wear-resistant, chemical and heat
resistant;
ceramic inserts, wire drawing dies, biomedicine
Zirconium
oxide
ZrO2
5.5
800
210000
0.000010
High stability, high strength, heat and chemical
resistant, wear-resistant;
drawing dies, ex1rusion d ies
Sil icon
carbide
SiC
3.1
600
440000
0.000005
Hard, wear-resistant, thermal-shock resistance,
corrosion-resistant even at high temperatures;
abrasives, valves, bearings, combustion chambers
Silicon
nitride
Si3N4
3.2
900
330000
0.000004
High stability, thermal-shock resistance,
high strength; cutting ceramics, guide and runner
blades for gas t urbines
Aluminum
nitride
AIN
3.0
200
300000
0.000005
High thermal conductivity, high electrical
insulation property;
semiconductors, housings, heatsinks, insulating parts
Name
Aluminum
silicate
ll
Ob
N/mm2 N/mm2
1/K
Alu-
minum
oxide
178
Material science: 4.10 Other materials
Sintered metals
Designation system for sintered metals
Designation example:
cf. DIN 30910-1 (1990-101
Sint - A 1 0 sintered smooth
J~
ISintered metal I
I
Code letters for material class
2. 2nd number for further differentiation
without systematics
1. 1st number for chemical composition
Code letter
Volume ratio
R""in %
AF
< 73
A
75 ± 2.5
plain bearings
B
80 ± 2.5
Formed parts with
Number Chemical composition
Area of application
mass fraction in %
Filter
plain bearings
0
1
2
Sintered iron, sint. steel, Cu < 1 % w ith or without C
Sintered steel, 1% to 5% Cu, with or without C
Sintered steel, Cu > 5 %, with or w ithout C
3
Sintered steel, with or without Cu or C, other
alloying elements< 6 %, e. g. Ni
4
Sintered steel, with or without Cu or C, other
alloying elements> 6%, e. g. Ni, Cr
5
Sintered alloys, Cu > 60%, e.g. sintered CuSn
6
Sintered nonferrous heavy metals, except for no. 5
Sintered light alloys, e.g. sintered aluminum
Reserved numbers
sliding properties
C
85 ± 2.5
plain bearing, formed parts
D
90 ± 2.5
Formed parts
E
94± 1.5
Formed parts
F
>95.5
Sintered forged
7
8,9
formed parts
TreatmMrt condition
Treatment condition of the material
• sintered
• calibrated
• heat treated
-:::,
Treatment condition of the surface
• steam treated
sintered forged
• isostatically pressed
sintered smooth
calibrated smooth
sized and coined smooth
Sintered metals (selection, soft m agnetic sintered m etals not inc luded)
Designation
Hanln- T_.atnngth
Chemical composition
HS_,
R,.N/mm2
-
80- 200
Sintered steel, Cr 16-19 %, Ni 10-14 %
Sint-AF 50
40-160
Sintered bronze, Sn 9 - 11 % , rem. Cu
Sinl-AF 40
Sint-A OO
>25
>60
Sintered iron, C < 0.3 %, Cu< 1%
Sint-A20
>40
> 150
Sintered steel, C < 0.3%, Cu 15- 25%
Sintered bronze, C < 0.2% , Sn 9 - 1 %, rem. Cu
Sint-A50
>25
> 70
Sint-A51
> 18
>60
Sintered bronze, C 0.2-2% , Sn 9-11 %, rem. Cu
Sint-800
> 30
>80
Sintered iron, C < 0.3 %, Cu < 1 %
Sint-B 10
>40
> 150
Sintered steel, C < 0.3%, Cu 1- 5 %
Sint-850
>30
>90
Sint-C 00
>45
> 150
Sintered bronze, C < 0.2%, Sn 9- 11 %, rem. Cu
Sintered iron, C < 0.3 %, Cu < 1 %
Sint-C 10
>60
>200
Sintered steel, C < 0.3 %, Cu 1- 1,5 %
Sinl-C40
> 100
>300
Sintered steel, Cr 16-19%, Ni 10- 14 %, Mo 2 %
Sint·C 50
>35
>140
Sintered bronze, C < 0.2%, Sn 9 - 11 %, rem. Cu
Sint-D 00
>50
>250
Sintered iron, C < 0.3%, Cu < 1 %
Sint-D 10
>80
>300
Sintered steel, C < 0.3 %, Cu 1- 5 %
Sint·D 30
> 11 0
>550
Sintered steel, C < 0.3 %, Cu 1- 5 %, Ni 1- 5 %
Sint-D 40
> 100
>450
Sintered steel, Cr 16- 19 %, Ni 10- 14%, Mo 2 %
Sint·E 00
Sint-E 10
> 60
>200
> 100
>350
Sintered iron, C < 0.3 %, Cu < 1%
Sintered steel, C < 0.3%, Cu 1-5%
machined
surface treated
cf. DIN 30910-2-6 (1990-10)
Properties,
application examples
Filter parts for gas and
liquid filters
Bearing materials w ith
exceptionally large pore volume for the best emergency
running properties; bearing
liners, bearing bushings
Plain bearings w ith very
good dry running properties,
low stressed formed parts
Plain bearings, formed parts
with average stress w ith
good sliding properties; auto
parts, levers, clutch parts
Formed parts for higher
stresses; wear-resistant
pump parts, gears, some are
corrosion-resistant
Sint-E 73
>55
>200
Sintered aluminum Cu 4- 6%
Formed parts for precision
engineering, for household
appliances, for the electrical
industry
Sint-F OO
> 140
>600
Sint-F 31
>180
>nO
Sinter forged steel, containing C and Mn
Sinter forged steel, containing C, Ni, Mn, Mo
Sealing rings, flanges for
muffler systems
179
Material science: 4.11 Plastics
Overview of plastics
General
properties
Disadvantages:
Advantages:
lower strength and heat resistance in
comparison to metals
some are combustible
some are nonresistant to solvents
limited material reutilization
low density
electri cally insulating
heat and sound absorbing
decorative surface
economical forming
• weather and chemical resistance
Classification
Thermoplas1ic:s
Thermosets
Elastomers
Processing
Hot workable
Weldable
Generally glueable
Machinable
Not workable
Non-weldable
Glueable
Machinable
Not workable
Non-weldable
Glueable
Machinable at low temperatures
Fabrication
Injection molding
Injection blow molding
Extruding
Pressing
Transfer molding
Injection molding, molding
Pressing
Injection molding
Extruding
Recycling
Easily recyclable
Not recyclable,
possible reuse as filler
Not recyclable
Temperature behavior
Structure
Amorphous thermoplastica
brittle hard
t hermo-
thermo- viscous
elastic
plast,c
/"""
r~
\
of uw
o1ongation at
.!!!'~ !.--_,,,,
Filamentary macromolecules
without cross-linking
20°c
\
\
C
0
:,:
·~
r
a welding range, b hot-working; ..,
temperature T~
Semi-crystalline thermoplastic
~----1amella (crystalline)
c injection molding, edrusion
t ough
tensile siren th
range of use
C
0
hon at tra~!-
~"'l!!!---~ - - -- -.::::: amorphous
Crystalline areas have
intermediat
greater cohesive forces
layers
20°(
temperature T- - .
Filamentary thermoset plastics
= J
C
a welding range; b hot-working;
c injection molding. extrusion
hard
t ensile st ren th
range of use
--------
elongation at ~ ~ - - - - - -
Macromolecules w ith
many cross-links
20°c so·c
Filamentary elastomers
brittle
hard
temper ature T ~
rubber-elastic
t ion at fracture
--~ne---range of use
Macromolecules in random
condition with few cross-linkages
.[
o• c 20°c
temperature T _____,..
180
Material science:· 4.11 Plastics
,r.~,,-11 "" 1111:.IL.-•lll:.19-"Yolll i ■ l:.llllll••-1111
11~1r.1
Designations for basic polymers
Desi9- MMning
Type"
nation
ABS
T
AMMA Acrylonitrile-methylmethacrylate
T
ASA
Acrylonitrile-styrene--acrylate
CA
Cellulose acetate
Cellulose acetate butyrate
Cresci-formaldehyde
Carboxymethyl cellulose
T
T
T
D
CAB
CF
CMC
CN
CP
EC
EP
Ethyl cellulose
Epoxide
Polyamide
Type1
PAN
PB
PBT
Polyacrylate
Polyacrylonitrile
Polybutene
Polybutylene terephthalate
T
T
T
T
PTFE
PUR
PVAC
PVB
Polyvinyl butyral
PC
Polycarbonate
PCTFE
PE
PET
PF
Polychlorotrifluoroethylene
Polyethylene
Polyethyleneterephthalate
Phenol formaldehyde
T
T
T
T
D
PVC
PVOC
PVF
PVFM
Polyvinyl chloride
Polyvinylidene chloride
Polyvinyl fluoride
Polyvinyl formaldehyde
PVK
SAN
SB
Poly-N-vinylcarbazole
D
Ethylene-vinyl acetate
Melamine formaldehyde
MF
PA
Type" Desi9- Meaning
nation
MNM
MNM PIB
Polyisobutene
T
PMMA Polymethylmethacrylate
MNM POM Polyoxymethylene;
Cellulose nitrate
Cellulose propionate
EVAC
DesigMeaning
nation
PAK
Acrylonitrile
butadiene styrene
cf. DIN EN ISO 1043-1 (2002-06)
T
T
T
Polyformaldehyde
E
PP
D
T
PS
PSU
Polypropylene
Polystyrene
Polysulfone
T
T
T
Polytetrafluoroethylene
Polyurethane
Polyvinyl acetate
T
D
T
T
T
T
T
T
T
T
T
SI
SMS
Styrene-acrylonitrile
Styrene-butadiene
Silicone
Styrene-a-methylstyrene
D
T
UF
UP
VCE
Urea-formaldehyde
Unsaturated polyester
Vinyl chloride-et hylene
D
D
T
11 M NM modified natural materials; E elastomers; D thermoset plastics; T thermoplastics
Code letters for designation of special properties
Special
CL1I
properties
Special
CL1I
properties
flexible; liquid
high; homo
impact t ough
linear, low
moderate, molecular
cf. DIN EN ISO 1043-1 (2002-06)
Special
CL1I
properties
N
B
C
block, brominated
chlorinated; cryst alline
F
H
D
E
density
foamed;
elastomer
L
=>
PVC-P: Polyvinylchloride, plasticized; PE-LLD: linear Polyethylene low density
I
M
CL1I
normal; novolak
oriented
plasticized
raised; resol; hard
saturated; sulphonated
0
p
R
s
T
u
V
w
X
Special
properties
temperature
ultra; no plasticizers
very
weight
cross-linked, cross-linkablE
11 code letter
Code letters and abbreviations for fillers and reinforcing materials cf. DIN EN ISO 1043-2 (2002-04)
Abbreviation for materia111
Designation
Material
Designation
B
C
Boron
Carbon
G
K
Material
Designation
p
Glass
Calcium carbonate
Q
Material
Mica
Silicate
Designation
T
w
Material
Talc
Wood
D
Aluminum trihydrate
L
Cellulose
R
Aramid
X
not specified
E
Clay
M
Mineral, metal21
s
Synthetic mat erials
z
other
Shape, structure
Designation
Abbreviations for shape and structure
Designation
Shape, structure
Designation
Shape, structure
Designation
Shape, structure
pearls, balls,
beads
G
ground stock
whiskers
N
p
nonwoven (thin)
H
paper
vv
w
C
chips, shavings
knitwear
R
roving
X
not specified
D
powder
K
L
laminates
s
peelings, flakes
y
yarn
F
fibers
M
matted, thick
T
spun yarn, cord
z
other
=>
GF: glass fiber; CH: carbon whisker; MD: mineral powder
B
ven eer
woven
11 The materials can be further designat ed, e.g. by its chemical symbol or another symbol from relevant international standards.
2 1 For metals (M) the type of metal must be specified by the chemical symbol.
181
M ateri al science: 4. 11 Plast ics
Identification, Distinguishing characteristics
Methods for identifying plastics
Roatlng Solution density
Plastics
in g/cm3
floating
0.9- 1.0
PB, PE, PIB, PP
1.0- 1.2
ABS, ASA, CAB, CP,
PA, PC, PMMA,
PS,SAN,SB
1.2- 1.5
CA, PBT, PET,
POM, PSU, PUR
1.5- 1.8
Organically filled
molding material
1.8-2.2
Solubility in
solvents
Thermosets and
PTFE are not soluble.
VisualAppearance of the specimen is
transparent
cloudy
CA,CAB,CP,
EP, PC, PS,
PMMA,PVC,
SAN
ABS.ASA,
PA. PE,
POM,PP,
PTFE
Other thermoplastics are soluble Touch
in certain solvents;
e.g. PS is soluble in Waxy to the touch:
benzene or acePE, PTFE, POM, PP
tone.
PTFE
Behavior when
heated
• Thermopl. soften and melt
• Thermosets and elastomers
decompose without softening
Burning test
• flame color
• fire behavior
• soot formation
• odor of the smoke
Distinguishing characteristics of plastics
Density
g/cm3
Burning behavior
0th. characteristic:
ABS
~ 1.05
Yellow flame, soots strong ly, smells like
coal gas
Tough elastic, is not dissolved by carbon
tetrachloride, sounds dull
CA
1.31
Yellow, sputtering flame, drips, smells like
distilled vinegar and burnt paper
Pleasant to the touch, sounds dull
CAB
1.19
Yellow, sputtering flame, drips burning,
smells like rancid butter
Sounds dull
MF
1.50
Very flammable, chars with white
edges, smells like ammonia
Very brittle, rattling sound
(compare to UF)
PA
~ 1.10
Blue flame w ith yellow edges, drips
in fibers. smells like burnt horn
Tough elastic, not brittle, sounds dull
PC
1.20
Yellow flame, goes out after flame is
removed, soots, smells like phenol
Tough hard, not brittle, rattling sound
PE
0.92
Light flame with blue core, drips off burning,
odor like paraffin, smoke hardly
visible (compare w ith PP)
Wax like surface, can be scratched with the
fingernail, not brittle, working
temperature> 230°C
PF
1.40
Very flammable, yellow flame, chars,
smells like phenol and burnt wood
Very brittle, rattling sound
PMMA
1.18
Luminous flame, fruity odor,
crackles, drips
Clear w hen uncolored, sounds dull
POM
1.42
Bluish flame, drips, smells like
formaldehyde
Not brittle, rattling sound
pp
0.91
Light flame with blue core, drips off burning,
odor like paraffin, smoke hardly
visible (compare with PE)
Cannot mark w ith fingernail,
not brittle
PS
1.05
Yellow flame, soots strongly, smells sweet
like coal gas, drips off burning
Brittle, sounds like tinny metal, is dissolved
by carbon tetrachloride among others
PTFE
2.20
Nonflammable, strong odor when red hot
Waxy surface
Yellow flame, very strong odor
Polyurethane, rubber elastic
Polyurethane foam
Very flammable, extinguishes after the flame
is removed, smells like hydroch loric acid, chars
Rattling sound (U = hard)
Designation11
PUR
PVC-U
PVC-P
1.26
= 0.05
1.38
1.20-1.35 Can be more flammable than PVC-U, depending
on plasticizer, smells like hydrochloric acid, chars
Rubbery flexible, no sound (P = soft)
SAN
1.08
Yellow flame, soots strongly, smells
like coal gas, drips off burning
Tough elastic, is not dissolved by carbon
tetrachloride
SB
1.05
Yellow flame, soots strongly, smells like
coal gas and rubber, drips off burning
Not as brittle as PS, is dissolved by
carbon tetrachloride among other things
UF
1.50
Very flammable, chars with white
edges, smells like ammonia
Very brittle, rattling sound
(compare to MF)
UP
2.00
Luminous flame, chars, soots, smells
like styrene, glass fiber residue
Very brittle, rattling sound
11 Compare to page 180
182
Material science: 4.11 Plastics
Thermoplastics (selection)
~.....-..
W011cin9
Abb,.,,.
iatlon
Designation
Density
TensileImpact
strengtt,1I tough.- long-t.,.,,, Application examples
g/cm3
N/mm2
mJ/mni'-
°C
~ 1.05
35-56
80n.f.3I
85- 100
1.14
43
n.f.31
80-100
1.14
57
2141
80- 100
0.96
20- 30
n.f.31
80- 100
0.92
8- 10
n.f.31
60-80
Trade name
ABS
AcrylonitrileTerluran.
butadiene-styrene Novodur
PA6
Polyamide 6
PA66
Polyamide 66
PE-HD
Polyethylene.
high density
Durethan,
Maranyl,
Resistane,
Ultramid,
Rilsan
Hostalen,
Lupolen,
Vestolen A
Telephone housings,
instrument panels.
surf boards
Gears.
plain bearings,
screws,
cables,
housings
Battery cases,
f uel containers.
garbage cans,
pipes,
cable insulatio n,
films.
bottles
PE-LO
Polyethylene,
low density
PMMA
Polymethylmethacrylate
Plexiglas.
Degalan,
Lucryl
1.18
70-76
18
70- 100
Optical lenses,
warning lig hts,
dials.
light ed letters
POM
Polyoxymethylene;
Delrin,
Hostaform,
Ultraform
1.42
50- 70
100
95
Gears,
plain bearings,
valve bodies.
housing parts
pp
Polypropylene
Hostalen PP,
Novolen,
Procom,
Vestolen P
0.91
21 - 37
n.f.3>
100-110
Heating ducts,
washing machine
parts,
fittings.
pump housings
PS
Polystyrene
Styropor,
Polystyrol.
Vestyron
1.05
40- 65
13- 20
55-85
Packaging material,
flatware,
fil m cartridges,
insulating boards
PTFE
Polyletrafluorethylen
Hostaflon,
Teflon,
Fluon
2.20
15- 35
n.f.31
280
Maintenance free
bearings,
piston rings,
seals, pumps
1.20
- 1.35
20-29
2•1
60- 80
1.38
35-60
n.f.3I
< 60
PVC-P
PVC-U
Polyvinylchloride.
Hostalit,
plasticized
Vinoflex,
Vestolit,
Polyvinylchloride Vinnolit.
no plasticizers
Solvic
Hoses.
seals,
cable sheathing,
pipes,
fittings,
containers
SAN
Styreneacrylnitrile
copolymer
Lu ran,
Vestyron,
Lustran
1.08
78
23- 25
85
Graduat ed dials,
battery housings,
headlight housings
SB
Styrenebutadiene
copolymer
Vestyron.
Styrolux
1.05
22-50
40 •
n.f.31
55- 75
Television housings,
packaging material,
clothes hangers,
distribution boxes
11 Values depend on temperature and test speed.
2> Duration of temperature application has a significant effect.
3> n.f. " no fracture of the specimen
41 Impact toughness
183
Material science: 4.11 Plastics
Designation of thermoplastic molding materials
Polyethylene PE
Polypropylene PP
cf. DIN EN ISO 1872-1 (1999-101
cf. DIN EN ISO 1873-1 (1995-12)
Designation system
Name
Standard
block:
number block
Example:
Thermoplastic
ISO 1873 -
I
Data block
1
II
Data block
2
PP-R
II
Data block
3
11
Data block
4
Data block
5H
.
2)
06-16-003
EL
II
I
ISO8773
Data block 1
In data block 1 the molding material is designated by its abbreviation PE or PP after the hyphen.
For polypropylene the additional information follows: PP-H homopolymers of the propylene, PP-B thermoplastic,
impact tough PP (so-called block-copolymerl; PP-R thermoplastic, static copolymers of the propylene.
Datablock2
Intended applications and/or
processing methods for PE and PP
Important properties, additives and coloring
for PE and PP
SymPosition 1
bol
SymPositions 2 to 8
bol
SymPosition 1
bol
SymPositions 2 to 8
bol
B
C
Blow molding
Calendering
L
M
Monofilam. extrusion
Injection molding
A
B
Process stabilizer
Anti-blocking agent
L
N
p
R
E
F
Extrusion
Extrusion (films)
0
R
Stamping
Rotomolding
C
D
Artificial color
Powder
C
H
General use
Coating
s
Powder sintered
Unspecified
E
F
Blowing agent
Fire extinguisher
s
X
K
Cable insulation
y
Fiber production 31
C
H
Pellets
Thermal aging stabilizer
X
y
T
z
Light stabilizer
Natural colors
Impact to ugh
Mold release agent
Sliding and lubricating agent
Increased transparency
Cross-linkable
Increased electr. conductivity
Static inhibitor
Data block 3
3
Density of PE in kg/m
Modulus of elasticity
for PP in MPa (N/mm2 )
Symbol
above- to
Symbol
above- to
00
03
08
- 901
901-906
906- 911
02
06
10
- 400
400-800
800- 1200
13
18
23
9 11 - 916
916- 921
921- 925
27
33
40
925- 930
930-936
936- 942
1200- 2000
16
28
2000- 3500
40
3500
Impact toughness for PP in kJ/m2
02
-3
3- 6
05
45
50
57
62
942- 948
948-954
954-960
960
09
15
25
35
Melting mass flow rate in g/10 min
Conditions for PE
Temp.
Load
in °C
in kg
190
190
190
190
E
D
T
G
0.325
2.16
5.00
21.6
-
6- 12
12-20
20-30
30
Symbol
for PP and PE
000
001
003
- 0.1
0.1- 0.2
0.2-0.4
006
012
022
0,45
090
200
400
700
0.4- 0.8
0.8-1.5
1.5- 3.0
3.0- 6.0
6-12
12-25
25-50
50
above-to
-
Data block 4 for PE and PP
Position 1: Symbol for filler/reinforcer grade
Symbol Material
B
C
G
Boron
Carbon
Glass
K
Chalk
Cellulose
Mineral, metal
L
M
Symbol Material
s
T
w
X
z
Position 2: Symbol for physical form
Symbol Fo rm
Synthetic,
o rganic
Talcum
B
D
F
Pearls, balls
Powder
Fiber
Wood
Not specified
Other
G
H
Ground stock
W hiskers
Symbol Fo rm
s
X
Lamina
Flakes
Not specified
z
Other
Position 3: Mass percentage of the filler material
⇒
Thermoplastic ISO 1873-PP-H, M 40-02-045, TD40: Polypropylene molding material, homopolymer,
fabricated by injection molding, modulus of elasticity 3500 MPa; Impact toughness 3 kJ/m2, melting mass
flow rate 4.5 g/10 m in, filler 40% talcum powder
11 Data block 5 optional • ent ry of additio nal requirements
21 2 commas - data block m issing
31 only for PP
184
Material science: 4.11 Plastics
Thermoset molding materials, Laminated material
Designation and properties of thennoset plastic molding materials
Type
DIN 7708-2
(old standard)
Type
ISO 14526
cf.
page 180
Resin
Flexural
strength 11
N/mm2
Filler
Pourable phenolic plastic molding materials (PF PMCI
Impact
toughness11
k.J/m2
Water
absorption
mg
cf. DIN EN ISO 14526-3 (2000-08)
31
PF(WD30+
MD20)
30% wood flour
20% mineral flour
Q: a, 40
M :a, 50
Q: a, 4.5
M:a, 5.0
s 100
51
PF (LF20+
MD25)
20% cellulose fibers
25% mineral flour
O: a, 40
M : a,50
O:a, 4.5
M: a,5.0
s 150
84
PF (SC20+
LF15)
20% synthetic chips
15% cellulose fibers
Q:a, 35
M :ae 45
Q:a, 5.5
M: ae 6.5
s 150
40% (to 50%) flaky
organ. synthesis product
O:a, 30
M :a, 45
0 :., 7.0
M:a, 9.0
s 200
40% (1060%)
m ica fibers
Q: ;, 30
M: a, 40
Q: ;, 2.5
M:a, 3.5
s 30
Phenolic
(formal dehyde)-resin
(PF)
74
PF (SS40
t o SS50l
13
PF (PF40
to PF60)
83
PF (LF20+
MD25)
20% cellulose fibers
25% m ineral fibers
Q:;, 35
M :a, 45
Q:a, 5.5
M:a, 6.0
s 150
12
PF (GF20+
GG30)
20% fiber glass
30% glass grist
Q:;, 50
M :a, 60
Q:a, 6.0
M:a, 7.0
s 30
-
PMC ISO 14526- PF(WD30+MD20), M: Pourable m olding compound (PMC), phenolic (formaldehyde)
resin (PF), approx. 30% of wood flour (WD30), approx. 20% of mineral flour (MD20); recommended
machining process: injection molding (M)11
cf. DIN EN ISO 14527-3 (2000-08)
Urea formaldehyde molding materials (UF PMCI and
urea/melamine formaldehyde molding materials (UF/MF-PMCI (UF/MF-PMCI
131.5
UF(LD10+
MD30),X,E2>
131
UF(LD10+
MD30)
130
UF(WD30+
MD20)
-
UF/MF
(LF20+S10)
-
Urea
(formaldehyde)
resin
(UF)
Urea/melamine
(form aidehyde) resin
20% cellulose powder
30% mineral flour
Q: a, 45
M :a, 55
Q:a, 5.0
M:a, 7.5
s 150
20% cellulose fibers
30% mineral flour
O: ae 45
M: ae 55
Q:;,, 5.0
M:ae 7.5
s 150
30% wood flour
20% mineral flour
Q: a, 35
M: a, 40
Q;a, 4.5
M: a,5.0
s 200
-
Q;a, 6.5
M: -
s 100
20% cellulose fibers
10% o rganic
synthesis product
PMC ISO 14527 - UF(LD20+MD20}, M : Pourable molding com pound (PMC), urea formaldehyde resin
(UF), approx. 20% of cellulose powder (LD20), approx. 20% of mineral flour (MD20}; recommended
machining process: injection molding (M)11
Laminated materials31
cf. DIN EN 60893 (2004-12)
Types of reinforcing materials
Resin types
Type of resin Designation
EP
MF
PF
UP
SI
Pl
Nominal
thicknesses
tin mm
-
Epoxy resin
Melamine (formaldehyde) resin
Phenolic (formaldehyde) resin
Unsaturated polyester resin
Silicone resin
Polyimide resin
Abbreviation Designation
cc
CP
CR
GC
GM
WV
Cotton fabric
Cellulose paper
Combined reinforcing material
Glass fiber fabric
Fiber glass mat
Wood veneer
0.4; 0.5; 0.6; 0.8; 1.0; 1.2; 1.5; 2; 2.5; 3; 4; 5; 6; 8; 10; 12; 14; 16; 20; 25; 30; 35; 40; 45; 50; 60; 70; 80; 90; 100
Board EC 60893 - 3 -4- PF CP 201, 10 x 500 x 1000: Board made of phenolic (formaldehyde} resin/cellulose
paper(PF CP 2011 according to IEC standard"> 60893-3-4 with t = 10 mm, W = 500 mm,/ = 1000 mm.
11 Q = compression molding compound; M = injection molding compound
21 X = machining process not specified; A = free of ammonia; E = specific electric properties
31 Applications: insulators for electrical equipment for instance, or bearing liners, rollers and gears for machine construction
4 1 IEC = International Electrotechnical Commission (international standard)
185
Material science: 4. 11 Plastics
Elastomers. Foam materials
Elastomers (rubber)
AbbreDesignation
vi•
tion'l
Tensile
Elong: at Working
Density strengtt,>1
Properties,
fracture t ~
%
"C
2 (18)
450
- 60 to +90
1.27
- 1.36
5 ( 15)
250
g/crn3
N/mm2
0.94
application examples
BR
Butadiene
rubber
co
Epichlorhydrin
rubber
CR
Chloroprene
rubber
1.25
11 (25)
400
- 30 t o+110
Oil and acid resistant, very flammable,
seals, hoses, V-belts
CSM
Chlorosulfonat ed
polyethylene
1.25
18 (20)
300
-30 to+ 120
Aging and weather resistant, oil resistant;
insulating material, molded goods, films
EPDM
Ethylenepropylene rubber
0.86
4 (25)
500
Good electrical insulator, not resistant
- 50to+120 against oil and gasoline; seals, profiles,
bumpers, cold water hoses
1.85
2 (15)
450
Abrasion resistant, best thermal resistance;
- 10 to +190 aerospace and automotive industries;
rotary shaft seals, O-rings
lsobutenelsoprene
rubber
0.93
5 (21)
600
- 30 to+ 120
Weather and ozone resistant;
cable insulation, automotive hoses
IA
lsoprene
rubber
0.93
1 (24)
500
- 60 to +60
Low resistance to oil, high strength;
truck tires, spring elements
NBA
Acrylonitrilebutadiene
rubber
1.00
6 (25)
450
Abrasion resistant, oil and gasoline resistant,
-20 to +110 electr. conductors, O-rings, hydraulic hoses,
rotary shaft seals, axial seal
NA
Natural rubber
lsoprene rubber
0.93
22 (27)
600
-60 to +70
Low resistance to oil, high strength;
truck t i res, spring elements
PUA
Polyurethane
rubber
1.25
20 (30)
450
-30 to +100
Elastic, wear-resistant; timing belts,
seals, couplings
SIA
Styrene-lsoprene
rubber
1.25
1 (8)
250
Good electr. i nsul ator, water repellant
-80 to +180 O-rings, spark plug caps, cylinder
head and joint sealing
0.94
5 (25)
500
-30 to +80
FKM
IIA
SBA
Fluoro rubber
Styrene-Butadiene
rubber
1l cf. DIN ISO 1629 (1992-03)
High abrasion resistance;
tires, belts, V-belts
Vibration damping, oil and gasoline
- 30 to +120
resistant; seals, heat
- 10 to +120
resistant dampers
Low resistance to oil and gasoline;
tires, hoses, cable sheathing
21 Value in parentheses = with additive or filler reinforced elastomer
Foam materials
cf. DIN TT26 (1982-05)
Foam materials consist of open cells, closed cells or a mixture of closed and open cells.
Their raw density is lower than that of the struct ural substance. A d istinction is made between hard, medium hard,
soft, elastic, soft elastic and integral foam material.
S1ilfMa. Raw material base of the
...-m- foammatsial
Cell structure
Polystyrene
Polyvinylchlo ride
Hard
Polyethersulfone
Predominantly
closed
cell
Polyurethane
Phenolic resin
Urea-formaldehyde resin
Po lyethylene
Medium- Polyvinylchloride
hard
Melamine resin
to softPolyurethane polyester type
elastic
Polyurethane polyether type
Open cell
Max. worl<ing
Thermal
conductivity
W/(K-ml
Wat• absorption In 7 days
-c•t
15 - 30
75 (100)
0.035
2- 3
50 - 130
60 (80)
0.038
<1
45 - 55
180 (210)
0.05
15
20 - 100
80 (150)
0.021
1- 4
40 - 100
130 (250)
0.025
7- 10
5-15
90 (100)
0.03
20
0.036
1-2
Density
kg/m3
temperature
Vol.-%
Predominantly
closed
cell
25- 40
up to 100
50-70
- 60 to +50
0.036
1- 4
10.5-11.5
up to 150
0.033
approx. 1
Open cell
20- 45
- 40 to +100
0.045
-
1l Long-term working temperature, short-term in parentheses
186
Material science: 4.11 Pl astics
Plastics processing
Injection molding and extrusion
Tolen,,- group11 for
Injection molding
temperature In
Injection pres- Extrusion
process
sure
In bar
temperature
in °C
·c
Abbreviation
Shrinkage
in%
Dimensions
with
deviations
ranees Series 121 Saries2 2
General
tole-
Substa,-
Mold
PE
160- 300
20 - 70
500
190-230
1.5- 3.5
150
140
130
pp
170- 300
20- 100
1200
235- 270
0.8-2 31
150
140
130
PVC, hard
170-210 41
30-60
1000- 1800
170- 190
0.2-0.5
130
120
110
PVC, soft
170- 20041
20- 60
300
150- 200
1-2.5
-
-
-
PS
180-250
30-60
-
180-220
0.3-0.7
130
120
110
SB
180- 250
20-70
-
180-220
0.4- 0.7
130
120
110
SAN
200-260
40- 80
-
180- 200
0.5-0.6
130
120
110
ABS
200- 240
40- 85
800- 1800
180-220
0.4-0.7
130
120
110
PMMA
200-250
50- 90
400-1200
180- 250
0.3- 0.8
130
120
110
PA
210- 290
80- 120
700-1200
230-275
1- 2
130
120
110
POM
180- 23041
50- 120
800- 1700
180- 220
1- 3.5
140
130
120
PC
280- 3204 1
80- 120
> 800
240- 290
0.7- 0.8
130
120
110
PFSI
90- 110 4 1
170- 190
800- 2500
-
0.5- 1.5 31
140
130
120
MF61
95- 1104)
160- 180
1500-2500
-
0.6- 1.7 31
130
120
110
UFSl
95- 110
150- 160
1500- 2500
-
0.4-0.6
140
130
120
21 Series 1: Can be maintained without special effort, Series 2: Requires high finishing effort
II See table below
31 Transverse and longitudinal shrinkage may differ
41 W ith screw injection molding machine
61 With inorganic filler material
SI W ith organic filler material
Tolerances for plastic molded parts
Tolerance
group
Codefrom table
letter"
above
cf. DIN 16901 (1982-11)
Nominal dimension range over - up to in mm
0-1
1-3
3-6
6- 10
10-15 15- 22 22- 30 30- 40 40- 53 53- 70 70-90
90120
120160
General tolerances
150
140
130
A
B
A
B
A
B
ct0.23 ct0.25 ±0.27
±0.13 ±0.15 ±0.17
±0.30 ±0.34 ±0.38 ±0.43 ±0.49 ±0.57
±0.20 ±0.24 ±0.28 ±0.33 ±0.39 ±0.47
±0.20 ±0.21 ±0.22 ±0.24
±0.10 ±0.11 ±0.12 ±0.14
±0.68 ±0.81 ±0.97 ±1.20
±0.58 ±0.71 ±0.87 ±1.10
±0.27 ±0.30 ±0.34 ±0.38 ±0.43 ±0.50 ±0.60 ±0.70 ±0.85
±0.17 ±0.20 ±0.24 ±0.28 ±0.33 ±0.40 ±0.50 ±0.60 ±0.75
±0.18 ±0.19 ±0.20 ±0.21 ±0.23 ±0.25 ±0.27 ±0.30 ±0.34 ±0.38 ±0.44 ±0.51 ±0.60
±0.08 ±0.09 ±0.10 ±0.11 ±0.13 ±0.15 ±0.17 ±0.20 ±0.24 ±0.28 ±0.34 ±0.41 ±0.50
Tolerances for d imensions with deviations
B
0.40
0.20
0.42
0.22
0.44
0.24
0.48
0.28
0.54
0.34
0.60
0.40
0.68
0.48
0.76
0.56
0.86
0.66
1.00
0.80
1.20
1.00
1.40
1.20
1.70
1.50
130
A
B
0.36
0.16
0.38
0.18
0.40
0.20
0.42
0.22
0.46
0.26
0.50
0.30
0.54
0.34
0.60
0.40
0.68
0.48
0.76
0.56
0.88
0.68
1.02
0.82
1.20
1.00
120
A
B
0.32
0.12
0.34
0.14
0.36
0.16
0.38
0.18
0.40
0.20
0.42
0.22
0.46
0.26
0.50
0.30
0.54
0.34
0.60
0.40
0.68
0.48
0.78
0.58
0.90
0.70
A
0.18
0.08
0.20
0.10
0.22
0.12
0.24
0.14
0.26
0. 16
0.28
0.18
0.30
0.20
0.32
0.22
0.36
0.26
0.40
0.30
0.44
0.34
0.50
0.40
0.58
0.48
140
110
A
B
11 A For dimensions which do not depend on mold dimensions; B For dimensions which depend on mold dimensions
187
Material science: 4.11 Plastics
High-temperature plastics, Polyblends, Reinforcing fibers
High-temperature plastics
AbbreDesignation
viation
Tensile Working
strength temperature
N/mm2 from to
Special properties
Application examples
PTFE
Polytetrafl uoretylene
trade name
· Teflon"
10
- 20 to 260°C,
short-term to
3oo•c
High-temperat ure strength
and chemical resistance, low
strength, hardness and
coefficient of friction
Bearings, seals, coatings, highfrequency cable, chemical
equipment
PEEK
Polyetheretherketone
97
- 65 to 250°c,
short-term to
300•c
High-temperature strength
and chem ical resistance, good
sliding behavior
Bearings, gears, seals, air and
space travel (instead
of metals)
Polyphenylensulfide
- 200 to 220°c,
PPS
70
short-term to
260°c
High st rength, hardness, stiffness, high chemical, weather
and radiation resistance
Pump housings,
bearing bushings, space travel,
nuclear power stations
PSU
Polysulfone
- 40 to 150°c,
140-240 short-term to
200°c
High strength, hardness, stiffness, high chemical and radiation resistance, clear
Microwave dishes, spools,
circuit boards, o il level indicators, needle bearing cages
Pl
Polyimide
trade name
·vespeI•
- 240 to 360°c,
75- 100 short-term to
400°c
High strength in large
temperature range,
radiation resistant, dark, nontransparent
Jet engines, aircraft noses,
piston rings, valve seats, seals,
electronic connection
components
Polyblends
Polyblends (also known as "blends") are mixtures of different thermoplastics. The special properties of these copolymers result from numerous possible combinations of the properties of the original materials.
Components
Special
properties
Application examples
90% polystyrene,
10% butadiene rubber
Brittle hard, at low t emperatures not impact tough
Stacking boxes, fan
housings, radio housings
Brittle hard, impact tough
even at low temperatures
Telephones, dash-boards,
hubcaps
Polyphenylenether +
Polystyrene
High hardness, high cold
various compositions;
impact toughness to
possibly can be reinforced
-40°C, physiologically
with 30% glass fiber
harm less
Radiator grill, computer
parts, medical equipment,
solar panels,
trims
Polycarbonate +
Acrylnitrile/Butadiene/
Styrene
various
compositions
High strength, hardness,
toughness, dimensional
stability under heat.
impact t ough, shock-proof
Polycarbonate + Polyethyleneterephthalate
different
compositions
Exceptional impact tough- Motorcycle helmets,
ness and shock resistance automotive parts
Abbre-- Designation
viation
S/B
Styrene/butadiene
ABS
Acrylonitrile/butadiene/ 90% styrene-acrylonitrile,
styrene
10% nitrile rubber
PPE +
PS
PC+
ABS
PC+
PET
Instrument panels,
fenders, office machine
housings, lamp housings
in motor vehicles
Reinforcing fibers
Designation
Density
kg/dm3
Tensile
stnngth
N/mm2
Elongation
at fracture
"·
Special properties
Application examples
4.5
Isotropic11, good strength, high- Body parts, aircraft manufacluring, sailboats
temp. strength, inexpensive
3400
- 3800
2.0- 4.0
Highly stressed light parts,
Lightest reinforcing fiber,
ductile, fracture t ough, strongly crash helmets,
anisotropic", radar-penetrable bulletproof vests
1750
- 5000 21
0.35- 2.121
Parts for racing cars, sails for
Extremely anisotropic 11, highstrength, light, corrosion resist- racing yachts,
aerospace applications
ant, good electr. conductor
Glass fiber
2.52
GF
3400
Aramide
fibers
AF31
1.45
Carbon
fiber
CF
1.6-2.0
Thermosets (e.g. UP and EP resins) and thermoplastics with high working temperatures (e.g. PSU, PPE, PPS, PEEK,
Pl) are used as embedding materials (so-called matrix).
11 Isotropic = the same material properties in all directions; anisotropic = material properties in the direction of the
fibers are different from those transverse to fibers
21 Depends significantly on the fiber defect sites occurring during the manufacturing process
31 Trade name "Kevlar"
T-a.test
page 190
Standard tensile test specimens are pulled to
fracture.
Determination of material characteristic
values, for example
The changes in tensile force and strain are
measured and plotted on a g raph. This is converted to a stress-strain curve.
- calculation of static load strength
- prediction of forming behavior
- obtaining data for machining processes
Ha""- test by Brlnell H8
I
• Indenter ball is loaded with standardized
test load F
- test load depends on ball diameter D and
on the material group
- Degree of loading, see page 192
• Indentatio n diameter d is measured
page 192
Hardness test, e.g. on steels, cast iron
materials, non-ferrous metals, which
- are not hardened
- have a metallic bright testing surface
- are softer than 650 HB
• Hardness is determ ined based o n the test
load and the surface area of indentation
page 193
Hardness·- by Rockwell
• Indenter (diamond cone, carbide ball) is loaded
with minor test load - measurement baseline
Hardness testing by different methods, e.g.
on steels and non-ferrous metals,
• Impact w ith major test load
- permanent deformation of the test piece
- in soft or hardened condition
- with small thicknesses
Removal of the major load
• Hardness is displayed directly on the test
device and is based on the depth of penetration h
Methods HRA, HRC:
hardened and high-strength metals
Methods HRB, HRF:
soft st eel, non-f errous metals
~ test by Viclcen
• The diamond pyramid is loaded with
variable loads
- test load is a function of parameters such
as test piece thickness or grain size in
matrix structure
page 193
Universal method for testing
- soft and hardened materials
- thin layers
- individual microstructural components of
metals
• The diagonals of the indentation are measured
Hardness is determined based on the test
load and surface area of indentation
HerdMss • - by penetrant testing (Martens hardness)
• Diamond pyramid is loaded w ith variable
loads
- test load is based on parameters such as
test piece thickness or grain size
• The load is logged continuously as a
functio n of penetration depth
page 194
Method for testing all materials, e.g.
- soft and hardened metals
- thin layers, also carbide coatings and paint
coating
- individual m icrostructure components
- ceramic, hard material, etc.
Martens hardness is determined during
loading
lwdness test by ball penetration test
• The test ball is loaded w ith initial load
- measurement baseline
• Impact with est ablished test load
- test load must produce a penetration
depth of 0.15- 0.35 mm
• The penetration depth is measured after 30 s
loading time
• Ball indentation hardness is determined
page 195
Testing of plastics and hard rubber.
Ball indentation hardness provides com parison values for research, development and
quality control.
Material science: 4.12 Material testing
189
page 195
Hardness test by Shore
• The testing device (durometer) is pressed on
the test piece with contact pressure F
• The spring loaded indenter penetrates
into the test piece
• Working time 15 s
Control of plastics (elastomers).
It is hardly possible to derive any relationships to other material properties from the
shore hardness.
• The shore hardness is displ. directly on the device
page 191
Shear test
.. Cylindrical specimens are loaded in standardized equipment until fractured due to shearing
Used to determine the shear strength r 58 , e.g.
- for strength calculations of shear loaded
Breaking strength is determined from the
parts, e.g. pins
maximum shearing force and cross-sectional - to predict cutting forces in forming
area of the test specimen
Notched-bar impact bending test
• Notched test specimens are subjected to
bending load by pendulum impact and are
fractured
• Notch impact toughness = energy required
to deform and fracture the test specimen
page 191
Erichsen cupping test
BIB
page 191
- To test metallic materials for behavior after
impact bending loads
- To monitor heat treatment results, e.g.
with quenching and tempering
- To test the temperature behavior of steels
Sheet metal clamped on all sides is
deformed until crack formation by a ball
• The deformation depth until crack propagation is a measure of deep drawing capability
- For testing of sheet metal and strip for
their deep drawing capability
- Evaluation of the sheet surface for
changes during cold working
Cylindrical specimens with polished surface
are alternately loaded with constant mean
stress am and variable alternating stress
amplitude aA, until fracture. The graphical
representation of the series of tests yields
the Wohler (S-N) curve
Used to determine material properties with
dynamic loading, e.g.
Fatigue test
n-
- fatigue strength, fatigue endurance and
fatigue strength under alternating stresses
- endurance limit
Ultrasonic testing
A transducer sends ultrasonic signals
through the workpiece. The waves are
reflected by the front wall, the back w all and
by defects of a certain size
• The screen of the testing device displays the
echoes
- Nondestructive testing of parts, e.g. for
cracks, cavities, gas holes, inclusions, lack
of fusion, differences in microstructure
- To determine the type of defect, the size
and the location of the defect
- To measure wall and layer thicknesses
• The test frequency determines the detectable
defect size which is limited by the grain size
of the test specimen
Metallography
Etching metallographic test specimens (microsections) develops the microstructure which can then
be observed under the metallographic microscope.
Specimen preparation:
Removal
- avoid structural transformation
Embedding - sharp edged microsections
Grinding
- removal of layers of deformation
Polishing - high surface quality
Etching
- structural development
- To check the crystalline structure
- To monitor heat treatments, forming and
joining processes
- To determine grain distribution and
grain size
- Defect testing
190
Material science: 4.12 Material testing
Tensile test, Tensile test specimens
Tensile test
cf. DIN EN 10002-1 (2001-12)
Stress-strain diagram
with distinct yield point,
e. g. for soft steel
~ R.
I
z ~ R,
.s
"O
~
~
.,,
t
I
I
I
I
I
I
I
I
I
EL elongation at fracture
F tensile force
Fm maximum force
Fe force at yield
strength lim it
Fp0.2 force at yield
strength lim it
at 0.2% strain offset
Lo initial gage length
Lu gage length
after fracture
do initial diameter of
the test specimen
So
init ial cross sectio n
of the test specimen
Su smallest test
specimen cross
section after fracture
normal strain
z reduction of area at
fracture
a, tensile stress
Rm tensile strength
Re yield strength
R0 02 yield strength at
0.2% strain offset
v. yield strength ratio
,
EL
strain e in % ~
a= -
z
F
So
Tensile strength
Y"teld strength
Yield strength at
0.2 % strain offset
Rm
Normally, round proportional bars w ith an initial gage
lengt h of L0 =5 • d0 are used.
Unmachined specimens are allowed with
- uniform cross sections, e.g. for specimens of sheet
metal, profiles, wires
- cast test specimens, e.g. of cast iron materials or
non-ferrous casting alloys
R po2
Elongation at fracture EL
I
If tensile test specimens are used that contract during
the test, the initial gage length Lo has an effect on the
elongation at fracture EL.
Elongation at fracture
Stress-strain diagram
without distinct yield point,
e .g . for quenched and
tempered steel
zr~
Tensile test _.:imens
Tensile stress
Smaller initial gage length Lo fracture EL
greater elongation at
Yield strength ratio: v. = Re (R0 0.2l/Rm
It provides information about the heat treatment condition of the steels:
0.2
EL
strain E in % ~
normalized
V5 , . 0.5-0.7
quenched & tempered v•.. O.7- 0.95
Tensile test specimens
R
p0.2
F.
po.2
- So
Normal strain
E = ~ - 100%
I
EL= ¥
-100%
I
Reduction of area at fraction
Z - So - Su - 100%
So
cf. DIN 50125 (2004-011
Round tensile test apec:im- with smooth cylindrical ends, shapes A end B
do
4
5
6
8
10
12
14
Shapes, application
Lo
Le
20
24
25
30
30
36
40
48
50
60
60
70
84
Shape A; Machined test spe-
Shape Ad,
5
65
6
80
8
95
Shape B d,
MS
40
Shapes, application
4
Li
72
cimens fo r clamping in the
tensioning wedge
10
12
15
17
115 140 160 185 Shape B: Machined test specimens w it h threaded heads
MS M10 M12 M16 M 18 M20 produce more precise mea75
50
60
90 110 125 surem ent of the elongation
Tensile test specimens, other shapes
ShapeE
a
3
4
5
6
7
8
10
b
Shape E Lo
10
35
15
10
40
15
20
60
27
22
70
29
25
80
B
8
30
12
25
90
33
Le
L,
38
115
Flat specimens w ith heads
for tensioning wedges,
tensile test specimens of
45
50 80 90 105 115 strips, sheets, flat bars and
135 140 210 230 260 270 profiles
33
Shape C
Shape D
Shape F
Machined round test specimens w ith shouldered ends
Machined round test specimens w ith conical ends
Unmachined sections of round bars
Shape G
Shape H
Unmachined section s of flat bar steel and profiles
Flat specimens for testing sheets with thicknesses between 0.1 and 3 mm
=>
Tensile test specimen DIN50125 - A10x50: Shape A,~ = 10 mm, Lo= 50 mm
191
M aterial science: 4.12 Material testing
Shear test. Notched bar impact bending test. Cupping test
Sheartest
cf. DIN 50141 (2008-07), withdrawn
So init ial cross section
Fm maximum shear force
do initial diameter of
the test specimen
specimen length
of t he test specimen
r,8 shear strength
The test is carried out on tensile t est machines w it h
st andardized shear devices.
Sheer test specimens
3
do
Lim it
- 0.020
deviations -0.370
4
5
6
8
10
12
16
- 0.020
- 0.370
- 0.030
- 0.390
- 0.030
- 0.345
- 0.040
- 0.370
- 0.013
- 0.186
- 0.016
- 0.193
- 0.016
- 0.193
50
50
50
50
110
110
110
50
Charpy impact test
cf. DIN EN 10045 (1991-04)
KU Notch impact energy in J , measured on a test specimen w ith U-not ch
KV Notch impact energy i n J, m easured on a test specimen w ith V-notch
Test specimen
The test specimen must be completely machined. Fabrication of the test material
should alter the material's microstructure as little as possible. No notch should be
visible with the naked eye at the notch root w hich runs parallel to the notch axis.
Notch impact test specimens
Test dimension in mm or degree (0 )
h
b
r
h,
lw
Notch
shape
Designation
Test specimen cross section
Normal test specimen
~
Explanation
11 Deutscher Verband fUr MaterialprGfung
J-..j
~trnl
u
55
40
10
10
Normal test specimen
V
55
40
10
DVM test specimen11
u
55
40
10
-
Erichsen cupping test
1.0
10
8
0.25
10
7
1.0
a
45°
(German Association for Material Test ing)
KU = 115 J :
Normal t est specimen w ith U-notch, Notch
impact energy 11 5 J , work capacity of t he
pendulum impact tester 300 J
KV150 = 85 J : Normal t est specimen w ith V-notch, Notch
impact energy 85 J , work capacity of t he pendulum impact tester 150 J
cf. DIN EN ISO 20482 (2003-12), replacement for DIN 50101 and 50102
IE Eric hsen cupping depth value in mm
F sheet metal holding force in kN
length of the test sheet
test specimen
5
die
ho le diameter of the die
ball diameter of t he punch
t hickness of t he test sheet
w w idth of t he test sheet
D
d
Test specimens
The t est specimens must be fl at and not have any burrs. Before clamping, the
sheet s are to be lig htly greased over with a graphite lubri cant.
Tools end test specimen dimensions
Abbrev iation
sheet metal
holder
punch
Tool dimensions
D
mm
d
mm
F
kN
Test specimen dimensions
I
w
t
mm
mm
mm
Applicatio n
IE
27
20
10
a: 90
a: 90
0.2-2
Standard test
IE40
40
20
10
;,,90
;,,90
2-3
IE21
21
15
10
a: w
55- 90
0.2- 2
11
8
10
a: b
30 - 55
0.1- 1
Tests on
th icker or
narrower
strips
IE11
-
IE = 12 mm: Erichsen cupping depth = 12 mm, standard test
192
Material science: 4.12 Material testing
Hardness test by Brinell
Hardness test by Brinell
D
F
test load in N
ball diameter in mm
0
d
diameter of the impression in mm
d 1, d2 individual measurement values of the
impression diameter in mm
h
depth of impression in mm
minimum thickness of the test specimen
s
inmm
distance from edge in mm
a
h71
<c~
t
~
g "'
.I
t-L-
Test conditions
Impression diameter
0.24 • 0 s d s 0.6 • 0
Minimum test specimen thickness s >= 8 - h
Distance from edge a>: 3 - d
" (.~) ll\ '.~,Jg•'
• 'i~ :~ r~
{;
..=. _-,..
_;'
d1
cf. DIN EN ISO 6506-1 (2006-03)
I
Impression diameter
I
d - d, +dz
I
2
Brinell hardness
0.204 • F
HBW=
1t .
D. (D-JDLd2)
Test specimen surface: metallic bright
0esignetion examples:
180 HBW 2.5 / 62.5
600HBW 1 / 30 / 25
~TT
I
I
Hardness value
Indenter
BaH
diameter
Testfon:e F
Impact time
Brinell hardness 180
Brinell hardness 600
W carbide ball
2.5mm
1 mm
62.5 • 9.80665 N = 612.9 N
30 • 9.80665 N = 294.2 N
Unspecified:
Value entry:
!Oto 15s
25 s
Degree of loading. ball diameter, test loads and test materials
Test load Fin N
w ith ball diameter 011 in mm
1
2.5
10
5
Degree of
loading
0.102 • F/02
Test range
Brinell
hardness
HBW
Materials
30
294.2
1839
7355
29420
Steel, nickel and titanium alloys
Cast iron
Copper, copper alloys
15
-
-
-
14710
Light metal, light metal alloys
>35
< 140
> 35
35 - 200
s 650
>: 140
> 200
10
98.07
612.9
2452
9807
Cast iron
Light metal, light metal alloys
Copper, copper alloys
5
49.03
306.5
1226
4903
Copper, copper alloys
Light metals, light metal alloys
< 35
35-80
2.5
24.52
153.2
612.9
2452
Light metals, light metal alloys
< 35
1
9.807
61.29
245.2
980.7
Lead, t in
-
11 Small ball diameters for fine-grained materials, thin specimens or hardness tests in the outer layer. For hardness tests
on cast iron, the ball diameter O m ust be~ 2.5 mm. Hardness values are o nly comparable if the tests were carried o ut
wit h the same degree of loading.
Minimum thickness s of the specimens
Ball diameter
O inmm
1
Minimum thickness sin mm for impression diameter do in mm
0.25 0.35 0.5
2
2.5
5
10
0.6
0.8
1.0
1.2
0.23 0.37 0.67 1.07
16
1.3
1.5
2.0
2.4
3.0
0.13 0.25 0.54 0.8
,_
,_
·-- . ·- . ·-
n ,n
nco
no,
3.5 1 4.o 1 4.5 1 5.o 1 5.5 1 6.o
Example: 0 = 2.5 mm, d = 1.2 mm
- m inimum specimen thickness
s= 1.23mm
. 3 1.46 2.0
0.58 0.69 0.92 1.67 2.45
4.0
I
I
I
I
I
I
I
1.17 1.84 2.53 3.34 14.28 5.36 6.59 8.0
11 Table fields without thickness indicated lie outside of the test range 0.24 . 0 s d s 0.6 . 0
193
Material sci ence: 4.12 Material testing
Hardness test by Rockwell, Hardness test by Vickers
Hardness test by Rockwell
Hardness test
1st step
2nd step 3rd step
cf. DIN EN ISO 6508-1 (2006-03)
I
Rockwell hardness HRA, HRC
F0 m ino r load in N
F1 m ajor load in N
h permanent i ndentation depth
HRA, HRC = 100-
in mm
s
a
Rockwell hardness HRB, HRF
Surface of specimen is ground to
Ra = 0.8- 1.6 µm. The m achining of the
specimen must not result in any
changes to t he m icrostructure.
Distance from edge a" 1 mm
100 ~~~~-~~~
90 ........-+---++-t--+---+---1
65
70
"'I:: 60
50
~
40 t--1--t-\--t-- t- +-'t-t
~
h
0.002 mm
Test method
HRCRockwell hardness - C,
test w it h diamond cone
HRBW Rockwell hardness - B,
t est w ith carbide ball
Test method, applications (selectio n)
C:
jg
~
HRB, HRF = 130-
Designation examples:
65HRC
70HRBW
T
Hardness value
~
I
test specimen thickness
d istance from edge
Test conditions
reference pl ane for measurement
h
0.002 mm
30 t--t--t~ \1-- t- + --'I
HRA
20
HRC
0 0.5 1 1.5 2 mm 3
minimum test - - - specimen thickness
Fo
F1
in N
in N
Measurement
range from - to
Diamond cone,
cone ang le 120°
98
490.3
20- 88 HRA
98
1373
20- 70 HRC
Carbide ball (W)
1.5785 mm
98
882.6
20- 100 HRB
98
490.3
60- 100 HRF
Met hod Indenter
HRB
HRF
Hardness test by Vickers
136°
Application
Hardened steel,
hig h-strength
metals
Soft steel,
non-ferrous metals
cf. DIN EN ISO 6507-1 (2006-03)
F
d
s
a
t est load in N
d iagonal of the indentation in mm
test specimen thickness
distance from edge
Test conditions
Surface of specimen is ground t o
Ra = 0.4- 0.8 µm . The machining of
t he specimen must not result in any
changes to t he m icrostruct ure.
Distance from edge a" 2.5 • d
Vickers hardness
F
HV = 0.1891 • d 2
Designation examples:
540HV1/20
650HV 5
2000
1000 t-¼--+!-t+-++--t--1
t
Hardness value
Test load F
Working time
Vickers hardn. 540
Vickers hardn. 650
1 • 9.80665 N = 9.807 N
5 • 9.80665 N = 49.03 N
Value entry
Unspecified:
20 s
10 to 15 s
:,::
> 500
Test conditions and applied loads for the Vickers hardness test
~ 250
Test condition
HV100
HV50
HV30
HV20
HV10
HV5
~ 100 ~~-~~-~~-~
,,:; 0.0, 0025 0.1 015 1 2.5 10
Test load in N
980.7
490.3
294.2
196.1
98.07
49.03
Test condition
HV3
HV2
HV1
HV0.5
HV0.3
HV0.2
Test load in N
29.42
19.61
9.807
4.903
2.942
1.961
min. test specimen t hickness - -
194
Material science: 4.12 Material testing
Martens hardness, Conversion of hardness values
Martens hardness by penetrant testing
F
1360
ind
~ nter
test
specimen
F
h
-<::
s
"'
cf. DIN EN ISO 14577 (2003-05)
test load in N
depth of penetration in mm
specimen thickness in mm
Mertens hardness
Test specimen surface
Test characteristics
'I'[ cl
Aluminum
Steel
0.08
0.30
2.20
h-
Carbide
0.03
i
0.80
h,,.,
0.1 N
2N
100 N
0.13
0.55
4.00
I
I
0.10
!!f'1
Designation:
ITest method
I I 20s
2 N ,. F ,. 30 kN
Micro range
F < 2 N o r H > 0.2 µm
Nano range
I
Application of load
I
within 20 s
h ,s 0.2 µm
N/mm2
255
285
320
350
385
80
90
100
110
120
76
86
95
105
114
415
450
480
510
545
130
140
150
160
170
124
133
143
152
162
575
610
640
675
705
180
190
200
210
220
171
181
190
199
209
740
770
800
835
865
230
240
250
260
270
900
930
965
1030
1095
280
290
300
320
340
Rm
Tensile
strength
Rockwell hardness
HRC
HRA
-
-
-
-
-
-
-
-
-
219
228
238
247
257
-
-
20
22
24
26
61
62
62
63
266
276
285
304
323
27
29
30
32
34
64
65
65
66
68
-
I IMartens hardn. value I
I I 5700 N/mm2
I
Universal hardness test, e.g. fo r all metals,
plastics, carbides, ceramic materials;
m icro and nano ranges: thin layer measurement,
microstructure components
Conversion tables for hardness values and tensile strength 11
Brinell
hardness
HB30
I
Applications
Conditions
Macro range
Vickers
hardness
HV
(F ~ 98N)
F
26.43 • h2
I
'-------7
I
Test range
Tensile
strength
HM =
/.al/ 2J2- ,;700 w-m2
I ITest duration
I Test load F
I Martens hardness I 0.5 N
I
Average roughness Ra at F
Material
-
HRB21 HRF21
cf. DIN EN ISO 1826512004-02)
N/mm2
Vickers
hardness
HV
(F~ 98N)
Brinell
hardness
HB30
HRC
HRA
360
380
400
420
440
342
361
380
399
418
37
39
41
Rm
Rockwell hard-
ness
-
-
48
56
62
67
83
87
91
94
1155
1220
1290
1350
1420
45
69
70
71
72
73
71
75
79
82
85
96
99
(101)
(104)
(106)
1485
1555
1595
1665
1740
460
480
490
510
530
437
456
466
485
504
46
48
48
50
51
74
75
75
76
76
87
90
92
94
95
(107)
(109)
(1 10)
(111)
(112)
18 10
1880
1955
2030
2105
550
570
590
610
630
523
542
561
580
599
52
54
55
56
57
77
78
78
79
80
97
98
100
(101)
(102)
(113)
(114)
(115)
2180
650
670
690
720
760
618
-
-
58
59
60
61
63
80
81
81
82
83
800
840
880
920
940
-
64
65
66
68
68
83
84
85
85
86
(104)
(105)
-
-
-
-
11 Applies to unalloyed and low alloy steels and cast steel. Special tables of this standard are to
43
be used for
quenched and tempered, cold worked and high-speed steels, as well as for various carbide types. Considerable
deviations are to be expected for high-alloyed and/or work-hardened steels.
21 The values in parentheses lie outside of the measurement range.
195
Material science: 4.12 Material testing
Testing of plastics: Tensile properties, Hardness testing
Determination of the tensile properties on plastics
Typical stress-strain
curves
t
I brittle
I
/
I ,,- duct ile
Oyz
~ OM3
~
aM = ~
yield strength
6.LFY change in length with
CM
maximum elongation Yield strength
yield strain
fy
I
So
Oy
Fy
ay = -
I
So
without
y /,ductile
For each property, e.g. tensile strength, yield strength,
Maximum elongation
yield point I
£H1 £Y2
£H2 £HJ
strain , - - - Test specimens
%JL~.,t
8 So
h
Test Specimens
yield strain, at least five test specimens must be tested.
Application
- thermoplastic injection molded and extrusion
molding materials
- thermoplastic slabs and films
- thermoset molding materials
- thermoset slabs
- fiber reinforced composite materials, thermoplastic
and thermoset plastic
Toler- Type
ance Lo
mm
Test speed
in mm/min
1
2
5
20
50
100
I
I
EM = -c.LFM
• 100OYo
Lo
Yield strain
I
Ey = t.4Y
· 100%
Lo
I
Test specimen according to
DIN EN ISO 527-2 for molding materials
DIN EN ISO 527-3 for films
Test speed
⇒
I
I
OM tensile strength
maximum load
y ield strength
. I
Tensile strength
Lo gage length
So initial cross section
'/
t:,
~
maximum force
yield stress
6 4M change in length with
OHi >-0H2
FM
Fy
cf. DIN EN ISO 527-1 (1996-041
I 10 ±20% h
I 200 ±1Cl% b
1A
1B
SA
5B
2
4
5
50 ± 0.5
50 ± 0.5
20 ± 0.5
10 ± 0.2
50 ± 0.5
50 ± 0.5
25 ± 0.25
" 1
25.4 ± 0.1
" 1
6 ± 0.4
mm
4 ±0.2
4 ± 0.2
.. 2
.. 1
" 1
mm
10 ± 0.2
10 ± 0.2
4 ± 0.1
2 ± 0.1
10- 25
Tensile test ISO 527-2/lA/50: Tensile test according to ISO 527-2; specimen type 1A; test speed 50 mm/min
Hardness test on plastics
d . DIN EN ISO 2039-1 (2003-061
Fo preload 9.8 N
Fm t est load
Ball indentation test
Fm
h
a
depth of penetration
distance from edge
s
specimen thickness
Test Specimens
distance from edge a .- 10 mm, minimum specimen thickness s " 4 mm
,::i
.-
..
··- t
_\
I
Ball indentation hardness Hin N/mm2 for indentation depth h in mm
0.16
0. 18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
0 .34
Test load
FminN
F
V,
I
I .
a
Test specimen
49
22
19
16
15
13
12
11
10
9
9
132
59
51
44
39
35
32
30
27
25
24
358
160
137
120
106
96
87
80
74
68
64
961
430
370
320
290
260
234
214
198
184
171
⇒
Ball indentation hardness ISO 2039-1 H 132: H- 31 N/mm2 at Fm= 132 N
Hardness test by Shore on plastics
I
I I sprmen F test load
F••
- '
,,,,
~
'Q
,,..,
~
s
specimen thickness
Test conditions for the Shore A and Shore D methods
_J
Shore D
0
0
depth of penetration
distance from edge
Distance from edge a " 9 mm, minimum specimen thickness s " 4 mm
Test
method
lndenters for
~
8
Test Specimens
' I
s; ~1
h
FA contact pressure in N
F Test
V,
cf. DIN EN ISO 868 (2003-061
".
Fmax
in N
FA
in N
Application
A
7.30
10
if Shore hardness with Type D is< 20
D
40.05
50
if Shore hardness with Type A is> 90
⇒
85 Shore A: Hardness value 85; test method Shore A
196
Material science: 4.13 Corrosion, Corrosion protection
Corrosion
Electrochemical series of metals
In galvanic corrosion the same processes occur as in electrical elements where the base metals are corroded. The
voltage produced between two dissimilar metals under influence of a conducting liquid (electrolyte) can be taken
from the standard potentials of the electrochemical series. Standard potential refers to the voltage produced between
the electrode material and a platinum electrode immersed in hydrogen.
Passivation (formation of protective layers) alters the voltage between the elements.
Electrode
materials
~
.,~
.,~
Mg
Al
Mn
I
I
I
;'.\
I
I
-2.5
-3
..-
"' -
;J
~
9 9
9 "9 9 0
Zn Cr
Fe
N i Sn H
~
~
0
~
0
Cu
~
Ag
+
- 0.5
-2
- 1.5
- 1
+0.5
0
Standard potentials of the e lectrode materials in volts
~
I increasingly noble
adr;a"rbase
ll
<-;
+
+
Pt
+1
+1 .5 1
'
f
Example: The standard potentials of Cu = + 0.34 V and Al = - 1.7 V y ield a voltage of U = +0.34 V - (- 1.67 V) = 2.01 V
between Cu and Al.
Corrosion behavior of metallic materials
Resistance in following environment
Materials
Corrosion behavior
Dry
ambient air
Unalloyed and
alloy steels
Only resist corrosion in dry
areas
Stainless
steels
Resistant, but not against
aggressive chemicals
Aluminum and
Al alloys
Resistant, except t he Al
alloys containing Cu
Copper and
Cu alloys
Resistant, especially
Cu alloys containing Ni
Sah
Country
air
Industrial
air
Sea
air
water
0
0
0
0
()
()
()
()
()
etoO
()
()
•
•
•
•
•
•
()
• resistant () fairly resistant
~
non•resistant
e toO
0 unusable
Corrosion protection
Preparation of metal surfaces before coating
Processing step
Purpose
Process
Mechanical cleaning
and creating a good
surface for adherence
Removal of m ill scale, rust and
dirt
Grinding, brushing, blasting with
water jet mixed w ith silica sand
Chemical cleaning and
creating an optimal
surface finish
Removal of mill scale, rust and grease
residues
Roughing or smoothing the surface
Etching with acid or lye;
degreasing w ith solvents;
chemical or electrochemical polishing
.
Preventative actions for corrosion protection
Actions
Examples
Select suitable materials
Stainless steel for parts fo r preparation in the
paper production
Observe corrosion protection principles in design
Same material o n contact points, insulation layers
between the pans, avoiding gaps
Protective layers: • protective oil or lubricant
• chemical surface treatment
• protective paint
Oiling sliding tracks and measuring tools
Phosphatizing, burnishing
Lacquer coat, possible after previous phosphatizing
Metallic coatings
Hot-dip galvanizing,
galvanic metal plating, e.g. chrome plating
Cathodic corrosion protection
Pan to be protected, e.g . a ship propeller,
is connected to a sacrificial anode
Anodic oxidatio n of Al materials
A corrosion-resistant permanent oxide layer is p roduced
o n the part, e.g. a rim
M at erial science: 4. 14 Hazardous m at erials
197
Disposal of substances*
Waste management laws
cf. Closed Substance Cycle and Waste Management Act (2001-10)
Important principles of recycling management
Avoid wast e, e.g. by in-house recycling management or a low-waste product design.
• Utilize material waste, e.g. by recovery of raw materials from waste (secondary raw materials).
• Use waste for recovery of energy (energy use), e.g . use as substitute fuel.
• Waste m ust be recycled properly w ithout adverse effect on the well being of the general public.
The disposal of waste is subject to monitoring by the responsible authorities (usually the administrative dist rict). In
panicular, w astes hazardous to health, air or water, explosive, and flammable especially need to be monitored.
The w aste producer is responsible for proper disposal and documentation of disposal.
Examples of w aste requiring special monitoring (hazardous w asteI in metal processing industry11
Disposal
code
Description of the
type of waste
Appearance, description,
source
150199D1
Packaging containing
hazardous impurities
Barrels, canisters, buckets and Emptied, drip free, brush or spatula clean
cans contain residues of
cond itions are not wastes requiring
paints, lacquers, solvents,
special monit oring. They are considered
cleaning agents, rust preventa- retail packaging. Disposal using the dual
t ives, rust and silicone
system or in metal bins using a waste
removers, spackle, etc.
management company. Bins w ith dried
paint are sim ilar to house-hold commercial
waste.
Spray cans with residual
Spray cans should be avoided if possible;
contents
they must be disposed as hazardous waste.
160602
Nickel cadmium
batteries
160603
Mercury dry cells
Special instructions,
actio ns
160604
A lkaline batteries
Rechargeable batteries, e.g.
All batteries containing contaminants are
from drills and screwdrivers, etc. labeled. The dealer must accept their return
at no charge.
Coin cell batteries, mercury
Consumers are required to return t hem to
containing monocell batteries
the dealer or to a public recycling center.
Non-rechargeable batteries
060404
Mercury containing
waste
Fluorescent lamps
(so-called ·neon tubes")
Can be recycled. Return to dealer or to
waste disposer.
Do not put in g lass recycling!
120 106
Used mach ining oils,
containing halogens, no
emulsio n
Water free drilling, turning,
g rinding and cutting oils,
so-called cooling lubricants
120107
Used machining oils,
Old, water free
halogen free, no emulsion ho ning o il
110
Synthetic machining oils
Avoid cooling lubricants as much as possible, e. g. by
• dry machining
• m inimum quantity cooling lubricatio n
Separat ed collection of different cooling
lubricants, emulsions, solvents. Inquire
with supplier for reprocessing or
combustion (energy recycling) options.
130202
Non- chlorinated machine, Used oil and gear oil,
hydraulic oil, compressor oil
gear and lubricating oils
from piston air compressors
150299D1
Vacuumed and filter materials, wipe cloths and protective clothing w ith hazardous contam inants
For example, used rags, clean- Option of using a rental service for cleaning
ing cloths; brushes contamicloths.
nated with oil or wax, oil
binders, oil and lubricant cans
130505
Other emulsions
Condensation water from
compressors
Use compressor oils w ith de-emulsifying
properties; inquire about t he optio n of oil
free compresso rs.
140102
Other halogenated
solvents and solvent
m ixtures
Per (-chloroet hane)
Tri (-chlo roethene)
Mixed solvents
Recycling by suppliers and t est replacement w ith aqueous cleaning solution.
Cooling lubricants fro m synt hetic o ils, e.g. on ester-based
Recycling through supplier or a licensed
waste disposal service.
Used oils of known orig in may be recycled
by secondary refi ning or energy recovery.
Do not m ix w ith other materials I
11 Regulation governing wastes requiring special monitoring - BestbuAbN ( 1999-01), Appendix 1: Wastes listed in
the European Waste Catalog (EAK w ast e) are considered t o be especially hazardous. Appendix 2: EAK wast e
req uiring special mo nitoring as w ell as waste types not on the EAK list ( Letter "D" in Disposal code).
*) According to European Standards
198
Material science: 4.1 4 Hazardous materials
Hazardous materials and material characteristics of hazardous gases
Identification and handling of hazardous materials
cf. EC Directive R 67/548/EEC11
Substance
ldentification21
Symbol A-phrases
S-phrases
Acetone
F,Xi
11; 36; 66; 67
9; 16; 26
Acetylene
F+
5; 6; 12
(2); 9; 16; 33
Kerosine
Acrylonitrile
F, T, N
45; 11; 23/24;
25; 37/38; 41;
43; 51/53
9; 16; 45;
53; 61
Phenol
Ammonia
C;N
34; 50
26; 36/37/39;
61
Phosphoric acid
Arsenic
T;N
23/25; 50/53
20/ 21; 28; 45;
60;61
Substance
Tetrachlorethane (•Per•)
ldentification21
Symbol A-phrases
S-phrases
X n;N
40; 51/53
23; 36/37;
61
T
45
53; 45
T;C
23/24/25; 34;
48/20/21/22;
68
24/25; 26;
28; 36/37;
39; 45
C
34
23; 45
Propane
F+
12
9; 16
T;N
23; 33; 50/53
7; 45; 60; 61
Asbestos
T
45; 48/23
53; 45
Mercury
Gasoline
T
45; 65
53; 45
Hydrochloric acid C
Benzene
F;T
45; 46;11;
36/38; 48/23/
24/25; 65
53; 45
Oxygen
Lead
compounds
T;N
61 ; 20/22; 33;
62; 50/53
Chromium
compounds
T;N
Hydrofluo ric acid
(HF)
34;37
26; 45
0
8
17
53; 45; 60; 61
Lubricating grease T
45
53; 45
49; 43; 50/53
53; 45; 60; 61
Lubricating oil
T
45
53; 45
T+;C
26/27/28;
35
7/9; 26;
36/37; 45
Sulphoric acid
C
35
26; 30; 45
Ceramic
m ineral fibers
T
49; 38
53;45
Styrene
Xn
10; 20; 36/38
23
Carbon
monoxide
F+;T
61; 12; 23;
48/23
53;45
Turpentine, oil
Xn;N
10; 20/21;
36/38; 43;
51/53; 65
36/37; 46;
61; 62
Fiber glass
Xn
38; 40
35/37
Trichlorethylene
(Tri)
T
45; 36/38;
52/53; 67
53; 45; 61
Nicotine
T+; N
25; 27; 51/53
36/37; 45; 61
Hydrogen
F+
12
9; 16; 33
11 As per Art. la of the Regulation on Hazardous Materials applicable in Germany since 31 October 2005
21 Cf. A-phrases on page 199, S-phrases on page 200, Safety signs on page 342; t he slash(/) between the number indi-
cates a combinatio n of A-phrases or S-phrases.
Material characteristics of hazardous gases
Density
ratio to air
Ignition
temperature
0.91
305°C
Argon
1.38
incombustible
Butane
2.11
365°C
Carbon dioxide
1.53
incombustible
Carbon monoxide
0.97
Hydrogen
Gas
Lower I Upper
ignition limit
vol.-% gas in air
Additional info rmation
82
W ith a pressure Pe> 2 bar self-disintegration
and explosion
-
-
Loss of breath; danger of suffocation
1.5
8.5
Narcotic effect; suffocating effect
-
-
Liquid CO2 and dry ice lead to serious frostbyte
605°c
12.5
74
Potent blood poison; damage to vision,
lungs, liver, kidneys and hearing
0.07
570°C
4
75.6
Spontaneous combustion w ith high escaping
speeds; forms explosive m ixtures w ith air, 0 2
and Cl
Nitrogen
0.97
incombustible
-
-
Lose of breath in enclosed spaces; danger of
suffocation
Oxygen
1.1
incombustible
-
-
Greases and oils react with oxygen explosively;
fire-promoting gas
Propane
1.55
470°C
2.1
9.5
Loss of breath; liquid propane causes damage
to skin and eyes
Acetylene
1.5
199
Material science: 4.1 4 Hazardous materials
Hazardous substances, R-phrases*
Hazardous substances adversely affect the safety and health of humans and endanger the environment. They must
be specially labeled (see page 342). The following R Phrases1I are standard phrases and point out the special risks
when handling a hazardous substance. Special safety data sheets for each hazardous substance contain further
extensive information.
cf. RL 67/548/EWG21 (2004-04)
R-Phrases: Notes on special risks
IR-Phrases•1
R1
R2
R3
-
Meaning
R-Phrases31
Meaning
Explosive when dry
R34
Causes burns
Risk of explosion by shock, friction,
R35
fire, or other sources of ignition
R36
Causes severe burns
Irritating to the eyes
Extreme risk of explosion by shock, friction,
fire, or other sources of ignition
R4
Forms very sensitive explosive metallic
compounds
R5
Heating may cause an explosion
R6
Explosive with or w ithout contact w ith air
R7
May cause fire
RS
Contact w ith combustible material may
cause fire
R37
Irritating to respiratory system
R 38
R39
R40
Irritating to the skin
R41
Risk of serious damage to eyes
R42
May cause sensitization by inhalation
Danger of very serious irreversible effects
Limited evidence of a carcinogenic effect
R43
May cause sensitization by skin contact
R44
Risk of explosion if heated under confinement
R 10
Flammable
R45
May cause cancer
R 11
Highly flammable
R46
May cause heritable genetic damage
R 12
Extremely flammable
R48
R 13
Extremely flammable liquid gas
Danger of serious damage to health by
prolonged exposure
R 14
Reacts violently with water
R 15
Contact with water liberates extremely
flammable gases
R 16
Explosive when mixed with
R49
May cause cancer by inhalation
R50
Very toxic to aquatic organisms
R 51
Toxic to aquatic organisms
R 52
Harmful to aquatic organisms
R 53
May cause long-term adverse effects
in the aquatic environment
R54
Toxic to flora (plants)
vapor-air mixture
R 55
Toxic to fauna (animals)
R 19
May form explosive peroxides
R 56
Toxic to soil organisms
R 20
Harmful by inhalation
R 57
Toxic to bees
R 21
Harmful in contact with skin
R 58
May cause long-term adverse effects
Dangerous to the ozone layer
May impair fertility
oxidizing substances
R 17
Spontaneously flammable in air
R 18
In use, may form flammable/explosive
in the environment
R 22
Harmful if swallowed
R 59
R 23
Toxic by inhalation
R 60
R 24
Toxic in contact with skin
R 25
Toxic if swallowed
R 26
Very toxic by inhalation
R27
Very toxic in contact with skin
R 28
Very toxic if swallowed
R 29
Contact with water liberates toxic
R61
May cause harm to the unborn child
R 62
Possible risk of impaired fertility
R 63
Possible risk of harm to the unborn child
R64
May cause harm to breastfed babies
R 65
Harmful: May cause lung damage if
swallowed
R66
Repeated exposure may cause skin dryness
or cracking
gases
R30
Can become highly flammable in use
R31
Contact with acids liberates toxic gases
R32
Contact with acids liberates very toxic
gases
R 33
Danger of cumulative effects
21 EU-Directive, Appendix Ill
11 R = Risk
31 Combinations of the risk phrases are possible; e.g.
*) Accordi ng to European Standards
R 67
Vapors may cause drowsiness
R 68
and dizziness
Possible irreversible damage
R 23/24: Toxic by inhalation and in contact with skin
200
Mat erial science: 4.14 Hazardous materials
Hazardous substances, S-Phrases*
The following standardized recommended saf ety measures (S phrases)'' are t o be followed while handling hazardous
substances and preparations. By complying with them dangers can be avoided or reduced.
S (safety) phrases: Recommended Safety Measures
Sphr- 31
Meaning
Sphrase31
d . RL 671'548,1EWG 21 (2004-04)
Meaning
S1
Keep locked up
S39
Wear eye/face protection
S2
Keep out of the reach of children
S40
S3
Keep in a cool place
To clean t he floor and all objects contam. by this
material, use ... (to be specif. by the manufacturer)
S4
Keep away from living quarters
S 41
S5
Keep contents under ... (appropriate liquid to
be specified by the manufacturer)
In case of fire and/or explosions do not breathe
fumes
S42
S6
Keep contents under ... (appropriate Iinert gas
to be specified by the manufacturer)
During fumigation/spraying wear suitable
respiratory equipment (appropriate
wording to be specified by the manufacturer)
S7
Keep container t ightly closed
S43
S8
Keep container dry
In case of fire, use ... (indicate in the space
the precise type of fire-fighting equipment
if water increases risk, add: 'Never use water')
S 45
In case of accident or if you feel unwell,
seek medical advice immediately
(show the label where possible)
S9
Keep container in a well-ventilated place
S 12
Do not keep the container sealed
S 13
Keep away from food, drink and animal
feeding stuffs
S46
S 14
Keep away from ... (incompatible materials
to be indicated by the manufacturer)
If swallowed, seek medical advice immediately
and show this container or label
S47
Keep at temperature not exceeding ... °C
S 15
Keep away from heat
S 16
Keep away from sources of ignition - no smoking
S48
Keep wet with ... (appropriate material
to be specified by the manufacturer)
(To be specified by the manufacturer)
S 17
Keep away from combustible materials
S 18
Handle and open container with care
S49
Keep only in the original container
S20
When using do not eat or drink
S 50
S 21
When using do not smoke
Do not mix w ith ... (to be specified
by the manufacturer)
S22
Do not breathe dust
S 51
Use only in well-ventilated areas
S23
Do not breathe gas/fumes/vapor/spray
(appropriate wording to be specified by t he
manufacturer )
S 52
Not recommended for interior use on large
surface areas
S53
S24
Avoid contact w ith skin
Avoid exposures"', obtain special
instructions before use
Dispose of this material and its container
at hazardous or special waste collection point
S 25
Avoid contact with eyes
S56
S 26
In case of contact w ith eyes, rinse immediately
with plenty of water and seek medical advice
S57
S 27
Take off immediately all contaminated
clothing
S 28
After contact w ith skin, wash immediately with
plenty of ... (to be specified by the manufacturer)
S 29
Do not empty into drains
S30
Never add water to this product
S33
Take precautionary measures against
static discharges
S35
This material and its container must be
disposed of in a safe w ay
S36
Wear suitable protective clothing
S37
Wear suitable gloves
S38
In case of insufficient ventilation,
wear suitable respiratory equipment
Use appropriate container to avoid 51
environmental contamination
S59
Refer to manufacturer/supplier for information
on recovery/recycling
S60
This material and its container must be
disposed of as hazardous waste
S61
Avoid release to the environment.
S62
If swallowed, do not induce vomiting:
seek medical advice immediately
and show this container or label
S63
In case of accident by inhalation: move victim to
fresh air and keep at rest
S64
If swallowed, rinse mouth with water (only if the
person is conscious)
Refer to special instructions/safety data sheets
11 S - safety
21 EU- Directive, Appendix IV
31 Combinations of t he S phrases are possible; e. g. S 20/21: when using do not eat. drink or smoke.
4 1 i.e. do not expose yourself to this hazard
51 Contamination, infestat ion
•) According to European Standards
Table of Contents
201
5 Machine elements
~
--
tF·--- -3t
5.1
Threads (overview) . . . . . . . . . . . . . . . . . . . . . . . . . 202
Metric ISO threads . . . . . . . . . . . . . . . . . . . . . . . . . 204
Whitworth threads, Pipe threads . . ........... 206
Trapezoidal and buttress threads . . . . . . . . . . . . . 207
Thread tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . 208
5.2
Bolts and screws (overview) . . . . . . . . . . . . . . . . . 209
Designations, strength . ..................... 210
Hexagon head bolts & screws ..... . ..... . ... 212
Other bolts & screws .. ........... . .... . . . .. 215
Screw joint calculations ..... . .... . .... .. .... 221
Locking fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Widths across flats, Bolt and screw drive systems 223
5.3
Countersinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
Countersinks for countersunk head screws . .. . 224
Counterbores for cap screws ... . . .. ..... . ... 225
5.4
Nuts (overview) . . . . .......... .. .... . .... . . 226
Designations, Strength .... . .. . ............. 227
Hexagon nuts ...... . ........... . ..... . .... 228
Other nuts ........... . ... . .... . ... . .. . ... . 231
5.5
Washers (overview) . . . . . . . . . . . . . . . . . . . . . . . . 233
Flat washers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
HV, Clevis pin, Conical spring washers . .... .. . . . 235
5.6
Pins and clevis pins (overview) . . . . . . . . . . . . . . . 236
Dowel pins, Taper pins, Spring pins .......... 237
Grooved pins, Grooved drive studs, Clevis pins . 238
5.7
Shaft-hub connections
Tapered and feather keys ... . ............ . ... 239
Parallel and woodruff keys .................. 240
Splined shafts, Blind rivets .. . ............... 241
Tool tapers ......... . .... .. ................ 242
5.8
Springs, components of jigs and tools
Springs .. . ........... . .......... . .. . ..... .244
Drill bushings . .... .. .. ...... .. ............ 247
Standard stamping parts .................... 251
5.9
Drive elements
Belts ................. . .. . ... .. . . ......... 253
Gears ....... . ..... . ...................... 256
Transmission ratios .. .. .. . . ..... . .... . . ... . 259
Speed graph .. ... .. ...... . .......... .. .... 260
___)
(
~ -=--
......
~
-
-~
5.10 Bearings
Plain bearings (overview) ..... . . . . ... .... .. . 261
Plain bearing bushings . .... . . . ... . . . .. . .. . . 262
Antifriction bearings (overview) ........... . .. 263
Types of roller bearings . ... ..... . ... . ....... 265
Retaining rings .. . . . ... . ............. . ..... 269
Sealing elements . . . . . . . . . . . . . . . . . . . . . . . . . . 270
Lubricating oils ..... . .... .. .......... . ..... 271
Lubricating greases ... . .. . .... .. . ... . . ..... 272
202
Machine elements: 5.1 Threads
Types of threads, Overview
cf DIN 202 11999 111
Right-hand threads, single-start
Thread
name
Metric threads
ISO threads
Metric threads with
large clearance
Metric straight
internal threads
Thread profile
II
Code Designation
letter example
Nominal Biz•
Application
DIN 14 - M 08
0.3to0.9 mm
Clocks, precision
mechanisms
DIN 13 - M 30
1 to 68 mm
General purpose
(coarse t hread)
DIN 13- M 20 x 1
1 to 1000 mm
General purpose
(fine thread)
DIN 2510 - M 36
12 to 180 mm
Bolt s/screws w ith
anti-fatigue shank
DIN 158- M 30 x 2
6to60 mm
Drain plugs and
grease nipples
DIN 158- M 30 x 2 keg
6 1060 mm
Drain plugs and
grease nipples
M
Metric
taper
external threads
;s:
M
Pipe threads,
st raight
~
G
60°
-
Parallel
pipe threads
(internal threads)
Taper
p ipe threads
(external th reads)
Metric ISO
trapezoidal
threads
Buttress threads
Knuckle threads
Tapping screw
threads
DIN ISO 228-G11/ 2 (internal)
1
DIN ISO 228 G112A (external) /a to 6 inches
DIN 2999-Rp 112
1
DIN 3858- Rp 11a
'la to 1 112 inch
DIN2999-R ½
1/
16 to 6 inches
DIN 3858- R 1ls-1
'ts to 1 ''2 i nches
Tr
DIN 103- Tr 40 x 7
8 10300mm
General purpose as
motion screw
threads
s
DIN 513-S 48 x 8
10 to 640 mm
General purpose as
motion screw
threads
DIN 405- Rd 40 x 116
8to 200 mm
General purpose
DIN 20400- Rd 40 x 5
10to300 mm
Knuckle threads wilt
large thread overlap
ISO 1478- ST 3,5
1.5 to 9.5 mm
For tapping
screws
0
/,s t o 6 inch
Rp
D t i-- ~ 16
g
-&
Does not seal on
t hread
R
Rd
ST
Designation of left-hand and multiple start threads
Pipe t hreads,
seals on thread;
for threaded pipe,
fittings, screwed
pipe joints
cf. DIN ISO 965-1 (1999-11)
Type of thread
Explanation
Left-hand threads
T he code designation "LH" is placed after the complete M30- LH
Tr 40 x 7 - LH
t hread designat ion (LH = Left-Hand).
Code designation (examples)
Mult iple start
The lead Ph and the pitch Pfollow the code designatio n M 16xl't,3 P 1,5or
right-hand thread and the t hread diameter.
M 16 x Ph 3 P 1,5 (double-start)
Multiple start left- " LH " is placed after the thread designation of the mult i- M 14 x Pt, 6 P 2-LH or
hand thread
p ie start. 11
M 14 x Pt, 6 P 2 (triple-start)-LH
11 For parts which have right-hand and left-hand threads, "RH" (Right-Hand) is placed after the thread designation of
the right-hand thread and "LH" (Left-Hand) after the left-hand t hread. The number of starts fo r multiple-starts is
found by: no. of starts = lead Ph/ pitch P.
203
Machine elements: 5.1 Threads
Thread standards of various countries (selection) 1)
Thread name
Thread profile
Code
Thread designation
Country 21
Example
Meaning
UNC
1/4- 20 UNC- 2A
ISO-UNC-thread
with 1/4 inch
nominal diameter,
20 threads/inch,
Class 2A
ARG,AUS,
CAN,GBR,
IND,JPN,
NOR, PAK,
SWE
and others
UNF
1/ -28 UNC-3A
4
ISO-UNF threads
w ith 1/4 inch
nominal diameter,
28 threads/inch,
Class 3A
ARG,AUS,
CAN,GBR,
IND, JPN,
NOR, PAK,
SWE
and others
UNEF
1
/ 4-32 UNEF - 3A
ISO-UNEF thread
with 1/4 inch
nominal diameter,
32 threads/inch,
Class 3A
ARG,AUS,
CAN, IND,
NOR, PAK,
SWE
and others
Unified National
Special Thread,
special diameter/lead
combinations
UNS
1
/4-27 UNS
UNS threads with
1/ inch nominal
4
diameter,
27 threads/inch
ARG,AUS,
CAN, NZL,
USA
Straight Pipe
Threads for
Mechanical Joints
NPSM
1/,- 14 NPSM
NPSM threads
with 1/ 2 inch
nominal diameter,
14 threads/inch
USA, CAN
NPT
3ia-18NPT
NPTthread
with 3ia inch
nominal diameter,
18 threads/inch
BRA,CAN,
FRA,USA
and others
NPTF
1
/ , - 14 NPTF
(dryseal)
NPTF threads
with 1/ 2 inch
nominal diameter,
14 threads/inch,
(dry sealing)
BRA.CAN,
USA
Acme threads
with 13/ 4 inch
nominal diameter
4 threads/inch,
Class 2G
AUS, CAN,
GBR, NZL,
USA
Stub Acme threads
w ith 1/ 2 inch
nominal diameter,
20 threads/inch
CAN, USA
Unified National
Coarse Thread
...
Unified National Fine
Thread
internal thread
Unified National
Extra Fine
Thread
external thread
p
straight
external thread
American Standard
Taper Pipe Thread
tape r
internal thread
American Taper Pipe
Thread, Fuel
taper
external thread
American trapezoidal
threads
h = 0.5 • P
Acme
American truncated
trapezoidal threads
h = 0.3- P
Stub
Acme
1/z-20 Stub
Acme
external thread
11 cf. Kaufmann, Manfred: "Wegweiser zu den Gewindenormen verschiedener Lander"
DIN, Beuth-Verlag
21 Three-letter codes for countries, cf. DIN EN ISO 3166-1 (2008-06)
203 a
Machine elements: 5.1 Threads
Imperial Threads
Imperial Threads for general purposes
p
internal thread
\
"Aff '
N
~
~IN
II
::i::
:i':
::£
~J
.,,
~
co
:i':
,,, , ,,,,,,
~
:J
.,,
external t hread
c:5"
Major diameter
Pitch
Depth of external t hread
Depth of internal t hread
Radius at root
Basic pitch 0
M inor 0 of external thread
M inor 0 of internal thread
Tap hole drill 0
Thread angle
h3 = 0.6134 • P
H1 = 0.5413 • P
R = 0.1443 • P
di = 0-, = d - 0.6495 • P
OJ = d- 1.1904-P
0 1 = d- 1.0825 • P
= d-P
60°
Stress area
s =
d =D
p
Basic sizes for Unified National Coarse Threads (UNCI
Minor
No.
size
o r inches
6
8
10
12
1/4
5/16
318
7/16
1/2
9/16
5/8
3/4
7/8
1
1 1/8
11/4
1318
1 1/2
1 3/4
2
Major
per inch diameter
D
inches
32
0.1380
32
0.1640
24
0.1900
24
0.2160
20
0.2500
18
0.3125
16
0.3750
14
0.4375
13
0.5000
12
0.5625
11
0.6250
10
0.7500
9
0.8750
1.0000
8
7
1.1250
7
1.2500
6
1.3750
6
1.5000
1.7500
5
4.5
2.0000
Pitch
Threads
diameter
External
threads
Internal
threads
p
inches
0.0313
0.0313
0.0417
0.0417
0.0500
0.0556
0.0625
0.0714
0.0769
0.0833
0.0909
0.1000
0.111 1
0.1250
0.1429
0.1429
0.1667
0.1667
0.2000
0.2222
d:,~D,
d:,
0,
inches
0.1177
0.1437
0.1629
0.1889
0.2175
0.2764
0.3344
0.3911
0.4500
0.5084
0.5660
0.6851
0.8028
0.9188
1.0322
1.1572
1.2668
1.3918
1.6201
1.8557
inches
0.1008
0.1268
0.1404
0.1664
0.1905
0.2464
0.3006
0.3525
0.4084
0.4633
0.5168
0.6310
0.7427
0.8512
0.9549
1.0799
1.1766
1.3016
1.5119
1.7355
inches
inches
inches
0.1042
0.1302
0.1449
0.1709
0.1959
0.2524
0.3073
0.3602
0.4167
0.4723
0.5266
0.6418
0.7547
0.8647
0.9704
1.0954
1.1946
1.3196
1.5335
1.7594
0.01920
0.01920
0.02558
0.02558
0.03067
0.03411
0.03834
0.04380
0.04717
0.05110
0.05576
0.06134
0.06815
0.07668
0.08765
0.08765
0.10225
0.10225
0.12268
0.13630
0.01691
0.01691
0.02255
0.02255
0.02706
0.03007
0.03383
0.03866
0.04164
0.04511
0.04921
0.05413
0.06014
0.06766
0.07732
0.07732
0.09021
0.09021
0.10825
0.12028
,,,
R
Stress
area 5
inct,2
inches
0.0045
0.0045
0.0060
0.0060
0.0072
0.0080
0.0090
0.0103
0.011 1
0.0120
0.0131
0.0144
0.0160
0.0180
0.0206
0.0206
0.0241
0.0241
0.0289
0.0321
0.0093
0.0142
0.0179
0.0246
0.0324
0.0532
0.0786
0.1078
0.1438
0.1842
0.2288
0.3382
0.4666
0.6120
0.7713
0.9781
1.1664
1.4179
1.9171
2.5207
Radius
Basic sizes for Unified National Fine Threads (UNFI
No.
Threads
Major
per inch diameter
size
or inches
D
inches
6
8
10
12
1/4
!i/16
318
7/16
1/2
9/16
5/8
3/4
7/8
1
11/8
11/4
1 318
11/2
40
36
32
28
28
24
24
20
20
18
18
16
14
12
12
12
12
12
0.1380
0.1640
0.1900
0.2160
0.2500
0.3125
0.3750
0.4375
0.5000
0.5625
0.6250
0.7500
0.8750
1.0000
1.1250
1.2500
1.3750
1.5000
Pitch
p
inches
0.0250
0.0278
0.0313
0.0357
0.0357
0.0417
0.0417
0.0500
0.0500
0.0556
0.0556
0.0625
0.0714
0.0833
0.0833
0.0833
0.0833
0.0833
(d2; cf.Jr
ANSI/ASME 81.1 (1989)
Thread depth
External
Internal
threads
threads
H,
Pitch
Minor
Pitch
External Internal
diameter threads threads
i·
Drill bit for tap hole
Drill size Decimal
equival.
#36
#29
#25
#16
#7
F
5/16
u
27/64
31/64
17132
21132
49/64
7/8
63/64
1 7/64
1 7132
111132
1 9/16
125/32
0.1065
0.1360
0.1495
0.1 770
0.2010
0.2579
0.3125
0.3680
0.4219
0.4843
0.5313
0.6562
0.7656
0.8750
0.9844
1.1093
1.2187
1.3437
1.5625
1.7812
ANSI/ASME 81.1 (19891
Thread depth
External
Internal
threads
threads
d:, • D,
d:,
0,
,,,
inches
0. 1218
0.1460
0.1697
0.1928
0.2268
0.2854
0.3479
0.4050
0.4675
0.5264
0.5889
0.7094
0.8286
0.9459
1.0709
1.1959
1.3209
1.4459
inches
0.1082
0.1309
0.1528
0.1735
0.2075
0.2629
0.3254
0.3780
0.4405
0.4964
0.5589
0.6756
0.7900
0.9008
1.0258
1.1508
1.2758
1.4008
inches
0.1109
0.1339
0.1562
0.1773
0.2113
0.2674
0.3299
0.3834
0.4459
0.5024
0.5649
0.6823
0.7977
0.9098
1.0348
1.1598
1.2848
1.4098
inches
0.0153
0.0170
0.0192
0.0219
0.0219
0.0256
0.0256
0.0307
0.0307
0.0341
0.0341
0.0383
0.0438
0.0511
0.0511
0.0511
0.0511
0.0511
H,
inches
0.01353
0.01504
0.01691
0.01933
0.01933
0.02255
0.02255
0.02706
0.02706
0.03007
0.03007
0.03383
0.03866
0.04511
0.04511
0.04511
0.04511
0.04511
Radius
R
inches
0.0036
0.0040
0.0045
0.0052
0.0052
0.0060
0.0060
0.0072
0.0072
0.0080
0.0080
0.0090
0.0103
0.0120
0.0120
0.0120
0.0120
0.01 20
Stress
areas
inch2
Drill bit for tap hole
Drill size Decimal
equival.
0.0103
0.0149
0.0203
0.0262
0.0368
0.0587
0.0886
0.1198
0.1612
0.2046
0.2578
0.3754
0.5127
0.6674
0.8607
1.0785
1.3208
1.58n
#33
#29
#21
#14
I
I
Q
25/64
29/64
33/64
37/64
11/16
13/16
59/64
1 3/64
1 11164
119/64
1 27/64
0.1130
0.1360
0.1590
0.1820
0.2720
0.2720
0.3320
0.3906
0.4531
0.5156
0.5781
0.6875
0.8125
0.9219
1.0469
1.1719
1.2968
1.4219
203 b
Machine elem ents: 5. 1 Threads
Imperial Threads
Basic sizes National Pipe Taper (NPT)
ANSI/ASME 8 1.20. 1 - 1983 (R 1992)
p
internal
thread
Cl..
a,
N
,,,
Thread depth h3 = 0.8 • P
Hight
H = 0.865 • P
C>
C>
outside
diameter
~;~
Cl..
a,
N
,,,
~
C>
Thream
Outside
diam. of pipe
No. size
D
1/16
1/8
1/ 4
3/8
1/ 2
3/4
1 1/4
11/2
2 1/2
27
27
18
18
14
14
11 1/2
11 1/2
11 1/2
11 1/2
8
0.3125
0.4050
0.5400
0.6750
0.0625
1.0500
1.3150
1.6600
1.9000
2.3750
2.8750
Pitch
p
0.03704
0.03704
0.05556
0.05556
0.07143
0.07143
0.08696
0.08696
0.08696
0.08696
0.12500
Gauge
length
d;, - 0,
L,
all dimensions in inches
0.28120
0.1598
0.37360
0.1613
0.49163
0.2275
0.62701
0.2398
0.77843
0.3199
0.98887
0.3391
1.23863
0.3997
1.58338
0.4197
0.4197
1.82234
2.29627
0.4354
2.76215
0.6825
Pitch
diameter
Usuable
length of
Depth of
Drill bit for tap hole
Drill size
Decimal
equival.
ext thread
external
thread
t,
"3 = 8P
0.2611
0.2639
0.4018
0.0478
0.5337
0.5457
0.6828
0.7068
0.7235
0.7565
1.1375
0.02963
0.02963
0.04444
0.04444
0.05714
0.05714
0.06957
0.06957
0.06957
0.06957
0.10000
C
a
7/16
9/16
45/64
29/32
1 9/64
1 31/64
1 23/32
2 3/16
2 39/64
0.2420
0.3320
0.4380
0.5620
0.7030
0.9060
1.1410
1.484
1.7190
2.1880
2.6090
Basic sizes American National Standard General !up. Acme Screw Thread ANSVASME B1.5 - 1988 (R 1994)
ac
ac
R,
R2
c:{
M inor 0 external threads
Major 0 internal threads
Minor 0 internal threads
Pitch 0
Thread depth
Width of flat
up to 10 tpi = 0.020
over 10 tpi = 0.010
0.06- P
0.12 • P
d:i = d-(P+2•ac)
04 = d+2-a,,
0 1 = d-P
<J., = 0, = d - 0.5 • P
h:, = H4 = 0.5 • P + ac
w = 0.370 • P - 0.259 • ac
Minor diameter
Pitch
p
No. size
Pitch diameter
External thread
d;, - 0,
D,
Thread depth
"3=H4
0.2917
0.3542
0.4000
0.5000
0.5833
0.7083
0.8000
0.9250
1.0500
1.1250
1.2500
1.5000
1.7500
1.9167
2.1667
2.4167
2.5000
3.0000
3.5000
4.0000
4.5000
0.0517
0.0517
0.0700
0.0825
0.1033
0.1033
0.1200
0.1200
0.1200
0.1450
0.1450
0.1450
0.1450
0.1867
0.1867
0.1867
0.2700
0.2700
0.2700
0.2700
0.2700
Internal thread
all dimensions in inches
3/8
7/16
1/2
518
3/4
7/8
11/8
11/4
1 3/8
1 1/2
1 3/4
2
2 1/4
2 1/2
2 3/4
3
3 1/2
4
4 1/2
5
12
12
10
8
6
6
5
5
5
4
4
4
4
3
3
3
2
2
2
2
2
0.3750
0.4375
0.5000
0.6250
0.7500
0.8750
1.0000
1.1250
1.2500
1.3750
1.5000
1.7500
2.0000
2.2500
2.5000
2.7500
3.0000
3.5000
4.0000
4.5000
5.0000
0.0833
0.0833
0.1000
0.1250
0.1667
0.1667
0.2000
0.2000
0.2000
0.2500
0.2500
0.2500
0.2500
0.3333
0.3333
0.3333
0.5000
0.5000
0.5000
0.5000
0.5000
0.3333
0.3958
0.4500
0.5625
0.6667
0.7917
0.9000
1.0250
1.1500
1.2500
1.3750
1.6250
1.8750
2.0833
2.3333
2.5833
2.7500
3.2500
3.7500
4.2500
4.7500
0.2717
0.3342
0.3600
0.4600
0.5433
0.6683
0.7600
0.8850
1.0100
1.0850
1.2100
1.4600
1.7100
1.8767
2.1267
2.3767
2.4600
2.9600
3.4600
3.9600
4.4600
204
Machine elements: 5.1 Threads
Metric threads and fine threads
Metric ISO threads for general purpose application, basic profiles
p
internal thread
Cl..
:i:
~ ,N
II
:i::
"£
?&a
~l
.i:]
,5'
-0
external thread
"t,
c:5"
d =D
p
Major diam eter
Pitch
Depth of external thread
Depth of internal thread
Radius at root
Basic pitch 0
M inor 0 of external thread
Minor 0 of internal thread
Tap hole drill 0
Thread angle
Stress area
ex,
\ .., ,, , ,,,,., :i:
N
d. DIN 13-19 (1999-1 1)
h3 = 0.6134 • P
H, = 0.5413 • P
R = 0.1443 • P
cJ-, = ~ = d-0.6495 • P
dJ = d- 1.2269 • P
0 1 = d- 1.0825 • P
= d- P
50•
S =~ - ( d-,;d3)2
Basic sizes for coarse threads Series 111 (dimensions in mm)
design&-
external
threads
internal
threads
threads
threads
root
Stress
area&
0 for
tap
Minor0
Pitch
Pltch0
tion
d . DIN 13-1 (1999-11)
Thread depth
external internal Rounded
Thread-
Drill bit
Hexagonal widtt1
across
flats31
d:D
p
da=Oz
d,
o,
h3
H1
R
mm2
hole 2l
M1
M 1.2
M 1.6
0.25
0.25
0.35
0.84
1.04
1.38
0.69
0.89
1. 17
0.73
0.93
1.22
0.15
0.15
0.22
0.14
0.14
0.19
0.04
0.04
0.05
0.46
0.73
1.27
0.75
0.95
1.25
-
M2
M2.5
M3
0.4
0.45
0 .5
1.74
2.21
2.68
1.51
1.95
2.39
1.57
2.01
2.46
0.25
0.28
0.31
0.22
0.24
0.27
0.06
0.07
0.07
2.07
3.39
5.03
1.6
2.05
2.5
4
5
5.5
M4
M5
M6
0.7
0.8
1
3.55
4.48
5.35
3.14
4.02
4.n
3.24
4. 13
4.92
0.43
0.49
0.61
0.38
0.43
0.54
0.10
0.12
0.14
8.78
14.2
20.1
3.3
4.2
5.0
7
8
10
MB
M10
M 12
1.25
1.5
1.75
7.19
9.03
10.86
6.47
8. 16
9.85
6.65
8.38
10.11
0.77
0.92
1.07
0.68
0.81
0.95
0.18
0.22
0.25
36.6
58.0
84.3
6.8
8.5
10.2
13
16
18
M 16
M20
M24
2
2.5
3
14.70
18.38
22.05
13.55
16.93
20.32
13.84
17.29
20.75
1.23
1.53
1.84
1.08
1.35
1.62
0.29
0.36
0.43
157
245
353
14
17.5
21
24
30
36
M30
M36
M42
3.5
4
4.5
27.73
33.40
39.08
25.71
31 .09
36.48
26.21
31.67
37.13
2.15
2.45
2.76
1.89
2.17
2.44
0.51
0.58
0.65
561
817
1121
26.5
32
37.5
46
55
65
M48
M56
M64
5
5.5
6
44.75
52.43
60. 10
41.87
49.25
56.64
42.59
50.05
57.51
3.07
3.37
3.68
2.71
2.98
3.25
0.72
0.79
0.87
1473
2030
2676
43
50.5
58
75
85
95
Basic sizes for fine threads (dimensions in mm)
Thread
3.2
cf. DIN 13-2- 10 (1999-11 )
Thread
Pltch 0
Mlnpr0
designation
ext. th. int. th.
dxP
o,
da=Dz d,
designation
d xP
da= Dz
"3
o,
dx P
da=Dz
"3
o,
M 2 x0.25
M 3 x 0.25
M4x0.2
1.84
2.84
3.87
1.69
2.69
3.76
1.73
2.73
3.78
M 10 x 0.25
M 10 x 0.5
M 10 x 1
9.84
9.68
9.35
9.69
9.39
8.77
9.73
9.46
8.92
M 24X 2
M30x 1.5
M30x 2
22.70
29.03
28.70
21.55
28.16
27.55
21 .84
28.38
27.84
M 4 x 0.35
M 5 x 0.25
M 5 x 0.5
3.77
4.84
4.68
3.57
4.69
4.39
3.62
4.73
4.46
M 12 x 0.35
M 12 x 0.5
M 12 x 1
11.77
11.68
11.35
11.57
11.39
10.77
11.62
11.46
10.92
M36x 1.5
M36X 2
M42x1.5
35.03
34.70
41.03
34.16
33.55
40.16
34.38
33.84
40.38
M 6 x 0.25
M 6 x 0.5
M 6 x 0.75
5.84
5.68
5.51
5.69
5.39
5.08
5.73
5.46
5.19
M 16 x 0.5
M 16 x 1
M 16X 1.5
15.68
15.35
15.03
15.39
14.77
14.16
15.46
14.92
14.38
M42 x2
M48x 1.5
M48 X 2
40.70
47.03
46.70
39.55
46.16
45.55
39.84
46.38
45.84
M 8 x 0.25
M 8 x 0.5
M8x 1
7.84
7.68
7.35
7.69
7.39
6.77
7,73
7.46
6.92
M 20 x 1
M20 x 1.5
M 24 x 1.5
19.35
19.03
23.03
18.77
18.16
22.16
18.92
18.38
22.38
M56x1.5
M 56 x 2
M 64 x 2
55.03
54.70
62.70
54.16
53.55
61 .55
54.38
53.84
61.84
Pitch 0
Thread
Minor0
Minor0
Pitch 0
ext. th. int. th. designation
ext. th. int th.
11 Series 2 and Series 3 also have intermediate sizes (e. g. M7, M9, M 14).
2 1 cf. DIN 336 (2003-07)
3) cf. DIN ISO 272 ( 1979-10)
205
Machine elements: 5.1 Threads
Metric taper threads
-
Metric taper external and mating
internal straight screw threads (standard design)11
p
ii
--,1 , 16
-
2
::r:::100
H
/1
jj""
2
reference
plane
O..g
t hread axis
---
--
-
Thread
designation
length
d x I'
M 5 keg
M 6keg
M 8x 1 keg
M 10 x 1 keg
M 12 x 1 keg
M 10 x 1.25 keg
M 12 x 1.25 keg
M 12 x 1.5 keg
M 14x 1.5 keg
M 16x 1.5keg
M 18 x 1.5 keg
M 2Qx 1.5keg
M 22X 1.5 keg
M 24 x 1.5 keg
M 26x 1.5 keg
M 30 x 1.5keg
M36x 1.5keg
M38x 1.5 keg
M42x 1.5 keg
M 45x 1.5 keg
M 48 x 1.5keg
M52x 1.5 keg
M27X2 keg
M 30x2 keg
M 33•2 keg
M 36 x 2 keg
M 39x2 keg
M 42 X2 keg
M45x2 keg
M 48 x 2 keg
M 52x2 keg
M 56x2 keg
M60x2 keg
⇒
.;;' -c:,_
-~
,.;;
b
~
reference
plane
,,
"3 max.
5
0.52
2
5.5
0.66
2.5
depth
7
0.82
3
8.5
0.98
3.5
Thread dimensions
d:021 d.z: D.z3I
5
30
6
33
36
39
42
45
1.34
48
52
56
60
Dimensions in inspection plane
Disstance
Thread dimensions
d '3
4.07
4.84
6.84
8.84
10.84
8.59
10.59
10.35
12.35
14.35
16.35
18.35
20.35
22.35
26.19
30.19
36.22
38.22
42.22
45.22
48.22
52.22
27.25
30.25
33.25
36.25
39.25
42.25
45.25
48.25
52.25
56.25
60.25
25.2
29.2
24.35
28.35
35.2
37.2
41.2
44.2
47.2
51.2
25.9
28.9
3 1.9
34.9
37.9
40.9
43.9
46.9
50.9
54.9
58.9
34.38
36.38
40.38
43.38
46.38
50.38
24.80
27.80
30.80
33.80
36.80
39.80
42.80
45.80
49.80
53.80
57.80
24.16
28.16
34. 16
36.16
40.16
43.1 6
46.16
50.16
24.55
27.55
30.55
33.55
36.55
39.55
42.55
45.55
49.55
53.55
57.55
1.32
R = 0.144. P
4.5
5.4
7.4
9.4
11.4
9.3
11.3
11.2
13.2
15.2
17.2
19.2
21.2
23.2
25.03
29.03
35.03
37.03
41.03
44.03
47.03
51.03
25.70
28.70
31.70
34.70
37.70
40.70
43.70
46.70
50.70
54.70
58.70
12
Root radius
H1 = 0.866 • P
d '2
26
4.5
"3 - 0.613 • P
5.05
6.06
8.06
10.06
12.06
10.13
12.13
12.19
14.19
16.19
18.19
20.19
22.19
24.19
11.35
9.19
11.19
11.03
13.03
15.03
17.03
19.03
21.03
23.03
1.01
Thread dept h
2.8
12
10
12
12
14
16
18
20
22
24
10.5
d3=d- 1.23 - P
d'
8
10
36
38
42
45
48
52
27
cl, = d-0.650 • p
M inor 0
Height
b
4.02
4.77
6.77
8.77
10.77
8.47
10.47
10.16
12. 16
14. 16
16. 16
18.16
20. 16
22.16
30
Pitch 0
d.i
4.48
5.35
7.35
9.35
5
6
Thread dimensions of
external threads
inspection
plane
Dimensions in reference plane
Thread
Distance
a
13
I
~
"'
inspection
-i-' --plane--
Thread dimensions
Thread
iI '--
v
300' 30°
' ::t::j-o
"' ;:;
;:;
:i1
,<::
,;'
/
cf. DIN 158-1 (1997-06)
3.5
5
6.5
8
9
10
Threads DIN 158 - M 30 x 2 keg: Metric t aper external threads, d • 30 mm, P • 2 mm,
standard design
1l For self -sealing jo ints (e.g. Drai n plugs, g rease nip ples). For larger nominal d iamet ers it is recommended to use
a joint compound to seal in the t hreads.
3> CJi Basic pitch diameter of internal thread
21 D Basic major diameter of internal thread
206
Machine elements: 5.1 Threads
Whitworth threads, Pipe threads
Whitworth threads
(not standardized)
external t hread
Major diameter
M inor diameter
d =D
d, = D, =d- 1.28 - P
Pit ch diameter
Threads/inch
Pitch
= d - 2 . t,
d2 = Di = d - 0.640 • P
N
25.4mm
p =- - N
Thread dept h
Radius
Thread angle
R = 0.137. P
h 1 = H1 = 0.640 • P
55°
Dimensions In mm for external and Internal threads Thread Dimensions in mm for external and internal threads
Thread
desig- Major Minor Pitch Threads Thread Core desig- Major Minor Pitch Threads Thread Core
nation
0
0
0
depth section
0
0
0
i=. depth . : . , nation
1
d
d:D d,:O, dz=D.,
N
h,:H, mm'
d
d : D d,=0, dz=D.,
N
h,:H, mm'
.=,
6.35
7.94
9.53
12.70
4.72
6.13
7.49
9.99
5.54
7.03
8.51
11.35
20
18
16
12
0.81
0.90
1.02
1.36
17.5
29.5
44.1
78.4
1¼"
11/2"
131,•
2·
3 1.75
38.10
44.45
50.80
27.10
32.68
37.95
43.57
29.43
35.39
41.20
47.19
7
6
5
4.5
2.32
2.71
3.25
3.61
577
839
1 131
1 491
15.88
19.05
22.23
25.40
12.92
15.80
18.61
21.34
14.40
17.42
20.42
23.37
11
10
9
8
1.48
1.63
1.81
2.03
131
196
272
358
2¼"
2½"
3"
3 1/2"
57.15
63.50
76.20
88.90
49.02
55.37
66.91
78.89
53.09
59.44
72.56
83.89
4
4
3.5
3.25
4.07
4.07
4.65
5.00
1886
2408
3516
4888
Pipe threads
cl. DIN ISO 228-1 (2003-05), DIN EN 10226-1 (2004-10)
Pipe threads DIN ISO 228-1
Pipe threads DIN EN 10226-1
for joints not sealed by threads;
straight i nternal and external threads
sealed by t hreads;
straight internal threads, taper external t hreads
p
55°
""' .;;
external thread
straight
internal t hread
cf. American Taper Standard-Pipe Threads NPT: page 203
Thread designation
DIN ISO 228-1
DIN EN10226-1
External and
External Internal
internal threads threads
threads
Major
Pitch
Minor
diameter diameter diameter
Profile
height
Usable
length ol
external
threads
d=D
dz = D.,
d, = 0,
p
Threads
per
Inch
N
Rp1/1s
Rp'/a
Rp' /•
7.723
9.728
13.157
7.142
9.147
12.301
6.561
8.566
11.445
0.907
0.907
1.337
28
28
19
0.581
0.581
0.856
6.5
6.5
9.7
G3ia
G'i,
G¾
R1/,s
R1/a
R1/ 4
R3ia
R'i,
Rl/4
Rp3ia
Rp1/,
Rpl/4
16.662
20.995
26.441
15.806
19.793
25.279
14.950
18.631
24.117
1.337
1.814
1.814
19
14
14
0.856
1.162
1.162
10. 1
13.2
14.5
G1
G11/4
G1'1,
R1
R1 1/4
R11/2
Rp1
Rp1¼
Rp11/2
33.249
41.910
47.803
31.770
40.431
46.324
30.291
38.952
44.845
2.309
2.309
2.309
11
11
11
1.479
1.479
1.479
16.8
19.1
19.1
G2
G21/2
G3
R2
R21!,
R3
Rp2
Rp2 1!,
Rp3
59.614
75.184
87.884
58.135
73.705
86.405
56.656
72.226
84.926
2.309
2.309
2.309
11
11
11
1.479
1.479
1.479
23.4
26.7
29.8
G4
G5
G6
R4
R5
R6
Rp4
Rp5
Rp6
113.030
138.430
163.830
111.551
136.951
162.351
110.072
135.472
160.872
2.309
2.309
2.309
11
11
11
1.479
1.479
1.479
35.8
40.1
40.1
G'i,s
G'ia
1
G /•
Pitch
h:h,:H,
"'
207
Machine elem ents: 5.1 Threads
Trapezoidal and buttress threads
Metric ISO trapezoidal screw threads
Dimension
cf. DtN 103-1 (1977-041
1.5
Fo r pitch P in mm
2- 5
6-12
14-44
0.15
0.075
0.15
0.25
0.125
0.25
1
0.5
1
0.5
0.25
0.5
n = Ph : p
d3 = d - (P+2·/Jc)
o. = d+2 • "c
D,
d- P
0, = d - 0.5-P
d,.
H• = 0.5 • P + Be
~
H, = 0,5 • P
Be
R1 and R2
W= 0.366 • P-0.54 • Be
30°
Minor 0
Minor 0
designation
dx P
Pltd,
p
Ph
Thread clmensions in mm
Thread dimensions in mm
Thread
d
Nominal diameter
Single start pitch
and multi ple start lead
Mult iple start pitch
No. of threads
M ino r 0 external threads
Major 0 internal threads
Minor 0 internal t hreads
Pitch0
Th read depth
Thread overlap
Crest clearance
Radius
Width of flat
Thread angle
Thread
Major Thread Width designation
0
depth of flat
axt. th. int. th.
dXP
Major Thread Width
0
depth of flat
d.,
0,
o. "3 =H.
w
o.
h;, =H.
w
Tr 10 X
Tr 12 x
2
3
9
10.5
7.5
8.5
8
9
10.5
12.5
1.25
1.75
0.60
0.96
Tr 40 X
Tr 44 X
7
7
36.5
40.5
32
36
33
37
41
45
4
4
2.29
2.29
Tr 16 X
Tr 20 X
4
4
14
18
11.5
15.5
12
16
16.5
20.5
2.25
2.25
1.33
1.33
Tr 48 X
Tr 52 X
8
8
44
48
39
43
40
44
49
53
4.5
4.5
2.66
2.66
Tr 24 x
Tr 28 x
5
5
21.5
25.5
18.5
22.5
19
23
24.5
28.5
2.75
2.75
1.70
1.70
Tr 60 X 9
Tr 70 X 10
55.5
65
50
59
51
60
61
71
5
5.5
3.02
3.39
Tr 32 X
Tr 36 x
6
3
29
34.5
25
32.5
26
33
33
36.5
3.5
2.0
1.93
0.83
Tr 80 X 10
Tr 90 X 12
75
84
69
77
70
78
81
91
5.5
6.5
3.39
4. 12
33
31
29
25
30
26
37
37
3.5
5.5
1.93
3.39
Tr 100 X 12
Tr 140 x 14
94
133
87
124
88
126
101
142
6.5
8
4.12
4.58
d, = Dz
Tr 36 X 6
Tr 36 x 10
Metric buttress threads
cf. DtN 513 (1985-04)
Nominal thread size
Pitch
Minor 0 external t hreads
Minor 0 internal threads
Pitch 0 external threads
Pitch 0 internal threads
Axial clearance
External thread depth
Internal thread depth
Radi us
Crest w idth on major 0
Thread angle
"t,
external t hread
Extemalthreads Internal threads
Thread
Pitch
h;,
Minor Thread
depth
0
H,
0,
S 12 X 3
S 16x 4
6.79
9.06
2.60
3.47
7.5
10.0
2.25
3.00
9.75
13.00
S 20 x4
S 24 X 5
13.06
15.32
3.47
4.34
14.0
16.5
3.00
3.75
17.00
20.25
S 28 X 5
5 32 X 6
19.32
21.58
4.34
5.21
20.5
23.0
3.75
4.50
24.25
27.50
S 36 X 6
S40x 7
25.59
27.85
5.2 1
6.07
27.0
29.5
4.50
5.25
31.50
34.75
Minor
designation
0
d x P
d.,
Thread
depth
0
d,
d =D
p
cl:!= d - 1.736 - P
D, = d-1 .5-P
d:, = d - 0.75-P
0, = d - 0.75 • P+ 3.176 - a
a =0.1 - l'P
~ = 0.8678 - P
H1 = 0.75 • P
R =0.124 - P
w = 0.264- P
33°
External threads Internal threads
Minor Thread Minor Thread
designation
depth
depth
0
0
d x P
d.,
h;,
0,
H,
Thread
s 44 x 7
s 48x 8
s 52 X 8
s 60x 9
s 70 X 10
s 80x 10
s 90x 12
S 100 X 12
Pitch
0
d,
31.85
34.12
6.07
6.94
33.5
36
5.25
6.00
38.75
42.00
38.11
44.38
6.94
7.81
40
46.5
6.00
6.75
46.00
53.25
52.64
62.64
8.68
8.68
55
65
7.50
7.50
62.50
72.50
69.17
79.17
10.41
10.41
72
82
9.00
9.00
81.00
91.00
208
Machine elements: 5.1 Threads
Thread tolerances
Tolerance classes for metric ISO threads
cf. DIN ISO 965-1 (1999-11)
Internal threads
Screw thread tolerances are to ensure the function Thread tolerance
and interchangeability of internal and external
pitch and m inor
threads. They are dependent on the diameter tole,- Applies to
diameters
ances set in this standard and on the precision of
the pitch and the thread angle.
upper case letters
l abeled by
The tolerance class (fine, medium and coarse) is
also dependent on the surface finish of the Tolerance class
5H
threads. Thick electroplated protective coatings (example)
require more clearance (e.g. Tolerance Class 6G)
Tolerance grade
than bright or phosphatized surfaces (Tolerance
5
(size of tolerance)
Class 5H).
Tolerance zone
H
(Position of zero line)
External threads
pitch and major
diameters
lower case letters
6g
6
g
Designation examples
Explanations
M12 X 1 -59 6g
EX1ernal fine threads, nominal 0 12 mm, pitch 1 mm; 5g ~ Tolerance class for pitch 0 ;
6g - Tolerance class f or major 0
M12 -6g
M24 - 6G/6e
EX1ernal coarse t hreads, nominal 0 12 mm; 69 - Tolerance class for pitch and major 0
~
M16
Thread fit for coarse threads, nominal 0 24 mm, 6G - Tolerance class of the internal
threads, 6e - Tolerance class of the external threads
Tolerance class medium 6H/6g applies to threads without tolerance indication
Tolerance Class 6H/6g
is assigned to the
"medium" (general
purpose) t olerance
class and ·normal"
engagement length in
DIN ISO 965-1 (see
table below).
~
7
~
7o
~ ~ -~ ~ " ' '
-~
\~
C
~
./,.
,.,,
~
~-y ~
_
l,;' ~ -1..
0
C
:§
~
·;.
is
0
C
is
"E"'
C..
CL
! ] l11J 'J.. "' "'
"'
e
£ ~
~ ~
c:,
-s.-s..g
ci""ci'"~
"'
'&
c:,
,~.
p
0
I .
'&
.!i
'&
~
0
E
Internal threads, tolerance zone location H
..
-5 5
'i i
=a. -~
0
C
'is
.€
E
~
'&
'&
B
0
·;.
·;.
E
E
EX1ernal threads, tolerance zone location g
Limits for external and internal threads (selection)
cf. DIN ISO 965-2 (1999-11)
Internal threads - Tolerance dau 6H
~
'&
'&
.c
External threads - Tolerance dau 6g
Minor0 11 dJ
Major
0D
min.
min.
max.
min.
max.
max.
min.
max.
min.
max.
min.
M3
M4
MS
M6
3.0
4.0
5.0
6.0
2.675
3.545
4.480
5.350
2.775
3.663
4.605
5.500
2.459
3.242
4.134
4.917
2.599
3.422
4.334
5.135
2.980
3.978
4.976
5.974
2.874
3.838
4.826
5.794
2.655
3.523
4.456
5.324
2.580
3.433
4.361
5.212
2.367
3.119
3.995
4.747
2.273
3.002
3.869
4.596
MS
MB x 1
M10
M10x1
8.0
8.0
10.0
10.0
7.188
7.350
9.026
9.350
7.348
7.500
9.206
9.500
6.647
6.917
8.376
8.917
6.912
7.153
8.676
9.153
7.972
7.974
9.968
9.974
7.760
7.794
9.732
9.794
7.160
7.324
8.994
9.324
7.042
7.212
8.862
9.212
6.438
6.747
8.128
8.747
6.272
6.596
7.938
8.596
M12
M12 x 1.5
M 16
M16 X 1.5
12.0
12.0
16.0
16.0
10.863
11.026
14.701
15.026
11.063
11.216
14.913
15.216
10.106
10.376
13.385
14.376
10.441
10.676
14.210
14.676
11.966
11.968
15.962
15.968
11.701
11.732
15.682
15.732
10.829
10.994
14.663
14.994
10.679
10.854
14.503
14.854
9.819
10.128
13.508
14.128
9.602
9.930
13.271
13.930
M20
M20 X 1.5
M24
M24 X 2
20.0
20.0
24.0
24.0
18.376
19.026
22.051
22.701
18.600
19.216
22.316
22.925
17.294
18.376
20.752
21.835
17.744
18.676
21.252
22.2 10
19.958
19.968
23.952
23.962
19.623
19.732
23.577
23.682
18.334
18.994
22.003
22.663
18.164
18.854
21.803
22.493
16.891
18.128
20.271
21.508
16.625
18.930
19.955
21.261
M 30
M30X 2
M36
M36X 3
30.0
30.0
36.0
36.0
27.727
28.701
33.402
34.051
28.007
28.925
33.702
34.316
26.211
27.835
31.670
32.752
26.771
28.210
32.270
33.252
29.947
29.962
35.940
35.952
29.522
29.682
35.465
35.577
27.674
28.663
33.342
34.003
27.462
28.493
33.118
33.803
25.653
27.508
3 1.033
32.271
25.306
27.261
30.655
31.955
Threads
Pitch 0
Minor0 0 1
1l cf. DIN 13-20 (2000-08) and DIN 13-21 (2005-08)
Major0 d
Pitch 0 d2
209
Machine elements: 5.2 Bolts and screws
Hexagon head bolts and screws
pages 212-214
The most commonly used
bolts/screws in machine, equipment
and automotive i ndustry
Fully threaded type:
higher fatigue strength
Partly threaded and
with coarse threads
M1.6-M64
DINEN
ISO 4014
Fully threaded with
fine threads
M1.6-M64
DIN EN
ISO 4017
Partly threaded and
with fine threads
M8x1-M64x4
DINEN
ISO 8765
Fully threaded with
fine threads
M8x1-M64x4
DINEN
ISO 8676
t =-=B-
With reduced shank
M3-M20
DINEN
ISO 24015
Waisted bolts; for dynamic loads, no
nut retention necessary when properly installed
i=·Je-
Fit bolt
M8--M48
DIN 609
Fixing position of parts against
movement, fit shank transmits transverse loads
-(f}-+--a-
is-++
Hexagon bolts and screws for steel structures
Compared to coarse threads:
smaller thread depth, smaller
pitch, higher load capacity, larger
minimum engagement depth'•
page 214
j=-5:3-
With larger
width across flats
M12- M36
DINEN
14399-4
High-strength structural bolting
assemblies (HV), with nuts as per
DIN EN 14399-4 (page 2301
~ -m-
Fit bolt with large
widths across flats
M12-M30
DIN 7999
Friction grip (FG) joints, shear/bearing
stress connection
Cap screws
~
-8E·3-
pages 215, 216
With hexagon socket,
with coarse threads
M1.6-M64
DIN EN
ISO 4762
With hexagon socket,
fine threads
M8x1- M64x4
DIN EN
ISO 21269
With hexagon socket
and low head
M3-M24
DIN 7984
Slotted
M1 .6-M10
DINEN
ISO 1207
Slotted
M1.6-M10
DINEN
ISO 2009
With hexagon socket
M3-M20
DINEN
ISO 10642
Slotted raised head
countersunk
M1.6-M10
DIN EN
ISO 2010
Recessed raised head M1.6-M10
countersunk cross
DIN EN
ISO 7047
Countersunk head screws
¥--➔-
tF-·➔
With low-profile head: small height,
low stress
Slotted bolts/screws: small screws,
low stresses
Fine threads: s maller thread depth,
capable of higher loads, larger
minimum engagement depth '•
pages 216, 217
Sheet metal screws with tapping threads
►
Machine, equipment and automotive
industry; low space requirements,
head sinkable
Variety of applications in m achine,
equipment and automotive industry
For screws with hexagon socket:
g reater load capacity
For screws with cross recess: Secure
tightening and loosening compared
to slotted screws
pages 217, 218
Round head screw
ST2.2- ST9.5
DIN
ISO7049
Countersunk
head screw
ST2.2-ST6.3
DIN
ISO7050
Round head
countersunk screws
ST2.2-ST9.9
DIN
ISO 7051
Vehicle body and sheet metal manufacturing.
The sheets to be joined have tap
holes. The threads are formed by the
screw. Locking fasteners are only
needed for thin sheets.
210
Machine elem ents: 5.2 Bolts and screw s
:@11...-.:11 · - - ·
lllus1ntion
• ,., •• ;,&,,,.11~'1
Standard range
, ..... u,11 ■ l ~ - ~ - •'-'•••-
from -to
Standard
Application, properti•
ST2.2-ST6.3
DINEN
ISO 15481
Round head counter- ST2.2- ST6.3
sunk with cross/recess
DIN EN
ISO 15483
Vehicle body and sheet metal
manufacturing
drilling screws bore the t ap hole
while being screwed in and form t he
threads.
M4-M24
M4-M48
M4-M48
DIN 835
DIN 939
DIN 938
For aluminum alloys
For cast iron materials
For steel
W ith dog point
and slotted
M1.6-M12
DINEN
27435
W it h dog point
and hex socket
M 1.6-M24
DIN EN ISO
4028
Compression loadable screws
for securing position of parts,
e.g. levers, bearing bushings, hubs
With cone point
and slotted
M1.6-M12
DINEN
27434
W ith cone point
and hex socket
M1.6-M24
DIN EN ISO
4027
With flat point
and slotted
M 1.6-M 12
DINEN
24766
With flat point
and hex socket
M 1.6-M24
DIN EN ISO
4026
Design
Drilling screws with tapping t hreads
Qi
&·
Flat head with
cross recess
Studs
page 219
~E-3I•
le ~ 2 • d
1.~ 1.25-d
le ~ 1. d
Setscrews
D
IG
i I ·$E---}
page 220
Set screws are not suitable for power
transmission of torques, e.g. for join ing shafts to hubs.
Drain plugs
-00
page 219
Heavy type w ith
hexagon socket or
hexagon head
M 10x1M52x1.5
DIN 908
DIN910
Gearbox manufacturing; Fill, overflow
and drain screws for gear oil; milling
of seating surface necessary
Thread forming screws
~
..
page 218
Various head forms
e.g . hexagon,
cheese head
M2-M 10
DIN 7500-1
For low loading in malleable
materials, e.g. 5235, DC01- DC04,
non-ferrous metals; use without
locking fastener
Eye bolts
t
page 219
With coarse threads
M8-M 100x6
DIN 580
Transport eyes on machines and
equipment; stress depends on the
angle of the applied load, milling of
seating surface necessary
Designation of bolts and screws
Examples:
Hex screw
Drain plug
Cap screws
I
I
Type
Reference standard,
e.g. ISO, DIN, EN;
Sheet number of
the standard 11
cf. DIN 962 (2001-11)
ISO 4017 - M 12 x 80 -A2-70
DIN 910 - M24 x 1.5 -St
ISO 4762 - M10 x 55 - 8.8
-r-~ ~
Nominal data, e.g.
M - metric screw t hread
12 -+ nominal diamet er d
80 - shank length /
I
Property class. e. g. 8.8, 10.9,
A2-70, A4-70
Material, e.g. St steel.
CuZn copper-zinc-alloy
11 Bolts and screws standardized according to ISO, DIN EN or DIN EN ISO have the abbreviation ISO in their desig-
nation. Bolts and screws standardized according to DIN have the abbreviation DIN in their designation.
211
Machine elements: 5.2 Bolts and screws
Property classes, Product grades, Clearance holes, Minimum engagement depth
Property classes of screws and bolts
cf. DIN EN ISO 898-1 (1999-111. DIN EN ISO 3506-1 (1998-031
Stainless steels
DIN EN ISO 3506-1
Unalloyed and alloy steels
DIN EN ISO 898-1
Examples:
A2-70
9.8
~
_ ~T~
~----''---~
Tensile strength ~
Rm= 9 · 100 N/mm2
= 900 N/mm2
l~_ ___,Tl
T.___ _ _ _ _-,
Yield strength R.
Stael microstr.
Stael group
Tensile strength ~
R0 = 9 . 8 . 10 N/mm2
= 720 N/mm2
A austenitic
F ferritic
2 alloyed w ith Cr, Ni
4 alloyed with Cr, Ni, Mo
Rm= 70 • 10 N/mm2
= 700 N/mm 2
Property classes and material properties
$
$
5.8
Property classes for bolts and screws m ade of
stainless steels11
unalloyed and alloyed steels
6.8
8.8
9.8
10.9
12.9 A2-50 A4-50 A2-70
Tens. strength Rm in N/mm 2
500
600
800
900
1000
1200
500
500
700
Yield strength Re in N/mm2
400
480
640
720
900
1080
210
210
450
12
10
8
Elong. at fracture EL in %
11 Material properties apply to threads s M20.
10
9
8
20
20
13
Material property
Product grades for bolts and nuts
iC
Product
grade
Toleranees
A
fine
cf. DIN EN ISO 4759-1 (2001-041
Explanation, application
I--- - - - + - - - - - , Dimensional, form a nd positional tolerances for bolts and nuts
B
medium
> - - -- - + - - - - - < w ith ISO threads are specified in tolerance grades A. B. C.
C
coarse
Clearance holes for bolts
Thread
~
d,
~
......
l
i
I==!=!
_!!._
cf. DIN EN 20273 ( 1992-02)
Clearance hole dh11
Thread
Series
med. coarse
d
Thread
Clearance hole dh 11
Series
d
fine
med. coarse
Clearance hole dh11
Series
fine
med. coarse
d
fine
M1
M1.2
1.1
1.3
1.2
1.4
1.3
1.5
MS
M6
5.3
6.4
5.5
6.6
5.8
7
M24
M30
25
31
26
33
28
35
M1.6
M2
1.7
2.2
1.8
2.4
2
2.6
MB
M10
8.4
10.5
9
11
10
12
M36
M42
37
43
39
45
42
48
M2.5
M3
M4
2.7
3.2
4.3
2.9
3.4
4.5
3.1
3.6
4.8
M12
M16
M20
13
17
21
13.5
17.5
22
14.5
18.5
24
M48
M56
M64
50
58
66
52
62
70
56
66
74
11 Tolerance grades for dh; fine series: H12, medium series: H13, coarse series: H14
Minimum engagement depth in blind hole
Area of application
I I I
l
0.8-d
1.2 • d
-
0.8 • d
1.2 • d
1.2 • d
-
0.8· d
1.2 • d
1.2- d
1.2- d
0.8 • d
1.2 • d
1.0 - d
1.0 • d
Cast iron materials
1.3• d
1.5• d
1.5 -d
Copper alloys
1.3 · d
1.3 - d
-
Aluminum casting alloys
1.6 • d
2.2 . d
-
-
Al alloys, age-hardened
0.8 · d
1.2 • d
1.6· d
-
Al alloys, not age-hardened
1.2 -d
1.6 -d
-
Plastics
2.5 • d
-
-
Rm s 400 N/mm 2
2
Struc. Rm= 400-600 N/mm
steel Rm> 600- 800 N/mm2
Rm > 800 N/mm 2
x ~ 3 • P (thread pitch)
e1 according to DIN 76,
see page 89
Minimum engagement depth /0 11
for coarse threads and property class
4.8- 6.8
8.8
10.9
3.6,4.6
1
1 Engagement depth for fine threads /0 = 1.25 • Engagement depth for coarse threads
212
Machine elements: 5.2 Bolts and screws
l:•~·~:11ro1•1r:J:Ti ■ ;'f;ill
Hexagon head bolt with shank and coarse threads
Valid standard
DIN EN ISO
4014
Thread d
M1.6
M2
M2.5
M3
M4
M5
M6
MS
M10
24014
WAF
k
dw
3.2
1.1
2.3
4
1.4
3.1
5
1.7
4.1
5.5
2
4.6
7
2.8
5.9
8
3.5
6.9
10
4
8.9
13
5.3
11.6
16
6.4
14.6
e
b
3.4
9
4.3
10
5.5
11
6
12
7.7
14
8.8
16
11.1
18
14.4
22
17.8
26
12
16
16
20
16
25
20
30
25
40
25
50
30
60
40
BO
45
100
1
931
from
~
•> tor/< 125mm
2>for /= 125- 200 mm
3>for I> 200 mm
s M12
Ml6- M24
;,,M30
I to
Property
classes
M12
M16
M20
M24
M30
M36
M42
M48
M56
WAF
k
18
7.5
24
10
30
12.5
36
15
46
18.7
55
22.5
65
26
75
30
85
35
dw
e
16.6
22
26.2
27.7
33
33.3
39.6
42.8
50.9
51.1
60.B
60
7 1.3
69.5
82.6
78.7
93.6
b'l
30
-
38
44
46
52
-
-
-
-
66
72
85
-
b3)
54
60
73
-
t,2)
84
97
96
109
108
121
137
50
120
65
160
BO
200
90
240
110
300
140
360
160
440
180
500
220
500
20
from
Grade
/ in mm
all
A
I s 150
A
/ ;,, 160
B
all
B
5.6, 8.8, 9.8, 10.9, A2-70, A4-70
Thread d
I to
Product grades (page 211)
Threads d
cf. DIN EN ISO 4014 (2001-03)
Repla ces
DIN EN
DIN
5.6, 8.8, 9.8, 10.9
Property
classes
Nominal
lengths/
=
12, 16. 20, 25, 30, 35-60, 65, 70, 80, 90-140, 150, 160,
180, 200- 460, 480,500 mm
Hexagon head boh ISO 4014 - M10 x 60 - B.B:
d = M 10, / = 60 mm, property class 8.8
Hexagon head bolts with coarse threads, fully threaded
Valid standard
DINEN ISO
4017
Thread d
M1.6
M2
M2.5
M3
M4
M5
M6
MB
M10
24017
WAF
k
3.2
1.1
4
1.4
5
1.7
5.5
2
7
2.8
8
3.5
10
4
13
5.3
16
6.4
dw
e
2.3
3.4
3.1
4.3
4.1
5.5
4.6
6
5.9
7.7
6.9
8.8
8.9
11.1
11.6
14.4
14.6
17.8
2
16
4
20
5
25
6
30
B
40
10
50
12
60
16
80
20
100
1
933
from
~
Property
classes
M12
M16
M20
M24
M30
M36
M42
M48
M56
WAF
k
18
7.5
24
10
30
12.5
36
15
46
18.7
55
22.5
65
26
75
30
85
35
dw
e
16.6
20
22
26.2
27.7
33
33.3
39.6
42.B
50.9
51.1
60.B
60
71.3
69.5
82.6
78.7
93.6
25
120
30
200
40
200
50
200
60
200
70
200
80
200
100
200
110
200
from
Product grades (page 211)
M l6- M24
;,, M30
/ inmm
Grade
a ll
A
/s 150
A
/ ;e 160
B
all
B
5.6, 8.8, 9.8, 10.9, A2-70, A4-70
Thread d
I to
sM12
cf. DIN EN ISO 4017 (2001-03)
Replaces
DINEN
DIN
I to
Threads d
as per
agreement
A2-50, A4-50
A2-70, A4-70
-
Property
classes
Nominal
lengths/
-
5.6, 8.8, 9.8, 10.9
A2-70, A4-70
A2-50, A4-50
as per
agreement
2, 3, 4, 5, 6, B, 10, 12, 16, 20, 25, 30, 35-60, 65, 70, 80,
90- 140, 150, 160,180,200 mm
Hexagon head boh ISO 4017 - MB x 40 - A4-50:
d = MS, / = 40 mm, property class A4-50
213
Machine elements: 5.2 Bolts and screws
; , ~... ,,, II 11111 IT:F.Ti:
I iTil I
Hexagon head bolt with shank and fine threads
cf. DIN EN ISO 8765 (2001-03)
Valid standard
DIN EN ISO
8765
Replaces
DIN EN
DIN
Thread d
MB Ml0 M12 M16 M20 M24
xl
x1 x1.5 xl.5 xl.5 x2
M30
x2
M36
x3
M42
x3
M48
x3
M56
x4
28765
WAF
13
5.3
36
15
46
18.7
55
22.5
65
26
75
30
85
35
11.6 14.6 16.6 22.5 28.2 33.6
14.4 17.8 20 26.2 33 39.6
42.8
50.9
51.1
60.8
60
71 .3
69.5
82.6
78.7
93.6
22
54
60
73
66
72
85
84
97
96
109
108
121
137
100
240
120
300
140
360
160
440
200
480
220
500
I
960
k
l
from
to
40
80
16
6.4
18
7.5
26
24
10
30
30
12.5
38
44
46
52
45 50 65 80
100 120 160 200
1-------- - -- -- ----< Nominal
Product grades (page 211)
lengths /
40, 45. 50, 55, 60, 65, 70, 80, 90-140, 150, 160,180,200,
220- 460, 480, 500 mm
,_T_h_r_ea_d_s_d_+-i_in_m_m---<_G_ra_d_e_, Property
s M12x1.5
all
A
classes
d s M24x2: 5.6, 8.8, 10.9, A2-70, A4-70
d = M30x2- M36x2: 5.6, 8.8, 10.9, A2-50, A4-50
M16x1.5-
s 150
A
M24x2
> 150
B
., M30x2
all
B
Explanations
1
1 for / < 125 mm
d "' M42x3: as per
agreement
21 for/= 125-200 mm
31 for / > 200 mm
Hexagon head bolt ISO 8765-M20 x 1.5 x 120 - 5.6:
d = M20 x 1.5, / = 120 mm, property class 5.6
Hexagon head bolts with fine threads, fully threaded
cf. DIN EN ISO 8676 (2001-03)
Valid standard
DIN EN ISO
MB Ml0 M12 M16 M20 M24
xl
xl xl .5 xl.5 xl.5 x2
M30
x2
M36
x3
M42
x3
M48
x3
M56
x4
13
5.3
36
15
46
18.7
55
22.5
65
26
75
30
85
35
11.6 14.6 16.6 22.5 28.2 33.6
14.4 17.8 20 26.2 33 39.6
42.8
50.9
51.1
60.8
60
71.3
69.5
82.6
78.7
93.6
l to
16
80
40
200
40
200
90
420
100
480
120
500
Nominal
lengths/
16, 20, 25, 30, 35- 60, 65, 70, 80, 90- 140, 150, 160,180,200,
220- 460, 480, 500 mm
Property
classes
d s M24x2: 5.6, 8.8, 10.9, A2-70, A4-70
d = M30x2- M36x2: 5.6, 8.8, 10.9, A2-50, A4-50
8676
Replaces
DIN EN
DIN
I
961
28676
Thread d
WAF
1 - - - - - -' - - -- - - - ' - - - - I k
from
Product grades aocording to
DIN EN ISO 8765
16
6.4
18
7.5
24
10
30
12.5
20 25 35
40
100 120 160 200
40
200
Hexagon head bolt ISO 8676 - MB x 1,5 x 55 - 8.8:
d = MB x 1.5, / = 55 mm, property class 8.8
Hex head bolt with reduced shank
cf. DIN EN 24015 (1991-12)
Thread d
M3
WAF
5.5
2
4.4
7
2.8
5.7
2.6
6
k
dw
M4
M6
MB
Ml0
M12
M16
M20
8
3.5
6.7
10
4
8.7
13
5.3
11.4
16
6.4
14.4
18
7.5
16.4
24
10
22
30
12.5
27.7
3.5
7.5
4.4
8.7
5.3
10.9
7.1
14.2
8.9
17.6
10.7
19.9
14.5
26.2
18.2
33
12
14
16
18
22
28
26
32
30
36
38
44
46
52
20
30
20
40
25
50
25
60
30
80
40
100
45
120
55
150
65
150
MS
b
t--
k
- ·>---<-
d "' M42x3: as per
agreement
from
- - - --
l to
Nominal
lengths/
Property
classes
Product grades (page 211)
Explanations
Threads d
I in mm
Grade
s M20
all
B
20, 25, 30-65, 70, 75, 80, 90, 100- 130, 140, 150 mm
5.8, 6.8, 8.8, A2-70
11 for/ s 120 mm
21
for / > 125 mm
Hexagon head bolt ISO 4015 - M8 x 45 - 8.8:
d = MB, / = 45 m m , property class 8.8
214
Machine elements: 5.2 Bolts and screws
Hexagon head bolts
Hexagon head frt bolts with long thread
cf. DIN 609 (1996-021
Thread d
MB
MB
x1
M10
M10
x1
M12
M12
x1.5
M16
M 16
x 1.5
M20
M20
x1.5
M24
M24
x2
M30
M30
x2
M36
M36
x3
M42
M42
x3
M48
M48
x3
WAF
k
13
5.3
16
6.4
18
7.5
24
10
30
12.5
36
15
46
19
55
22
65
26
75
30
d5 k6
9
14.4
11
17.8
13
19.9
17
26.2
21
33
25
39.6
32
50.9
38
60.8
44
71.3
50
82.6
14.5
16.5
17.5
19.5
20.5
22.5
-
-
-
-
-
-
28.5
30.5
35.5
-
-
25
27
32
36,5
41.5
43
48
49
54
56
61
63
68
25
80
30
100
32
120
38
150
45
150
55
150
65
200
70
200
80
200
85
200
WAF
'3'
-c,
{:
·......-41
b'I
k
t,21
t,31
·:·
I
k
e
from
to
l
Nominal
lengths/
25. 28, 30, 32, 35, 38. 40. 42, 45, 48. 50, 55, 60- 150, 160- 200 mm
8.8
Property
classes
Product grades (page 211)
din mm
/inmm
Grade
Explanations
s 10
all
A
=
a: 12
all
B
A2-70
21 for I = 50- 150 mm
11 for / " 150 mm
-c, I
~[:
·b
k
I
I
cf. DIN EN 14399-4 (2006-061,
replaces DIN 6914
Thread d
M12
M16
M20
M22
M24
M27
M30
M36
WAF
k
22
8
20.1
27
10
24.9
32
13
29.5
36
14
33.3
41
15
38
46
17
42.8
50
19
46.6
60
23
55.9
23.9
23
29.6
28
35
33
39.6
34
45.2
39
50,9
41
55.4
44
66.4
52
35
95
40
130
45
155
50
165
60
195
70
200
75
200
85
200
dw
-,:]
31 for I > 150 mm
Fit bolt DIN 609 - M16 x 1.5 x 125 -A2-70:
d = M16 x 1.5, / = 125 mm, property class A2-70
Hexagon head bolts with large width across flats
for high-strength structural bolting assemblies (HV)
WAF
as per
agreement
A2-50
e
b min
l
from
to
Nominal
35, 40, 45, 50, 55, 60, 65, 70-175, 180, 185, 190,195, 200 mm
lengths/
Property class,
10.9
normal - > w it h thin oil film, hot-galvanized - > code: tZn
surface
Hexagon head bolt EN 14399-4- M12 x 65 -10.9 - HV -tZn:
d = M12, / = 65 mm, property class 10.9, for high-strengt h bolting
assembl ies, w ith hot-galvanized surface
I
=
Product grade C
Hexagon fit bolts with large width across flats
Thread d
M12
M16
M20
M22
M24
M27
M30
WAF
dw
21
8
19
27
10
25
34
13
32
36
14
34
41
15
39
46
17
43.5
50
19
47.5
d, b11
e
b
13
22.8
18.5
17
29.6
22
21
37.3
26
23
39.6
28
25
45.2
29.5
28
50.9
32.5
31
55.4
35
from
to
40
120
45
160
50
180
55
200
55
200
60
200
65
200
k
WAF
I -,:] -c,~
~1
-c, I
.!. loo•
k
Product grade C
(2... t
I
cf. DIN 7999 (1983-121
l
Nominal
lengths /
Property
classes
=
40, 45, 50, 55, 60, 65- 180, 185, 190, 195,200 mm
All bolts: property class 10.9
Hexagon head bolt DIN 7999- M24 x 165:
d = M24, / = 165 mm. property class 10.9
215
Machine element s: 5.2 Bolts and screws
ii1~• .,-,111111as-. rw c• " ' r = , • ..-.1,as,.,~ .. , L
Hexagon socket head cap screws with coarse threads
Valid standard
DIN EN ISO
Replaces
DIN
4762
912
-
Thread d
Ml.6
M2
M2.5
MJ
M4
M5
M6
MS
MlO
WAF
k
d,
1.5
1.6
J
1.5
2
3.8
2
2.5
4.5
2.5
J
5.5
J
4
7
4
5
8.5
5
6
10
6
8
13
8
10
16
b
for I
-
16
20
17
25
18
,.. 25
20
,.. JO
22
,..30
24
,.. 35
28
,..40
32
,..45
1.1
" 16
1.2
" 16
1.4
" 20
1.5
"20
2. 1
s 25
2.4
s 25
J
s JO
3.8
s 35
4.5
s 40
2.5
16
J
20
4
25
5
30
6
40
8
50
10
60
12
80
16
100
,,
for I
from
I to
Property
classes
WAF
_ l_
~1
b.
~
"l:,
,,I
I
k
Stainless steels A2-70, A4-70
M12
M16
M20
M24
M30
M36
M42
M48
M 56
WAF
14
16
24
17
20
30
19
24
36
22
30
45
27
36
54
32
42
63
36
d,
10
12
18
41
56
84
b
for I
36
"' 55
44
a: 65
52
-, 80
60
., 90
72
84
96
108
124
a: 110 a: 120 a: 140 a: 160 a: 180
5.3
s 50
6
s 60
7.5
s 70
9
s 80
10.5
12
s 100 s 110
13.5
15
16.5
s 130 s 150 s 160
20
120
25
160
JO
200
40
200
45
200
60
300
,,
for I
from
I to
Thread d
Grade
M1.6- M56
A
Nominal
lengths/
=
45
200
8.8, 10.9, 12.9
Property
classes
Product grades (page 211)
8.8, 10.9, 12.9
by agreement
Thread d
k
b
cf. DIN EN ISO 4762 (2004-06)
A2-70, A4-70
~I ~
k
"l:,
.• ''"
b
Thread d
Grade
M3-M24
A
80
300
2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 30- 65, 70, 80- 150, 160,
180, 200, 220, 240, 260, 280, 300 mm
Cap screw ISO 4762 - M10 x 55 - 10.9:
d = MlO, / = 55 mm, property class 10.9
cf. DIN 7984 (2002-12)
M3
M4
M5
M6
MB
MlO
M12
M16
M20
M24
WAF
k
d,
2
2
5.5
2.5
2.8
7
3
3.5
8.5
4
4
10
5
5
13
7
6
16
8
7
18
12
9
24
14
11
30
17
13
36
b
for I
12
., 20
14
,.. 25
16
.. JO
18
,..30
22
.,35
26
., 40
30
.,50
38
a:60
44
a: 70
46
a: 90
1.5
s 16
2. 1
"20
2.4
s 25
3
"25
3.8
s JO
4.5
" 35
5.3
,. 45
6
" 50
7.5
s 60
" 80
I to
5
20
6
25
8
30
10
40
12
80
16
100
20
80
30
80
40
100
50
100
Nominal
lengths/
5, 6, B, 10, 12, 16, 20, 25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100 mm
Property
classes
8.8, A2-70, A4-70
,,
from
Product grades (page 211)
70
JOO
Thread d
for I
I
72
as per
agreement
A2-50, A4-50
Hexagon socket head cap screws, low head
WAF
48
=
Cap screw DIN 7984 - M12 x 50 -A2-70:
d= M12, / = 50 mm, property class A2-70
9
216
Machine elem ents: 5.2 Bolts and screws
Hexagon socket head cap screws with fine threads
MB M10 M12 M16 M20 M24
x 1 x1 xl.5 x1.5 xl.5 x2
M30 M36
x2
x3
M42
x3
M48
3x
M56
x4
k
dk
6
8
13
22
30
45
32
42
63
36
48
72
41
56
84
b
for I
28
32
36 44
52
,,40 ,,45 ,,55 a,65 a,80
72
124
60
84
96
108
ae90 " 11 0 a, 120 a, 140 a, 160 a, 180
for I
4.5 4.5 4.5
3
3
s 35 s 40 s 50 s 60 s 70
6
6
9
9
9
9
s 70 s 100 s 110 s 130 s 150 s 160
l to
12
80
40
200
Nominal
lengths I
12, 16, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 80, 90, 100, 110,
120, 130, 140, 150, 160, 180, 200, 220, 240, 260, 280, 300 mm
Thread d
WAF
WAF
cf. DIN EN ISO 21269 (2004-06)
,,
from
10
12
18
20
100
14
16
24
17
20
30
19
24
36
20
25 30
120 160 200
55
200
60
300
,,
A2-70, A4-70
70
300
80
300
as per
agreement
11 Property classes A2-50, A4-50 (stainless steels)
Cap screw ISO 21269 - M20 x 1,5 x 120-10.9:
d = M20x1.5, / = 120 mm, property class 10.9
Product grade A (page 211)
Slotted cheese head screws
cf. DIN EN ISO 1207 (1994-10)
Thread d
n
from
l to
Ml.6
M3
M6
MB
M10
8.5
3.3
10
3.9
13
5
16
6
1.2
1.1
1.2
1.3
1.6
1.6
2
2
2.5
2.4
5
40
6
50
8
60
10
80
12
80
M2
M2.5
M4
3
1.1
3.8
1.4
4.5
1.8
5.5
2
7
2.6
0.4
0.5
0.5
0.6
0.6
0.7
0.8
0.9
2
16
3
20
3
25
4
30
M5
b
for I < 45 mm - threads near to head
for / 2: 45 mm- b = 38 mm
Nominal
lengths/
2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25-45, 50, 60, 70, 80 mm
k
Property
classes
-
Product g rade A (page 211)
4.8, 5.8, A2-50, A4-50
Cheese head screw ISO 1207 - M6 x 25 - 5.8:
d = M6, / = 25 m m, property class 5.8
Hexagon socket head countersunk screws
cf. DIN EN ISO 10642 (2004-06). replaces DIN 7991
Thread d
M3
M4
M5
M6
MB
M l0
M12
M 16
M20
WAF
k
2
5.5
1.9
2.5
7.5
2.5
3
9.4
3.1
4
11.3
3.7
5
15.2
5
6
19.2
6.2
8
23.1
7.4
10
29
8.8
12
36
10.2
b
tor I
18
20
ae 30
22
"35
24
,, 40
28
"' 50
32
36
44
" 30
2: 55
;o 65
2: 80
52
100
1.5
s 25
2.1
s 25
2.4
s 30
3
s 35
3.8
s 45
4.5
s 50
5.3
s 60
6
s 70
7.5
s 90
8
30
8
40
8
50
8
60
10
80
12
100
20
100
30
100
35
100
dk
1,
for I
from
l to
Product grade A (page 211)
27
36
54
45
200
8.8, 10.9, 12.9
Property
classes
Explanation
8
10
16
Property
classes
8.8, 10.9, 12.9
Nominal
lengths/
8, 10, 12, 16, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 80, 90, 100 m m
-
Countersunk head screw ISO 10642 - M5 x 30 - 8.8:
d = M5, / = 30 mm, property class 8.8
217
Machine elements: 5.2 Bolts and screws
. . . 111111 ilil111l!1111:r. , - , .. , ....., L.... :~,lm:JIT1 ■ w1111111:111,,.'11111:-.'1-•'--'•"L
Slotted raised head countersunk screws
Raised head countersunk screws with cross rec:ess
Thread d
M2
M2.5
M3
M4
MS
M6
MB
M10
3
1
3.8
1.2
4.7
1.5
5.5
1.7
8.4
2.7
9.3
2.7
11.3
3.3
15.8
4.7
18.3
5
0.4
0.4
0.6
0.5
0.5
0.8
0.6
0.6
1.0
0.8
0.7
1.2
1.2
1.0
1.6
1.2
1.2
2.0
1.6
1.4
2.4
2
2
3.2
2.5
2.3
3.8
3
20
4
25
5
30
6
40
8
50
8
f
t
Cll
I
0
2.5
16
from
to
b
cross recess*
forms
H
Z
cf. DIN EN ISO 2010 11994-10)
cf. DIN EN 1
so 7047 (1994-10)
M1.6
n
f 'y
60
12
80
for I < 45 mm - b "' /;for/ a, 45 mm - b = 38 mm
Nominal
lengths /
2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25-45, 50, 60, 70, 80 mm
Explanation
11 C cross recess size, forms H and Z
Countersunk head screw ISO 7047 - M3 x 20 - 4.8 - H:
d = M3, I = 20 mm, property class 5.8, cross recess form H
Thread d
cf. DIN EN ISO 2009 (1994-10)
cf. DIN EN ISO 7046-1 (1994-10)
M1.6
M2
M2.5
M3
M4
MS
M6
MB
M10
3
1
3.8
1.2
4.7
1.5
5.5
1.7
8.4
2.7
9.3
2.7
11.3
3.3
15.8
4.7
18.3
5
0.4
0.5
0.5
0.6
0.6
0.8
0.8
0.9
1.2
13
1.2
1.4
1.6
1~
2
23
2.5
~6
3
20
4
25
5
30
6
40
n
t
2
0
I
from
to
2.5
16
b
3
8
50
8
60
4
10
80
12
80
for I< 45 mm - b "' I; for I" 45 mm - b = 38 mm
Property
classes
DIN EN ISO 2009: 4.8, 5.8, A2-50, A2-70
DIN EN ISO 7046-1: 4.8, A2-50, A2-70
Nominal
lengths/
2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25-45, 50, 60, 70, 80 mm
Explanation
11 C cross recess size, forms Hand Z (DIN EN 2010)
Countersunk head screw ISO 7046-1 - MS x 40 - 4.8 - H:
d = M3, / = 40 mm, property class 4.8, cross recess form H
Product grade A (page 211)
Rat head countersunk tapping screws
Raised heed countersunk tapping screws
"Ji(~" ,s~;:o, f"'''
cf. DIN EN ISO 7050 (1990-08)
cf. DIN EN ISO 7051 (1990-08)
ST2.2
ST2.9
ST3.5
ST4.2
ST4.8
STS.5
ST6.3
3.8
5.5
7.3
8.4
9.3
10.3
1.1
1.7
2.4
2.6
2.8
3
0.7
1.0
1.2
1.3
0.5
0.8
,_/_fr-om---+---+-----+---+-- - - + - ---1-- --1
4.5
6.5
9.5
9.5
9.5
13
to
16
19
25
32
32
38
Cll
0
1
2
Nominal
lengths I
4.5, 6.5, 9.5, 13, 16, 19, 22, 25, 32, 38 m m
Forms
Form C with cone point, form F with dog point
Explanation
Product grade A (page 211)
4
10
80
DIN EN ISO 2010: 4.8, 5.8, A2-50, A2-70
DIN EN ISO 7047: 4.8, A2-50, A2-70
Slotted flat head countersunk screws
Rat head countersunk screws with cross rec:ess
I
3
2
Property
classes
Product g rade A (page 211)
~ k
,m111111a,, __ ,..,., 1
1> C cross recess size, forms Hand Z (DIN EN 2010)
Tapping screw ISO 7050- ST4.8 x 32 - F - Z:
d = ST4.8, I = 32 mm, form F, cross recess form Z
3
11.3
3.2
1.4
13
38
218
Machine elements: 5.2 Bo lts and screws
Tapping screws, Thread forming screws
Pan head tapping screws
cf. DIN ISO 7049 (1990-081
Thread d
from
l to
ST2.2
ST2.9
ST3.5
ST4.2
ST4.8
ST5.5
ST6.3
4
1.6
5.6
2.4
7
2.6
8
3.1
9.5
3.7
11
4
13
4.6
4.5
16
6.5
19
9.5
25
9.5
32
9.5
32
13
38
13
38
0
2
3
Nominal
lengths I
4.5, 6.5, 9.5, 13, 16, 19, 22, 25, 32, 38 mm
Fo rms
Fo rm C with cone point, form F with dog point
Explanation
11 C cross recess size, forms Hand Z (DIN EN 2010)
=>
Product grade A (page 2111
Tapping screw ISO 7049 - ST2.9 x 13 - C - H:
d = ST2.9, I = 13 mm, form C, cross recess form H
Tap hole diameter for tapping screws (selection)
Sheet metal
thickness
sin mm
ST2.9
ST3.5
ST4.2
ST4.8
ST5.5
0- 0.5
0.6- 0.8
0.9- 1.1
1.6
1.7
1.8
2.2
2.3
2.4
2.6
2.7
2.8
3.2
3.2
3.7
3.7
4.2
4.9
1.2-1.4
1.5- 1.7
1.8-2.0
1.8
2.4
2.5
2.6
2.8
2.9
3.0
3.3
3.5
3.5
3.9
3.9
4.0
4.3
4.5
4.6
4.9
5.0
5.2
3.0
3.0
3.5
3.8
3.9
4.0
4.1
4.3
4.6
4.7
5.0
5.3
5.3
5.8
from-to
hi
I:-::
11 Holes bored or punched in
steel or copper alloy sheet
Tap hole diameter d for tapping screw threads1
ST2.2
2.0-2.5
2.6- 3.0
3.1-3.5
Thread forming screws
cf. DIN 7500-1 (2007-03)
M2
M2.5
M3
M4
M5
M6
MS
M10
k
4
1.4
5
1.7
5,5
2
7
2.8
8
3.5
10
4
13
5.3
16
6.4
e
2.3
3.4
3.1
4.3
4. 1
5.5
4.6
6
6
7.7
6.9
11.1
11.6
14.4
14.6
17.8
Form DE: hexagon head bolt
WAF
~~
~
ST6.3
WAF
DE
from
3
4
4
6
8
8
10
12
50
60
80
16
20
25
30
40
Form EE: hexagon socket head 1----- - + -----,1----1---+---+----+---+---+---4
cap bolt
WAF
1.5
2
2.5
3
4
5
6
8
WAF
k
2
2.5
3
4
5
6
8
10
EE
d,
3.8
4.5
5.5
7
8.5
10
13
16
"'j
I to
r q·I
~
Form NE: raised countersunk
head bolt with cross
1:::'"' ,',
,~
:.
:.
:.
e:.
~ ~
d,
3.8
1.2
0.4
4.7
1.5
0.5
5.5
1.7
1
8.4
2.7
1.2
9.3
2.7
1.4
11.3
3.3
1.4
15.8
4.7
2
18.3
5
2.3
4
16
5
20
6
25
8
30
10
40
10
50
12
60
20
80
k
f
NE
from
l to
c11
"
Product grade A (page 211 I
0
1
2
3
Nominal
lengths I
3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 30- 50, 55, 60, 70, 80 mm
Explanation
11 C cross recess size, forms Hand Z (DIN EN 20101
4
Screw DIN 7500 - DE - MB x 25 - St: DE Hex head, d = MB,
I = 25 mm (material: case hardened and tempered steel)
219
Machine elements: 5.2 Bolts and screws
Studs, Eye bolts, Drain plugs
Studs
cf. DIN 835, 938, 939 (1995-021
M3
M4
MS
M6
MS
MS
xl
M10 M12 M16
M10 M 12 M16
xl.25 xl.25 xl.5
bfor I< 125
I< 125
12
18
14
20
16
22
18
24
22
28
26
32
30
36
38
44
46
52
54
60
e
DIN 835
DIN 938
DIN 939
3
-
8
4
5
10
5
6.5
12
6
7.5
16
8
10
20
10
12
24
12
15
32
16
20
40
20
25
48
24
30
I
from
to
20
30
20
40
25
50
25
60
30
80
35
100
40
120
50
170
60
200
70
200
Thread d
""I
""I
- ...,..g---
H
,.,.
I
I
b
I
e
Product grade A (page 211 )
Property
classes
Nominal
lengths I
Application
DIN
For screwing into
Aluminum alloys
Steel
Cast iron
835
938
939
=
20, 25, 30-75, 80, 9(}- 180, 190, 200 mm
Stud ISO 939 - M10 x 65 - 8.8:
d = M 10, I = 65 mm, property class 8.8
cf. DIN 580 (2003-081
d1
l~'i f.
Thread d
MS M10 M12 M 16 M20 M24 M30
M36
M42
M48
M56
h
d,
18
36
20
22.5
45
25
26
54
30
30.5
63
35
35
72
40
45
90
50
55
108
60
65
126
70
75
144
80
85
166
90
95
184
100
20
13
25
17
30
20.5
35
27
40
30
50
36
65
45
75
54
85
63
100
68
110
78
8.60
6.10
11.5
8.20
cl-,
d:i
I
Case hardened steel C15E, A2, A3, A4, A5
Materials
~So
loading
direct ions ,.
vertical
(single line)
under 45°
(double line)
Carrying capacity int for loading direction
Vertical
under 45°
=
0.14 0.23 0.34 0.70 1.20 1.80
0.10 0.17 0.24 0.50 0.86 1.29
3.20
2.30
4.60
3.30
cf. DIN 910 ( 1992-011
Thread d
WAF
I
-
d,
I
:T
.
i
- -
---,:
M10
x1
M12
xl.5
M16
xl.5
M20
xl.5
M24
xl.5
M30
xl.5
M36
x l .5
M42
xl .5
M48
xl.5
M52
x1.5
14
17
8
17
21
12
21
21
12
25
26
14
29
27
14
36
30
16
42
32
16
49
33
16
55
33
16
60
33
16
3
10
10.9
3
13
14.2
3
17
18.7
4
19
20.9
4
22
23.9
4
24
26.1
4
27
29.6
5
30
33
5
30
33
5
30
33
"t)
C
WAF
e
_ ,__
i
C
Materials
I
=
St steel, Al Al-alloy, CuZn copper-zinc-alloy
Screw plug DIN 910 - M24 x 1.5 - St:
d = M24 x 1.5, mat erial: steel
Hexagon socket Drain plugs
cf. DIN 908 (1992-01)
Thread d
WAF -
.,, ..~
-
=--
C
..,
d,
I
C
I
WAF
t
1-t---
f
t--
I
6.30
4.50
Eye bolt DIN 580 - M20 - C15E: d = M20, material C15E
Hexagon head Drain plugs
.,, .,
M24
M24
x2
5.6, 8.8, 10.9
Eye bolts
l
M20
M20
x l .5
e
M10
xl
M12
xl.5
M16
xl.5
M20
xl.5
M24
xl.5
M30
xl.5
M36
xl.5
M42
xl.5
M48
xl.5
M52
x l .5
14
11
3
17
15
3
21
15
3
25
18
4
29
18
4
36
20
4
42
21
5
49
21
5
55
21
5
60
21
5
5
5
5.7
6
7
6.9
8
7.5
9.2
10
7.5
11.4
12
7.5
13.7
17
9
19.4
19
10.5
21.7
22
10.5
25.2
24
10.5
27.4
24
10.5
27.4
Materials
St steel, Al Al-alloy, CuZn copper-zinc-alloy
=
Screw plug DIN 908 - M20 x 1.5- CuZn:
d = M24 x 1.5, material: copper-zinc-alloy
220
Machine elements: 5.2 Bolts and screws
Slotted set screws
cf. DIN EN 27434, 27435, 24766 (all 1992-101
Thread d
with cone point
{~
f
I
d1
n
tii;;I;
z~
0N
from
l to
~ tpoint . , ;
z.,,
WM
z "
M6
M8
M10
M 12
0.2
0.3
0.8
0.3
0.4
1
0.3
0.4
1.1
0.4
0.6
1.4
0.5
0.8
1.6
1.5
1
2
2
1.2
2.5
2.5
1.6
3
3.6
2
3
2
6
2
8
3
10
3
12
4
16
6
25
8
30
5
35
10
40
12
55
16
60
0.8
1.1
1
1.3
1.5
1.5
2
1.8
2.5
2.3
3.5
2.8
4.3
3.3
5.5
4.3
7
5.3
8.5
6.3
0.3
0.7
0.3
0.8
0.4
1
0.4
1.1
0.6
1.4
0.8
1.6
1
2
1.2
2.5
1.6
3
2
3
-
2.5
8
3
10
4
12
5
16
6
20
8
25
8
30
10
40
12
50
16
60
0.6
0.2
0.5
0.8
0.3
0.7
1
0.3
0.8
1.5
0.4
2
0.4
1.1
2.5
0.6
1.4
3.5
0.8
1.6
4
1
2
5.5
1.2
2.5
7
1.6
3
8.5
2
3.6
2
6
2
8
2
10
2.5
12
3
16
4
20
5
25
6
30
8
40
10
50
12
60
n
t
c~
from
l to
d1
n
t
Zco
W<D
zr-0~
f
MS
0.2
0.3
0.7
z
fi i'! .~'
c::
M4
0.1
0.2
0.5
d1
with dog point
w{
M l.2 M l .6 M2 M2.5 M3
from
l to
I
Product grade A (page 21 1I
Valid standard
Replaces
DIN EN 27434
DIN EN 27435
DIN EN 24766
DIN 553
DIN 417
DIN 551
Property
classes
45H, A1-12H, A2-21H, A3-21H, A4-21H, A5-21 H
Nominal
lenglhs /
2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 30--50, 55, 60 mm
Set screw ISO 7434 - M6 x 25 -1 4H:
d = M6, / = 25 mm, property class 14H
=>
Set screws with hexagon socket
cf. DIN EN ISO 4026, 4027, 4028 (2004-051
Thread d
with cone point
z~
wo
z ..
- 0
o!!?
M2 M2.5 M3
M4
MS
M6
M8
M 10
M12
M 16
M20
d,
WAF
0.5
0.9
0.7
1.3
0.8
1.5
1
2
1.3
2.5
1.5
3
2
4
2.5
5
3
6
4
8
5
10
e
1
0.8
1.5
1.2
1.7
1.2
2.3
1.5
2.9
2
3.4
2
4.6
3
5.7
4
6.9
4.8
9.1
6.4
11.4
8
l to
2
10
2.5
12
3
16
4
20
5
25
6
30
8
40
10
50
12
60
16
60
20
60
d1
z
WAF
1
1.3
0.9
1.5
1.5
1.3
2
1.8
1.5
2.5
2.3
2
3.5
2.8
2.5
4
3.3
3
5.5
4.3
4
7
5.3
5
8.5
6.3
6
12
8.4
8
15
10.4
10
e
1
0.8
1.5
1.2
1.7
1.2
2.3
1.5
2.9
2
3.4
2
4.6
3
5.7
4
6.9
4.8
9.1
6.4
11.4
8
from 2.5
10
3
12
4
16
5
20
6
25
8
30
8
40
20
50
12
60
16
60
20
60
t
from
with dog point
.,;
z~
wo
z"
0
o!!?
t
l to
with flat point
f~t
I
SW
Product grade A (page 2111
Valid standard
Replaces
DIN EN ISO 4026
DIN EN ISO 4027
DIN EN ISO 4028
DIN913
DIN914
DIN 915
z ~
w o
z"
- 0
o!!?
d,
WAF
1
0.9
1.5
1.3
2
1.5
2.5
2
3.5
2.5
4
3
5.5
4
7
5
8.5
6
12
8
15
10
e
1
0.8
1.5
1.2
1.7
1.2
2.3
1.5
2.9
2
3.4
2
4.6
3
5.7
4
6.9
4.8
9.2
6.4
11 .4
8
2
10
2.5
12
3
16
4
20
5
25
6
30
8
40
10
50
12
60
16
60
20
60
t
from
I to
Property
classes
Nominal
lengths/
=>
45H, A1 -12H, A2-21H, A3-21H, A4-21H, A5-21H
2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 30-50, 60 mm
Set screw ISO 4026 - M6 x 25 -A5-21H:
d = M6, / = 25 mm, AS stainless steel, property class 21H
221
Machine elements: 5.2 Bolts and screws
111111,--;11M1IF.l II
Preselection of shank bolts11
Joint diagram
fp preload
(_ _
I . _~
F
i/'
f,
u..·
~
•static
2.5
4
6.3
10
16
25
40
F, joint clamp
force
• dynamic
1.6
2.5
4
6.3
10
16
25
40
M5
M6
MB
Ml0
M12
M16
M20
M24
F, tot al bolt load
~.,
5.8, 6.8
8.8
M5
M6
MB
MB
Ml 0
M16
M20 M24
f, bolt extension
eo 10.9
M4
M5
M6
MB
M l0
M12
M16
M20
12.9
M4
M5
M5
MB
MB
Ml0
M12
M16
r, joint compression
fj
Applied force per bolt F.21 in kN
Load
F• applied force
~:g
a..
63
11 It is necessary to check t he values of the selected bolts in accordance
M-
with VDI Guideline 2230 for instance.
21 For waisted bolts select next higher applied force level.
Preload and tightening torques
Shank bolts
Thread
f31
A."
in
mm2
I
Preload
Fp in kN
Waisted bolts
Tightening torque
Mi in N • m
Overall coefficient of friction µ 41
0.08 0.12 0.14 0.08 0.12 0.14
I
Preload
F p in kN
A_.21
in
mm2
Tightening torque
Mtin N -m
Total coefficient of friction µ41
0.08
0.12
0.14
0.08
0.12
0.14
11.8
17.3
20.2
11.2
16.4
19.2
13.6
20
23.4
17.6
25.8
30.2
19.2
28.2
33
36.6
18.6
27.1
31.9
17.2
25.2
29.5
16.5
24.2
28.3
17.9
26.2
30.7
23.1
34
39.6
25.3
37.2
43.6
26.6
12.9
19
22.2
8.8
10.9
12.9
39.2
20.3
29.7
34.8
18.8
27.7
32.4
18.1
26.6
3 1.1
18.8
27.7
32.4
24.8
36.4
42.6
27.3
40.1
47.1
29.2
14.6
21.5
25.1
13.4
19.6
23
12.7
18.7
21.9
13.6
20
23.4
17.6
25.8
30.2
19.2
28.2
33
M10
8.8
10.9
12.9
58.0
29.5
43.3
50.7
27.3
40.2
47
26.2
38.5
45
36
53
61
46
68
80
51
75
88
42.4
20.7
30.4
35.6
18.9
27.7
32.4
17.9
26.4
30.8
25
37
43
32
47
55
35
51
60
M10x1.25
8.8
10.9
12.9
6 1.2
31.5
46.5
54.4
29.4
43.2
50.6
28.3
41.5
48.6
37
55
64
49
72
84
54
80
93
45.6
22.7
33.5
39.2
20.9
30.6
35.9
19.9
29.2
34.4
27
40
46
35
51
60
38
56
65
M12
8.8
10.9
12.9
84.3
43
63
73.9
39.9
58.5
68.5
38.3 61
56.2 90
65.8 105
80
117
137
87
128
150
6 1.7
30.3
44.6
52.1
27.6
40.6
47.7
26.3
38.6
45.2
43
63
74
55
81
95
60
88
103
M12x1.5
8.8
10.9
12.9
88.1
48.2
70.8
82.7
45
66
72.3
43.2 65
63.5 96
74.3 112
87
128
150
96
141
165
65.8
35
52
61
32.6
47.8
56
31
45.7
53.4
48
71
83
63
93
108
69
102
119
M16
8.8
10.9
12.9
157
81
119
140
75.3 72.4 147
111
106
216
124
253
130
194
285
333
214
314
367
117
58.4
85.8
100
53.4
78.5
91 .8
51
106
74.8 156
87.5 182
137
202
236
150
221
258
M16x1.5
8.8
10.9
12.9
167
88
129
151
82.2 79.2 154
121
116
227
141
136
265
207
304
355
229
336
394
128
65.5 60.2
96.2 88.4
104
113
57.4 115
84.5 169
197
99
151
222
260
166
244
285
M20
8.8
10.9
12.9
245
131
186
218
121
173
202
117
166
194
297
423
495
391
557
653
430
615
720
182
92
134
157
86
123
144
82
117
137
215
306
358
278
395
462
304
432
505
M20x1.5
8.8
10.9
12.9
272
149
212
247
138
200
231
134
190
225
320
455
533
433
618
721
482
685
802
210
11 3
160
188
104
148
173
100
142
166
242
345
402
322
460
540
355
508
594
M24
8.8
10.9
12.9
353
188
268
313
175
250
291
168
238
280
512
730
855
675
960
1125
743
1060
1240
262
136
193
225
124
177
207
118
168
196
370
527
617
480
682
800
523
745
871
M24x2
8.8
10.9
12.9
384
210
300
350
196
280
327
189
268
315
545
776
908
735
1046
1224
816
1160
1360
295
158
224
263
145
207
242
139
198
230
410
582
682
543
775
905
600
852
998
MB
8.8
10.9
12.9
M8x1
During assembly, the bolts are under tensile and torsional stress. The tightening torque Mi utilizes approx. 90% of the
yield strength of the bolt material.
41 µ = 0.08: bolt MoS lubricated
11 A. stress area
2
21 ~ waist cross section
µ = 0.12: bolt l ightly oiled
31 F property class of bolt
µ = 0.14: bolt secured with microencapsulated plastic
222
Machine elements: 5.2 Bolts and screws
Locking fasteners
A locking fastener is generally not necessary for screw
joints which are sufficiently d imensioned and securely
mounted. T he clamping forces prevent the slipping o f
the screwed parts or loosening of the bolts and nuts. In
practice a loss of c lamping force can still occur due to
t he following causes:
100
%
90
BO
• Loosening of the screw joint caused by high surface
contact pressures which initiate plastic deformation
(so-called settling) and reduce the preload of the
screw joint.
Remedy: As little seperation as possible, m inimal surface roughness, use of high-strength bolts (large preload).
, mecroencapsu at
hesive: optimal
70
t
..
60
"O
0
~
50
Unscrewing of the screw joint: For joints dynamically loaded tran sverse to the bolt axis a fully self-actuated unscrewing can occur.
C.
40
30
20
This is remedied w ith locking elements. These are
divided into three g roups based on their effectiveness.
10
Ineffective locking elements (e.g. spring lock washers
and t ooth lock washers).
0
0
1000
2000
3000
4000
5000
load cycles - -
Vibration test DIN 65151 performed on various locking
elements
C&ptive fasteners, which allow a partial unscrewing,
but prevent the screw joi nt from coming completely
apart.
Threadlocking le. g. g lue or corrugated head screws).
The preload remains approximately constant. The nut
or bolt cannot loosen by itself (best method of locking).
The locking behavior of screw joints under transverse
loading on the bolt is tested
ISO 4014-Ml0.
Overview of locking fasteners
Joint
Locking element
Standard
Type, property
Loaded
together,
spring loaded
spring lock washer
spring washer
tooth lock washer
serrated lock washer
w ithdrawn
w ithdrawn
withdrawn
withdrawn
ineffective
ineffective
i neffective
ineffective
Interlocking
lock washer
castle nut with cotter pin
lock w ire
w ithdrawn
DIN 935-1+2
captive fastener
captive fastener
captive fastener
Force-fit
(gripping)
jam nut
bolts and nuts
with gripping
polyamide coating
Blocking
(force-fit and
interlocki ng)
Bonded
ineffective, loosening possible
DIN 267-28
ISO 2320
captive fastener or slight
anti-rotat ion lock
bolts with teeth
under the head
anti-rotation lock, not suitable for
hardened parts
detent edged ring
detent washer
self-locking pair
of washers
anti-rotation lock, not suitable for
hardened parts
anti-rotation lock
microencapsulated adhesives
in threads
liq uid adhesive
DIN 267-27
anti-rotation lock, sealing joint;
temperature range - 50°C to 150°C
anti-rotation lock
223
Machine elements: 5.2 Bolts and screws
Width across flats, Types of bolt and screw drives
Width across flats for bolts, screws, valves and fittings
@
ffl
I
e 1 = 1.4142 - s
s = 0.7071 • e 1
I
I
m
e 2 = 1.1547 - s
s = 0.8660· 8 2
I
@
I
8 3 = 1.0824 • s
s = 0.9239 • 8 3
I
cf. DIN 475-1 (1984-011
Length of diagonal
Width across
Two Square Hexa- flats(WAF-)
flats
gonal Nominal size
s
d
e,
Bi
length of diagonal
Two Square Hexa- Octaflats
gonal gonal
d
e,
Bi
8J
3.2
3.5
4
3.7
4
4.5
4.5
4.9
5.7
3.5
3.8
4.4
21
22
23
24
25
26
29.7
31.1
32.5
23.4
24.5
25.6
22.7
23.8
24.9
4.5
5
5.5
5
6
7
6.4
7.1
7.8
4.9
5.5
6.0
24
25
26
28
29
31
33.9
35.5
36.8
26.8
27.9
29.0
26.0
27.0
28.1
6
7
8
7
8
9
8.5
9.9
11.3
6.6
7.7
8.8
27
28
30
32
33
35
38.2
39.6
42.4
30. 1
31.3
33.5
29. 1
30.2
32.5
9
10
11
10
12
13
12.7
14.1
15.6
9.9
11.1
12.1
32
34
36
38
40
42
45.3
48.0
50.9
35.7
37.7
40.0
34.6
36.7
39.0
12
13
14
14
15
16
17.0
18.4
19.8
13.3
14.4
15.5
41
46
50
48
52
58
58.0
65. 1
70.7
45.6
51.3
55.8
44.4
49.8
54.1
15
16
17
17
18
19
21.2
22.6
24.0
16.6
17.8
18.9
55
60
65
65
70
75
77.8
84.8
91.9
61.3
67.0
72.6
59.5
64.9
70.3
18
19
20
21
22
23
25.4
26.9
28.3
20.0
21.1
22.2
70
75
80
82
88
92
99.0
106
113
78.3
83.9
89.6
75.7
81.2
86.6
=
DIN 475 -WAF 16: Width across flats with nominal size s = 16 mm
Width across
flats (WAf-)
Nominal size
s
Table values as per DIN 475 apply to finished stamped wrought products. bo lts,
screws, nuts and fittings. Diagonal lengths calculated by the formula e2 = 1.1547 • s
are larger than the table values, since they are based on the sharp-edged hexagon.
Calculation of regular polygons, page 27.
Screw drive systems
Type
$
Properties
High torque transmission, no axial
force required, relatively economical,
identical tool for bolt and nut, many
variations. tool relatively large
like hexagon head except the torque
transmission is slightly less, requires
less space for too l than with hexagon
head
•
I: r-'\
~ tJ
slotted
Higher torque transmission than with
hexagon head
Very good torque transmission, little
space required for tool
external
torx drive
hexagon socket
tamper resistant
hexagon drive
*
*@
Properties
internal
torx drive
hexagonal head
(f;
Type
Safety screw, can only be loosened
with a special tool, especially wellsuited as protection against damage
and theft, yet has good torque transmission
Safety screw, can only be loosened
with a special tool, especially wellsuited as protection against damage
and theft, yet has good torque trans-
mission
tamper resistant
torx drive
Inexpensive and popular, but it is difficult to center the tool, low torque
transmission, high contact pressure
on the loaded driving flats
cross recess
Pozidriv
Higher torque than with slotted bolts
& screws, better tool centering, lower
co ntact pressure, available without
diagonal notches and also with cross
recess Phillips form H
224
Machine elements: 5.3 Countersinks
Countersinks for countersunk head screws
Countersinks for countersunk screws with head forms as per ISO 7721 cf. DIN EN ISO 15ai5 (2005-05) Replaces DIN 66
90°!1°
~
-
Nominal sizes
1.6
2
2.5
3
3.5
4
Metric screws
M 1.6
M2
M2.5
M3
M3.5
M4
Tapping screws
-
ST2.2
-
ST2.9
ST3.5
ST4.2
3.9
4.5
d 1 H13
1.8
2.4
2.9
3.4
d 2 min.
3.6
4.4
5.5
6.3
8.2
9.4
d2 max.
3.7
4.5
5.6
6.5
8.4
9.6
r, ..
1.0
1.1
1.4
1.6
2.3
2.6
Nominal sizes
5
5.5
6
8
10
Metric screws
MS
-
M6
MB
M10
Tapping screws
ST4.8
STS.5
ST6.3
ST8
ST9.5
-
d 1 H13
5.5
6
6.6
9
11
-
10.4
11.5
12.6
17.3
20
10.7
11.8
12.9
17.6
20.3
2.6
2.9
3.1
4.3
4.7
-
,,
d:i min.
,.
c/:imax.
r, ..
=>
Countersink ISO 15065-8: Nominal size 8 (metric threads MB or
tapping screw threads STB)
DIN EN ISO 2009
DIN EN ISO 7046-1
DIN EN ISO 2010
DIN EN ISO 7047
DIN ISO 1482
DIN ISO7050
DIN ISO 1483
DIN ISO7051
Application for:
Slotted flat head countersunk screws
Cross recessed flat head countersunk screws
;~•~,
Cross rec. raised head countersunk screws
Slotted flat head countersunk tapping screws
Cross rec. flat head counters. tapping screws
~s
Slotted raised head countersunk tapping screws
Cross rec. raised head counters. tapping screws
Cross recessed flat head countersunk tapping screws ISO 15482
Cross recessed raised head countersunk tapping screws ISO 15483
Slotted raised head countersunk screws
Graphical representation,
see page 83;
Countersinks for countersunk head screws
90°!1°
~
3
Form A and Form F
6
7
d 1 H1311
1.8
2.4
2.9
3.4
4.5
5
5.5
6.6
7.6
9
E
d:i H13
3.7
4.6
5.7
6.5
8.6
9.5
10.4
12.4
14.4
16.4
LL
t, ..
0.9
1.1
1.4
1.6
2.1
2.3
2.5
2.9
3.3
Countersink DIN 74 - A4: Form A, thread diameter 4 mm
3.7
0
-
Application of
Form A for:
1.6
2
2.5
3
4
4.5
5
Countersunk flat head wood screws
Raised head count ersunk wood screws
w
E
0
3
FormE
Graphical representation,
see page 83;
Forms B, C and D are no
longer standardized
DIN 97 and DIN 7997
DIN 95 and DIN 7995
10
12
16
20
22
24
13
17
21
23
25
c:J..!H13
19
24
31
34
37
40
t, ..
5.5
7
9
11.5
12
13
d 1 H131>
a
~
8
10.5
Thread0
LL
a
cf. DIN 74 (2003-04)
<(
Thread0
600± 10
75° :t 1°
=>
Countersink DIN 74 - E12: Fo rm E, thread diameter 12 mm
Application of
Form E for:
Countersunk head bolts for steel structures
Thread0
LL
d 1 H131)
a.
d.! H13
3
4
5
6
8
10
12
14
16
20
3.4
4.5
5.5
6.6
9
11
13.5
15.5
17.5
22
6.9
9.2
11.5
13.7
18.3
22.7
27.2
31.2
34.0
40.7
t, ..
1.8
2.3
3.0
3.6
4.6
5.9
6.9
7.8
8.2
9.4
.,
.s=
"'
(/')
=>
Application of
Form Ffor:
DIN 7969
Countersink DIN 74- F12: Form F, thread d iameter 12 mm
Hexagon socket head countersunk screws
DIN EN ISO 10642
(replaces DIN 7991)
1 > Medium size clearance hole according to DIN EN 20273, page 211
225
M achine elements: 5.3 Counterbores
IRIIIIIH:-U1111~:+.-.111--;1 . , ,... :..... - - 11,
:1: 1:.a:r.111111111iT:J:TtliTill
Counterbores for cap screws
4
5
6
8
10
12
16
20
24
27
30
dt, H131l
4.5
5.5
6.6
9
11
13.5 17.5
22
26
30
33
39
Series 1
6.5
8
10
11
15
18
20
33
40
46
50
58
26
36
Series 2
7
9
11
13
18
24
-
-
-
-
-
-
-
Series 3
6.5
8
10
11
15
18
20
26
33
40
46
50
-.5" Series4
7
9
11
13
16
20
24
30
36
43
46
54
58
63
Series 5
9
10
13
15
18
24
26
33
40
48
54
61
69
Series 6
8
10
13
15
20
24
33
43
48
58
63
73
ISO 1207
2.4
3.0
4.3
-
-
-
12.6
16.6 20.6 24.8
DIN 7984
2.4
3.2
3.9
4.4
5.4 6.4 7.6 9.6 11.6 13.8
DIN 974 prov ides no code designations for co unt erbores.
-
-
4.4
6.6
10.6
-
3.4
5.6
8.6
-
ISO4762
3.7
5.4
Series
Cap screws without washer components
~
~
cf. DIN 974-1 (1991-05)
3
3.4
d
:c
d 1 H13
§f ~
3
✓= ~
6.4
1
Screws (bolts) ISO 1207, ISO 4762, DIN 6912, DIN 7984
2
Screws (bolts) ISO 1580, DIN 7985
31.0 37.0
-
-
Cap screws and the following washer components:
3
Screws (bolts) ISO 1207, ISO 4762, DIN 7984 with spring lock washers DIN 79803>
4
Washers DIN EN ISO 7092
Toot h lock washers DIN 579731
Spring washers DIN 137 Form A31
Serrated lock washers DIN 679831
Spring lock washers DIN 128 + DIN 690531 Serrated lock w ashers DIN 690731
5
Spring washers DIN 137 Form B31
Spring washers DIN 690431
Washers DIN EN ISO 7090
Washers DIN 6902 Form A 31
6
Conical spring washers DIN 6796
Graphical represen- 1l Clearance hole according to DIN EN 20273, series medium, page 211
talion, see page 83; 21 Fo r screws/bolts without washer components
31 Standards withdrawn
Counterbore for hexagon bolts/screws and hexagon nuts
d
4
5
Width across flats
7
di, H13
M
:i:
d 1 H13
10
12
14
16
20
24
27
30
33
36
8
8
13
16
18
21
24
30
36
41
46
50
55
65
4.5
5.5
6.6
9
11
13.5 15.5 17.5 22
26
30
33
36
39
45
Series 1
13
15
18
24
28
33
36
40
46
58
61
73
76
82
98
Series 2
15
18
20
26
36
26
43
46
73
76
93
107
33
48
54
82
61
89
30
54
40
69
73
82
8.3
9.6 10.8 13.3 16.0 18.2 20.1 22.4 23.9 27.4
if ✓= ~
cf. DIN 974-2 (1991-05)
6
10
-.5" Series 3
10
11
13
18
33
22
-;._
3.3
4.1
4.6
6.1
7.2
Hex bolt
42
DIN 974 prov ides no code designations for counterbores.
~
Series 1: For socket w rench DIN 659, DIN 896, DIN 3112 o r socket DIN 3124
Series 2: For box w rench DIN 838, DIN 897 or socket DIN 3129
Graphical represen- Series 3: For recesses in tight space conditions (not suitable for conical spring washers)
tation, see page 83; 1l For hexagon bolts/screws ISO 4014, ISO 4017, ISO 8765, ISO 8676 wit hout washer components
or
Calculation of counterbore depth for flush mounting (for DIN 974-1 and DIN 974-2)
Determining the allowance Z
washer
d,
bolt/screw
Thread
head
nominal 0 d
""
~
=---
~
k ""''
d
AllowanceZ
over 1
to 1.4
over 1.4
106
over6
t o 20
over 20
to 27
over 27
to 100
0.2
0.4
0.6
0.8
1.0
counterbore depth
kmax maxim um height of t he screw/bolt head
h max maxim um height of the washer compo nent
z
allowance based o n thread nominal diameter
(see table)
t
iI I
ld. H13
I~, H1~ I
H If values kmax and hmax are unavailable,
values k and h can be used as approximations.
Counterbore depth11
I
t= kmax + hmax + Z
I
226
Machine elem ents: 5.4 Nuts
Hexagon nuts, type 1
a$
page 228
Most commonly used nuts, used with
bolts up to equal property class
w ith coarse t hreads
M 1.6-M64
DIN EN ISO
4032
with fine threads
M8x1- M64x4
DIN EN ISO
8673
force than for coarse threads
Fine threads: greater transmitted
Hexagon nuts, type 2
f! $
page 229
w ith coarse threads
M5-M36
DINEN ISO
4033
Nut height mis approx. 10% higher
than nuts of type 1, used with bolts
up to equal property class
with fine t hreads
M8x1- M36x3
DIN EN ISO
8674
Fine threads: greater transmitted
force than for coarse threads
with coarse threads
M1.6-M64
DIN EN ISO
4035
Use wit h.low installation heights and
with fine threads
M8x1- M64x4
DIN EN ISO
8675
Low hexagon nuts
•
a•·
!
pages 229, 230
Prevailing torque hexagon nuts with locking insert
•
e•
a
with coarse threads
M3-M36
DIN EN ISO
7040
with fine threads
M8x1-M36x3
DIN EN ISO
10512
Fine t hreads: greater transmitted
force than for coarse t hreads
w ith coarse threads
M5-M36
DIN EN ISO
7719
w ith fine threads
M8x1- M36x3
DIN EN ISO
10513
Self-locking all-metal nuts w ith full
loading capacity
Fine threads: greater transmitted
force than for coarse threads
w ith large
w idth across flats,
pages 230, 232
M12-M36
DINEN
14399-4
coarse threads
w ith flange,
coarse threads
M5-M20
weld nuts,
M3-M 16
M8x1- M16x1.5
coarse threads
high form,
coarse o r
DIN 929
coarse or
cotter pins
Used in sheet metal structures; nuts
are usually joined to metal sheets by
projection welding
page 232
M4-M100
M8x1- M 100x4
DIN 935
M6-M48
M8x1-M48x3
DIN 979
0.6x12- 20x280
DIN EN ISO
1234
fine threads
low form,
Metal construction: high-strength
custom preloaded joints (HV), with
hexagon head bolts DIN EN 14999-4
(page 214)
M ight be used w ith large clearance
DIN EN 1661 holes or to reduce contact pressure
fine threads
•
force than coarse t hreads
page 230
Castle nuts, cotter pins
Ge)
Fine threads: higher transmissio n of
Self-locking nuts with full loading
capacity and non-metallic insert, up
to operating temperatures of 120°C
Hexagon nuts, other forms
8$
low stresses
Might be used for axial fixing of
bearings, hubs in safety joints lsteering area of vehicles)
Locking w ith cotter pin and t ransverse hole in t he bolt. At full
load of the bolt, the cotter pin is
sheared off above property class 8.8.
227
M achine elements: 5.4 Nuts
Acorn nuts
~ $
page 231
high form,
coarse or
fine threads
M4-M 36
M8x1-M24x2
DIN 1587
low form,
coarse or
fine threads
M4-M48
M8x1-M48x3
DIN 917
Decorative and sealing external joint
closures, protection fo r t hreads, protection from injuries
Eye nuts, eye bolts
{$
page 231
M~M100x6
M20x2M 100x4
DIN 582
lock nuts
wit h fine threads
M 10x1M200x1.5
DIN 70852
lock washers
10-200
DIN 70952
lock nut s
w ith fine threads
M 10x0.75M1 15x2
(KMO-KM23l
DIN 981
lock washers
10-115
(MBO-MB23)
DIN 5406
high form,
coarse t hreads
M1-M10
DIN 466
low form,
coarse threads
M 1-M1 0
DIN 467
M6-M30
DIN 1479
eye nuts,
coarse or
fine threads
Transport eyes on machines and
equipment; stress depends on t he
angle of the applied load, m illing of
seating surface necessary
Lock nuts, lock washers
~·<rt
t$
page 231
For axial positioning, e.g . of hubs,
with small mount ing heights and low
stresses, locking w ith lock washers
For axial positioning of roller bearings, for adjustment of the bearing
clearance, e. g. w ith tapered roller
bearings that are locked with lock
washers
Knurled nuts
tJ
page 232
Used in joints t hat are opened Irequently, e.g. in manufact uring of jigs
and fixtures, in contro l cabinets
Hexagon turnbuckle nuts
coarse t hreads
For joining and adjusting, e.g. of
t hreaded and connecting bars, with
left-hand and right-hand threads;
locked by jam nuts
Designation of nuts
Examples:
cf. DIN 962 (2001-11 )
Hexagon nut
Castle nut
Hexagon nut
I
I
Type
I
Reference standard, e.g.
ISO, DIN, EN;
sheet number of
the standard 11
ISO 4032 - M12 -8
OIN929 - M8 x 1 - St
EN 1661 - M12 - 10
T
Nominal data, e.g.
M - metric threads
8 - nominal diameter d
1 - thread pitch P
for fi ne t hreads
I
Property class, e.g . 05, 8, 10
Material, e.g.: St steel
GT malleable cast
iron
11 Nuts standardized according to ISO or DIN EN ISO, have the code ISO in their designation.
Nuts standardized according to DIN, have the code DIN in their designation.
Nuts standardized according to DIN EN, have the code EN in t heir designation.
228
Machine elements: 5.4 Nuts
Property classes, hexagon nuts with coarse threads
cf. DIN EN 20898-2 (1994-02),
DIN EN ISO 3506-2 (1998-031
Property classes of nuts
Stainless steels
DIN EN ISO 3506-2
Unalloyed and alloy steels
DIN EN 29898-2
Examples:
nut heig ht m ee 0.8 • d:
nut height m < 0.8 • d:
8
nut height m ee 0.8 • d:
T
nut height m < 0.8 • d:
A 2-70
3
1rQ ~
I
Code
S1INII micros1ructure
Steel group
Code
A austenitic
F ferrit ic
1 free machining alloys
70 proof stress = 70 • 10 N/mm 2
035 low nut,
proof stress= 35. 10 N/mm2
8 property class
04 low nuts, test
load = 4. 100 N/mm2
2 alloyed with Cr, Ni
4 alloyed wit h Cr, Ni, Mo
Allowable combinations of nuts and bolts
Nuts
~
Property class
of the nut
;1
~~
4.8
cf. DIN EN 20898-2 (1994-021
Usable bolts up to property class
St ainless steels
Unalloyed and alloy steels
5.8 6.8 8.8 9.8 10.9 12.9 A2-50 I A2-70 I A4-50 I A4-70
4
5
allowable combinations
of property classes for nuts
and bolts
6
8
9
•
' ~
10
12
A2-50
A2-70
' ---·
M -50
{L'1_'{J
~
A4-70
04, 05,
A2-025,
A4-025
Bolts
Property classes for low nuts. The nuts are designed for smaller load
capacity. Bolts and nuts of the same material g roup, e.g. stainless steel,
can be combined with each other.
Hexagon nuts with coarse threads, Type 11
Valid standard Replaces Thread d
DINEN ISO DIN ENI DIN
WAF
4032
24032 934 dw
e
m
..,
AF
Property
classes
~
T hread d
M2
M2.5
M3
M4
M5
M6
MS
M 10
3.2
2.4
4
3.1
5
4.1
5.5
4.6
7
5.9
8
6.9
10
8.9
13
11.6
16
14.6
3.4
1.3
4.3
1.6
5.5
2
6
2.4
7.7
3.2
8.8
4.7
11.1
5.2
14.4
6.8
17.8
8 .4
as per agreement
6, 8, 10
A2-70, A4-70
Thread d
M12
M16
M20
M 24
M30
M36
M42
M48
M56
WAF
dw
18
16.6
24
22.5
30
27.7
36
33,3
46
42.8
55
51.1
65
60
75
69.5
85
78.7
e
20
10.8
26.8
14.8
33
18
39.6
21.5
50.9
25.6
60.8
31
71.3
34
82.6
38
93.6
45
m
Product g rades (page 211)
cf. DIN EN ISO 4032 (2001-03)
M1.6
Property
classes
6, 8, 10
A2-70, A4-70
as per agreement
A2-50, A4-50
Grade
M1.6-M16
A
M20-M64
B
-
Explanation
11 Type 1: Nut height m ., 0.8 • d
Hexagon nut ISO 4032-M10-10: d = M10, property class 10
-
229
Machine elements: 5.4 Nuts
(;J:f:111111 ■ 111 I
Hexagon nuts with coarse threads, type 2 11
~
~
~ ~
W~F
cf. DIN EN ISO 4033 (2001-03), replaces DIN EN 24033
Thread d
MS
M6
MB
M10
M 12
M 16
M 20
M24
M30
M36
WAF
dw
8
6.9
10
8.9
13
11.6
16
14.8
18
14.6
24
22.5
30
27.7
36
33.2
46
42.7
55
51.1
e
m
8.8
5.1
11.1
5.7
14.4
7.5
17.8
9.3
20
12
26.8
16.4
33
20.3
39.6
23.9
50.9
28.6
60.8
34.7
Property
Product g rades (page 211) classes
Thread d
Grade
M 1.6 M 16
A
M20- M64
B
Explanation
=>
9, 12
11
Hexagon nuts of type 2 are approx. 10 % higher than nuts of type 1.
Hexagon nut ISO 4033 - M24 - 9: d = M24, property class 9
Hexagon nuts with fine threads, type 1 and type 2 11
Valid standard Replaces
Thread d
DIN EN ISO DIN EN DIN
8673
28673 934
WAF
28674 971 dw
8674
e
m1
"t::,
-r1~
QJ
W
A
11
m211
cf. DIN EN ISO 8673 and 8674 (2001-031
MS
x1
M 10
x1
M 12
x1.5
M16
x1.5
M20
x1.5
M24
x2
M30
x2
M36
x3
M 42
x3
M48
x3
M56
x4
13
11 .6
16
14.6
18
16.6
24
22.5
30
27.7
36
33.3
46
42.8
55
51.1
65
60
75
69.5
85
78.6
14.4
6.8
7.5
17.8
8.4
9.3
20
10.8
12
26.8
14.8
16.4
33
18
20.3
39.6
21.5
23.9
50.9
25.6
28.6
60.8
31
34.7
71.3
34
82.6
38
93.6
45
-
-
-
6, 8
Type 1
Property
classes
Type2
m
Product grades (page 211 I
T hread d
Grade
M8x1 M16x1.5
A
M20x1 .5- M64x3
B
Explanation
=>
A2-70, A4-70
8, 10, 12
11
as per
agreement
A2-50, A4-50
-
10
Hexagon nut type 1: DIN EN ISO 8673, nut height m 1 ,. 0.8. d
Hexagon nut type 2: DIN EN ISO 8674, nut height m 2 is approx. 10%
larger t han nuts of type 1.
Hexagon nut ISO 8673 - M8x1 -6: d = M8x1, property class 6
Low hexagon nuts with coarse threads11
cf. DIN EN ISO 4035 (2001-03)
Valid standard
DIN EN ISO
Replaces
DINEN
Thread d
M 1.6
M2
M2.5
M3
M4
M5
M6
MB
M10
4035
24035
WAF
dw
3.2
2.4
4
3.1
5
4.1
5.5
4.6
7
5.9
8
6.9
10
8.9
13
11.6
16
14.6
e
m
3.4
1
4.3
1.2
5.5
1.6
6
1.8
7.7
2.2
8.8
2.7
11.1
3.2
14.4
4
17.8
5
as per agreement
Property
classes
1P
~
A2-035, A4-035
Thread d
M 12
M 16
M20
M 24
M30
M 36
M42
M48
M 56
WAF
dw
18
16.6
24
22.5
30
27.7
36
33.2
46
42.8
55
51 .1
65
60
75
69.5
85
78.7
e
m
20
6
26.8
8
33
10
39.6
12
50.9
15
60.8
18
7 1.3
21
82.6
24
93.6
28
04, 05
Property
classes
Product grades (page 211) Explanation
Thread d
Grade
M 1.6- M 16
A
M20-M36
B
04, 05
=>
A2-035, A4-035
11
as per agreement
A2-025, A4-025
-
Low hexagon nuts (nut height m < 0.8 · di have a smaller load capacity as type 1 nuts.
Hexagon nut ISO 4035 - M16 -A2-035:
d = M 16, property class A2-035
230
Machine elements: 5.4 Nuts
Low hexagon nuts with fine threads11
cf. DIN EN ISO 8675 (2001-031
Valid standard
DIN EN ISO
Replaces
DINEN
Thread d
MB
xl
Ml0
x1
M12
x l .5
M16 M20
x l .5 x1.5
M24
x2
M30
x2
M36
x3
M42
x3
M48
x4
M56
x4
8675
28675
WAF
dw
13
11.6
16
14.6
18
16.6
24
22.5
30
27.7
36
33.3
46
42.8
55
51.1
65
60
75
69.5
85
76.7
e
m
14.4
4
17.8
5
20
6
26.8
8
33
10
39.6
12
50.9
15
60.8
18
71.3
21
82.6
24
93.6
28
~W ~1 P
~F
~
04, 05
Property
classes
Product g rades (page 21 1)
Thread d
Grade
M8x1 - M16x1.5
A
M20x1.5-M64x3
B
11 Low hexagon nuts (nut height m < 0.8. d) have a smaller load capacity
Explanations
of type 1 nuts (page 229).
21 Property classes for stainless steels: A2-025, A4-025
-
Hexagon nut ISO 8675 - M20x1 .5 - A2-035:
d ~ M20x 1.5, property class A2-035
Hexagon nuts with insert, type 111
Valid standard Replaces
DIN EN ISO DIN EN DIN Thread d
7040
10512
27040 982
WAF
dw
e
~
as per
agreement
21
A2-035, A4-035
h
m
Property cl.
Explanation
-
Product grades see
DIN EN ISO 4032
cf. DIN EN ISO 7040 and 10512 (2001-03)
M4
M5
M6
MB
MB
xl
MlO
Ml0
xl
M12
M 12
x l .5
M16
M16
x1.5
M20
M20
x l .5
M24
M24
x2
M30
M30
x2
M36
M36
x3
7
5.9
7.7
8
8.9
8.8
10
8.9
11.1
13
11.6
14.4
16
14.6
17.8
18
16.6
20
24
22.5
26.8
30
27.7
33
36
33.3
39.6
46
42.8
50.9
55
51.1
60.8
6
2.9
6.8
4.4
8
4.9
9.5
6.4
11 .9
8
14.9
10.4
19.1
14.1
22.8
16.9
27.1
20.2
32.6
24.3
38.9
29.4
for DIN EN ISO 7040: 5, 8, 10
fo r DIN EN ISO 10512: 6, 8, 10
11 Hexagon nuts type 1 (nut height m"' 0.8 • di
DIN EN ISO 7040: Nuts with coarse threads
DIN EN ISO 10512: Nuts with fine threads
Hexagon nut ISO 7040- M16-10: d= M10, property class 10
Hexagon nuts with large width across flats11
cf. DIN EN 14399-4 (2006-06), replaces DIN 6915
Thread d
M12
M16
M20
M22
M24
M27
M30
M36
WAF
22
20.1
27
24.9
32
29.5
36
33.3
41
38
46
42.8
50
46.6
60
55.9
23.9
10
29.6
13
35
16
39.6
18
45.2
20
50.9
22
55.4
24
66.4
29
dw
e
m
Property cl.,
surface
10
normal -> lightly oiled, hot-galvanized-> code: !Zn
Explanation
11 for high-strength structural bolting assemblies (HVI in metal construction. Used
in combination with hexagon head bolts as per DIN EN 143994 (page 2141.
Hexagon nut DIN EN 14399-4 - M16 -10 - HV: d = M24, property class 10,
high-strengt h preloaded
Product grade B
Hexagon nuts with flange
Thread d
M5
M6
MB
Ml0
M12
M16
M20
WAF
de
8
9.8
11.8
10
12.2
14.2
13
15.8
17.9
16
19.6
21 .8
18
23.8
26
24
31.9
34.5
30
39.9
42.8
e
m
8.8
5
11.1
6
14.4
8
17.8
10
20
12
26.8
16
33
20
dw
Product grades see
DIN EN ISO 4032
cf. DIN EN 1661 (1998-02)
Property
classes
8, 10, A2-70
Hexagon nut EN 1661 - M16-8: d = Ml 6, property class 8
231
Machin e elements: 5.4 Nuts
Hexagon acorn nuts, Lock nuts, Eye nuts
Hexagon acorn nuts. high form
M5
M6
-
MB
MB
x1
M10
M10
x1
M12
M12
x1.5
M16
M16
x1.5
M 20
M 20
x2
M24
M24
x2
WAF
d,
m
7
6.5
3.2
8
7.5
4
10
9.5
5
13
12.5
6.5
16
15
8
18
17
10
24
23
13
30
28
16
36
34
19
e
h
7.7
8
5.3
8.8
10
7.2
11.1
12
7.8
14.4
15
10.7
17.8
18
13.3
20
22
16.3
26.8
28
20.6
33.5
34
25.6
40
42
30.5
Thread d
m
WAF, - - -
"~t;f•
92
f
cf. DIN 1587 (2000-10)
M4
t
-
g,
h
-
g " 2 • P(P thread pitch)
Property
Product grade A or B
by choice of manufacturer
classes
=>
Thread undercut DIN 76-D
6, A1-50
Acorn nut DIN 1587 - M20 - 6: d = M 20, property class 6
Lock nuts
cf. DIN 70852 (1989-03)
Thread d
M1 2 M16 M20 M24 M30
x1.5 x 1.5 x1.5 x 1.5 x1.5
M35
x1.5
M40
x 1.5
M48
x 1.5
M55
x1.5
M60
x1.5
M65
x1.5
d,
d2
22
18
28
23
32
27
38
32
44
38
50
43
56
49
65
57
75
67
80
71
85
76
m
w
6
4.5
1.8
6
5.5
2.3
6
5.5
2.3
7
6.5
2.8
7
6.5
2.8
8
7
3.3
8
7
3.3
8
8
3.8
8
8
3.8
9
11
4.3
9
11
4.3
{;q1~ ~
r"'
m ....
t
St (steel)
Mat erial
=>
Lock nut DIN 70852 -M16x1 .5 -St: d= M 16x1.5, material steel
Lock washers
cf. DIN 70952 11976-05)
] i
hub
keyway
~
d
d,
t
a
w
w1 C11
t,
12
16
20
24
30
35
40
48
55
60
65
24
0.75
29
1
35
1
40
1
48
1.2
53
1.2
59
1.2
67
1.2
79
1.2
83
1.5
88
1.5
3
4
3
5
4
5
4
6
5
7
5
7
5
8
5
8
6
10
6
10
6
10
4
1.2
5
1.2
5
1.2
6
1.2
7
1.5
7
1.5
8
1.5
8
1.5
10
1.5
10
2
10
2
Material
=>
St (st eel sheet)
Lock washer DIN 70952-16- St: d = 16 mm, material steel
Eye nuts
cf. DIN 582 (2003-08)
d,
i
2
+
-<:
Thread d
MB M 10 M 12 M 16 M20
M24
h
d,
18
36
22.5
45
di
da
20
20
25
25
Vertical
under 45°
0.14 0.23 0.34 0.70
0. 10 0.17 0.24 0.50
d
l
~~
f
loading
directions
vertical
(singl e line)
, 50
under 45°
(double line)
26
54
30.5
63
35
72
45
90
30
30
35
35
40
40
50
50
M36
M42
M48
M56
55
108
65
126
75
144
85
166
95
184
60
65
70
75
80
85
90
100
100
110
M30
Load capacity11 in t for d irection of load application
1.20
0.86
1.80
1.29
3.20
2.30
4.60
3.30
6.30
4.50
8.60
6.10
11.5
8.20
Materials
Case hardened steel C15, A2, A3, A4, A5
Explanation
11 The values include a safety factor v = 6, based on the ultimate load.
=>
Eye nut DIN 582 - M36-C15E: d = M36x3, material C15E
232
Machine elements: 5.4 Nuts
Castle nuts, Cotter pins, Weld nuts, Knurled nuts
Castle nuts, high form
·:
•
·~
Product grades (page 211)
Thread d
Grade
M1.6-M16
A
M20- M100
B
cf. DIN 935-1 (2000-10)
M4
-
MS
M6
Thread d
-
MS
MS
xl
Ml0
Ml0
xl
M12
M12
xl.5
M16
M16
x l .5
M20
M20
x2
M24
M24
x2
M30
M30
x2
s
e
m
7
7.7
5
8
8.8
6
10
11.1
7.5
13
14.4
9.5
16
17.8
12
18
20
15
24
26.8
19
30
33
22
36
39.6
27
46
50.9
33
no cylindrical shoulder
2
2.5
2.8
\4
5
6.5
8
15.6
3.5
10
21.5
4.5
13
27.7
4.5
16
33.2
5.5
19
42.7
7
24
d,
~
)
n
1.2
3.2
w
-
I I
I
I
6, 8, 10
Property
classes
=
A2-70
A2-50
Castle nut DIN 935 - M20 - 8: d = M20, property class 8
Cotter pins
cf. DIN EN ISO 1234 (1998-02)
cf11
,:fW;i;Il
I
..;-
1
1.2
1.6
2
2.5
3.2
4
5
6.3
8
3
1.6
1.6
3
2
2.5
3.2
2.8
2.5
4
3.6
2.5
5
4.6
2.5
6.4
5.8
3.2
8
7.4
4
10
9.2
4
12.6
11.8
4
16
15
4
from
to
6
20
8
25
8
32
10
40
12
50
14
63
18
80
22
100
28
125
36
160
d 21 over
1
to
3.5
4.5
4.5
5.5
5.5
7
7
9
9
11
11
14
14
20
20
27
27
39
39
56
Nominal
lengths
6, 8, 10, 12, 14, 16, 18, 20, 22, 25, 28, 32, 36, 40, 45, 50, 56, 63, 7 1, 80,
90, 100, 112, 125, 140, 160 mm
b
C
a
I
Explanations
=
11 d Nominal sizes= cotter pin hole diameter
21 d applicable bolt diameter
1
Cotter pin ISO 1234- 2.5x32 - St:
d = 2.5 mm, I = 32 mm, material steel
Hexagon weld nuts
cf. DIN 929 (2000-01)
-, ~
Thread d
M3
M4
MS
M6
MB
Ml0
M12
M16
s
d1
7.5
4.5
8.2
9
6
9.8
10
7
11
11
8
12
14
10.5
15.4
17
12.5
18.7
19
14.8
20.9
24
18.8
26.5
3
0.3
3.5
0.3
4
0.3
5
0.4
6.5
0.4
8
0.5
10
0.6
13
0.8
e
m
h
:''
Material
=
Product grade A
St - steel w ith a maximum carbon content of 0.25%
Weld nut DIN 929 - M16- St: d = M16, material steel
Knurled nuts
..;
k
cf. DIN 466 and 467 (2006-08)
....-...
~t1~ ...\ f
E
f
h
--~·
~
--c>J
..... ,,,
Thread d
Ml.2 Ml.6
M2
M2.5
M3
M4
M5
M6
MS
Ml0
d•
d•
k
6
3
1.5
7.5
3.8
2
9
4.5
2
11
5
2.5
12
6
2.5
16
8
3.5
20
10
4
24
12
5
30
16
6
36
20
8
h' I
h2
4
2
5
2.5
5.3
2.5
6.5
3
7.5
3
9.5
4
11.5
5
15
6
18
8
23
10
Property
classes
Explanations
St (steel), A 1-50
11 Nut height for DIN 466 high form
2l Nut height for DIN 467 low form
=>
Knurled nut DIN 467 - M6 -Al-50: d = M6, property class A 1-50
233
Machine elements: 5.5 Washers
Flat washers, Overview
~'T-rT-¥"
Designation example:
I
I
I
I
Name
I
11 Stainless steel, steel group A2
I
Nominal size
(Thread nominal 0 )
I
Standard
I
I
Hardness
grade
Material
I
I
Overview
Design
Standard range
from-to
Illustration
~
~
t
Flat washers
with chamfer
Product grade A2 >
M5-M64
M 'l
Standard
Steel,
stainless
steel
DIN EN
ISO
7090
table below
Design
Standard range
from-to
Illustration
~
Flat washers
w ith chamfer,
for HV bolts
M12- M30
--
M11
Standard
Steel
DIN EN
14399-6
Steel
DIN 434
DIN 435
Steel
DINEN
28738
Spring
steel
DIN
6796
page 235
Flat washers
small series
Product grade A 2>
M1.6-M36
Steel,
stainless
steel
DINEN
ISO
7092
page 234
Flat washers
normal series
Product grade C21
M1.6-M64
Steel
DIN EN
ISO
7091
Steel
DIN
7989-1
g
Washers, square,
for channels and
!beams
M8-M27
~
Plain washers for
clevis pins
Product grade A 2>
d = 3-100 mm
t
Conical spring
washers for
screw joints
d=2-30mm
-=bl
page 234
n
Washers for steel
structures
Product grade
A21, C2l
M10-M30
page 234
page 235
page 235
page 235
11 Material is steel with corresponding hardness grade (e.g. 200 HV; 300 HV); other materials as agreed upon.
2> Product grades are differentiated by tolerance and by manufacturing process.
Flat washers with chamfer. normal series
- ---1/•h
h
h
4 ··2
30° to 45°
~..;
.-
Hardness grade 200 HV suitable for:
• Hexagon bolts and nuts of property classes" 8.8 or " 8 (nut)
• Hexagon bo lts and nuts made of
stainless steel
Hardness grade 300 HV suitable for:
• Hexagon bolts and nuts of property classes s 10.9 o r s 10 (nut)
cf. DIN EN ISO 7090 (2000-11 ), replaces for DIN 125-1+2
For threads
MS
M6
MS
M10
M12
M16
Nominal size
d 1 min.11
d2 max.11
5
6
8
10
12
16
20
5.3
6.4
8.4
10.5
13.0
17.0
21.0
10.0
12.0
16.0
20.0
24.0
30.0
37.0
hll
1
1.6
1.6
2
2.5
3
3
M24
M30
M36
M42
M48
MS6
M64
For threads
M20
Nominal size
24
30
36
42
48
56
64
d 1 m in.H
25.0
31.0
37.0
45.0
52.0
62.0
70.0
11
44.0
56.0
66.0
78.0
92.0
105.0
115.0
4
4
5
8
8
10
10
d2 max.
h'i
Ma1erial21
Type
Hardness grade
=
Steel
Stainless steel
-
-
A2, A4, F1, C1, C4 (ISO 3506)3>
200 HV
300HV
(quenched and
tempered)
200 HV
Washer ISO 7090-20-200 HV: Nominal size (= thread nominal 0 ) = 20 mm, hardness grade 200 HV, steel
1> These are all nominal dimensions
2> Non-ferrous metals and other materials as per agreement
31 Compare to page 21 1
234
Machine elements: 5.5 Washers
J;iliiliilij
..__, iT:]"r.lli Cll &.~ f:J':J a .. •~ 1 IW 1111
] 'J, l A'•T
Flat washers, small series
h
I '-'--
.,;; .,;;
■ '-
cf. DIN EN ISO 7092 (2000-11), replaces DIN 433-1+2
For threads
M1.6
M2
M2.5
M3
M4
MS
M6
Nominal size
1.6
2
2.5
3
4
5
6
8
d, min. 1I
1.7
2.2
2.7
3.2
4.3
5.3
6.4
8.4
1
di max. 1
3.5
4.5
5
6
8
9
11
15
hmax
0.35
0.35
0.55
0.55
0.55
1.1
1.8
1.8
For threads
M10
M12
M142l
M16
M20
M24
M30
M36
Nominal size
10
12
14
16
20
24
30
36
d 1 min. 1I
10.5
13.0
15.0
17.0
21.0
25.0
31.0
37.0
d 2 max.11
18.0
20 .0
24.0
28.0
34.0
39.0
50.0
60.0
hmax
1.8
2.2
2.7
2.7
3.3
4.3
4.3
5.6
Material31
Hardness grade 200 HV suitable for:
• Cap screws w ith property classes
" 8.8 or of stainless steel
• Cap screws w ith hexagon socket
and property classes
" 8.8 or of stainless steel
Hardness grade 300 HV suitable for:
• Cap screws w ith hexagon socket
and property classes
" 10.9
M8
Steel
-
-
A2, A4, F1, Cl, C4 (ISO 3506141
200 HV
300 HV
(quenched
and temoered}
200 HV
Type
Hardness grade
⇒
Stainless steel
Washer ISO 7092-8-200 HV-A2: Nominal size
(= thread nominal 0) = 8 mm, small series,
hardness grade 200 HV, of stainless steel A2
n These are all nominal dimensions
2> Avoid this size if at all possible
31
Non-ferrous metals and other materials as per agreement
4> Compare to page 21 1
Flat washers, normal series
__, hf--
L-
cf. DIN EN ISO 7091 (2000-11), replaces DIN 126
For threads
M2
M3
M4
MS
M6
MS
M10
M12
Nominal size
2
3
4
5
6
8
10
12
d 1 min.1>
2.4
3.4
4.5
5.5
6.6
9.0
11.0
13.5
d2 max.1I
5.0
7.0
9.0
10.0
12.0
16.0
20.0
24.0
h'I
0.3
0.5
0.8
1.0
1.6
1.6
2
2.5
.,;; .,;;
For threads
M16
M20
M24
M30
M36
M42
M48
M64
'
•- -
Nominal size
16
20
24
30
36
42
48
64
d 1 min. 11
17.5
22.0
26.0
33.0
39.0
45.0
52.0
70.0
11
30.0
37.0
44.0
56.0
66.0
78.0
92.0
115.0
3
3
4
4
5
8
8
10
--
d 2 max.
Hardness grade 100 HV suitable for:
• Hexagon bolts/screws, product
grade C, w ith property classes " 6.8
• Hexagon nuts, product grade C,
w ith property classes s 6
h11
⇒
Washer ISO 7091-12-100 HV: Nominal size
(= thread nominal 0 ), d = 12 mm, hardness grade 100 HV
1
1 These are all nominal dimensions
Washers for steel structures
-ffiJ
Suitable for bolts according to DIN
7968, DIN 7969, DIN 7990 joined
with nuts according to ISO 4032 and
IS04034.
cf. DIN 7989-1 and DIN 7989-2 (2000-04}
For threads11
M10
M12
M16
M20
M24
M27
M30
d 1 min.
11.0
13.5
17.5
22.0
26.0
30.0
33.0
d 2 max.
20.0
24.0
30.0
37.0
44.0
50.0
56.0
⇒
Washer DIN 7989-16-C-100 HV: Thread nominal 0
d = 16 mm, product grade C, hardness grade 100
Versions: Product grade C (stamped version} t hickness h = (8 ± 1.2) mm
Product grade A (turned version} thickness h = (B ± 1) mm
11 Nominal dimensions
235
Machine elements: 5.5 Washers
:c
Washers for HV bolts, Channels and I beams, Clevis pins, Conical spring washers
Rat washers with chamfer for HV screw joints
mark
ldentif~ication
45
~",,.
0
,
~ '
N
450
Sign of the manufacturer
cf. DIN EN 14399-6 (2006-06)
For threads
d 1 min.
M12
13
M16
17
M20
21
M22
23
M24
25
M27
28
M30
31
d-, max.
24
30
37
39
44
50
56
~
3
4
4
l--h_ __
- ---+W
- a-s_h_e_..
r _D_tN_ _E_N_..1_4399
_ _-&_,_-_2_0_~_N_o_..m
_ i_n-: -I s-iz_,_e_d
_ ~_2_0_,_m_
m_~_th-e--l
h
nominal size d corresponds to thread d iameter)
1--M-a1_er_i_a_l:-s-te_e_l.-q....u-e-nc_h_e_d_a_n_d_t_e_m_p_e_r-ed-'--to- 30-0- H
--V--37_0_H_V
__- - - - - - - - l
Square, tapered washers for channels and I beams
channel washer
DIN 434
I-beam washer
DIN 435
~:7:.:'1~~::.'4
cf. DIN 434 (2000-04), DIN 435 (2000-01)
For threads
M8
M10
M12
M16
M20
M22
M24
d 1 min. 11
9
11
13.5
17.5
22
24
26
a
22
22
26
32
40
44
56
b
22
22
30
36
44
50
56
h DIN 434
3.8
3.8
4.9
5.8
7
8
8.5
4.6
4.6
6.2
7.5
9.2
10
10.8
h DIN 435
I-Washer DIN 435-13.5: Nominal sizes d1 = 13.5 mm
Material: Steel, hardness 100 HV 10 to 250 HV 10
11 Nominal diameter
Washers for clevis pins, product grade A1>
d, min.21
cf. DIN EN 28738 (1992-101
6
8
10
12
12
15
18
20
1.6
2
2.5
3
20
22
24
27
34
37
39
100
3
4
6
8
5
10
16
18
24
28
30
0.8
h
d,min.21
14
d-,max.
22
h
4
3
5
d,min.2 1
30
36
40
50
60
80
d2 m ax.
44
50
56
66
78
98
10
6
8
Washer ISO 8738-14-160 HV: d 1 min. = 14 mm,
hardness grade 160 HV
h
5
120
12
Ma1erial: Steel, hardness 160 to 250 HV
Application: For clevis pins according to ISO 2340 and ISO 2341 (page 238),
used only on the cotter pin end.
11 Product grades are differentiated by
tolerance and manufacturing process 21 nominal dimensions
Conical spring washers for screw joints
s
M2
M3
M4
M5
M6
M8
M10
d, H14
2.2
5
3.2
7
4.3
9
5.3
11
6.4
14
8.4
18
10.5
23
hmax.
0.6
0.85
1.3
1.55
2
2.6
3.2
s
0.4
0.6
1.2
2
For threads
d 1 H14
M12
M16
1.5
M24
2.5
M30
hmax.
s
=>
h
cf. DIN 6796 ( 1987-10)
For threads
M22
23
M27
13
17
M20
21
25
28
31
29
39
45
49
56
60
70
3.95
5.25
6.4
7.05
7.75
8.35
9.2
3
4
5
5.5
6
6.5
7
Conical spring washer DIN 6796-10-FSt: for threads M10,
of spring steel
Ma1erial: Spring steel (FSt) according to DIN 267-26
Application: Conical spring washers should counteract loosening of the
screw joints. This does not apply to alternating transverse loads. Its application is therefore limited to predominantly axially loaded, short bolts/screws
of property classes 8.8 to 10.9.
236
Machine elements: 5.6 Pins and clevis pins
Pins and clevis pins, Overview
Designation example:
Name
Standard
Material
Pins with DIN-EN main numbers are designated with ISO numbers.
ISO number = DIN-EN number - 20000; example: DIN EN 22338 = ISO 2338
11 if available
Illustration
Designation,
Standard range
from-to
Standard
Dowel pin,
not hardened
d= 1-SOmm
Dowel pin,
hardened
d • 0.8- 20mm
e.g. St = steel
Stainless steels:
A 1 = austenitic
Cl = martensitic
Designation,
Standard range
from-to
Standard
DIN
ENISO
2338
Taper pin
d, - 0.6-50 mm
DINEN
22339
DIN
EN ISO
8734
Spring pin
(clamping
sleeves),
slotted
d, • 1-50 mm
DIN
ENISO
8752
DIN
ENISO
13337
DIN
ENISO
8740
Tapered grooved
pin
d 1 = 1.5-25 mm
DIN
ENISO
8744
Half length
reversed taper
grooved pin
d 1 = 1.5-25 mm
DIN
ENISO
8741
Half length taper
grooved pin
d 1 = 1.2- 25 mm
DIN
ENISO
8745
Center grooved
pin,
grooved 1/3 the
length
d, = 1.2 - 25 mm
DIN
EN ISO
8742
Round head
grooved pin
d, = 1.4- 20 mm
DIN
ENISO
8746
Center grooved
pin, with long
grooves
d 1 = 1.2-25 mm
DIN
ENISO
8743
Grooved pin with DIN
countersunk head EN ISO
d 1 • 1.4- 20 mm
8747
Clevis pins without head,
form A without
cotter pin hole,
form Bwith
d = 3-100mm
DIN EN
22340
Clevis pins with
head,
form A without
cotter pin hole,
form Bwith
d = 3 - 100mm
Illustration
Pins
1l tolerance m6 or h8
Grooved pins, grooved drive studs
f-a
Straight grooved
pin with chamfer
-of"'" ~
d 1 =1.5-25mm
Clevis pins
Form A
DIN EN
22341
237
Machine elements: 5.6 Pins and clevis pins
Dowel pins of unhardened steel
and austenitic stainless steel
a',
- - - ~ - ---~
1)
..,
-.0
E
cf. DIN EN ISO 2338 (1998-02)
dm6/h82l
from
to
l
0.6
2
6
d m6/h821
from
to
6
8
l
12
60
14
80
Nominal
lengths /
2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 35,
40-95, 100, 120, 140, 160, 180, 200 mm.
⇒
11 Radius and hollow allowed at
0.8
2
8
1.2
4
12
1.5
4
16
2
6
20
2.5
6
24
3
8
30
8
40
5
10
50
10
18
95
12
22
140
16
26
180
20
35
200
25
50
200
30
60
200
40
80
200
50
95
200
Dowel pin ISO 2338 - 6 m6 x 30 - St: d = 6 mm,
tolerance class m6, I = 30 mm, of steel
2> Available in tolerance classes m6 and h8
end of pin
Dowel pins. hardened
cf. DIN EN ISO 8734 ( 1998-03)
dm6
l
from
to
3
10
u
2
u
3
4
5
6
8
w n u
20
4
16
5
20
6
24
8
30
10
40
12
50
14
60
18
80
22
50
26 40
100
Nominal
lengths/
3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22. 24. 26, 28, 30, 32, 35, 40,
45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100 mm
Materials
• Steel: Type A pin fully hardened, type B case hardened
• Stainless st eel type Cl
1> Radius and hollow allowed on
⇒
end of pin
Dowel pin ISO 8734-6 x 30-C1: d = 6 mm, I= 30 mm,
of stainless steel of type Cl
Taper pin, unhardened
cf. DIN EN 22339 (1992· 10>
dh10
1
2
3
4
5
6
from
to
6
10
10
35
12
45
14
55
18
60
22 22 26 32 40
90 120 160 180
l
Nominal
lengths/
Type A ground, Ra= 0.8 µm;
Type B turned, Ra = 3.2 µm
⇒
8
,-1>
"i e - ~ 1 ~-6
~
12
16
20
25
30
45 50
200
55
Taper pin ISO 2339-A-10x40-St: Type A, d =10 mm,
I = 40 mm, of steel
cf. DIN EN ISO 8752 (1998-03)
cf. DIN EN ISO 13337 (1998-02)
Nominal0"1
d 1 max.
2
2.4
2.5
2.9
3
3.5
4
4.6
5
5.6
6
6.7
8
8.8
10
10.8
12
12.8
s ISO 8752
s ISO 13337
0.4
0.2
0.5
0.25
0.6
0.3
0.8
0.5
1
0.5
1.2
0.75
1.5
0.75
2
1
2.5
1
4
20
4
30
4
40
4
50
5
80
10
100
10
120
10
160
10
180
Nomlnal0"1 14
d 1 max.
14.8
16
16.8
20
20.9
25
25.9
30
30.9
35
35.9
40
40.9
45
45.9
50
50.9
s ISO 8752
s ISO 13337
3
1.5
4
2
5
2
6
2.5
7
3.5
7.5
4
8.5
4
9.5
5
from
l to
from
l to
3
1.5
10
200
14
200
20
200
Nominal
lengths I
4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 35, 40,
45- 95, 100, 120, 140, 160, 180, 200 mm
Materials
• Steel: Hardened and tempered 420 HV 30- 520 HV 30
• Stainless steel: Type A or type C
Application
The diameter of the location hole (tole rance class H12) m ust
have the same nominal diameter d 1 as the mating pin. After
installing the pi n in the smallest receiv ing hole, the slot
should not be completely closed.
1> Only one chamfer is allowed for
spring pins with nominal diameter d 1 "' 10 mm.
10
2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 35, 40,
45- 95, 100, 120-180, 200 mm
Spring pins (clamping sleeves), slotted, heavy duty
Spring pins (clamping sleeves), slotted, light duty
A
4
4
10
⇒
Spring pin ISO 8752 - 6 'x 30 - St: d 1 = 6 mm,/= 30 mm,
of steel
238
Machine elem ents: 5.6 Pins and clevis pins
• 1 ■ 1111..._.,. .. 1 ■ 111u1:.1, ■ 11t1 ,u:..-..., ■ 111~Mr:..u_. ....._,
• 11111
Grooved pins. grooved drive studs
d,
1.5
2
2.5
3
4
5
6
8
/ from
to
8
20
8
30
10
30
10
40
10
60
14
60
14
80
14 14 18 22 26 26
100 100 100 100 100 100
/ from
to
8
20
8
30
8
30
8
40
10
60
10
60
12
80
14 18 26 26 26 26
100 160 200 200 200 200
/ from
to
8
20
12
30
12
30
12
40
18
60
18
60
22
80
26 32 40 45 45 45
100 160 200 200 200 200
/ from
to
8
20
8
30
8
30
8
40
8
60
8
60
10
80
12 14 14 24 26 26
100 120 120 120 120 120
f:' :t
/ from
to
8
20
8
30
8
30
8
40
10
60
10
60
10 14 14 18 26 26 26
80 100 200 200 200 200 200
ffl1
d,
1.4
1.6
2
2.5
3
4
5
6
8
10
12
16
20
/ from
to
3
6
3
8
3
10
3
12
4
16
5
20
6
25
8
30
10
40
12
40
16
40
20
40
25
40
/ from
to
3
6
3
8
4
10
4
12
5
16
6
20
8
25
8
30
10
40
12
40
16
40
20
40
25
40
Nominal
lengths /
Pins: 8, 10-30, 32, 35, 40-100, 120, 140- 180, 200 mm
Studs: 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 30, 35, 40 mm
Full length straight ~
grooved pin with
-.,
chamfer
1
ISO 8740
1/2 length reversetaper grooved pin
ISO 8741
~~Z•''J
1:•:e:•1
1/3-1/2 length
center grooved pins
ISO 8742+8743
;
t ,;
Tapered groove pin
ISO 8744
I
~-
Full length taper
grooved pins
ISO 8745
=~
I
Grooved pins
with round head
ISO 8746
~
Grooved pins with
countersunk head
ISO 8747
cf. DIN EN ISO 8740- 8747 (1998-031
⇒
i:,~"t:l
t.
I
-,;~,:,
1.
"t:,
I
3
4
5
6
8
10
12
14
'
~- -.SI
/2
18
20
22
24
0.8
1
1.2
1.6
2
3.2
3.2
4
4
5
5
5
6.3
5
6
8
10
14
18
20
22
25
28
30
33
36
k js14
1
1
1.6
3
4
4.5
5
5
5.5
6
6
7
8
8
9
,.
I
from
to
Nominal
lengths I
⇒
b m in
b
16
d1 H13
d, h11
k
4
4
1.6 2.2 2.9 3.2 3.5
4.5 5.5
6
6
30
20 24 28 30 35 40 45 50
100 120 140 160 180 200 200 200
8
40
10
50
2
12
60
16
80
6, 8, 10-30, 32, 35, 40-95, 100, 120, 140- 180, 200 mm
Clevis pin ISO 2340 - B - 20 x 100 - St: Form B, d = 20 mm,
I = 100 mm, of free-cutting steel
t
8
cf. DIN 1445 (1977-021
10
12
14
16
18
20
24
30
40
50
17
20
20
20
25
29
36
42
49
11
14
d-,
M6
MB M10 M12 M12 M12 M16 M20 M24 M30 M36
m
<iJ h14
14
18
20
22
25
28
30
36
44
55
66
k js14
3
4
4
4
4.5
5
5
6
8
8
9
s
11
13
17
19
22
24
27
32
36
50
60
Nominal
16, 20, 25, 30, 35- 125, 130, 140, 150-190, 200 mm
lengths /2
⇒
1l
g ripping length
25
it. h14
Clevis pins with head and threaded stud end
/11)
20
cf. DIN EN 22340, 22341 (1992-101
d h11
Form A without cotter pin hole
Form B with cotter pin hole
~[
16
t.
Clevis pins with head ISO 2341
k
12
Grooved pin ISO 8740 - 6 x 50 - St: d 1 = 6 mm, / = 50 mm, of steel
Qevis pins with and without head
Clevis pins without head ISO 2340
10
Clevis pin DIN 1445-12h11 x 30 x 50 - St: d 1 = 12 mm, toierance class h l 1, / 1 = 30 mm, /2 = 50 mm, of 9SMnPb28 (SO
239
M achine elements: 5.7 Shaft-hub connections
Keys, Gib-head keys
I
I I
Name
Standard
I
Fo rmor Type
\
\widthxheight x length \
Designation,
Standard range Standard
from- to
Illustration
\ Material,e. g.steel \
Designation,
St andard range St andard
from- t o
Illustration
Overview of tapered keys
table below
b..1:100
I
Tapered key
S:::1
DIN 6886
2x2- 100x50
e
Form A:
sunk key
E33
Gib-head
tapered key
c~
wxh=
Form B:
d riving key
DIN 6887
w xh =
4 X 4--100 X 50
Overview of feather keys
FonnA
I
[
~,~
1 -c:I
I
page 240
~
I
I ~,
DIN 6885
Feather key
wxh =
2x2- 100x50
Form A - J
Woodruff keys
DIN 6888
wxh=
2.5x3.7- 10x16
Tapered keys, Gib-head tapered keys
d. DIN 6886 (1967-12) or DIN 6887 (1968-04)
Fonn A (sunk key)
b 010
_I
-<:t
Fonn B (driv ing key}
C: I _ I ::iiz:1
-<:t
~ 1:100
~
•
~@~m
-
~
-
-
-<:
~ ~
For shaft
diamet er d
over
to
10
12
12
17
22
22
30
30
38
38
44
44
50
50
58
58
65
65
75
75
85
85
95
95
110
Tapered keys
w 010
h
4
4
5
5
6
6
8
7
10
8
12
8
14
9
16
10
18
11
20
12
22
14
25
14
28
16
Gib-head tapered h,
keys
"2
4.1
7
5. 1
8
6.1
10
7.2
11
8.2
12
8.2
12
9.2
14
10.2
16
11.2
18
12.2
20
14.2
22
14.2
22
16.2
25
2.5
1.2
3
1.7
3.5
2.2
4
2.4
5
2.4
5
2.4
5.5
2.9
6
3.4
7
3.4
7.5
3.9
9
4.4
9
4.4
10
5.4
16
70
20
90
25
11 0
32
140
40
160
45
180
56
220
63
250
70
280
80
320
Shaft keyway depth
Hub keyway depth
r,
Allow. deviation
t,, t,
Key length /
from
to
t,
17
+0.2
+0.1
10 11
45
1211
56
50
200
Nominal lengt hs I
6, 8 - 20, 22, 25, 28, 32, 40, 45, 50, 56, 63, 70, 80- 100, 110, 125, 140, 160-200, 220,
250, 280, 320, 360, 400 mm
Lengt h to lerances
Key length/, from - t o
6 - 28
32- 80
Tolerances for
Key length
--0.2
--0.3
--0.5
Keyway lengt h (sunk key)
+0.2
+0.3
+0.5
11 Gib-head key lengths from 14 mm
90- 400
240
Machine elements: 5.7 Shaft-hub connections
Feather keys, Woodruff keys
Feather keys (high form)
cf. DIN 6885-1 (1968-08)
Form B
Form A
FormC
FormD
FormE
Form F
Tolerances f o r ~ keyways
..:::
Shaft keyway width w
tight fit
normal fit
P9
N9
Hub keyway width w
tight fit
normal fit
P9
JS 9
A llow. deviation for d 1
s22
s 130
> 130
Shaft keyway depth t1
Hub keyway depth t2
+0. 1
+0.1
+0.2
+0.2
+0.3
+0.3
90-400
..::
Alllow. deviation for length /
Length
for
tolerances
6 - 28
32-80
key
-0.2
-0.3
-0.5
keyway
+0.2
+0.3
+0.5
d, over
to
6
8
8
10
10
12
12
17
17
22
22
30
30
38
38
44
44
50
50
58
58
65
65
75
75
85
85
95
95
110
110
130
w
h
2
2
3
3
4
4
5
5
6
6
8
7
10
8
12
8
14
9
16
10
18
11
20
12
22
14
25
14
28
16
32
18
t,
t,
1.2
1
1.8
1.4
2.5
1.8
3
2.3
3.5
2.8
4
3.3
5
3.3
5
3.3
5.5
3.8
6
4.3
7
4.4
7.5
4.9
9
5.4
9
5.4
10
6.4
11
7.4
l to
from
6
20
6
36
8
45
10
56
14
70
18
90
20
110
28
140
36
160
45
180
50
200
56
220
63
250
70
280
80
320
90
360
Nominal
lengths I
6, 8, 10, 12, 14, 16, 18, 20, 22, 25, 28, 32, 36, 40, 45, 50, 56, 63, 70, 80, 90, 100, 110, 125, 140, 160, 180,
200, 220, 250, 280, 320 mm
=
Feather key DIN 6885-A-12 x 8 x 56: Form A, b= 12 mm, h = 8 mm, I = 56 mm
Woodruff keys
cf. DIN 6888 (1956-08)
Tolerances for Woodruff keyways
w
..:::
..::
over
to
d,
8
10
10
12
Shaft keyway width w tight fit
normal fit
P9 (P 8)11
N 9 (N 8)11
Hub keyway width w tight fit
normal fit
P9 (P8)11
J 9 (J 8) 11
Allow. devia. fo r w ,.5
5
and h s 7.5 > 7.5
6
,. 9
6
>9
8
10
Shaft keyway depth t 1 +0.1 +0.2
Hub keyway depth t 2 +0. 1 +0.1
+0.1
+0.1
+0.2
+0.1
+0.2
+0. 1
+0.2
+0.2
12
22
30
17
22
17
4
30
38
w h9
2.5
h
3.7
3.7
5
6.5
5
6.5
7.5
6.5
7.5
9
7.5
9
11
9
11
13
11
13
16
d,
10
10
13
16
13
16
19
16
19
22
19
22
28
22
28
32
28
32
45
t,
2.9
2.5
3.8
5.3
3.5
5
6
4.5
5.5
7
5.1
6.6
8.6
6.2
8.2
10.2 7.8
9.8
12.8
h12
3
1.4
t,
,..
=
9.7
9.7
1.7
5
6
2.2
2.6
8
3
10
3.4
12.7 15.7 12.7 15.7 18.6 15.7 18.6 21.6 18.6 21.6 27.4 21.6 27.4 31.4 27.4 31.4 43.1
Woodrufj key DIN 6888 - 6 x 9: w = 6 mm, h - 9 mm
11 Tolerance class for broached keyways
241
Machine elements: 5.7 Shaft-hub connections
Splined shaft joints and blind rivets
Splined shaft joints with straight flanks and internal centering
Light
series
d
N 11
8
D
d
N 11
D
B
N11
D
B
6
6
6
6
6
14
16
20
22
25
3
3.5
4
5
5
42
46
52
56
62
8
8
8
8
8
46
50
58
62
68
8
9
10
10
12
8
8
8
8
8
48
54
60
65
72
8
9
10
10
12
6
6
6
8
8
28
32
34
38
42
6
6
7
6
7
72
82
92
102
112
10
10
10
10
10
78
88
98
108
120
12
12
14
16
18
10
10
10
10
10
82
92
102
112
125
12
12
14
16
18
11
13
16
18
21
23
26
28
32
36
6
6
7
6
7
26
30
32
36
40
6
6
6
8
8
cf. DIN ISO 14 (1986-12)
Medium
series
N 11
D
B
Light
series
Tolerance cia- for the hub
Not heat
treated
dimensions
B
Internal
centering
D
Tolerame claues for the shaft
Heat
treated
d imensions
B
d
M edium
series
D
Dimen.
Sliding
fit
d
Type of fit
Transition
fit
Press fit
B
d 10
f9
h10
D
a11
a11
a11
d
f7
g7
h7
H9
HlO
=:,
Shaft (or hub) DIN ISO 14-6 x23 x 26: N = 6, d= 23 mm, D = 26 mm
H7
H11
H10
H7
11 N number of splines
Open end blind rivets with break mandrel and flat head
Open end blind rivets with break mandrel and countersunk head
Blind rivet with flat head
¢Jdh
broken
mandrel
original
head
=-
..,
head
'
set rivet joint
4
5
511
8.4
10.5
12.6
Head height k
1.3
1.7
2.1
2.5
Rivet mandrel 0 dm m ax.
2
2.45
2.95
3.4
Rivet hole 0 d,,1
3.1
3.2
4.1
4.2
5.1
5.2
6.1
6.2
l max + 3.5
lmax + 4
lmax + 4.5
lmax + 5
min.
Shaft length I
min.
max.
set rivet joint
-
3
6.3
Fitting length b
Blind rivet with countersunk
¢id•
head
br oken ~
mandrel
original
Rivet 0 d(Nominal size)
Head 0 (/i. m ax.
max.
for med
head
formed
head
cf. DIN EN ISO 15977 (2003-04)
cf. DIN EN ISO 15978 (2003-08)
Recommended grip range
4
5
0.5-1.5 11
6
7
2.0-3.5
1.5-3.5 11
1-311
1.5-2.511
8
9
3.5-5.0
2- 5
3-511
2.5-4.0
2- 3
3-5
10
11
5-7
5.0-6.5
44i
12
13
7- 9
6.5-8.5
6-B
5-7
16
17
9-13
8.5-12.5
8-12
7- 11
11- 15
20
21
13-17
12.5-16.5
12-15
25
26
17- 22
16.5-21.0
15-20
15-20
30
31
20-25
20-25
Property
classes
L (low) and H (high) are differentiated by the minimum shear
and m inimum tensile forces of the rivet.
Materials21
Rivet body of aluminum alloy (AIA)
Rivet mandrel of steel (SI)
Blind rivet ISO 15977 - 4 x 12 - AIA/St - L: Blind rivet w it h flat
head; d = 4 m m, I= 12 mm, rivet body of alum inum alloy, rivet
mandrel of steel, property class L (low )
11 Only for flat head rivets ISO 15977
21 Other standard ized material combinations for rivet body/mandrel include:
St/St; AIA/AIA; A2/A2; Cu/St; NiCu/St etc.
242
Machine element s: 5.7 Shaft-hub connections
Metric tapers, Morse tapers, Steep tapers
Morse tapers and metric tapers
cf. DIN 228-1 (1987-05}
Form A: Taper shank with tightening thread
Form 8: Taper shank w ith tang
~1 re-±,;JF:1€
~ 1
4f!:=:;;;p€
~ 1
Form C: Taper sleeve for t aper shanks with draw-in threads
.~,
Form D: Taper sleeve for taper shanks with tang
--z
-b' +---I- -----k/RzE
I
/4
- z
- - - -,.-/Rz 2.5 .~!
I--
•~
I
"'"'
/4 "'"'
/3
/3
The Forms AK, BK CK and DK each have a feed for cooling lubricants.
•
Type of
taper
Metric
t aper
(ME}
Morse
taper
(MT}
Taper
/3
3
25
20
0.5
3
-
4.6
34
28
0.5
d-,
d.i
ct.
~
4
4
4.1
2.9
-
-
23
2
6
6
6.2
4.4
-
-
32
•
z11
Taper
ratio
~
1: 20
1.432°
2
0
9.045
9.2
6.4
-
6.1
50
3
56.5
6.7
52
45
1
1 : 19.212
1.491°
1
12.065
12.2
9.4
M6
9
53.5
3.5
62
9.7
56
47
1
1 : 20.047
1.429°
2
17.780
18.0
14.6
M10
14
64
5
75
14.9
67
58
1
1 : 20.020
1.431°
3
23.825
24.1
19.8
M12
19.1
81
5
94
20.2
84
72
1
1 : 19.922
1.438°
4
31.267
31.6
25.9
M16
25.2
102.5
6.5 117.5
26.5
107
92
1
1 : 19.254
1.488°
5
44.399
44.7
37.6
M20
36.5
129.5
6.5 149.5
38.2
135
118
1
1 : 19.002
1.507°
6
63.348
63.8
53.9
M24
52.4
182
8
210
54.8
188
164
1
1 : 19.180
1.493°
80
170
1.5
240 200
1.5
1 : 20
1.432°
80
80.4
70.2
M30
69
196
8
220
71.5 202
100.5
88.4
M36
87
232
10
260
90
120 120
120.6
106.6
M36 105
268
12
300
108.5 276 230
1.5
160 160
160.8
143
M48 141
340
16
380
145.5 350 290
2
200 200
201.0
179.4
M48 177
412
20
460
182.5 424 350
2
Taper shank DIN 228 - ME - 8 80 AT6: Metric taper shank, Form B, Size 80,
Taper angle tolerance quality ATS
11 Control d imension d
1 may lie a maximum distance z in front of the taper sleeve.
Steep taper shanks for tools and chucks form A
. Ill
24
'°I
.
~H11
d,
,.
Taper shank
,
,,
100 100
Metric
t aper
(MT}
=>
Taper shank
~
iej
,,
~
::, w
a
_,l'fWI., ,
I
cf. DIN 2080-1 (1978-12}
dJ
<4-0.4
,,
M12
50
68.4
1.6
16.1
25.3
M16
63
93.4
1.6
16.1
69.85
39.6
M24
97.5
126.8
3.2
25.7
107.95
60.2
M30
156
206.8
3.2
25.7
No.
d,
d,a10
30
31.75
17.4
40
44.45
50
60
a± 0.2 b H12
70
165. 1
92
M36
230
296
4
32.4
80
254
140
M48
350
469
6
40.5
=>
Steep taper shank DIN 2080 - A 40 AT4: Form A,
No. 40, Taper angle tolerance quality AT4
b
Machine elements: 5.7 Shaft-hub connections
243
Tool holding fixtures
Tool holding fixtures join the tool with the spindle of the machine tool. They transmit the torque and are responsible
for precise concentric running.
Type of design
Function, advantages(+) and d i - - - H
Metric taper (MEI and Morse taper (MT)
Torque transmission:
• force-fit over the taper surface
machine tool spindle
+ reduction sleeves fit different taper
diameters
- not suitable for automatic tool change
Metric taper 1 : 20;
Morse taper 1: 19.002 to 1: 20.047
Steep taper shank ISKI
machine
tool
spindle
+ DIN 69871-1 suitable for automatic tool
change
Fastening in the machine spindle:
Form A: with draw-in bar
Form B: by front fastener
Taper 7: 24 (1: 3.429) according to
DIN 254
Torque transmission:
• force-fit using the taper and contact surfaces
• drive slots on shaft end produce interlock.
Taper 1 : 9.98
'vcontact surface
Taper shank numbers:
ME4;6
MT 0; 1; 2; 3; 4; 5; 6
ME 80; 100; 120; 1140); 160;
(180); 200
Use with CNC machine tools,
especially machining centers;
less suited for high-speed cutting IHSCJ
Steep taper numbers:
• DIN 2080-1 (form Al: 30; 40;
45; 50; 55; 60; 65; 70; 75; 80
• DIN 69871-1: 30; 40; 45; 50; 60
- high weight, therefore less suited for
quick tool change w ith high axial repeating clamping accuracy and for high revolution speeds
Hollow taper shanks (designation HSKI
driver
cf. DIN 228-1 and -2 (1987-05)
Clamping device for conventional drilling and milling.
cf. DIN 2080-1 (1978-12) and -2 (1979-09) and DIN 69871-1 (1995-10)
Torque transmission:
• grooves on taper edge produce interlock.
The steep taper is not meant for transmission of forces, it only centers the tool.
Axial locking is achieved by the thread or
the ring groove.
'vcontact
surface
Application, siz•
+ low weight, therefore
+ high static and dynamic
rigidity
+ high repeated clamping accuracy (3 µm)
+ high rotational speeds
- more expensive than steep taper
cf. DIN 69893-1 and -2 12003-05)
Safer use with high-speed cutting
Nominal sizes: d 1 = 32; 40; 50;
63; 80; 100; 125; 160 mm
Form A: with shoulder and
clamping keyway for automatic
tool change
Form C: only manual change is
possible
Shrinkage chucks
Torque transmission like HSK.
Clamping the tool by quick, inductive heating (approx. 340°C) of the holding shank in
the shrinkage chuck. A shrinkage joint is
formed by the oversize of the tool (approx.
3- 7 µml after the joining and cooling.
holding
shank
available with HSK or steep taper
+ transmission of high torques
+ high radial rigidity
+ higher cutting values possible
+ shorter machining times
+ good runout
+ greater running smoothness
+ better surface quality
+ reliable tool changes
- relatively expensive
- additional induction and cooling devices
required
Universally applicable in
machine tools with steep taper
or hollow shank tool holders;
suitable for tools with cylindrical shank of HSS o r carbide.
Shank diameters: 6; 8; 10; 12;
14; 16; 18; 20; 25 mm
244
M achine elem ents: 5.8 Springs, compo nents of jigs and t ools
Cylindrical helical tension springs
,13~·~
+~:, }-~;_
German loop DIN 2091
L,
c::,
~\ l J . : ~t..--;:;
c,
HI
-
d
~
r.:~[\
~--->-
s,c'. ['.'.'. I/ ['.'.'.I/
.
..
d
~
Sz
L,
o.
minimum sleeve diameter in mm
free length, with no load on spring in mm
L,
length of spring body w it h no load in mm
4,
L,,,.. maximum spring lengt h
internal prestress in N
Fmax maxim um allowable spring force in N
R
L,
0.
spring rate in N/mm
maxim um allowable spring displacement
for Fmax in mm
Sm
L..,,
o.
w ire diameter in mm
outside coil diameter
Fa
I Sm
L,
d
Do
i.
4
Fo
F..,..
...,
R
Tension springs of patented drawn unalloyed spring steel wire11
d . DIN EN 10270-1 (2001-12)
0.20
0.25
0.32
0.36
0.40
3.00
5.00
5.50
6.00
7.00
3.50
5.70
6.30
6.90
8.00
8.6
10.0
10.0
11.0
12.7
4.35
2.63
2.08
2.34
2.60
0.06
0.03
0.08
0. 16
0. 16
1.26
1.46
2.71
3.50
4.06
0.036
0.039
0.140
0.1 73
0.165
33.37
36.51
18.85
19.23
23.67
0.45
0.50
0.55
0.63
0.70
7.50
10.00
6.00
8.60
10.00
8.60
11. 10
7. 10
9.90
11.40
13.7
20.0
13.9
19.9
23.6
3.04
5.25
5.78
7.88
9.63
0.25
0.02
0.88
0.79
0.83
5.31
5.40
11.66
12. 13
14. 13
0.207
0.078
0.606
0.276
0.239
24.41
68.79
17.78
4 1. 15
55.78
0.80
0.90
1.00
1.10
1.25
10.80
10.00
13.50
12.00
17.20
12.30
11.70
15.40
14.00
19.50
25.1
23.0
31.4
27.8
39.8
10.20
9.45
12.50
11.83
15.63
1.22
1.99
1.77
2.99
2.77
19. 10
28.59
28.63
41.95
42.35
0.355
0.934
0.454
1.18 1
0.533
50.36
28.49
59.22
32.98
74.25
1.30
1.40
1.50
1.60
1.80
11.30
15.00
20.00
21.60
20.00
13.50
17.50
22.70
24.50
23.20
134.0
34.9
48.9
50.2
46.0
118.95
15.05
21.75
20.00
19.35
5.771
5.44
3.99
3.99
6.88
70.59
66.08
60.54
67.40
100.90
0.322
1.596
0.603
0.726
1.819
20 1.60
38.00
93.72
87.38
51.70
2.00
2.20
2.50
2.80
3.00
27.00
24.00
34.50
30.00
40.00
30.50
27.80
38.90
34.70
45.10
62.8
55.6
79.7
69.8
140.0
25.00
23.10
31.25
29.40
86.25
6.88
9.81
9.88
17.77
11.50
101.20
148.00
148.50
233.40
214.20
0.907
2.425
1.056
3.257
0.587
104.00
57.02
131.33
65.85
345.31
3.20
3.60
4.00
4.50
5.00
43.20
40.00
44.00
50.00
50.00
46.60
46.00
50.60
57.60
58.30
100.0
92.1
11 7.0
194.0
207.0
40.00
37.80
58.00
128.25
142.50
11.88
19.60
24.50
28.00
47.00
238.40
357. 10
436.30
532.30
707.90
1.451
3.735
3.019
1.613
2.541
156. 13
90.38
136.43
3 12.74
260. 12
5.50
6.30
7.00
8.00
60.00
70.00
80.00
80.00
69.30
80.00
92.00
94.00
236.0
272.0
306.0
330.0
156.75
179.55
199.50
228.00
38.00
45.00
70.00
120.00
774.50
968.50
1132.00
1627.00
2.094
2.258
2.286
4.065
351.72
429.00
464.83
370.91
Tension springs of stainless steel spring steel wire11
d. DIN EN 10270-3 (2001-08)
0.20
0.40
0.63
0.80
1.00
3.00
7.00
8.60
10.80
13.50
3.50
8.00
9.90
12.30
15.40
8.60
12.70
19.90
25.1
31.4
4.35
2.60
7.88
10.20
12.50
0.05
0. 121
0.631
0.971
1.411
0.99
3.251
9.861
15.67
23.77
0.031
0.142
0.237
0.305
0.390
1.25
1.40
1.60
2.00
4.00
17.20
15.00
21.60
27.00
44.00
19.50
17.50
24.50
30.50
50.60
39.8
34.9
50.2
62.8
117.0
15.63
15.05
20.00
25.00
58.00
2.211
4.351
3.211
5.501
19.600
35.50
55.72
56.93
84.86
366.50
0.458
1.371
0.623
0.779
2.593
30.54
22. 11
38.97
48. 19
57.40
/
72.73
37.48
86. 19
101.86
133.83
11 In addition t o t he springs listed, other springs w it h different outside diameters and lengths are commercially
available for each w ire diameter.
245
M achine elem ents: 5.8 Springs, components of jigs and tools
10 1
Cylindrical helical compression springs cf DIN 2098 12<1968
, • 970 08
w ire diameter
d
Fma,
t
/
F1
/
V>
~
Spring
characteristic
curve
block
.E F, /
height
en
mean coil diameter
Od
mandrel diameter
o.,
sleeve diameter
Lt
free length, unloaded spring
C
L1
Sm,1x
maximum allowable spring force at Smax
Fmax
Lmin
s1, s2 spring displacement at F 1, F2
Lt
maximum allowable spring displacement at Fmax
Smax
P•
On,
i,
number of spring coils
;,
t otal number of coils (ends groundl
R
spring rate in N/m m
⇒
0.,
0.,
Fmax
max.
min.
in N
2.5
2
1.6
2.0
1.5
1.1
3.1
2.6
2.1
6.3
4
2.5
12.5
8
5
20
12.5
8
5.3
3. 1
1.7
2
I
= is+ 2
F1, F2 spring force at L1, L2
L1
S1
I 4
minimum allowable t est length of the spring
Lm1n
s,
Tot al number of coils
L1, L2 length of loaded spring at F1 , F2
·;:
5;-
Dm
Compression spring DIN 2098 - 2 x 20 x 94:
d = 2 m m, Om = 20 mm and L, = 94 mm
Li
Smsx
R
Li
Smax
R
Li
i,-8.5
R
Sma,
1.00
1.24
1.50
5.4
4.0
3.0
3.8
2.4
1.5
0.26
0.51
1.0
8.2
5.9
4.4
6.0
3.8
2.4
0.17
0.33
0.65
12.4
8.7
6.4
9.3
5.9
3.6
0.11
0.21
0.42
17.S 13.7 0.07
12.E 8.6 0.15
9.2 5.4 0.28
6.6
9.3
10.4
22
33.2
43.8
13.5
7.0
4.4
9.2
3.3
0.9
0.73
2.84
11.6
0.46
1.81
7.43
30.0
15.0
8.7
14.6
5.7
1.9
1.49
5.68
23.2
23.1
8.9
3.0
0.95
3.61
14.8
55.5
28.5
17.0
21.3
7.9
2.2
36.1
14.2
4.4
0.30
1.17
4.80
24.0
13.0
8.5
20.0
10.0
6.1
36.5
19.0
12.0
14.0
4.9
1.4
10.8
6.5
3.6
17.5
10.3
5.9
7.5
5.0
3.4
14.4
9.6
6.5
44.C 31.8
21.5 11.7
12.C 3.0
80.5 53.1
40.5 20.6
24.C
6.6
22.6
14.7
10.1
84.9
135
212
48.0
24.0
14.5
35.6
14.0
5.5
2.38
9.76
37.3
73.5
36.0
21.5
55.9
21 .9
8.9
1.52 11 0
6.23 53.5
23.7
31.5
25
16
10
22.0
13.4
7.5
28.0
18.6
12.5
128
198
318
58.0
30.0
18.0
43.0
17.5
6.8
67.1
27.3
10.9
1.90 135 104
1.23 195
7.24 68.0 42.5 4.69 98
29.7
38.5 16.5 19.2
55
2.5
32
25
20
16
28.3
21.6
16.8
12.9
36.0
28.4
23.2
19.1
71.5
49.0
36.0
27.5
3.2
40
32
25
20
35.6
27.6
21.1
16.1
44.6
36.5
28.9
23.9
82.0
58.5
42.5
33.5
52.2
32.2
20.5
12.9
60.8
38.7
23.4
15.0
50
40
32
25
56.0
45.2
37.0
29.7
5
63
50
40
32
44.0
34.8
27.0
20.3
56.0
43.0
34.0
26.0
70.0
57.0
46.0
38.0
99.0
71.0
53.5
41.0
120
85.0
64.0
51.0
71.6
45.8
29.5
18.1
87.7
54.1
34.4
22.3
7.27 180
14.5 130
28.4
95.5
75.0
55.4
82.1
50.5
32.1
20.5
95.3
61 .1
37.2
23.6
111
69.9
46.2
28.3
135
86.8
54.5
34.8
2.22 170 129
1.43 245 187
0.97
2.04
4.64 115
80.2 3.0 165 11 6
9.05 81.5 50.0 5.86 120
75.7 3.98
17.7
61 .0 31.7 11.5
88.C 49.9 7.78
1.96 275 216
1.33
3.03 190 148
96.2 3.82 190 136
2.61
5.92 135
12.4
94.5 57.4 8.0 135
83.4 5.45
24.2
74.0 36.9 15.7 105
53.4 10.7
4
182
233
292
365
288
361
461
577
427
533
666
852
623
785
981
1226
2.98 88.5
11.4
45.0
46.6
26.5
3.48 11 0
7.29 74.5
14.2
54.0
27.8
41 .0
4.76 125
9.3
88.5
19.4
63.5
38.2
49.5
3.79 230 175
2.45 335
110
4.79 235
7.41 160
14.4 120
72.8 9.35 170
30.3
89.5 43.5 19.6 130
4.63 275 210
2.99 395
9.25 195 133
5.98 280
18.1 140
81.6 11.7 205
35.3 110
52.5 22.9 160
257
1.65
165
3.26
104
6.36
65.5 13.3
304
2.03
194
4.07
124
7.95
79.5 15.5
6.3
80
63
50
40
71.0
55.0
42.0
32.6
89.0 932
71.5 11 77
58.0 1481
47.5 1854
145
103
105
65.0
80.0 42.0
60.0 24.0
8.96 220
18.3 155
36.7 115
71.7
90.0
160
99.0
62.0
39.7
5.70 335
11.7 235
23.3 175
45.6 135
250
3.69 490
155
7.55 340
100
15.1 250
63.2 29.5 195
370
2.51
277
5.1 3
145 10.3
95.0 20. 1
8
100
80
63
50
89.0
69.0
53.0
40.5
111
91.0
73.0
60.0
170
11 8
125
76.0
95.0 48.0
75.0 30.0
11.9
23.2
47.0
95.4
187
111
74.0
46.8
7.58 390
14.8 285
30.3 205
60.8 160
286
4.9 570
186
9.58 410
112 19.6 300
70.0 39.2 230
423
271
169
103
d
0.2
0.5
1
1.6
1413
1766
2237
2825
i 6 • 3.5
;, • 5.5
5.95 150
11.7 105
79.5
22.8
47.7
60.5
260
180
140
11 0
0.61
2.33
9.57
;, • 12.5
Li
Sn,.,,
R
0.21
0.79
3.27
0.41
1.59
6.51
84.5 0.99 165 129
0.67
33.4 4.0
78.C 50.0 2.73
13.6 15.4
45.C 20.2 10.4
151
0.83
62.1 3.19
24.4 13.0
3.34
6.51
13.3
26.7
246
Machine elements: 5.8 Springs, components of jigs and tools
Disc springs
I
Single spring
D.
¾~I
=1=
ho "' lo- t
I•
t
'-l. 2
~
(a)
.ej,,
0
~1
C:
·;:
a.
Vl
~
-•
{di
(b)
-/
.. /
,r
----
outside diameter
inside diameter
1
thickness of the single
d isc spring
ho
spring height (theoretic
spring displacement to flat
position)
lo
overall height of the
unloaded single spring
s
spring deflection of a single
spring
Stotal
spring deflection of stack of
disc springs
F
load generated by a single
disc spring
(c)
-
31
E :1J
E~
"'::,
Nu,
,....: t,
v~
-.. C:
0
-
u
ci 5
::, 0
0 .c
o·J
E.,
Eli:
CD 't:
I ::,
"'.,ti
N
,....: ~
.. o
u
..,,_
'
0,
H12
8
10
14
16
4.2
5.2
7.2
8.2
20
25
28
40
10.2
12.2
14.2
20.4
-
25
28
40
45
12.2
14.2
20.4
22.4
50
56
63
71
I
Fiotal =
length of unloaded spring
st ack
n
number of disc springs in
parallel stack
number of disc springs in
series stack
i
I
Fl Stotal = i • si
Spring length
I Lo= I
i • lo
Parallel stack
a : a
Spring
deflection
Spring force
I
I
Fi01a1= n-
I
Fl Stotal = s I
Spring length
Lo=io+(n- 1)- t
I
Series C: soft springs
0.11 .. 40: hc,/1,. 1.3
Fin
s21
t
lo
kN 11
Series B: medium hard springs
0.,1 .. 28; ho/1 .. 0.75
Fin
s21
t
lo
kN 11
1
lo
Fin
kN 11
s21
0.4
0.5
0.8
0.9
0.6
0.75
1.1
1.25
0.21
0.33
0.81
1.00
0.15
0.19
0.23
0.26
0.3
0.4
0.5
0.6
0.55
0.7
0.9
1.05
0.12
0.21
0.28
0.41
0.19
0.23
0.30
0.34
0.2
0.25
0.35
0.4
0.45
0.55
0.8
0.9
0.04
0.06
0.12
0.16
0.19
0.23
0.34
0.38
0.8
0.9
1.0
1.35
1.6
1.8
0.75
0.87
1.11
0.41
0.53
0.60
0.5
0.7
0.8
1
1.15
1.6
1.8
2.3
0.25
0.60
0.80
1.02
0.49
0.68
0.75
0.98
-
-
-
-
-
1.25
2.85
1.89
1.20
1.1
1.55
1.53
0.34
-
-
-
-
-
-
-
-
-
-
1.5
1.5
2.2
2.5
2.05
2.15
3.15
4.1
2.91
2.85
6.54
7.72
0.41
0.49
0.68
0.75
-
-
-
-
1.5
1.7
2.6
3.0
2.62
3.66
0.86
0.98
25.4
28.5
31
36
3
3
3.5
4
4.3
4.9
5.6
6.7
12.0
11.4
15.0
20.5
0.83
0.98
1.05
1.20
2
2
2.5
2.5
3.4
3.6
4.2
4.5
4.76
4.44
7.18
6.73
1.05
1.20
1.31
1.50
1.25
1.5
1.8
2
2.85
3.45
4. 15
4.6
1.55
2.62
4.24
5.14
1.20
1.46
1.76
1.95
80
90
100
125
41
46
51
64
5
5
6
7
8.2
8.5
33.7
31.4
48.0
1.28
1.50
1.65
-
-
-
-
3
3.5
3.5
5
5.3
6
6.3
8.5
10.5
14.2
13.1
30.0
1.73
1.88
2.10
2.63
2.25
2.5
2.7
3.5
5.2
5.7
6.2
8
6.61
7.68
8.61
15.4
2.21
2.40
2.63
3.38
140
160
180
72
82
92
-
-
-
-
5
6
6
9
10.5
11.1
27.9
41.1
37.5
3.00
3.38
3.83
3.8
4.3
4.8
8.7
9.9
11
17.2
21.8
26.4
3.68
4.20
4.65
C:
Cl. ::,
::, 0
0
4,
o.tt .. 18; t1o11 .. o.4
o.
Spring
Spring force deflection
of disc springs
Serles A: hard springs
h12
~
ftotal total load generated by stack
1
2
3
4
Spring deflection s - Spring force graph for various disc spring
combinations: (a) single spring;
(bl parallel stack of 3 single sprin gs: 3 times fo rce;
le) series stack of 4 single springs: 4-fold deflection;
Id) series stack of 3 parallel stacks w ith 2 single
springs each: 3-fold deflection, 2-fold force
Group
Series stack
o.
0,
f+J
D;
without contact surface:
Groups 1 & 2
3
I
cf DIN 2093 12006 03>
-s
t'; ~
=
-
Disc spring DIN 2093 - A 16: Series A, outside diam eter 0 0 = 16 mm
11 Spring force F of a single disc with spring deflection s .. 0.75 • ho
21 s .. 0,75 • ho
31 Size 3: !> 6-14 mm, with contact surface, 0 = 125, 140, 160,180,200,225.250 mm
8
/
Press-fit drill bushings
FormB
Form A
cf. DIN 179 (1992-11); Standard sheet w ithdrawn
d1 F7 over
to
m
1,
1 1.8 2.6 3.3 4
1.8 2.6 3.3 4 5
5
6
short
6
8
10
12
16
20
25
medium
9
12
16
20
28
36
45
16
20
25
36
45
56
long
cl, n6
4
5
7
6
10 12 15 18 22 26 30 35 42
8
r
Hardness 780 + 80 HV 10
1.5
=
Form B
d,
d2
· rn
✓=._/Rz4
2
Drill bushing DIN 179 -A 18 x 16: Form A, d 1 = 18 m m,
cf. DIN 172 (1992-11); Standard sheet withdrawn
d1 F7 ~;er
1,
1 1.8 2.6 3.3 4
1.8 2.6 3.3 4 5
5
6
8 10 12 15 18 22 26
10 12 15 18 22 26 30
6
8
short
6
8
10
12
16
20
25
medium
9
12
16
20
28
36
45
20
25
36
45
56
long
16
d2n6
4
d-;
7
5
6
8
9
7
10 12 15 18 22 26 30 35 42
8
10 11 13 15 18 22 26 30 34 39 46
2
12
2.5
3
4
~(~JRzT3)
=
3
Drill bushing DIN 172 - A 22 x 36: Form A, d1 = 22 mm,
/ 1 =36mm
Slip type jig bushings
cf. DIN 173-1 (1992-11); Standard sheet w ithdrawn
Form K Quick-change bushings for
right hand cutting tools
d 1 F7 ~;er
4
6
Form L Removable bushings
(dimensions same as form K)
cl,m6
10
short
1,
6
8
8
10
10 12
12 15
15 18 22 26 30 35 42 48
18 22 26 30 35 42 48 55
12
15
18 22
26 30 35 42 48
12
17
20
25
55 62
35
67
medium
20
28
36
45
56
25
36
45
56
67
31
78
36 43
50 57
d-;
6.5 8.5 10.5 12.5 15.5 19
d4
18
22
26 30 34 39 46 52 59 66 74 82 90
els
15
18
22
~ H7
2.5
3
12
8
10
a
65°
so·
23 27
70
30
long
26 30 35 42 46 53 60 68 76 84
5
6
so·
16
30•
35°
25°
1.5
14
4.25
6
7
15
3
4
5.5
Is
8
12
13
2
9
8
7
medium
8
12
16
20
26
32
long
13
20
25
31
37
43
4
5
2
r,
Hardness 780 + 80 HV 10
5
2
1.5
Hardness 780 + 80 HV 10
~ (._/Rz4 JRzT3)
3
/ 1 = 16mm
Headed press-fit drill bushings
Form A
8 10 12 15 18 22 26
10 12 15 18 22 26 30
6
8
7
8
9
10
12
3
'2
7
e,
13 16.5 18
=
6
8.5
10.5
20 23.5 26 29.5 32.5 36
14
3.5
12.5
1.5 45.5 49 53
Drill bushing DIN 173 - K 15 x 22 x 36: Form K,
d 1 = 15 mm, d2 = 22 mm, / 1 = 36 mm
248
Machine elements: 5.8 Springs, components of jigs and tools
Grub screws, Thrust pads, Ball knobs
Grub screws with thrust point
cf. DIN 6332 (2003-041
Form S (M6 to M20)
Application examples as d emping screws
with star knob 1l with knurled
DIN 6335
nut
M6 t o M20
DIN 6303
M6 to M10
with w ing nut
DIN 315
M6toM10
d,
M6
M8
M10
M12
M16
cJ.,
4.8
6
8
8
12
d:,
4
5.4
7.2
7.2
11
r
3
5
6
6
9
/2
6
7.5
9
10
12
/3
2.5
3
4.5
4.5
5
c4
32
40
50
63
80
O;
24
30
36
65
73
e
11
51
39
33
60
60
80
60
80 100 80 100 125
27
47
44
64
40
60
30
50
48
68
-
30
50
/4
20
40
/5
22
42
=
Grub screw DIN 6332 - S M 12 x 60: Form S w ith
threads d 1 = M 12, /1 = 60 mm
1,
40
or scallop knob DIN 6336 M6 to M16
Thrust pads
cf. DIN 6311 (2002-061
dz
4
12
4.6
10
7
4
16
6.1
12
9
5
20
8.1
15
11
6
8
M10
25
8.1
18
13
7
8
M12
32
12.1
22
15
7.5
12
M16
15.6
28
16
8
16
M20
Form S with snap ring
di
H12
Snap rlng
DIN7993
snap ring
thrust points
40
=
EHT (450 HV 1) 0.3 + 0.2mm,
surface hardness 550 + 100 HV 10
FormM
with conical hole
Grub-DIN 8332
M6
MB
Thrust pad DIN 6311 - S 40: Form S, d 1 = 40 m m,
with inserted snap ring
Ball knobs
FormC
with threads
-
80
cf. DIN 319 (2002-041
Form L
with clamping sleeve
FormE
with threaded bushing
-c:
16
20
25
32
40
50
cJ.,
M4
M5
M6
MB
M10
M12
t,
7
9
11
14.5
18
21
6
7.5
9
12
15
18
4
5
6
11
13
16 15 15 15 20 20 20 23 23 20 23 28
10 8 10 12 10 12 16 12 16 20
lit;
4
5
6
-
8 10 -
10 12 -
12 16 -
ts
9
12
15 15 -
15 15 -
20 20 -
22 22 -
h
15
18
22.5
29
37
46
=
Color:
8
Ball knob DIN 319 - E 25 PF: Form E, d 1 = 25 mm,
of phenolic molding compound PF (thermoset plastic].....
Material:
Other f orms no longer standardized.
8
Ball knob of phenolic molding compound PF (thermo set plasticl; threaded bushing of st eel (Stl by
choice of manufacturer; other materials by agreement.
black
249
M achine elements: 5.8 Springs, components of jigs and tools
l.fiTilwa ■ ,1w.111111r.111 , .... ~ .. 1111
!I'
Star knobs
cf. DIN 6335 (1996-01}
Form A
FormB
di
da
dJ
ct.
4
h,
"2
l'3
t,
32
12
18
6
M6
21
20
10
40
14
21
8
MB
26
25
14
12
15
50
18
25
10
M10
34
32
20
18
63
20
32
12
M1 2
42
40
25
22
80
10011
25
40
16
M 16
52
50
30
28
32
48
Form Description
20
M20
65
60
38
36
A to E M etal kno bs
FormK
FormC
A
rough part of metal
B
w ith through bore d4
C
w ith blind bore d4
D
w ith t hrough t hreaded bore els
E
w ith blind t hreaded bore els
K21
of molding mat. (plastic} w ith threaded bushing els (of metal}
L21
of molding material (plastic} with t hreaded pin els (of metall
⇒
Star knob DIN 6335 - A 50 AL: Form A. d 1 = 50 mm,
of aluminum
11 This size is not available in molding material.
2 1 Sometimes with insignificant ot her dimensions; material l ike
flut ed knobs DIN 6336
Autedknobs
cf. DIN 6336 ( 1996-01}
~ ,a
@'3
Form A
Form E
h,
"2
l'3
t,
di
da
ct.
32
12
M6
21
20
10
12
20
30
40
14
MB
26
25
13
15
20
30
50
18
M10
34
32
17
18
25
30
63
20
M 12
42
40
21
22
30
40
80
25
M16
52
50
25
28
30
40
⇒
Fluted knob DIN 6336 - L 40 x 30: Form L (mold ing
material) d 1 = 40 mm,/= 30 mm
Forms A to E (met al knobs) as well as K and L (knobs of molding
material! correspond to star knobs DIN 6335.
Materials: Cast iron, aluminum, molding compounds (PF 3 1 N
RAL 9005 DIN 7708-2)
Locating and seating pins
Form A
Seating
pin
d. DIN 6321 (2002-10}
FormB
Locating
pin
cylindrical
FormC
Locating
pi n
-
-
d,
15°
-!::'
di
l1
b
l1
g6 Form A Form Bend C
h9
short long
truncate d
d,
-!::'
6
5
8
-
10
6
12
-
16
8
20
-
25
10
⇒
hardened 53 + 6 HRC
I
7
11
da
,.
l2
n6
12
1
16
1.6
4
6
1.2
4
18
2.5
6
9
1.6
6
13
22
3.5
8
12
2
8
15
25
5
12
18
2.5
9
10
0.02
0.04
Clevis pins DIN 6321 - C 20 x 25: Form C, d1 = 20 mm, / 1 = 25 mm
11 Appropriate bore tolerance: H7
T-slots and nuts for T-slots
cf. DIN 650 (1989-10) and 508 (2002-06)
Width a
10
8
Deviation from a - 0.3/- 0.5
b
14.5 16
12
14
22
28
19
- 0.3/- 0.6
23 30 37
46
56
68
Deviation from b 1.5/0
7
C
+2/0
9
8
12
+3/0
16 20
+4/0
25
32
25
20
+2/0
36 45
30 38
Deviation from c
18
15
h max.
mm.
Thread d
11 Tolerance class HB for pilot T-slots and
clamping slots; H1 2 for clamping slots
e
h,
k
Deviation from k
=>
7
+ 1/0
21
17
M6
13
10
6
28
23
18
42
36
- 0.4/- 0.7
+3/0
71
85
61
74
56
48
MB M10 M12 M16 M20 M24 M30 M36
15
18 22
28
35 44
54 65
12
14
16 20
28
36 44 52
7
10
14 18 22
26
6
8
0/- 0.5
01-1
Nut DIN 508 - M10 x 12: d = M10, a = 12 mm
Bolts for T-slots
cf. DIN 787 (2005-021
d
MB
M10
M12
M16 M20 M24 M30
22
28
36
a
8
10
12
14
18
from
22
30
35
45
70
80
55
b
to
120
150
50
60
190
240
300
13
15
18
e
22
28
35
44
54
12
14
16
24
h
41
20
32
50
k
6
6
7
10
14
18
22
8
Nominal 25, 32, 40, 50, 63, 80, 100, 125, 160,200,250,315,400,
lengths/ 500mm
e2 e 1
so
uptoM12x12: ~
asd1
M12x 14 and
up: a>d,
h
1
!">
=;,
Bolt DIN 787 - M10 x 10 x 100-8.8: d 1 = M10,
a = 10 mm,/= 100 mm. properly class 8.8
Loose slot tenons
vgl. DIN 6323 (2003-08)
b, h6
~ h6
Form
h,
A
12
6
12
•tt
20
dimensions
and indications
8
10
12
B
12
14
A
36
42
liketormA
14
18
22
28
28.6
5
9
12
C
16
19
20
32
5.5
18
61.5
76.5
90.5
24
7
30
36
40
50
cf. DIN 6319 (2001- 101
d:z
Conical seat
120°
ffi4
Form D
9
50.5
Spherical washers and conical seats
FormC
5.5
Slot tenon DIN 6323 - C 20 x 28:
Form C, b 1 = 20 mm, ~ = 28 mm
hardened, hardness 650 + 100 HV10
Spherical washer
20
3.6
FormG
H13
liJ
cJ.
Form
els
h:3
Form
D
G
R
Sphere
H13
7.1
D
G
6.4
12
12
17
11
8.4
9.6
17
17
24
14.5
2.3
3.2
2.8
3.5
4
5
9
12
10.5
12
21
21
30
18.5
4
14.2
24
24
36
20
4.6
4.2
5
5
6
15
13
17
19
23.2
30
36
30
36
44
26
31
5.3
6.3
6.2
7.5
7
50
22
27
21
8
Spherical washer DIN 6319 - C 17: Form C, d 1 = 17 mm
251
Machine elements: 5.8 Springs, components of jigs and tools
Punch holder shanks, Punches, Machined plates
Punch holder shanks form A 11
Form A
cf. DIN ISO 10242-1 and -2 (2000-031
~
1,
12
/3
/4
/5
WAF
15
M16 x 1.5
40
2
12
58
4
17
25
20
M16 x 1.5
M20 x 1.5
45
2.5
16
68
6
21
32
25
M20 x 1.5
M24 x 1.5
56
3
16
79
6
27
40
32
M24 x 1.5
M27 x 2
M30x 2
70
4
26
93
12
36
42
M30 x 2
80
5
26
108
12
41
d, f9
cJ.,
20
d,
Joo
~
A -::-
~o
--=-i
:,
w~ ~ ~
~
?fo
~ !(I
...:f
- , -!:''i
~ I
V\~·
~
50
J
Punch holder shanks ISO 10242-1 A-40x M30 x2: Form A,
d 1 = 40 mm. ~ = M30 x 2
=>
thr ead undercut DIN 76-A
11 Form C with mounting flange instead of screw threads
Round punch Form D 11
~
60°
'
.I
-~
d,
-
~
d1h6
from -to
0.5- 0.95
0.05
1.0- 2.9
0.1
3.0- 6.4
o. 1
6.5- 20
0.5
=>
-
d;, - (1.1 - 1.8) • d, (depending on 0 d,)
80
100
HSS41
....
I
~
80
160
-
250
Ra 3,2
315
400
500
{~
-
630
~ (~)
-
25, 32, 40
-
-
-
-
-
-
-
-
-
25, 32, 40
-
32, 40, 50
-
32, 40, 50
500
630
-
-
-
32, 40. 50
-
32, 40, 50, 63
Machined plate ISO 6753-1 1 -315 x 200 x 32: Fabricated by flame
cutting (1), /= 315 mm, W= 200 mm, t = 32 mm
Code
Note: These surface roughness
values only apply lo milled
edges.
Plat e thickness t for plate dimension w
250
315
400
I 100 I 125 I 160 I 200
20, 25, 32
200
.,,-/if,·'·•
50 ± 5 HRC
cf. DIN ISO 6753-1 (2006-091
I
~
64 ± 2 HRC
11 Form DA with allowable enlargement below the head
21 WS alloyed cold-work steel
31 HWS high-alloyed cold-work steels
41 HSS high-speed steels
Machined plates for press tools
and for fixtures
-1 ff 10 01/100 I A I
45 ± 5 HRC
Punch DIN 9861 D - 5.6 x 71 HWS: Form D, d1 = 5.6 mm,
I = 71 mm, of high-alloyed cold-work steel
I
d 1h6
62 ± 2 HRC
HWS31
71
4-
I
ws21
-
80
Hardness
Shank
Head
Material
I 0/+0.5
71
I
I
'
cf. DIN 9861-1 (1992-071
Graduation
Fabrication method
Limit deviations for
leng1h / and width w
(ws630mm)
Limit deviations
for thickness t
1
Flame cutting
Beam cutting
+4
+1
±2
2
Milling
+0.4
+0.2
+ 0.5
+0.3
252
Machine elements: 5.8 Springs, components of jigs and tools
Pillar die sets
Pillar die sets with rectangular working
surface forms C and CG11 cf. DIN 9812 (1981-121
Pillar die sets with circular working surface
cf. DIN 9812 (1981-121
forms D and DG21
.;-
I
i==a'I
I
~ --~l---~• ~
a, ·X b,
80 X 63
100 X 63
100 X 80
160 X 80
125x 100
250 X 100
160 X 125
315 X 125
200 X 160
315 X 160
250 X 200
315 X 250
"1
D.?
OJ
di
"3
50
30
80
19
M20 x 1.5
50
30
80
25
M20X 1.5
125
145
155
215
160
160
50
40
90
25
32
M24 x 1.5
180 170
315 180
56
40
90
32
M24 x 1.5
225 180
380
265 200
395 220
330
220
395
56
63
63
50
50
32
40
100
100
40
M30x 2
M30X 2
Center pillar die set DIN 9812 - C 100 K 80:
Form C, a1 x b, = 100 mm x 80 mm
⇒
11 Form C w ithout threads; form CG with threads
•
di
"1
D.?
OJ
di
"3
50
63
40
25
65
16
M16 x 1.5
80
95
125
125
140
50
30
80
M20 x 1.5
155
160
19
80
100
125
25
25
180
160
180
40
56
90
32
225
180
M24 x 1.5
245
180
265
190
M30 X 2
330
395
200
220
200
250
315
⇒
56
63
50
100
40
Pillar die set DIN 9812 - D 160: Form D.
d= 160mm
21 Form D w ithout threads; form DG w ith threads d:i
d:i
Pillar die sets with centrally positioned
pillars and thick pillar guide plate, form DF
Pillar die sets with diagonal
pillars, forms C and CG31
cf. DIN 9816 (1981-121
cf. DIN 9819 (1981-121
e
C
.;-
di
80
100
125
"1
50
50
160
200
⇒
D.?
80
85
90
di
19
25
100
56
110
• ,,
'2
125
16
18
155
180
225
32
265
23
'3
., X b,
":z
10
36
80 X 63
11
40
125 X 100
250 X 100
135 180
215
190
235
325 255
50
160 X 125
315 X 125
235
56
390
11
45
Pillar die set DIN 9816 - DF 100 GG: Form OF,
d 1 = 100 mm, cast iron slide guide
170
180
190
220
240
125 X 80
⇒
bz
280
"1
D.?
OJ
di
.,
19
75 103
30
80
40
90
25
25
40
90
32
":z
160
128
148 170
245 158
155
180
183
310
120
Pillar die set DIN 9819 - C 160 K 80 GG:
Form C, a1 = 160 mm, b1 = 80 m m, cast iron
31 Form C w ithout threads; form CG w ith threads
d:i
253
Machine elements: 5.9 Drive elements
V-belts, Positive drive belts
Design types
Range of dimensions
Designation
h 11 inmm
Standard for the belts
Speed
range
p~
range
L21 in mm
Standard for pulleys
3
Vmax in rn/S P'max in kW
For higher maximum tensile
Classic V-belts
~
DIN 2215, ISO 4184
Properties,
application
4- 25
strengths, reliable tractive power;
185- 19000
30
/
65
DIN 2217, ISO4183
machine construction
Narrow V-belts
~
construction equipment, variable drives for the mining
industry, agricultural machinery, conveyors, general
8-18
Good power transmission,
twice the power with the same
width as classic V-belts;
630-12500
40
70
gearbox manufacturing,
machine tools, HVAC
DIN 2211, ISO 4183
DIN 7753, ISO 4184
Cogged V-belts
4- 25
"
,
800- 3150
50
70
Low elongation, small pulley
diameter, high temperature
resistance from - 30' C to +80' C;
automotive alternator drives,
transmission design, pumps,
DIN 2211, DIN 2217
HVAC
DIN 2215, DIN 7753
Joined V-belts
(Power Band)
V-ribbed belts
(ribbed belts)
Insensitive to vibration or
10-26
1250- 15000
30
65
DIN 2211, DIN 2217
impact, no twisting of single
belts in the pulleys, absolutely
uniform force distribution, high
tensile strength, for long distances between axles;
paper machines
Large transmission ratios
3-17
possible, low vibration running
behavior;
600- 15000
60
20
DIN 7867
automotive alternator drives,
compressor drives in
HVAC, small machines
DIN 7867
85
Excellent transverse strength,
very high tensile strength,
flexible;
speed control gears,
machine tools, textile
machines, printing machines,
agricultural machinery
20
Good power transmission for
drives with several pulleys
and alternating direction of rotalion, 10% less efficiency than
classic V-belts; agricultural
machinery, textile machines,
general machine building
Wide V-belts
6-18
468- 2500
30
DIN7719
DIN 7719
Double V-belts
(Hexagonal belts)
•
10- 25
2000-6900
30
DIN 2217
DIN 7722, ISO 5289
Positive drive belts
0.7-5.0
100-3620
40-80
DIN ISO 5294
machine drives, automotive
industry, CNC spindle drives
DIN 7721, DIN ISO 5296
11 Belt height (pages 254, 255)
0.5-900
Efficiency 1/max ., 0.98,
synchronous running, low prestress forces, therefore lower
bearing load;
precision machine drives, office
21 Belt length
31 Transmittable power per belt
254
Machine elements: 5.9 Drive elements
Narrow V-belts
Narrow V-belt
pulley
DIN 2211-1 (1984-03)
DIN 7753-1 (1988-01)
Narrow V-betts,
V-beltpulleys
Designations
Wu
w0
h
hw
Belt profile (ISO designation codes)
SPZ
SPA
SPB
SPC
upper belt width
effective w idth
9.7
8.5
12.7
11
16.3
14
22
19
belt heig ht
distance
8
2
10
2.8
13
3.5
18
4.8
63
9.7
90
12.7
140
16.3
224
22
distance from effective 0 to outer 0
minimum allowable groove depth
2
11
2.8
13.8
3.5
17.5
4.8
23.8
g roove spacing for multi-groove
pulleys
groove spacing from outer edge
12
15
19
25.5
8
10
12.5
17
34° for effective 0 up t o
80
118
190
315
dmin minimum allowable effective 0
w 1 upper groove width
C
t
Ie
Effective diameter
= Narrow V-belt DIN 7753 - XPZ 710:
Narrow V-belt, cogged profile,
reference length 710 mm
a
38° for effective 0 over
Angle factor c 1
,so•
Wrap angle /J
80
118
190
315
1.02
1.05
1.08
1.12
1.16
1.22
1.28
1.37
1.47
170°
,so• ,so•
140°
130°
120°
110°
100°
90°
Service factor c,
Daily operating time in hours
up to 10
from 10 t o 16
over 16
Driven machines (examples)
1.0
1.1
1.1
1.2
1.2
1.3
Centrifugal pumps, fans, conveyor belts for light material
Machine tools, presses, sheet metal shearers, printing machines
1.2
1.3
1.3
1.4
1.4
1.5
Grinding gears, piston pumps, textile and paper machines
Stone crushers, mixers, winches, cranes, excavat ors
Efficiency values for narrow V-belts
Belt profile
smaller
pulley dmin
SPZ
63
100
d . DIN 7753-2 ( 1976-04)
SPA
SPB
180
250
140
smaller
pulley I\
SPC
400
224
400
630
Power rating P,.,.., in kW per belt
3.62
5.88
7.60
1.92
3.02
3.83
4.86
7.84
10.04
8.64
13.82
17.39
5.19
8.13
10.19
12.56
19.79
24.52
21.42
32.37
37.37
10.53
12.85
14.13
5.19
6.31
7.15
13.66
16.19
16.44
22.02
22.07
9.37
13.22
14.58
11.89
29.46
25.81
3 1.74
400
700
950 ,__--,--,;....,.,_.-,_ ._.__......._._,...,.._.....
1450
2000
2800
250
0.93
1.17
1.45
2.36
3.05
3.90
5.19
6.63
8.20
2.02
2.49
3.00
6.01
7.60
9.24
Profile selection for narrow V-belts
p
Prated
N
c1
power to be transmitted
power rating per belt
number of belts
angle factor
Number of belts
service f actor
N = P • c, -c2
P,ated
r::."
~
630 H -A--t--t-+-lf-d'+ -tl+-ifA-++i...iH~
~ 500hlt-t- -+-+--W-+-,i-n-+....-+-+-,IIF-li-+..,_
-;;; 400
C:
315
250 1-11""''' -,llt-t200 .....__._...._.__._...__..._._.__._.....__._."--J'-"'-L...-'-'_,l,,_J
2.5 4 6.3 10 16 25 40 63 100 160 250
1
i
calculated power P- c2 in kW -
Example:
Transmission parameters P - 12 kW with c 1 = 1.12;
c, = 1.4; dm;n = 160 mm, n, = 950 1/min; /J, % 7, N = 7
1. p . c,~ 12kW• 1.4= 16.SkW
2. From the diagram n, = 950 1/min and
P • c2 = 16.8 kW- profile SPA
3. P.ated = 4.27 kW from the table
_ N = P-c1 - c2 = 12kW- 1.12 - 1.4 _ _
44
4
P.ated
4.27 kW
•
5. Selected: N = 5 belts
255
M achine elements: 5.9 Drive elements
Positive drive belts
Positive drive belts (timing belts)
cf. DIN 7721-1 (1989-06)
Tooth spacing
200
20°
.c: -<:
~
p
s
h,
2.5
1.5
0.7
0.2
1.3
-
4
6
10
T5
5
2.7
1.2
0.4
2.2
6
10
16
25
10
5.3
2.5
0.6
4.5
16
25
32
50
No. of t eeth for
T2.5
T5
120
150
160
200
245
<'oo 'l.r;,o
~
-c"
A
<'oo I /
•• • w
HT profile
30
64
80
98
40
49
-
54
168
192
200
112
122
126
-
660
144
156
168
-
900
84
91
96
100
-
No. of teeth for
T5
Tl0
700
720
780
840
880
61
66
78
w
hs
530
560
610
630
-
132
=
Non-standardized tooth fonns
-
114
420
455
480
500
Effective
length11
-
48
270
285
305
330
390
.c:
-<:"
'\;If
p
T2.5
T l0
Double-sided
.c:
Code
,
Effective
lengt h 1I
s
Positive drive belt width
Nominal
thickness
Tooth size
Single-sided
180
184
920
960
990
53
56
61
63
66
1010
1080
11 50
1210
1250
101
108
115
121
125
70
72
78
84
88
1320
1390
1460
1560
1610
132
139
146
156
161
-
1780
1880
1960
2250
178
188
196
225
92
96
-
-
198
Belt DIN 7721 -6 T2.5 x 480: w = 6 mm, spacing p = 2.5 mm,
effective length= 480 mm, single-sided
The code letter D is added f or double-sided positive drive belts.
11 Effective lengths from 100-3620 mm, in custom-made products up to
25000mm
LAHN profile
liming belt pulleys
cf. DIN 7721-2 (1989-06)
Pulley o uter 0
Pulley out er 0
Pulley outer 0
Pulley
Pulley
Pulley
~ for
~ f or
~for
groove
groove
groove
T2.5 T5
Tl0
T2.5 T5
Tl0
T2.5 T5
Tl0
Pulley groove dimensions
1s0
\ t __"''
250
-;;
~
"
-,!f-,,
Effective diameter
I
d=do+2-a
I
Form N for> 20 grooves
Pully dimensions
!!!
!!!
7.4
8.2
9.0
9.8
15.0
16.6
18.2
19.8
36.3
39.5
17
18
19
20
13.0
13.8
14.6
15.4
26.2
27.8
29.4
31.0
52.2
55.4
58.6
61.8
32
36
40
48
24.9
28.1
31.3
37.7
14
15
16
10.6
11.4
12.2
21 .4
23.0
24.6
42.7
45.9
49.1
22
25
28
17.0
19.3
21.7
34.1
38.9
43.7
68.2
77.7
87.2
60
72
84
47.2 94.6 189.1
56.8 113.7 227.3
66.3 132.9 265.5
-
50.1
56.4
62.8
75.5
100.0
112.7
125.4
150.9
Pulley groove dimensions
Code
T2.5
T5
Tl0
Groove width Wr
Fo rm SE11
Form N2I
1.75
2.96
6.02
I
1.83
3.32
6.57
Groove height hg
Form SE11
Form N 2I
0.75
1.25
2.6
2a
0.6
1
2
1
1.95
3.4
Pulley w idth
w ith flange w,
w ithout flange w't
Letter symbols
Beltwidth w
T2.5
4
6
10
5.5
7.5
11.5
8
10
14
T5
6
10
16
25
7.5
11.5
17.5
26.5
10
14
20
29
Tl0
16
25
32
50
18
27
34
52
21
30
37
55
with pulley f lange
without pulley flange
-
10
11
12
13
11 Form SE for "' 20 grooves
21
Effective No. of teeth for
lengt h 11
Tl0
256
Machine elements: 5.9 Drive elements
Straight-toothed spur gears
Unmodified spur gears with straight teeth
External teeth
Number of teeth
Outside diameter
I
d 0 = d + 2 • m = m • (N + 2)
Root diameter
dr = d-2-(m+c)
Center distance
a = d1 + d 2 = m • (N1+ N 2 )
2
2
External and internal teeth
Pitch
p =rr - m
d=m-N
m module
N, N 1, N2
no. of teeth
Pitch diameter
pitch
d, d 1, d,
C
clearance
pitch
diameter
out side
diameter
root
diameter
Clearance
whole depth
ha addendum
hd dedendum
a
d0 , d0 1, d 0 2
d,, d,,, dr2
center distance
Example:
d
m =-=rr. N
p
h
P
Module
c = 0.1 • m to 0.3 . m
often c = 0.167 • m
Addendum
Dedendum
External spur gear,
m = 2 mm; N = 32; C= 0.167 • m; d = ?; d0 = ?; h = ?
d = m- N =2 mm-32 = 64mm
do = d + 2 • m = 64 mm + 2 • 2 mm = 68 mm
h = 2 - m+ c = 2 • 2 mm +0.167 • 2 mm= 4.33mm
Whole depth
h =2 -m+c
Internal teeth
Number of teeth
r-7
Outside diameter
d 0 = d + 2 · m = m · (N + 2)
N,
Root diameter
dr = d - 2-(m+c)
Center distance
a = d 2 - d1 = m • (N2 - N1)
2
2
Example:
Int ernal spur gear, m = 1.5 mm; N = 80;
c = 0.167 • m ; d = ?; d0 = ?; h =?
d = m • N = 1.5 mm • 80 = 120 mm
do= d - 2 • m ~ 120 mm - 2 • 1.5 mm = 111 mm
h = 2 - m+c = 2 -1.5mm+ 0.167-1.5mm= 3.25mm
I
257
Machine elements: 5.9 Drive elements
Helical gears. Module series for spur gears
Unmodified helical gears
f71t
transverse module
m,
real pitch module
Pt
transverse pitch
p,
real pitch
fJ
helix angle (normally fJ = 8° to 25°)
N, N1, N2 no. of teeth
d, d 1, d2 pitch diameter
d0
a
outside diameter
center distance
m,
Transverse pitch
Pr
n. mr
Pt = - - = - -
Pitch diameter
d = mt•N =-
cos/3
cos/3
N· m
- -r
cos/3
d
In helical gears t he teeth run in a screw-like pattern on
the cylindrical wheel body. The tools fo r manufacturing spur gears and helical gears conform to the real
pitch module.
Real pitch module
In the case of parallel shafts the two gears have the
same helix angle, but opposit e direction of rotation,
i.e., one gear has a right-hand helix and the other a
left-hand helix ({J1 = -{J 2).
Real pitch
n- d
N =-=mt
Pt
Number of teeth
Example:
Pt
m = --= t
cos/3 n
Transverse module
Pr = n • mr = Pt· cos/3
Outside diameter
Helical gear, N = 32; m, = 1.5 mm;
/J= 19.5°;c=0.167 • m;f71t= 7;d0 = 7; d= 7; h= 7
m = ~ = 1.5mm = 1. 591mm
'
cos{J
cos 19.5°
Center distance
do = d + 2 • m, = 50.9 mm + 2 • 1.5 mm z 53.9 mm
d
h
=f71t•N= 1.591mm -32 = 50.9mm
= 2•m,+c=2 • 1,5mm+0.167 - 1.5mm
= 3.25mm
Calculations of w ho le dep h, addendum, dedendum. clearance and root diameter are the same as those for spur
gears with straight teeth (page 256). In the formulae the
module mis replaced by the real pitch module m,.
Module series for spur gears (Series II
cf. DIN 780-1 (1977-05)
Module
0.2
0.25
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.25
Pitch
0.628
0.785
0.943
1.257
1.571
1.885
2.199
2.513
2.827
3.142
3.927
Module
1.5
2.0
2.5
3.0
4.0
5.0
6.0
8.0
10.0
12.0
16.0
Pitch
4.712
6.283
7.854
9.425
12.566
15.708
18.850
25. 132
31.416
37.699
50.265
Classification of• tool set of 8 module side miling cutters (up tom= 9 mm)11
Cutter no.
1
2
3
4
5
6
7
8
No. of teeth
12-13
14- 16
17-20
21-25
26- 34
35- 54
55- 134
135 to toothed rack
11
The manufacture of gears with side milling cutters is not an involute process. Only an approximate involute form
of the tooth flank is produced. Therefore this manufacturing process is only suitable fo r secondary gears. For gears
with m > 9 mm a tool set with 15 module side milling cutters is used.
258
Machine e le ments: 5.9 Drive elem e nts
Bevel gears, Worm drive
Unmodified bevel gears with straight teeth
m
module
N, N,, N 2 no. of teeth
d, d1, cl,
pitch diameter
6, 61, o2
pitch angle
do, d,,1, do, outside diameter
y1, y2
tip angle
:1:
shaft angle (normally 90")
Pitch and whole depth narrow to the cone point, so that at
every point of the tooth width a bevel gear has another
module, outside diameter, etc. The outermost module corresponds to the standard module.
d=m•N
Pitch diameter
d0 = d + 2 • m • coso
Outside diameter
In addition to the dimensions given on the outside
edges, the dimensions in the centers and inner edges
of gear teeth are also important for manufacturing.
Tip angle gear 1
Example:
Tip angle gear 2
Bevel gear drive, m = 2 mm; N 1 = 30; N2 = 120;
:1: = 90°. Calculate the dimensions for turning the
driving bevel gear.
tano, =
d1
d01
=
=
2500;
N1+ 2· coso,
N2 - 2. s ,n81
Pitch angle gear 1
s, = 14. 04•
=m• N1 = 2 mm• 30 = 60 mm
= d 1 +2- m · coso,
= 60mm+2 . 2 mm. cos 14.04°= 63.88 mm
tanr ,
r,
f: ,3! o.
N, +2 • cos8
tanr, = ~ - - - ~1
N2 -2 • sin81
30 + 2 -cos 14.04: = 0.2fil
120 - 2. sm 14.04
Pitch angle gear 2
Shaft angle
Whole depth, addendum, clearance, etc. are calculated like
spur gears with straight teeth (page 256).
= 14.95°
Worm drive
m
module
d, d 1, cl,
pitch diameter
d0 , d0 ,- d0 2 outside d iameter
r,
throat radius
-J
Worm
Pitch diameter
N, (no. of teeth)
Px=:it•m
Outside diameter
d0 1 = d, + 2 • m
Pn = Px • N, = :it • m • N 1
Worm gear
Pitch diameter
Worm drive m ~ 2.5 mm; N 1 = 2; d 1 = 40 mm;
N2 = 40; d0 1 = ?; d2 = ?; cf,_=?; r1 = ?;a = ?
d1 = nominal size
Axial pitch - worm
Lead
Example:
N,,N2 no. of teeth
lead
Pn
Px,P (axial ) pitch
cf,_
tip 0
Pitch
d2 = m•N2
p=:it•m
d 0 1 = d, +2 • m = 40 mm+2 • 2.5 mm = 45 mm
d 2 = m • N 2 = 2.5 mm • 40
= 100 mm
d.,_= d 2 + 2 • m = 100 mm + 2 - 2.5 mm = 105 mm
d, "' do2+m = 105mm+2.5 mm
= 107.5mm
Outside diameter
Tip diameter
dt_., d0 2 + m
r, = ~-m = 40mm _2.5mm
= 17.5mm
Throat radius
1j = 2 - m
8
= 70mm
Clearance, whole depth, addendum, dedendum and center
distance like spur gears (page 2561.
.
2
2
= d 1 + d 2 = 40 mm+ 100 mm
2
2
do2= d2+2 • m
d,
259
Machine elements: 5.9 Drive elements
Transmission ratios
Gear drives
Single gear ratio
driving
driven
N,, NJ, Ns ... no. of teeth
driving
gears
n,, flJ, ns ... speeds
N2, N4, N5 ... no. of teeth
driven
gears
ni, n4, n6 ... speeds
initial speed
n;
final speed
n,
total gear ratio
individual gear ratios
;,, i2, i3 ...
Gear ratio
Example:
Total gear ratio
J
i
Multiple gear ratio
Drive formula
J
i = 0.4; n 1 = 180/min; N2 = 24; n, = ?; N, =?
n2 = !i = i80/min = 450/min
i
0.4
i = N2 =n1 = ni
N1 f1i n1
i = N2. N4• Ns· ··
N1 -N3 -N,, ...
N = n 2 • N2 = 450/min • 24
60
1
n,
180/min
Torque for gears, page 37
Belt drives
Single gear ratio
d 1, d:i, els ... diameters1l
n 1, "3, ns ... speeds
di, d., c4; ... diameters1l
n 2, n., ns ... speeds
initial speed
n;
driving
J pulleys
driven
J pulleys
i 1, i2 , i3 ...
fina l speed
total gear ratio
individual gear ratios
v, v,, v2
circumferential velocity
Drive formula
Gear ratio
.
Multiple gear ratio
d
n
n2
d,
n 1 = 600/min; n, = 400/min;
d 1 = 240 mm; i= ?; di=?
i _ !i _ 6QC¥min _ 1,5 _ ,,5
n2 400{min 1
d , _ n, • d 1 _ 60C¥min • 240 mm _ 360 mm
n,
400{min
i = d2. d4. ds···
d1 • d 3 • d 5 . . .
effective diameter d8 ; for positive drive
belts (page 2551 calculate w ith the number
of teeth on the pulley.
Worm drives
N1 n o. of teeth (no. of threads) of the worm
Drive formula
n 1 speed of the worm
N 2 no. of teeth of the worm gear
n, speed of the worm gear
Gear ratio
gear ratio
Example:
i = 25; n 1 = 1500/min; N1 = 3; n2 =?
n, = ! i = 150Q'min = 60/min
;
25
n1
Total gear ratio
11 For V-belts (page 254) calculate w ith the
driving
n;
2 =1 =1= -
Example:
260
Machine elements: 5.9 Drive element s
Speed graph
The speed n of a machine t ool from the workpiece or tool diameter d and the selected cutting speed Ve can be determined
• on a comput er/calculator using the formu la, or
• g raphically using the speed graph.
Speed g raphs have the speeds under load which can be set on the machi ne.
These are stepped geometrically. For infinitely variable drives the calculated speed
can be set precisely.
Speed
I
n= - v_c_
n•d
.__________.
Speed graph with logarithmicaHy scaled coordinates
<::, ;-
/
V
/
,
/
100
/
90
80
70 I/ I/
/
/
~~ 60
,,
V
V
V /
I/
/
V
,,v I/
/
/
/
/
/
/
QJ
/
V
~ 40
/
CJ"\
V
C
/
V
V
/
V
/
I/
/
/
/
V
/
V /
/
V I/
/
/
/
, ,,
6
/
I/
/
/
V
/
V
V
/
/
/
/
V
/
/
/
I/
/
/
,
,
V
/
V
,,v
/
V
,,,
/
4
5
6 7 8 9 10
V
V
/
15
/
,I
/ /
/
20
/
/
/
'/
/
/
/
/
/
/
/
/
//
/
V/
40
/
50 60
V
'/
/
/
V
/
/
/
/
/
V
V '\.~ ~
"-"-""
~
/
/
/
V
/
/
/
/
,,,
/
I/
/
/
,,, / /
/
/
/ /
/
,,, ,,,
/
,
/
/
/
/
/
/
/
'/
/
/
/
/
//
/
/
/
/
/
/
/
/
/
/
,, / /
/
/
/
/
/
/
/
,,,,.:E
/
/
/
/
V
/
/
/
ro
C
,_<,.!2
/
/
/
QJ
'->'° 0..
V1
/
/
/
C:
'\'- "Cl
QJ
/
;,,r
/
80 100
150
200 mm 300
diameter d Example: d = 100mm; ve = 22D~;n=?
mm
220~
1
Calculation: n = _ e_ = ---1!l!!l. = 700.3 ; read from the speed graph above: n
" • d n • 0.1 m
min
V
I/
,,, / / /
/
~~
V
/ /,, /
V
// / /v/ / / /
/
/
, ,,v ,,,
/
/
/
/
I/
/
30
,,,
/
I/
/
/
/
V
/
/
I/
/
/
/
/
/
/
/
/
/
/
/
V
/
/
/
/
/
,
/
/
/
/
/
/
;/
/
/ /
/
/
,, / /
,
V
/
/
/
/
V I/
V v/
V
/
/
/
V I/
/
/
'/
/
/
,,v V /
/
/
// /
/
V
/
/
,,v V V / / I/ /
/
V
V
/
/
vv V /
/
/
V "-"'~
'\,~
/
/
..,.'->~
V -,,'->"
I/
/
V
/
/
/
,,,, ,,,
,I
/
I/
V
/
V
/
V
/
V
V V ,, V / V /
,, I /
,, / / V
/
V /
/
/
/
/
/
/
/
/VI/
/
/
/
/
/
V / / V / / V/ I/ ,,v/ / / / /
V
/
V
V
V
/
/
V I/
/
/
/
V
£::, 30 / V
V /
/
u
!.Iv I/ / vv /
/
/
/
/
/
/
I/
/
/
/
/
V
/
/
/
/
I/
/
/
V
/
/v
/
/
/
/
/
I/
V
// /
V /
;/
I#
V / // I/ / / / / / / / I/ / / / I/ / / / v/ V
/
V
/
/
°a': 50
/
IV
/
/
V /
VI/
/
I/
/ ~
/
V
/
<-J
V
V/ A
... 4 V /
Ai'
/
/
/
,
I/
/
<::,
V
I/
V V
/ /
A
I/ / , V
,,, / ,,, V / ,,,, / ,,, ,,,I/
,,, I/
/
/
/
V
V
V
I/
I/
/
/
/
/
/
/
/
I/
/
I/
V /
/
/
/
I/
I/
/
V
/
/
/
/
V
/
/
<::,
/
/
/
/
I/
/
/
/
/
/
/
I/
/
/ I/ V /
I/
I/
/
V
/
/
V/
V /
/
/
/
~
'\,~ ~"5 . ._. ,."5 ❖"-~ °'~~ '\~ I)~
/
V
/
/
220
200
180
160
140
120
4
/
/
/
300
5
<::,
V
400
10
9
8
<::,
I/
/
500
20
18
16
14
12
<::,
""'"5 ~f..,.'->"5 4r9 "-"'"5
800
m/min
600
=700 - 1
min
400
261
Machine elements: 5.10 Bearings
Plain bearings, Overview
Plain bearings11 (Selection by type of lubrication)
Ory-running
plain bearings
Hydrostatic
plain bearings
Hydrodynamic
plain bearings
•
I
Suitable for
I
T
Suitable for
Suitable for
- low-wear continuous operation
- wear-free continuous operation
- maintenance free or low
- high speeds
- high impact loads
- low friction losses
- low speeds possible
- with or w ithout lubrication
Areas of application
maintenance operation
Areas of application
Areas of application
- main and big end bearings
- gearboxes
- electric motors
- turbines, compressors
- lifting equipm., agricul. machinery
- precision bearings
- space telescopes and
antennae
- machine tools
- axial bearings for high f orces
- construction equipment
- armatures and devices
- packaging machines
- jet engines
- household appliances
11 Other plain bearings: air or gas and water lubricated plain bearings, magnetic bearings
Properties of plain bearing materials
Designation,
Material
number
Elongationlim it
Rpo.2
N/mm2
Specific
bearing
load
PL
11
N/mm2
Shaft
min.
hard·
ness
Sliding
properties
ErnerSliding gency- Properties, application
speed running
behavior
I
..
cf. DIN ISO 4381 (2001-021
Lead and tin casting alloys
G-PbSb15Sn102I
2.3391
43
7
160 HB
~
0
~
Medium loading;
all purpose plain bearing
G-SnSb12Cu6Pb
2.3790
61
10
160 HB
• •
'-
Good impact loading; turbines, com•
pressors, electric machines
cf. DIN ISO 4382·1 and ·2 (1992-11)
Cast copper alloys and copper wrought alloys
CuSn8Pb2-C
2.1810
130
21
280 HB
CuZn31Si1
2.1831
250
58
55HRC
CuPb10Sn10-C2I
2.1816
80
18
CuPb20Sn5-C
2.1818
60
11
~
~
0
250 HB
~
'-
0
150 HB
• • •
High loading, high vertical and
horizontal impact loading
POM
(Polyoxymethylene
High surface pressures; vehicle bearings, bearings in hot-rolling mills
Suitable for water lubrication,
resistant t o sulfuric acid
cf. DIN ISO 6691 (2001-05)
Thermoplastics
PA6
(Polyamide)
Low to moderate loading.
sufficient lubrication
-
12
50 HRC
-
18
50 HRC
•
1)
Bearing force based on the projected bearing surface
21 Composite material according to DIN ISO 4383 for thinwalled plain bearings
0
•
•
very good
O limited
Impact and wear resistant;
bearings in farm machinery
Harder and capable of higher compressive loads than PA; bearings in precision
mechanics, suitable for dry-running
~ good
0 poor
Cl normal
262
Machine elements: 5.10 Bearings
Plain bearing bushings
Bushings made of copper alloys
d . DIN ISO 4379 ( 1995-10)
a-
FormF
FormC
~
-0
.,,
~
-0
10
V,
V,
u.J
u.J
e- - - - ,-- - - - ,;;
12
,5" "t5"
-0
15
18
20
all
22
bJs13
chamfers 45° b1s13 '
25
b, js13
1l Force fitting produces
30
tolerance class HS
35
Recommended tolerance classes for mounting dimensions 40
Location hole
I H7
e7 or g7 (depending on
Shaft
⇒
application)
.,,.
-0
-0
FormC
Form F
Series 1
Serias2
Lengths
"2
"2 "3 "2 "2 "3 "2
b,
d,
-
I
16 20 3
12 14 16 12 14 1
- 10 10 15 20
18 22 3
14 16 18 14 16 1
10 15 20
21 27 3
17 19 21 17 19 1
20 22 24 20 22 1
24 30 3
12 20 30
15 20 30
23 24 26 23 26 1.5 26 32 3
15 20 30
25 26 28 25 28 1.5 28 34 3
28 30 32 28 31 1.5 32 38 4 20 30 40
34 36 38 34 38 2
38 44 4 20 30 40
45 50 5 30 40 50
39 41 45 39 43 2
44 48 50 44 48 2
50 58 5 30 40 60
Diameter range d 1: 6- 200
Bushing ISO 4379 - F22 x 25 x 30 - CuSn8P: Form F,
d1 = 22 mm, di - 25 mm, b 1 • 30 m m, of CuSn8P
Bushings made of sintered metal
FormJ
-e
.,,.
FormV
....,,
~ ----
LC!
-0
~
cf. DIN 1850-3 (1998-07)
.-
f
....,, - -- - -
,.,
LC!
bJs13
bijs13 '
V,
~
-
bJs13
all chamfers 45°
Recommended tolerance classes for mounting dimensions
Location hole
I H7
Shaft
I-
FormJ
FormV
"2
"2
10
12
15
18
20
22
25
30
35
40
16
14
16
22
18
16
18
24
21
27
21
19
24
22
24
30
26
25
26
32
28
27
28
34
30
32
39
32
46
38
35
38
41
45
55
45
50
46
50
60
Diameter range d 1: 1-60
2
3
3
3
3
3
3.5
4
5
5
⇒
Bushing DIN 1850 -V18 x 24 x 18 - Sin1-B50:
d 1 = 18 mm, di= 24 mm, b 1 = 18 mm,
sintered bronze Sint-850
"2
Bushings made of thermosets and thermoplastics
Thermoset plastics
d,
FormR
Form P
·i t,Jl
.,,. .,,
-1'. ,.,
,;;
---b 1j s13
all chamfers 45°
-0
-
bJs13
"2
_)('30°
b 1 h13
b 1 h13
"3
"2
R,,,..
16
20
25
30
25
25
30
30
40
50
Lengths
0.3
16
20
3
6
18
22
3
0.5
10
21
27
0.5
10
3
24
30
3
0.5
12
0.5
15
26
32
3
28
34
3
0.5
15
4
0.5
20
32
38
4
0.5
20
44
38
45
0.8
50
5
30
Diamet er range d 1 for thermosets: 3- 250,
for thermoplastics: 6-200
b,
10
15
15
20
20
20
30
30
40
20
20
30
30
30
40
40
50
- - - ,;;
-0
vr -
Toleranceclaa
Fabrication l'8Mllting.,..,
35 42 method
force fitting di
40 55
D12
A +0.21 +0.2 +0.4 +0.6 .-0.69 +0.90 injection
+0.07 0
+0.1 .-0.1 +0.23 .-0.30 molded
B
Tolerance class zbl 1
machined
Cll
Additional codes for bushings made of thermoset plastics
Circular grooves on y Assembly bevel 15' (inst. of 45'1
from 10
to 14
,.,
~"l5"'
10
12
15
18
20
20
25
25
35
40
d:i
)v1fl,'.'._
.,,-J
b,
8
8
10
12
15
15
20
20
25
30
d. DIN 1850-5 and -6 (1998-07)
FormT
30~
.,,. - --
10
12
15
18
20
22
25
30
35
R,,,..
0.6
0.6
0.6
0.6
0.6
0.6
0.8
0.8
0.8
0.8
Limit deviations d:i and d, of tolerance classes A and B for
bushings made of thermoplastics
Thermoplastics
Form S
Lengths
"3
d,
b1 h13
15 20 28
18 25 32
I
I
Recommended tolerance classes for mounting dimensions w
outer diameter di
z Undercut instead of
I Thermosets I Thermoplastics
radius R
Location hole
H7
H7
I
I
Bushing DIN 1850 - S20 A20 - PA 6: Form S; d 1 •
⇒
20 mm, tolerance cl. A, b 1 = 20 mm, polyamide 6
Shaft
h7
h9
I
I
Other stand. designs: Wraooed bushings DIN 1494, internal tension bushings DIN 1498, external tension bushings DIN 1499
263
Machine elements: 5.10 Bearings
Antifriction bearings, Overview
Roller bearings (selection)
I
I
I
I Antifrlction bearings
I
I
I
Axial and radial
load
For rotation
I
Radial
load
I
I Ball bearing I
Roller bearing!
I
I
Deep groove ball Cylindrical roller
bearings DIN 625 bearings DIN 5412
I Ball bearing I
For linear
movement
I
I
I Linear bearings
I
I
I
Axial
load
I Ball bearing I
JRoller bearing
Angular ball
Tapered roller
bearings DIN 628 bearings DIN 720
I
I
!Roller bearing
Axial-deep groove Axial-cyl. roller
ball bear. DIN 711
bear. DIN 722
•
~
A 8 R Pl
j_ B A A a±n- ~
Self-aligning ball Needle bearings
bearing DIN 630
DIN617
Cylindrical roller
bearings DIN 628 bearings DIN 5412
Angular contact ball
Spherical roller
bearings DIN 628 bearings DIN 728
Four-point contact
Properties of roller bearings
Bearing design 11
High
Inside 0 Radial Axial
loading loading speed
d
High
loads
Quiet
Application
running
Ball bearings
Deep groove ball
bearings
1.5 - 600
~
()
()
•
Universal bearings in machine and
Self -aligning ball
bearings
•
5-120
~
0
~
0
0
Compensation with misalignment
Angular contact ball
bearings single-row
10- 170
~
~
.
~
~
Only used in pairs, large forces,
automotive manufacturing
Angular contact ball
bearings double-row
10- 110
~
~
()
~
0
Large forces, automotive manufacturing,
with limited space requirements
Axial deep groove
ball bearings
8 - 360
0
~
()
()
0
Acceptance of very high axial forces,
drill spindles, tail stock centers
Four-point contact
bearings
20- 240
0
~
0
()
0
Very tight spaces, spindle bearing layouts
gear and roller bearing assemblies
2)
3)
automotive manufacturing
Roller bearings
Cylindrical roller
bearings (form N)
17- 240
Cylindrical roller
bearings (form NUP)
15- 240
Needle bearings
90- 360
Tapered roller
bearings
15- 360
Axial cylindrical
roller bearings
15-600
Spherical
roller bearings
60- 1060
1)
•
•
•
•
•
• •
•
0
()
~
0
0
0
0
•
Mounted in pairs
~
()
Acceptance of very large radial forces,
roller bearing assemblies, transmissions
0
Like Form N, with flanged w heel
additional acceptance of axial forces
()
High carrying capacity w ith tight
mounting space
0
Usually mounted in pairs, w heel bearings
in automobiles, spindle bearings
()2)
.
0
~
0
Stiff bearing requiring minimal axial
space, high friction
0
~
0
Angular displacement thrust bearings,
thrust bearings in cranes
For all radial bearings the prefix "radial" is omitted.
2) Reduced suitability with paired mounting
3)
~
3)
Suitability levels:
• very good
~ limited
() normal
~ good
0 not suitable
264
Machine elements: 5.10 Bearings
Antifriction bearings, Designation
Designation of antifriction bearings
Example:
Tapered roller bearings DIN 720 - S 30208 P2
I
Name
I
cf. DIN 623-1 (1993-05)
~ , TT
I
I
I
Standard
I
I Basic numbers I
I
I Prefix symbol I
Prefix symbols
I
I
Suffix symbol
I
.
Suffix symbols (selection)
K
cage with roller elements
L
R
free ring
ring with roller set
s
stainless steel
K
f'
bearing w ith tapered bore
bearing with shield on one side
bearing w ith shield o n both sides
reinforced design
bearing with seal on one side
bearing w ith seal on both sides
highest precision: dimensional, form and
running
z
2Z
E
RS
2RS
P2
3 0 2 08
Example of basic numbers:
TTTT
I
I
Bearing series 302
I
I
I Width series O I I Diameter series 2 I
I
Bearing type 3
I
I
I
Dimension series 02
I
Bore code 08
I
Bearing type
0
Design
Angular contact ball bear., double row
Borecode
Bore 0
d
Bore 0
d
Bore
code
1
Self-aligning ball bearing
00
10
12
60
2
Barrel and spherical roller bearings
01
12
13
65
3
Tapered roller bearings
02
15
14
70
Deep groove ball bear., double row
03
17
15
75
Axial deep groove ball bearin gs
04
20
16
80
25
17
85
4
5
6
Deep g roove ball bear., single row
05
7
Angular contact ball bear., single row
06
30
18
90
8
Axial cylindrical roller bearings
07
35
19
95
NA
Needle bearings
08
40
20
100
QJ
Four-point contact bearing
09
45
21
105
N, NJ, NJP, NN,
NNU, NU, NUP
Cylindrical roller bearings
10
50
22
11 0
11
55
23
115
Dimension series (selection)
Explanation
The dimension plans in DIN 616
contain diameter series in
which each nominal d iameter
of a bearing bore d (= shaft
diameter) is assigned a number
of:
• outside diameters and
• width series (for radial
bearings) or
• height series (f or axial
bearings).
cf. DIN 616 (1994-06)
Structure of the dimension series
■ ■ •■
r
=~1~
Example: Tapered roller bearings11
Dimension series 02
Bore
code
07
08
09
10
Bore
0
D
B
72
80
85
90
17
18
19
20
d
35
40
45
50
.
11 other d imensions, see page 267
265
Machine elements: 5.10 Bearing s
Ball bearings
Deep groove ball bearings (selection)
"l"~
R --bl#
d. DIN 625-1 (1989-04)
Bearing series 60
Bearing series 62
Bearing series 63
w
w
d
D
w
10
12
15
26
28
32
8 0.3 1
8 0.3 1
9 0.3 1
17
20
25
h
Basic
D
max min number
r
h
Basic
D
max min number
r
~ .AJ'~ I I
~---
.,, c:,
~ -tl
"'"'"w~ '
d from 1.5 to 600 mm
Mounting dimensions
according to DIN 5418:
•
l
,,
-
-c::I
I'
6000
6001
6002
30 9 0.6 2.1
32 10 0.6 2.1
35 11 0.6 2.1
6200
6201
6202
35 11 0.6 2.1
2.8
37 12 1
42 13 1
2.8
6300
6301
6302
35 10 0.3 1
42 12 0.6 1.6
47 12 0.6 1.6
6003
6004
6005
40 12 0.6 2.1
47 14 1
2
52 15 1
2
6203
6204
6205
47 14 1
52 15 1
62 17 1
2.8
3.5
3.5
6303
6304
6305
30
35
40
55 13 1
62 14 1
68 15 1
2.3
2.3
2.3
6006
6007
6008
62 16 1
72 17 1
80 18 1
2
2
3.5
6206
6207
6208
72 19 1
3.5
80 21 1.5 4.5
90 23 1.5 4.5
6306
6307
6308
45
50
55
75 16 1
80 16 1
90 18 1
2.3
2.3
3
6009
6010
6011
85 19
90 20
100 21
1
3.5
1
3.5
1.5 4.5
6209
6210
6211
100 25 1.5 4.5
110 27 2
5.5
120 29 2
5.5
6309
6310
6311
60 95 18
65 100 18
70 110 20
1
1
1
3
3
3
6012
6013
6014
110 22
120 23
125 24
1.5 4.5
1.5 4.5
1.5 4.5
6212
6213
6214
130 31 2.1 6
140 33 2.1 6
150 35 2.1 6
6312
6313
6314
75 115 20
80 125 22
85 130 22
1
3
1
3
1.5 3.5
6015
6016
6017
130 25 2
5.5
140 26 2
5.5
150 28 2.1 6
6215
6216
6217
160 37 2.1 6
170 39 2.5 7
180 41 2.5 7
6315
6316
6317
90 140 24
95 145 24
100 150 24
1.5 3.5
1.5 3.5
1.5 3.5
6018
6019
6020
160 30 2.1 6
170 32 2.1 6
180 34 2.1 6
6218
6219
6220
190 43 2.5 7
200 45 2.5 7
215 47 2.5 7
6318
6319
6320
I = Deep groove ball bearing DIN 625 - 6208 - 2Z - P2: Deep groove ball bearing (bearing type 6). w idth series 0 11. diameter series 2, bore code 08 (d = 8 - 5 mm = 40 mm).
A
design w ith 2 shields, bearing w ith highest precision (tolerance class 2)
---'---
Angular contact ball bearings (selection)
;f--
d
D
q.i_
r.r.U/.
.-----
.,, c:,
rLL".t'Zi
~ :iiF
~
w
dfrom 10 to 170 mm
Mounting dimensions
according to DIN 5418:
V"
t
-C::lJ:s
, ",\
r//r:r.a
• ={~
t
-c::I
" / . / ri
I'
_
___ . _
A.
cf. DIN 628-1 (1993-12)
Bearing series 72
Bearing series 73
Bearing ser. 33 (double row)
w
w
r
h
Basic
max min '1Umber2
D
13
14
15
17
1
1
1
1
'"fY. T/.
l_
r
h
Basic
max min number
.,
r
h
Basic
D
max min number2I
w
r
h
Basic
max min number3I
15 35 11 0.6
17 40 12 0.6
20 47 14 1
25 52 15 1
2.1
2.1
2.8
2.8
7202B
7203B
7204B
7205B
42
47
52
62
2.8
2.8
3.5
3.5
7302B
7303B
7304B
7305B
42 19 1
47 22.2 1
52 22.2 1
62 25.4 1
2.8
2.8
3.5
3.5
3302
3303
3304
3305
30
35
40
2.8
3.5
3.5
7206B
7207B
7208B
72 19 1
3.5
80 21 1.5 4.5
90 23 1.5 4.5
7306B
7307B
7308B
72 30.2 1
3.5
80 34.9 1.5 4.5
90 36.5 1.5 4.5
3306
3307
3308
45 85 19 1
3.5
3.5
50 90 20 1
55 100 21 1.5 4.5
7209B
7210B
7211B
100 25 1.5 4.5
110 27 2
5.5
120 29 2
5.5
7309B
7310B
7311B
100 39.7 1.5 4.5
110 44.4 2
5.5
120 49.2 2
5.5
3309
3310
3311
60 110 22
65 120 23
70 125 24
1.5 4.5
1.5 4.5
1.5 4.5
7212B
7213B
7214B
130 31 2.1 6
140 33 2.1 6
150 35 2.1 6
7312B
7313B
7314B
130 54 2.1 6
140 58.7 2.1 6
150 63.5 2.1 6
3312
3313
3314
75 130 25 1.5 4.5
5.5
80 140 26 2
85 150 28 2
5.5
7215B
7216B
7217B
160 37 2.1 6
170 39 2.1 6
180 41 2.5 7
7315B
7316B
7317B
160 68.3 2.1 6
170 68.3 2.1 6
180 73 2.5 7
3315
3316
3317
5.5
90 160 30 2
95 170 32 2.1 6
100 180 34 2.1 6
7218B
7219B
7220B
190 43 2.5 7
200 45 2.5 7
215 47 2.5 7
7318B
7319B
7320B
190 73 2.5 7
200 77.8 2.5 7
215 82.6 2.5 7
3318
3319
3320
62 16
72 17
80 18
1
1
1
Angular contact ball bearing DIN 628 - 73098: Angular contact ball bearing
= (Bearing
type 7), w idth series 0 11, diameter series 3, bore code 09 (bore diameter
d = 9 - 5 mm = 45 mm). contact angle a= 40° (B)
11 In the designations for deep g roove and angular contact ball bearings the 0 for the
width series is someti mes omitted according to DIN 623-1.
31 Contact angle not standardized
21 Contact angle a = 40°
266
Machine elements: 5.1 0 Bea ri ngs
Ball bearings, Roller bearings
Axial deep groove ball bearings (select ion)
cf. DIN 711 (1988-02)
Bearing series 512
d
I
d
I
~;,'j
I
-<-il-
.....
~y
D,
D
d from 8 to 360 mm
Mounting dimensions according t o DIN 5418:
_ J]._i-
~,
m~ •
•
!
lY
~
!
I
~
i
0,
D
T
25
30
35
27
32
37
47
52
62
40
45
50
42
47
52
68 19
73 20
78 22
55
60
65
Bearing series 513
r
h
Basic
max min number
15 0.6
16 0.6
18 1
T
r
h
Basic
max min number
6
6
7
51205
51206
51207
52 18 1
60 21 1
68 24 1
7
8
9
51305
51306
51307
1
1
1
7
7
7
51208
51209
51210
78 26 1
85 28 1
95 31 1
10
10
12
51308
51309
51310
57
62
67
90 25 1
95 26 1
100 27 1
9
9
9
51211
51212
51213
105
110
11 5
35 1
35 1
36 1
13
13
13
513 11
513 12
51313
70
75
80
72
77
82
105
110
115
9
9
9
51214
51215
51216
125
135
140
40 1
14
44 1.5 15
44 1.5 15
51314
513 15
513 16
=
Axial deep groove ball bearing DIN 711 - 51210: Axial-deep
groove ball bearing of the bearing series 512 w ith bearing
type 5, width series 1, diameter series 2 and bore code 10
27
27
28
1
1
1
Cylindrical roller bearings (selection)
Form N
D
cf. DIN 5412-1 (2005-08)
Bearing series
N2, NU2, NJ2, NUP2
Form NU
Bearing series
N3, NU3, NJ3, NUP3
h, r, ,.,_ D
max min max min
w r,
h, r, ,.,_
max min max min
w r,
Bore
code
d
D
17
20
25
40 12 0.6 2.1 0.3 1.2
47 14 1
2.8 0.6 2.1
52 15 1
2.8 0.6 2.1
47 14 1
2.8 1
52 15 1.1 3.5 1
62 17 1.1 3.5 1
2.8
2.8
2.8
03
04
05
30
35
40
62 16 1
72 17 1
80 18 1
72 19 1.1 3.5 1
80 21 1.5 4.5 1
90 23 1.5 4.5 2
2.8
2.8
5.5
06
07
08
3.5 100 25 1.5 4.5 2
3.5 110 27 2
5.5 2
3.5 120 29 2
5.5 2
5.5
5.5
5.5
09
10
11
Form NJ
~ --·
-c,
c:,
~ - ,ar,, ,-,r
Form NUP
~
~
w
dfrom 15 to 500mm
M ounting dimensions according to DIN 5418:
Form N
Form NU
unflanged
w ith fixe!l flange
i \' /~
•
.,q , : " = s • ..q
-<:
I
I
I
, r ,1 . ,.,
l__~--~✓' l__~-- ~~·
2.8 0.6 2.1
3.5 0,6 2.1
3.5 1
3.5
45 85 19 1
3.5 1
50 90 20 1
3 .5 1
55 100 21 1.5 4.5 1
60 110 22 1.5 4.5 1.5 4.5 130 31 2.1 6
65 120 23 1.5 4.5 1.5 4.5 140 33 2.1 6
70 125 24 1.5 4.5 1.5 4.5 150 35 2.1 6
2
2
2
5.5
5.5
5.5
12
13
14
75 130 25 1.5 4.5 1.5 4.5 160 37 2.1 6
80 140 26 2
5.5 2
5,5 170 39 2.1 6
7
85 150 28 2
5.5 2
5.5 180 41 3
2
2
3
5.5
5.5
7
15
16
17
90 160 30 2
5.5 2
5.5 190 43 3
95 170 32 2.1 6
2.1 6 200 45 3
100 180 34 2.1 6
2.1 6 215 47 3
7
7
7
3
3
3
7
7
7
18
19
20
105 - - 110 200 38 2.1 6
120 215 40 2.1 6
7
7
7
3
3
3
7
7
7
21
22
24
-
-
2.1 6
2. 1 6
225 49 3
240 50 3
260 55 3
=> Cylindrical roller bearing DIN 5412 - NUP 312 E: Cylindrical
roller bearing of bearing series NUP3 with bearing type NUP,
width series 0, diameter series 3 and bore code 12, reinforced
design
The normal desig n of the d imension series 02, 22, 03 and 23 were
deleted from the standard with no replacement and t hen
replaced with the reinforced design (suffix symbol E).
267
M achine elements: 5.10 Bearings
Roller bearings
Tapered roller bearings (selection)
cf . DIN 720 {1979-02) and DIN 5418 { 1993 -02)
Bearing series 302
Dimensions
dt,
o.
Di,
c.
q,
'•• fbs Basic
no.
20
25
30
47 14
52 15
62 16
12 15.25 33.2
13 16.25 37.4
14 17.25 44.6
27
31
37
26
31
36
40
44
53
41
46
56
43
48
57
2
2
2
3
2
3
35
40
45
72 17
80 18
85 19
15 18.15 51.8
16 19.75 57.5
16 20.75 63
44
49
54
42
47
52
62
69
74
65
73
78
67
74
80
3
3
3
3
1.5 1.5 30207
3.5 1.5 1.5 30208
4.5 1.5 1.5 30209
w
50 90 20
55 100 21
60 110 22
17
18
19
21.75 67.9
22.75 74.6
23.75 81.5
58
64
70
57
64
69
79 83 85
88 91 94
96 101 103
3
4
4
4.5 1.5 1.5 30210
4.5 2
1.5 3021 1
4.5 2
1.5 30212
~
65 120 23
70 125 24
75 130 25
20 24.75 89
21 26.25 93.9
22 27.25 99.2
77
81
86
74 106 111 113
79 11 0 116 118
84 115 121 124
4
4
4
4.5 2
2
5
5
2
/ /~
80 140 26
85 150 28
90 160 30
22 28.25 105
24 30.5 112
26 32.5 118
91 90 124 130 132
97 95 132 140 141
103 100 140 150 150
4
5
5
6
2.5 2
6.5 2.5 2
6.5 2.5 2
95 170 32
100 180 34
105 190 36
27
30
39
126
133
141
110 107 149 158 159
116 112 157 168 168
122 117 165 178 177
5
5
6
7.5 3
8
3
9
3
2.5 30219
2.5 30220
2.5 30221
110 200 38
120 215 40
32 41
34 43.5
148
161
129 122 174 188 187
140 132 187 203 201
6
6
9
3
9.5 3
2.5 30222
2.5 30224
~
-- - - -
"' ..,-
k~
[
T
T
da
D
-,.,
lwa
-
C
d
~...
c::,
w
Mount ing dimension
34.5
29 37
d,
max min min max min min min max max
1
1
1
1
1
1
30204
30205
30206
1.5 30213
1.5 3021 4
1.5 30215
30216
30217
30218
Bearing series 303
Dimensions
Mounting dimensions
according to DIN 5418:
,~/-rr
1'.1': --✓
~
cr ~
~
~ ~
I,.
~
~- - - - ---
c::,'
..,.
"'
~
--0 cf c::,
In t he case o f t apered roller bearings t he cage proj ects beyond the
lat eral face of the outer ring.
The mounting dimensions of DIN
5418 must be maintained so that
the cage does not rub against
other parts.
'•• ,,,,
Di, Ca q,
Basic
do dt,
o.
max min min max min min min max max no.
d
D
w
C
20
25
30
52
62
72
15
17
19
13 16.25 34.3
15 18.25 41.5
16 20.75 44.8
28
34
40
27
32
37
44
54
62
45
55
65
47
57
66
2
2
3
1.5 1.5 30304
3
1.5 1.5 30305
3
4.5 1.5 1.5 30306
35 80 21
40 90 23
45 100 25
18 22.75 54.5
20 25.25 62.5
22 27.25 70.1
45
52
59
44
49
54
70
77
86
71
81
91
74
82
92
3
3
3
4.5 2
5
2
5
2
50 110 27
55 120 29
60 130 31
23 29.25 77.2
25 31.5
84
91.9
26 33.5
65
71
77
60 95 100 102
65 104 110 111
72 112 11 8 120
4
4
5
6
2.5 2
30310
6.5 2.5 2
30311
7.5 3
2.5 30312
65 140 33
70 150 35
75 160 37
28 36
30 38
31 40
98.6
105
11 2
83
77 122 128 130
82 120 138 140
87 139 148 149
5
5
5
8
8
9
3
3
3
2.5 30313
2.5 30314
2.5 30315
80 170 39
85 180 41
90 190 43
33
34
42.5
44.5
46.5
120
126
132
102 92 148 158 159
107 99 156 166 167
113 104 165 176 176
5
6
6
9.5 3
10.5 4
10.5 4
2.5 30316
3
30317
30318
3
95 200 45
100 215 47
105 225 49
38 49.5
39 51.5
41 53.5
139
148
155
118 109 172 186 184
127 114 184 201 197
132 119 193 211 206
6
6
7
11.5 4
12.5 4
12.5 4
3
3
3
30319
30320
30321
110 240 50
120 260 55
42
46
165
178
141 124 206 226 220
152 134 221 246 237
8
8
12.5 4
13.5 4
3
3
30322
30324
cage
~~ ~~
Mounting dimension
-
36
T
54.5
59.5
d,
89
95
1.5
1.5
1.5
30307
30308
30309
Tapered roller bearing DIN 720 - 30212: Tapered roller bearing of bearing
series 302 with bearing type 3, w idth series 0, diameter series 2, bore code 12
268
Machine elements: 5.10 Bearings
Needle bearings, Lock nuts, Lock washers
Needle bearings (selection)
Ill _
- ---
.,,
cf. DIN 617 11993-04)
d
L&..t::i
-
Mounting dimensions
according to DIN 5418:
D
r
F
max
h
min
Bearing series NA49 Bearing """"" NA69
Basic
Basic
w
number
w
number
17
17
17
NA4904
NA4905
NA4906
30
30
30
NA6904
NA6905
NA6906
20
25
30
37
42
47
25
28
30
0.3
0.3
0.3
35
40
45
55
62
68
42
48
52
0.6
0.6
0.6
1.6
1.6
1.6
20
22
22
NA4907
NA4908
NA4909
36
40
40
NA6907
NA6908
NA6909
50
55
60
72
80
85
58
63
68
0.6
1
1
1.6
2.3
2.3
22
25
25
NA4910
NA4911
NA4912
40
45
45
NA6910
NA6911
NA6912
65
70
75
90
100
105
72
80
85
2.3
2.3
2.3
25
30
30
NA4913
NA4914
NA4915
45
54
54
NA691 3
NA6914
NA6915
=>
NA6907 and up:
Needle bearing DIN 617 - NA4909:
Needle bearing of bearing series NA49 with bear- double row
ing type NA w idth series 4, diameter series 9,
bore code 09
Lock nuts for antifriction bearings (selection)
cf. DIN 981 (1993-02)
Code
Code
d,
d-i
h
M10 x 0.75
M12 x 1
M15 x 1
18
22
25
4
4
5
KMO
KM1
KM2
M60 x 2
M65 x 2
M70 x 2
80
85
92
11
12
12
KM12
KM13
KM14
M17 x 1
M20 x 1
M25 x 1.5
28
32
38
5
6
7
KM3
KM4
KM5
M75 x 2
M80x 2
M85 X 2
98
105
110
13
15
16
KM15
KM16
KM17
M30 x 1.5
M35 x 1.5
M40 x 1.5
45
52
58
7
8
9
KM6
KM7
KM8
M90X2
M95X 2
M100 x 2
120
125
130
16
17
18
KM18
KM19
KM20
M45 x 1.5
M50 x 1.5
M55 x 2
65
70
75
10
11
11
KM9
KM10
KM11
M105 x 2
M110x 2
M115 x 2
140
145
150
18
19
19
KM21
KM22
KM23
h
Lock nut DIN 981 - KM6: Lock nut of d1
=>
E
M30 x 1.5
d1 from M10 to M200
Lock washers (selection)
cf. DIN 5406 (1993-02)
d,
d,C11
Code
I
21
25
28
1
1
1
4
4
5
2
2
2
MBO
MB1
MB2
60
65
70
86 1.5
92 1.5
98 1.5
9
9
9
4
4
5
MB12
MB13
MB14
1
17
20
25
32
36
42
1
1
1.2
5
5
6
2
2
3
MB3
MB4
MB5
75
80
85
104 1.5
112 1.7
119 1.7
9
11
11
5
5
5
MB15
MB16
MB17
30
35
40
49
57
62
1.2
1.2
1.2
6
7
7
4
4
4
MB6
MB7
MB8
90
95
100
126 1.7
133 1.7
142 1.7
11
11
14
5
5
6
MB1 8
MB19
MB20
45
50
55
69
74
81
1.2
1.2
1.5
7
7
9
4
4
4
MB9
MB10
MB11
105
110
115
145 1.7
154 1.7
159 2
14
14
14
6
6
6
MB21
MB22
MB23
=>
Lock washer DIN 5406 - MB6: lock washer of
d 1 = 30 mm
r ,;-
~-
I.._
d, from 10 to 200 mm
d,
10
12
15
I
Mounting dimensions
Code
269
Machine elements: 5.10 Bearings
Internal and external retaining rings, Circlips
Retaining rings in standard design1I (selection)
For shafts !external)
Nomi-
cf. DIN 471 (1981-09)
s
ct.
d:,
w
dz
mm
9.3
11
13.8
16.5
18.5
20.5
23.2
25.9
27.9
29.6
32.2
35.2
36.5
38.5
41.5
44.5
45.8
55.8
60.8
65.5
70.5
74.5
84.5
94.5
Norn~
Slot
Ring
"811ize
d,
10
12
15
18
20
22
25
28
30
32
35
38
40
42
45
48
50
60
65
70
75
80
90
100
1
1
1
1.2
1.2
1.2
1.2
1.5
1.5
1.5
1.5
1.75
1.75
1.75
1.75
1.75
2.0
2.0
2.5
2.5
2.5
2.5
3.0
3.0
1.8
1.8
2.2
2.4
2.6
2.8
3
3.2
3.5
3.6
3.9
4.2
4.4
4.5
4.7
5
5.1
5.8
6.3
6.6
7.0
7.4
8.2
9
=
Retaining ring DIN 471 -40 x 1.75:
17
19
22.6
26.2
28.4
30.8
34.2
37 .9
40.5
43
46.8
50.2
52.6
55.7
59.1
62.5
64.5
75.6
81.4
87
92.7
98.1
108.5
120.2
9.6
11.5
14.3
17
19
21
23.9
26.6
28.6
30.3
33
36
37.5
39.5
42.5
45.5
47.0
57.0
62.0
67.0
72.0
76.5
86.5
96.5
m
H13
1.1
1.1
1.1
1.3
1.3
1.3
1.3
1.6
1.6
1.6
1.6
1.85
1.85
1.85
1.85
1.85
2.15
2.15
2.65
2.65
2.65
2.65
3.15
3.15
For bores !internal)
n
min
0.6
0.8
1.1
1.5
1.5
1.5
1.7
2.1
2.1
2.6
3
3
3.8
3.8
3.8
3.8
4.5
4.5
4.5
4.5
4.5
5.3
5.3
5.3
nal size
d,
cf. DIN 472 (1981-09)
Ring
s
Slot
ct.
d:,
mm
10
12
15
18
20
22
25
28
30
32
35
38
40
42
45
48
50
60
65
72
75
80
90
100
1
1
1
1
1
1
1.2
1.2
1.2
1.2
1.5
1.5
1.75
1.75
1.75
1.75
2.0
2.0
2.5
2.5
2.5
2.5
3.0
3.0
=
Retaining ring DIN 472 - 80 x 2.5:
d 1 = 40 mm, s = 1.75 mm
10.8
13
16.2
19.5
21.5
23.5
26.9
30.1
32.1
34.4
37.8
40.8
43.5
45.5
48.5
51.5
54.2
64.2
69.2
76.5
79.5
85.5
95.5
105.5
3.3
4.9
7.2
9.4
11.2
13.2
15.5
17.9
19.9
20.6
23.6
26.4
27.8
29.6
32
34.5
36.3
44.7
49.0
55.6
58.6
62.1
71.9
80.6
1.4
1.7
2
2.2
2.3
2.5
2.7
2.9
3
3.2
3.4
3.7
3.9
4.1
4.3
4.5
4.6
5.4
5.8
6.4
6.6
7.0
7.6
8.4
3-10
12- 22
24-100
d 1 in mm
8-22
h10
h11
h12
d2
H11
11 Standard design: d 1 from 3- 300 mm; heavy duty design: d 1 from 15- 100 mm
1.1
1.1
1.1
1.1
1. 1
1. 1
1.3
1.3
1.3
1.3
1.6
1.6
1.85
1.85
1.85
1.85
2.15
2.15
2.65
2.65
2.65
2.65
3.15
3.15
0.6
0.8
1.1
1.5
1.5
1.5
1.8
2.1
2.1
2.6
24-100
H12
d2
Circlips (selection)
3
3
3.8
3.8
3.8
3.8
4.5
4.5
4.5
4.5
4.5
5.3
5.3
5.3
100-300
H13
ct. DIN 679911981-091
relaxed
Cirdlps
loaded
ll
~
n
Shaft
h11
loaded
els
a
s
d,
from- to
6
7
8
12.3
14.3
16.3
5.26 0.7
5.84 0.9
6.52 1
7- 9
8-11
9-12
d2
n
min
m
0.74 + 0.05 1.2
0.94
0
1.5
1.05 1.8
-
9
18.8
7.63 1.1
10- 14 1.15
2
10
20.4
8.32 1.2
11 - 15 1.25
2
12
23.4
10.45 1.3
13- 18 1.35 + 0.08 2.5
t-1-5 -+--2-9.- 4-+-12-.6
-1-+--,_5-+-1-6--24- +-1-.5-5-1
3
°
19
24
d:, from 0.8 to 30 mm
n
min
Tolerance dassas for dz
d 1 in mm
Mounting
dimensions:
10.4
12.5
15.7
19
21
23
26.2
29.4
31.4
33.7
37
40
42.5
44.5
47.5
50.5
53.0
63.0
68.0
75.0
78.0
83.5
93.5
103.5
m
H13
d 1 = 80 m m , S • 2.5 mm
Tolerance classes for dz
~
dz
w
37.6
44.6
15.92
21 .88
1.75
2
20- 31
25- 38
= Circlip DIN 6799-15: d = 15 mm
2
1.80
2.05
3.5
4
270
Machine elements: 5.10 Bearings
Radial seals (selection)
cf. DIN 3760 (1996-091
Form AS
"2
d,
10
w
22 26
25 -
12 22 30
25 -
d.i
"2
d,
7
8.5 28
7
10
30
40 52
47 40 47
42 52
w
d.i
7 25.5
50
8 27.5
55
non-rot ating
✓= ✓
-
70 80
72
-
8 46.5
8 51
30 40
5262837
80 100 110 10 75.5
40 >--+--+--+--+--+----+--+--+---I
7 18
35 55 85 110 120 12 80.5
t-+--+----t-+--t--+----t--, 8 38.5 t--+-+---+-+------i
35 47
42 55 62
90 110 120 12 85.5
22
7 19.5 l----+----+--+--+---+----+--+--1---+----t
40 60 65 8 41.5 95 120 125 12 90.5
t-+--+----t- +----t 45 t-+--+---+- --+- +----t--+---+- ---t
35 47
62 120 130
25
7 22.5 1----+---+---t 8 44.5 100
12 94.5
40 52
48 62 125 20
with
Ra0.2 to
Ra0.8
or
Rz1 bis RzS
a) = edges rounded
=
d1 from 6 to 500 mm
RWDR DIN 3760 -A25 x 40 x 7 - NB: Radial seal (RWDR) of
form A w ith d 1 = 25 mm, d, = 40 mm and W= 7 mm,
elastomer part of Nitrile-Butadiene rubber (NBR)
Felt rings (selection)
cf. DIN 5419 (1959-091
Mounting dimensions:
Dimensions
d,
20
25
30
35
40
45
50
55
Mounting dim.
Dimensions
w
d,
30
37
42
47
52
57
66
71
4
5
5
5
5
5
6.5
6.5
w
21
26
31
36
41
46
51
56
31
38
43
48
53
3
4
4
4
4
4
5
5
58
67
72
Mounting dim.
<1J
60 76 6.5 61.5 77 5
65 81 6.5 66.5 82 5
70 88 7.5 71.5 89 6
75 93 7.5 76.5 94 6
80 99 7.5 81.5 99 6
85 103 7.5 86.5 104 6
111 7
90 110 9.5 92
125 8
100 124 10 102
= Felt ring DIN 5419 MS-40: Felt ring of d = 40 mm, felt hardn. M5
d, from 17 to 180 mm
1
O-rings
DIN 3771 (withdrawn)
d,
externally sealing
0° to 5°
w+0.25
d 1 from 1.8 to 670 mm,
ct,from 1.8 to 7 mm
axially sealing
68
d.i
w
65 72
14 24 30 7 12
45 52
75 85
8 29
60
8 56
t-+--+----t-+----t 32
47 26 35
80 15
7 13
47 52 8 32
65 85 90 10 61
30
1---+---+----+-+------t 35 >--+---+--+--+--+---+--+---+---I
16 30 35 7 14
50 55
70 90 95 10 66
t-+--+----t-+-- t--+----t--, 8 35
18 30 35 7 16
38 55 62
75 95 100 10 70.5
Mounting dimensions:
w
"2
d,
"2
d,
"2
"2
d,
18
56
6
58
20
1.8
25 2.65 3.55 60
8
9
28
63
t-1-'-0+-~---+""'3"-0-+--+---1 67
14
40
69
45
71
15
16 1.8 2.65 50 3.55 5.3 75
17
53
80
5
"2
85
90
95
100
3.55 5.3 103 3.55 5.3
106
109
112
115
Mounting dimensions for static loading
internally sealing
internally & extern. sealing
,,
w
1.8
2.65
w+0.25
3.55
5.3
0.3
0.2
0.6
0.2
internal external
h
axially sealing
w
h
1.3
2.4
1.4
1.3
2.6
3.6
2.1
1.95
3.8
4.8
2.85
2.65
7.1
4.3
4.15
2.75
7.3
4.25
271
M achine elem ents: 5.10 Bearings
Lubricating oils
Designation of lubricating oils
cf. DIN 51502 (1990-08)
Designation using symbols
Designation using code letters
0 ~
PGLP220
JTT
I
;I
Code letters
for lubricating oils
I
=>
=>
I
Additional code
letters
00
I
I
I
ISO viscosity
g rade
0
o il based
I Mineral
lubricating oil
Silicon based
lubricating oil
Lubricating oil DIN 51517 - CL 100: Circulating mineral oil based lubricating oil (C), increased corrosion and
aging resist ance (L), ISO viscosity grade VG 100 (100)
Lubricating oil DIN 51517 - PGLP 220: Polyglycol o il (PG), increased corrosio n and aging resist ance (U,
increased wear protect ion (Pl, ISO viscosity grade VG 220 (220)
Types of lubrication oils
cf. DIN 51502 (1990-08)
Code letters Type of lubricant and properties
Standard
A pplication
Mineral oils
AN
Normal lubricating oils without
additives
DIN 51501
Once-t hrough and circulating
lubrication at oil temperatures up to 50 •c
B
Bitumen containing lubricating oils
w ith high adhesion
DIN 51513
Manual, continuous flow and oil bath lubrications, mainly fo r open lubrication points
C
Circulating lubricating oil, without
addit ives
DIN 51517
Plain bearings, antifriction bearings, gears
CG
Sliding track oil with active ingredients
for reducing wear
DIN 8659
T2
In mixed frict ion operations for slideways and
guideways, and for worm gears
Synthetic liquids
E
Est er oils with especially low
change in v iscosity
-
Bearings with widely varying
temperatures
PG
Polyglycol oils with hig h aging
resistance
-
Bearings w ith frequent mixed friction
cond itions
SI
Silicon oils w ith high aging
resistance
-
Bearings w ith very high and low
temperatures, very water repellant
Additional code letters
cf. DIN 51502 (1990-08)
Additional
Application and explanation
code letters
E
For lubricants t hat are m ixed w ith wat er, e.g. cooling lub ricant SE
F
For lubricant s with solid lubricant additive, e.g . graphite, molybdenum sulfide
L
For lubricants w ith act ive ingredients to improve corrosion protection and/or aging
resist ance
p
For lubricants w ith act ive ingredients for reducing friction and wear in
mixed frict ion areas and/or to increase the load capacity
ISO viscosity grade for liquid industrial lubricants
Viscosity
grade
Kinetic viscosity
in mm2/s at
20·c 40•c 50•c
Viscosity
grade
ISOVG 2
ISOVG 3
ISO VG 5
3.3
5
8
2.2
3.2
4.6
1.3
2.7
3.7
ISOVG 22
ISOVG32
ISOVG 46
ISOVG 7
ISOVG 10
ISOVG 15
13
21
34
6.8
10
15
5.2
7
11
ISOVG 68
ISO VG 100
ISO VG 150
cf. DIN 51519 (1998-08)
Kinetic viscosity
in mm2 /sat
V,scosity
grade
20°C
40•c
50•c
-
22
32
46
15
20
30
ISO VG 220
ISO VG 320
ISO VG 460
68
100
150
40
60
90
ISOVG680
ISO VG 1000
ISO VG 1500
-
-
Kinetic viscosity
in mm2 / s at
40•c
20°c
50°C
-
220
320
460
130
180
250
680
1000
1500
360
510
740
272
Machine e lements: 5.10 Bearings
Lubricating grease, Solid lubricants
cf DIN 51502 11990 081
Designation of lubricating greases
Designation by code letters
Designation by symbols
KSl3R - 10
TT IT
I
I
I
Code for
1Code ~etter for! I Addi tional 11
viscosity o r
lubncat1ng
code letters
consist ency
grease
1
Additional! I IAdditionall I
letters
code
I
6 ◊
Silicon based
Mineral oil based
lubricating grease lubricating grease
Lubricating grease DIN 51517 - K3N -20: Lubricating grease for antifriction and plain bearings (K) based on
mineral oil (NLGI grade 3) (3), upper working temperature+140°C (N), lower working temperature -20°C (-20)
Lubricating grease DIN 51517- KSI3R-10: Silicon based lubricating grease for antifriction and plain bearings
(K) (SI), NLGl-grade 3 (3), upper working temperature+180°C (R), lower working temperature - 10°C (- 10)
⇒
⇒
Lubricating greases
Code letters Application/additives
Code letters Application
K
General: antifriction bearings, plain bearing,
sliding surfaces
G
Closed gears
KP
Like K, but with additives for
reducing friction
OG
Open gears
(adhesive lubricant w ithout bitumen)
KF
Like K, but w ith solid lubricant
additives
M
For plain bearings and seals
(low requirements)
Consistency11 dassification for lubricating greases
,,
NLGIgracle3l
Worked penwation21
NLGIgrade31
000
00
0
445-475 (very soft)
400-430
355-385
1
2
3
Worked penetration21
NLGIgradrl
310-340
265--295
220-250
4
5
6
Worked penetration"
175--205
130-160
85--115 (very firm)
Code for the viscoelasticity
21 M easure of the penetration depth of a standardized test ball in the kneaded (worked) grease
31
National Lubrication Grease Institute (NLGI)
Additional letters for lubricating greases
Addit.
letter1 )
Upper working
temperature
·c
Acklt.
letter1 I
G
H
+100
+100
0 or 1
2 or 3
N
p
R
K
M
+120
+120
0 or 1
2 or 3
·c
Addit.
letter1I
C
D
+60
+60
0 or 1
2 or 3
E
+80
+80
0 or 1
2 or 3
F
Upper working
temperature
Grede 2l
Grade Z1
s
T
u
Upper working
temperature
·c
+ 140
+ 160
+ 180
+200
+220
+220
Grade 21
as per
agree~
ment
11 The
number value for the lower working temperature can be appended to the additional code letters;
e.g. - 20 for - 20°C
21 Grades for behavior when subjected to water, cf. DIN 51807-1:
0: no change; 1: small change; 2: moderat e change; 3: large change
Solid lubricants
Lubricant
Code
Working
temperature
Application
Graphite
C
-18 to +450 •c
As powder or paste and as an addit ive to lubricating oils and
lubricating g reases, not in oxygen, nitrogen and vacuums
Molybdenum
Polytet rafluorethylene
MoS2 - 180 to +400 •c As mineral oil-free paste, sliding lacquer or additive to lubricating oils sulfide
and lubricating greases, suitable for very high surface pressures
PTFE
-250 to +260 •c As powder in sliding lacquer and synthetic lubricating greases and as
bearing material, very low coefficient of sliding frictionµ= 0.04 to 0.09
Table of Contents
273
6 Production Engineering
inflection
point
frequency
curve
6.1
Quality management
Standards, Terminology .................... 274
Quality planning, Quality testing .......... .. . 276
Statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . . 277
Statistical process control . . . . . . . . . . . . . . . . . . . 279
Process capability ......... ..... .. ...... .... 281
6.2
Production planning
Time accounting according to REFA ... . .... .. 282
Cost accounting .... . ... ..... .......... .... 284
Machine hourly rates .. ................. ... . 285
6.3
Machining processes
Productive time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
Machining coolants ..................... .. . 292
Cutting tool materials, Inserts, Tool holders .. .. 294
Forces and power . . . . . . . . . . . . . . . . . . . . . . . . . . 298
Cutting data: Drilling, Reaming, Turning ....... 301
Cutting data: Taper turning .................. 304
Cutting data: Milling ... ................. .... 305
Indexing .................................. 307
Cutting data: Grinding and honing ..... .... ... 308
6.4
Material removal
Cutting data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Processes .. ........... .............. ... . .. 314
6.5
Separation by cutting
Cutting forces ...... ... .... ........ ..... ... 315
Shearing ................................. 316
Location of punch holder shank .. ... ... ..... . 317
6.6
Forming
Bending ........ . . ... ..................... 318
Deep drawing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
6.7
Joining
Welding processes ......................... 322
Weld preparation ... ... .. ................. . 323
Gas welding .............................. 324
Gas shielded metal arc welding ..... .... ..... 325
Arc welding .............. ..... ...... ... ... 327
Thermal cutting . . .... .... .. ........... .... 329
Identification of gas cylinders ... .. ... ........ 331
Soldering and brazing . ...... . .............. 333
Adhesive bonding . ... ... .... ... .. .. ....... 336
6.8
Workplace safety and environmental protection
Prohibitive signs .. ......................... 338
Warning signs ....................... ... . . . 339
Mandatory signs, Esc. routes and rescue signs . 340
Information signs . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Danger symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
Identification of pipe lines . . . . . . . . . . . . . . . . . . . 343
Sound and noise ......... .. ................ 344
x ,..
Material overhead
in percent of material direct
costs, e.g. purchasing costs,
warehousing costs, etc.
Wear safety
glasses
Wear hard
hat
274
Production Engineering: 6.1 Quality management
Standards ISO 9000, 9001, 9004
Standards of the ISO-9000 family should help organizations of all types and sizes to implement quality management
systems, t o work with existing quality management systems, and to facilitate mut ual understanding in national and
international trade.
Quality management standards
cf. DIN EN ISO 9000 (2005-12), 9001, 9004 (2000-12)
Standard
Explanation, contents
DIN EN ISO
9000
Fundamentals of quality management systems
Principle of quality management
customer focus
leadership
involvement of people
process approach
• system approach to management
• continuous i mprovement
• factua l approach to decision making
• m utually beneficial supplier relationships
Fundamentals of quality management systems (QM systems)
evaluation of QM systems
reasons for OM systems
continuous improvement
requirements of QM systems and
products
role of statistical methods
progressive implementation of QM syst ems
QM systems as part of the total
p rocess oriented evaluation
management system
quality policies and goals
requirements of OM systems and
comparative evaluation of organizations
role of t op management in the QM system
documentation; advantages and types
based on criteria of excellence models
Terminology for quality management systems
For a selection of definitions and explanations of t erms, see page 275.
DIN EN ISO
9001 1 )
Requirements of a quality management system
This international standard applies to organizations in any industry or business sector regardless of
products offered. It establishes requirements for a QM system, based on fundamentals outlined in
ISO 9000, if an organization:
must demonstrate capability to offer product s w hich fulfill both customer and
regulatory requirements,
strives t o improve customer satisfaction, including the process of continuous improvement of the
system.
Specified requirements can be used for:
internal applications by organizations
• certification purposes
• contract purposes
The standard is based on a process oriented evaluation, i.e. every activity o r sequence of activities
which uses resources to convert input into results is regarded as a process.
Requirements
The organization must:
recognize all necessary processes for the OM system and their use in the organization,
establish the flows and interdependencies of these processes,
establish criteria and methods for ensuring implementation and co ntrol of these processes,
ensure availability of resources and information for these processes,
monitor, measure and analyze these processes,
t ake necessary actions for continuous improvement of these processes,
fulfill documentation requirements for the QM system, and
observe regulations for document control.
1
DIN EN ISO
9004
)
This standard also replaces previous standards 9002 and 9003.
Guideline for assessing the overall performance, effectiveness and efficiency of
quality management systems
The goal of this standard is to improve the organization and t o improve the satisfaction of customers
and other relevant parties.
It is not intended for certification or contract purposes.
Quality-related terms
Quality
Extent to which the characteristics of a product fulfill the requirements for that product.
Requirement
Specified or mandatory demands for characte ri stics of a unit, e.g. nominal values, tolerances, functional capability or safety.
Customer satisfaction
Customer's perception of degree to w hich its requirements have been fulfilled.
Capability
Suitability of an organization, system or process to provide a product that fulfills that product's quality requirements.
Characteristic and conformity related t erms
Quality characteristic
Identifying attribute of a p roduct or p rocess, which is utilized in assessing quality based o n
the specified quality requirem ent s.
Quantitative (variable) charact eristics:
discrete characteri stics (who le numbers), i.e. number of holes, piece count
cont inuous characteristics (measured values). e.g. length, positio n, mass
Qualitative charact eristics:
o rdinal charact eristics (with ranking), e.g. light blue - blue - dark blue
nominal characteristics (without ranking), e.g. good - bad, blue - yellow
Identifying attribute of a product, a process or system relating to a requirement.
Conformity
Fulfilling a specified requirement, e.g. a dimensional tolerance.
Defect
Not fulfillin g a specified requirement, e.g. not conforming to a required d imensio nal
tolerance or surface quality.
Rework
Action taken on a defective product so that it fulfills requirements.
Process and product related terms
Process
Mutually interactive resources and activities which convert inputs into results. Some exam-
Method
Defined manner in which an activity or process is performed. In written form also referred
Product
Result of a process, e.g. pan, assembly, service, processed item, knowledge, concept, document, contract, pollutant.
ples of resources are personnel, finances, facilities and manufacturing methods.
to as process instructions.
Terms related to organization
Organization
Group of persons and facilities w ith a matrix of responsibilities, authorities and relationships.
Customer
Organizatio n or person which receives a product from a supplier.
Supplier
Organization or person which provides a product to a customer.
Terms relating to management
Quality
management system
Organization and organizational structures, methods and processes of an operation required
to put a quality management into practice.
Quality
management
All coordinated activities for managing and cont rolling the quality-related aspect s of an
o rganization by:
quality control
est ablishing a quality policy
• setting quality goals
quality assurance
• quality planning
q uality improvement
Quality planning
Activ ities di rected toward establishi ng quality goals and required implementation processes, as well as associated resources for attaining quality goals.
Quality control
Work acti vities and techniques to continually fulfill requirement s despite unavoidable variations in quality. Consists prim arily of process monitoring and elimination of weak points.
Quality assurance
Perfo rming and generating required documentation for all activities relating to the QM system, with the goal of creating an atmosphere of trust, both in-house and wit h the customer,
that quality requirements will be fulfi lled.
Quality
improvement
Actions taken throughout the organization to increase p roduct quality.
Quality manual
Document describing the quality policy, quality goals and quality management system of an
o rganization.
276
Production Engineering : 6.1 Quality management
Quality planning, Quality control, Quality testing
Quality planning
Rule-of-ten (for costs)
Costs required to eliminat e defects or costs resulting
from def ects increase by about a factor of 10 from
phase to phase in the product life cycle.
100
product planning process planning
and development and production
testing
and customer
Example: A t olerance error on a single part can be
corrected d uring the design p hase w it h negligible
increase of costs. If t he defect is first noticed in prod uction. much larger costs result. If t he defect leads
to problems in assembly or has an adverse impact
on the fu nct ionality of the finished product o r even
leads to a recall, eno rmous costs are incurred.
Quality control
Factors causing variance in quality
Quality control circle
l
human
ma\
environment
~
Factor
Examples
Human
q ualificatio n, motivation,
degree of utilization
Machine
machine rigidity, positioning
accu racy, wear condition
Material
deviat ions. material properties,
mat erial variat ions
Method
work st eps, production process.
test conditions
Surroundings
(environment)
temperature, v ib rations,
light, no ise. d ust
Management
poor q uality goals or policies
Measurability
m easurement inaccuracy
testing
raw parts
(/
Quality testing
cf. DIN 55 350-17 (1988-08)
Concepts
Explanations
Quality testing
Determine t o what extent a unit meets specified q uality requirement s.
Test plan
Test instructions
Define and describe the type and scope of test ing, e.g. measuring and monitoring devices,
frequency of testing, t est personnel, testing location.
Complete t esting
Testing of a un it for all specified q uality characteristics, e. g. co mplete inspectio n of a
single wor kpiece regarding a ll requirements.
100% testing
Testing of all units within a test lot, e. g . v isual inspecti on of all delivered parts.
Statistical testing
(sampling test)
Quality testing w ith the aid of stat istical methods, e. g. evaluation of a large q uantity
of parts by analyzing a number of sampled parts.
Test lot
(sampling test)
All of t he units being tested, e.g. a production of 5000 identical workpieces.
Sample
One or more units which are taken from the population o r a subset of the population.
e.g. 50 pa rts from a daily production of 400 parts.
Probability !Probability of defect)
Probability of a defective part w ithin a defined t ot al number of parts.
P probability in%
n number of defective parts
m t ot al number of parts
Example:
In a crate there are m = 400 parts, w here n = 10 parts have a d imensio nal defect.
W hat is the probability P of o btaining a def ective part w hen taking one part out
of the crate?
Probability P = !!._ · 100 % = ~ • 100% = 2.5%
m
400
277
Production En gineering: 6.1 Quality management
Statistical analysis
Statistical analysis of continuous characteristics
Presentation of -
data
Raw dat a list
Raw data is the documentation of all
observed values from the test lot or
sample in the sequence in which they
occur.
Example
Sample size: 40 parts
Test characteristic: part diameter d = 8 :t 0.05 mm
Measured part diameter din mm
7.98
7.96
7.99
8.02
Parts 1- 10
Parts 11- 20
Parts 21-30
Parts 31-40
Tally sheet
The tally sheet provides a clear presentalion of the observed values and
assignment into classes (ranges) of a
specific class interval size.
n
k
i
R
"i
hi
number of individual values
number of classes
class interval
range (page 278)
absolute frequency
relative frequency in %
vgl. DIN 53 804-1 (2002-04)
7.96
7.99
8.05
8.01
7.99
8.00
8.03
8.05
8.01 8.02 7.96
8.02 8.02 7.99
8.00 8.03 7.99
7.94 7.98 8.00
Class Menuredvolut
Tally sheet
<
no.
.,
in%
I
1
2.5
Ill
3
7.5
7.98
8.00
8.00
8.02
.lilt .lilt I
4
.lilt .lilt Ill
11
13
27.5
32.5
5
8.02
8.04
.lilt .lilt
10
25
6
8.04
8.06
II
2
5
40
100
2
3
C=
fn = )'40 = 6.3 ~ 6
i = -
~~
.0 Q)
co.::
I
I
R
i ,,,_
I
k
Relative frequency
h- = __l_
n- • 100%
J
n
AQi-
i::.-
>,
a,O
-c
b✓
n
I
6
t
A histogram is a bar g raph for visualizing the distribution of individual test
data.
7.99 8.01
8.01 8.Ql
8.Ql 8.02
8.02 8.00
Class interval size
= - - - - = 0.0 18 mm ~ 0.02 mm
C
Histogram
1 r=
I
0.11 mm
R
7.99
8.00
7.99
8.01
Number of classes
hi
n;
7.94 7.96
7.96 7.98
1
8.03
8.02
7.98
8.01
11
7.94
7.96
7.98
8.00
8.02
8.04
mm
I
8.08
part diameter d
Cumulative frequency curve in
probability system
The cumulative frequency curve in the
probability system is a simple and
clear graphical method used to check
for the existence of a normal distribu •
tion (page 278).
If the cumulative relative frequency in
the probability system approximates
a straight line, then a normal distribution of the individual values can be
assumed, i.e. a further evaluation can
be conducted per DIN 53 804-1 (page
278).
In this case specific values can additionally be determined from the samples.
I
t
if.
.£
84.13%):
x * 8.003 mm; s * 0.02 mm
The probability model of the example
shows t hat i n t he entire lot approximately 0.6% of parts can be expected
to be too thin and 3% too thick.
,
95
90
,.;_- 84.13
80
>,
C
70
Q)
::,
60
er
x
50
1Q) 40
.,!;
30
1§
~
I
,
/
/
20
"S
E
::,
"
~
10
5
II'
I
I
--
j
t
U@
7.96
i
I
I
' I
7.94
90
95
I
/
7.98
8.00
8.003 -
j
8.02
8.04
part diameter d
LLV lower lim it value; ULV upper limit value
20
if.
.£
-
I[""
0
0
80
I
/
1
0.6%
0. 1 0.05
.__s
5
10
30
40
50
60
70
,/
___.,. ~--~
Q)
.,!;
/ 0.5
1
J(- - - 3%
- - - - - - - >-- ->-- - ~ L -+- - - -
"
iii
Example of problem solving using the
graph:
Arithmetic mean x (for Fj = 50%) and
standard deviation s (as difference
68.26% .;. 2 between Fj = 50% and
n = 40
99.5
99
!
99
99.5
99.9
99.95
-
mm
8.08
278
Production Engineering: 6.1 Quality management
Normal distribution
Gaussian distribution
99.73%
95.44 %
68.26%
VA I l
t
I inflection
1(1 point
x
oi
i
_,
-3a
I
" . . . _l-
Continuous data values often exhibit a characteristic in their distribut io n w hich is approxi mated mathem atically by the Gaussian
normal distribution model. For an infinite number of ind iv idual values the probability density of a normal distribut ion y ields the typical
bell curve. This sym metrical and continuo us distribution curve is
clearly d escribed by the following parameters:
The meanµ lies o n the curve maxim um and ident ifies t he position of
the distribut ion.
The standard deviation o is a measure of the variations, i.e. how values deviate from the mean.
-o , +o +2o +3a
µ
characteri stic value x ~
-20
11 Carl Friedrich GauB (1777-1855), German mathematician
Normal distribution in sampling
cf. DIN 53804-1 (2002-04) or DGO 16-31 (1990)
number of indiv idual values
(sample size)
value of measurable properties,
e .g. i ndividual value
Xm ax largest measurement value
Xmin smallest measurement value
X
arithmetic mean
median value 11, m iddle value of
measured values arranged in
o rder of magnit ude
s
st andard deviation
R
range
D
mode (measurement value
occurring most freq uently
in a test series)
9ixl probabi lity density
n
Arithmetic
mean 2•
x,
x
-3sI
-2s
Xmin
I•
R
I
X
Xmax
,I
chafacteristic value x
number of samples
x
mean of multiple sample means
I
R mean of m ult iple sample ranges
s mean of standard deviations
R= R, + R2: · •• + Rm
Example: Evaluation of sample values fro m page 277:
x= 8.00225mm
R = 0.11 mm
x = 8.005mm s= 0.02348mm D= 7.99mm
11 M edian value f or
odd number of i ndiv id ual values:
e.g. x 1; x2; x 3; ><4; x 5:
X = X3
2
/Dx-x)
I
-v n - 1
5-
Mean of sample ranges
When evaluating several samples:
m
Standard deviation21
even number of individual values:
e.g. x, ; x2; x3; X4; x5; x6:
X = (X3 + X4)/2
21 M any pocket calculato rs have special functio ns for calculating the mean and
I
M ean of sample means
Ix= x , +xz
: ---+xm
I
Mean of standard
deviations
st andard deviatio n.
Repeated occurrences of identical measurement values can be represented by a
suitable factor.
Normal distribution in an inspection lot
Parameters of the population are estimated using a sampling method based o n characteristic values from t he sample (confirmatory statistics). To d ifferent iate sampling characteristics clearly from parameters of the population,
other designations are used. These estimated values are disting uished from the calculated process values for a
100% inspection (descriptive stati stics) by adding a • mark.
Characteristic values and designations in quality testing
Sampling test (confirmatory statistics)
Sample
Population
100 % inspection
(descriptive statistics)
Number of measured values n
Num ber of measured values m . n
Number of measured values N
Arit hmetic mean x
Estimat ed process meanµ
Process mean µ
Standard deviatio n s
Estimat edp rocess standard
deviation o (calculator 0 0 _ 1)
Process standard deviation a
(calculator 0 0 )
279
Productio n Engineering: 6.1 Quality management
Statistical process control
Quality control charts
Process control charts
Acceptance control charts
Process control charts are used for monitoring a
process for changes compared to a target value or a
previous process value. The intervention and w arning
limits are determined by the process estimated value of
a population or a preliminary run.
Acceptance control charts are used to monitor a process
in reference to set specification l imits (limit values).
Control limits are calculated as tolerance limits for the
location of the process mean and a tolerance range for
process variance.
Process control charts for quantitative characteristics (Shewhart-contro l charts)1>
Raw data chart
Control limits
-X
The raw data chart is a documentation of all measurement values by entering directly
on the chart It assumes an approximate normal distribulion process and is relatively
complex because of the
number of entries.
UWL
LWL
UCL
LCL
USL
LSL
Example: 5 individual values for each sample
characteristic mean
(mean of the characteristic, target val ue, ideal
value)
5.06
..
"'a,
USL
5.04
5.02 1-
:,
>
•E
5.00
~ E
upper warning limit
lower warning limit
upper control limit
lower control lim it
:l!:
upper specification limit
lower specification limit
Sample
number
-- -- - - - l --- -- --
- -- - - --
4.98 1-
~
.,"'
.- -
1-
UCL
UWL
i-- X
4.96
LWL
LCL
4.94
LSL
1
2
--1-
4
3
5 ...
Median value range chart (ii-R-chart)
Mean standard deviation chart (x-s-chart)
These charts are used to clearly represent production
dispersion without requiring much calculation. They are
suitable for manual control chart management.
These charts are used to show the trend of the mean
and exhibit g reater sensitivity than ii-A-charts. They
require computer-aided control chart management.
Example:
Example:
Inspect. characteristic: Cont rol dimensio n:
diameter
5±0.05
I
l
'
Sample size
Cont rol i nterval
60min
n=5
x, 4.98 4.96 5.03 4.97
E
a,"'
X2
4.97 4.99 5.01
4.96
::i ~ E X3 4.99 5.03 5.02 5.01
::i .. E
4.99 4 .99 4.99
a,>
X4 5.01
~
5.00 4.98 5.02
X5 5.01
Ix 24.96 24.97 25.03 24.95
x 4.99 4.99 5.01 4.99
R 0.04 0.07 0.05 0.06
\
5.04
a,
:,
E 5.02
UCL '
UWL
~ E
--tC: C: 5.00
-~ -LSL
"fil•>< 4 .98
4.96
LCL
~
0.08
U CL
:
UWL
., E 0.06
~
-- x
g> E 0.04 7"'F-LWL
"' C:
a:·LCL
:
Q; 0.02
0
'
"'
---
,__.-
-
-
--x
'
Sample no
1
2
Ti me
5 00
7 00
3
8 00
4
9 00
j
11 Walter Andrew Shewhart (1891- 1967), American scientist
Inspect . characteri stic: Control dimension:
diam eter
5±0.05
Sample size:
Control i nterval!:
n= 5
60min
x, 4.98 4.96 5.03 4.97
E
a,"'
X2
4.97 4.99 5.01 4.96
:5 ~ E X3 4.99 5.03 5.02 5.01
::l .. E
., >
X4
5.01 4.99 4.99 4.99
~
X5 5.01
5.00 4 .98 5.02
4.992 4.994 5.006 4.990
s 0.0 18 0.025 0.021 0.025
5.02
UCL '
UWL
-=1E
5.01
~E
5.00
~
c: c:
,o·4.99
LWL
a, I)(
~
4.98
LCL
0.026
UCL
I
0.024
,.
UWL
I
•I
,,._
"E C: 0.022
""'0
--:_..,
-o-~
~ - -X
0.020
C: "'
I
'
ci5 1J~ 0.018
LWL
0.016
LCL
Sample no.
3
4
1
2
6 00
8 00
9 00
7 00
Time
J
'
x
.,"'
- -+-
"'
.,,--
-. - --x
-·
,,
- -~-
"'-+-
280
Production Engineering: 6.1 Quality management
Process trend, Acceptance sampling and plan
Process trends
Process trend
(e.g. from an trace)
x
Designetion/observations
Possible causes - Actions
Natural run
The process is under control and can continue without interruption.
2/3 of a ll values lie in t he range
± standard deviation sand all values lie w ithin the contro l limits.
Exceeding the control limits
The values are outside of the control limits.
RUN (sequential)
7 or more sequential values lie on
one side of the mean line.
Over-adjusted machine, different material,
damaged or worn equipment
-
Stop process and 100% inspect parts
since the last sampling
Tool wear, other material charge, new t ool,
new personnel
-
Tightened observation of the process
LCL
Trend
7 or more sequential values show
an increasing o r decreasing t rend.
Middle Third
At least 15 consecutive values lie
w ithin ± standard deviation s.
~
~• 4 • X
~
\ ii ,,,..
- - -- - - - -- LCL
$NF
WN--x
Cyclical
« ~CL
►
LCL
The values cross the mean line
periodically .
Wear on tool. equipment or measuring dev ices, operator fatigue
-
Stop process to determine reasons for
adjust ment
Improved production, better supervision,
corrected test results
..... Determine how the process was
improved or check the test results
Different measuring devices, systematic
spread of t he data
-
Examine manufacturing process f or
infl uences
Acceptance sampling (attribute sampling)
cf. DIN ISO 2859-1 (2004-011
An attribute inspection is an acceptance sampling inspection in which the acceptability of the inspection lot is determined based on defective units or defects in individual sampling.
The percentage of nonconforming units or the number of defects per hundred units of the lot identifies the quality level. The acceptable quality level is the quality level defined for continuously presented lots; it is a quality level
that is specified by the customer in most cases. The associated sampling i nst ructions are summarized in control
tables.
Acceptance sampling plan for single sampling inspection as the normal inspection
(excerpt from a control table)
Acceptable quality level AOL (preferred values)
Lot size
0.04
0.065
0.10
0.15
0.25
0.40
0.65
1.0
1.5
2-
8
I
I
I
I
I
I
I
I
I
9-
15
I
I
I
I
I
I
I
I
8
0
5
0
16-
25
I
I
I
I
I
I
I
13
0
8
0
5
0
26-
50
I
I
I
I
I
20
0
13
0
8
0
5
0
51-
90
I
I
I
I
50
0
32
0
20
0
13
0
8
0
20
1
91- 150
I
I
I
80
0
50
0
32
0
20
0
13
0
32
1
20
1
I
2.5
I
151- 280
I
I
125
0
80
0
50
0
32
0
20
0
50
1
32
1
32
2
281- 500
I
200
0
125
0
80
0
50
0
32
0
80
1
50
1
50
2
50
3
501- 1200
315
200
0
125
0
80
0
50
0
125
1
80
1
80
2
80
3
80
5
0
Explanation: [ [ : Use first sampling instruction of this column. If the sample size is g reater than or equal to
so 2
the batch size: Carry out a 100% inspection.
Second number: Acceptance number = number of the accepted delivered defective units
First number: Sample size = number of units to be tested
281
Production Engineering: 6. 1 Quality management
Process and machine capability, Quality control charts
Capability, Quality control charts
During an evaluation of the q uality-related capability of a process through capability characteristics (capability indices), differentiation must be made between short•
term capability (machine capability) and long-term capability (process capability).
s
X
LLV
If Cm " 1.67 and Cm,;,, 1.67, t h is means that
99.99994% (range± 5 s) of t he quality characteristics lie wit hin the limits and the mean xii es
at least an amount of 5 s away from the tolerance
l imits.
C
=_I_
C
Likrit
m
Machine capability is an evaluation of t he
machine, i .e. whether there is sufficient probability
that it can produce within specified limits given its
normal fluctuations.
tolerance T ?. 10 s
L\crit
M achine capability index
6 -s
mk=~
Requirement 11 e.g.
C.., ;,, 1.67 and C...• ;,, 1.67.
ULV
charcteristic value LLV
ULV
x
s
Process capability index
lower limit value
upper limit value
arithm etic mean
standard deviati on
Llcrit
smallest interval between
m ean and a tolerance limit
Cm, Cm, machine capability index
C
Process capability is an assessment of t he manufacturing process, i.e. w hether
t here is sufficient probability that it can fulfill specified requirements g iven its
normal fluctuations.
o
estimat ed standard deviation
Cp, C pk
process capability index
_ Licrit
pk - 3 •0"
Requirement 11 e.g.
<;, ;,, 1.33 and<;,. ;,, 1.33
Example:
Examination of machine capability for production dimension 80 ± 0.05;
Values from preliminary run: s = 0.009 mm; x = 79.997 mm
C = _!__ = 0, 1mm
m
6- s 6 -0.009 mm
11 Customer or oontract
specific requirements;
in large scale production,
e.g. automotive industry,
tendency to higher requir&ments, e.g. c;,, ~ 2.0.
_ ; C
1 852
_ Llcrit _ 0.047mm
_
1 74
mk - ~
- 3- 0.009 m m
The machine capability is below requi rements.
Quality control charts for qualitative characteristics
Defect chart
cf. DGQ 16-33 (1990); DGQ 11-19 (1994)
Example:
Def ect charts record t he def ective
units, t he defect types and their frequency in a sampling.
Example of reading from the graph
for F3:
Part: Cov•
Defect type
Paint damaoe
Dents
Corrosion
n=9-50=450
Burr
defects in% = I i; • 100%
n
Crackinas
Anole error
Bent
Threads missino
=-2.._ -100% = 0. 66%
450
Sample size n = 50
Test interval: 60 min
D- % Pere. of total
Frequency of defect ii
2 0.44 ,I
Fl
1
1
14 3.11
:
I
F2 1 2
2 1 22 2 2
3 0.66 I
F3
1
1
1 0 .22
F4 1
FS
1 0.22
12 2.66
,
I
F6 2
3 1
3 1
2
1 0.22
1 0.22
FB
1
35
4 6 3 3 3 5 4 3 4
Sample no.
Pareto11 diagram
The Pareto diagram classifies criteria (e. g. defect s) accord ing to type
and frequency and is therefore an
impo rtant aid i n analyzing criteria
and establishing priorit ies.
Example for F2:
Percentage of total defects
14
=35 - 100%= 40 %
11 Pareto - Italian sociologist
1 2 3 4 5 6 7 8 9
Example:
100
t
.;
%
60 +-- --t'""'!lll~""'i- - - + - ---11--- - + - - t - - - - + - 40
I/
~-.,~
.s- 20 -t--~ ✓
-t-- -t - - - + - - - i -- ,--B~
0 /7J
F2
F6
F3
F1
--t--t---
F4
F7
FS
defect types -
Example of graphic represent ation: Dents (F2) and angle error
(F6) together make up approx. 74 % of t he total erro rs.
F5
282
Production engineering: 6.2 Production planning
Job time 11
Structure of types of time for workers
I
Basic setup time
I
t.,.
I
Setup recovery time I
t., = z • fbs/100%
I
I
I
Setup time
I ts = t bs + fsr + tus
~
Unproduc. setup time I
fus=Z• ft,s/100%
I
I
I
Activity time
t ac= ftv + ftf
I
Floor-to-floor time ~
(ff = tac + fw
Job time
T = t, + tp
I
Waiting time
fw
Recovery time
,,. = z • 111/100%
I
I
H
Material unprodue. time t m
lime per unit work
Productio n time ~
fp :c Q•fuw
fuw == ftt+ fu + tre
Unproductive time ~
l u = z • f1t/100%
Personnel
unproduc. time Ip
I
Symbol
~H
z = percentages of the respective floor-to-floor time
Designation
Explanation with examples
T
Job t ime
Tome allowed for manufacturing a lot size
i,
Setup time
Setup for an entire job
basic setup time 1.,.
• set up recovery time fsr
• setup unproductive time fus -
fp
,,.
,.
--
turn on machine
recovery time after strenuous changeover
repair of brief machine malfunction
Production time
Tome allowed for production of a lot size (without setup)
Recovery time
Personnel break time to reduce work-related fatigue
-
Unproductive t ime • job-related interruption time Im • personnel interruption time tp
unforeseen tool sharpening
checking work times, taking care of needs
--
Activity time
Tomes in which the actual job is processed
• variable times ltv
assembly or deburring work
cycle of a CNC program
• fixed t i mes ltf
lw
Waiting t ime
Waiting for the next workpiece in the continuous flow production
q
Job volume
Number of units to be produced for a job (lot size)
tac
Example: Turning three shafts on a lathe
Setup times:
Setup job
Setup of machine
Setup of tool
i.,.
Basic setup time
Setup recovery time
fsr = 4% of tbs
Unproduc. setup time lus = 14% of lb,
Setup time
t.=tm+t.,+~
min
= 4.50
= 10.00
= 12.50
= 27.00
= 1.08
= 3.78
= 31 .86
Production times:
Activity time
Waiting time
Floor-to-floor time
Recovery time
Unproductive time
Tome per unit work
Production time
m in
lac
1w
ltt=lac+lw
f re compens. for in fw
l u=8%of ltt
fuw= ftt+fre+fu
fp=Q·t.,w
= 14.70
= 3.75
= 18.45
-
= 1.48
= 19.93
= 59.79
Job time T: t. + t,, ., 32 m in+ 60 min= 92 min(= 1.53 hr)
11 According to REFA (Verband fur Arbeitsgestaltung, Betriebsorganisation und Unternehmensentwicklung e.V.)
International Association for Work Design, Industrial Organization and Corporate Development
283
Production engineering: 6.2 Production planning
Utilization time 1)
Structure of the types of times for production resources (PR)
PR
basic setup t ime
tbsp
I
I
unproduc'.":etup time
tusP = z. r.,.p/100%
I
I
I
I
Main
productive time
fmp = ftv + ft1
~
l
H
I
floor-t:ri~or time
tffp = tmp + t8 p + t;d
Aux.
~
productive time
tap • f av + fat
I
Idle time
t id
I
Symbol
unprod.'.:~ive time
tup = z • tffp/100%
~
H
PR
setup time
tsP = tt,sp + fusP
Utilization
time
Tu,P = t.p + tpp
~
H
PR time
per unit work
'tuwP = tffP + fup
~
~
PR production time
tpP = q • l uwP
H
I
~
z = percentage rate of the respect ive floor-to-floor time
Designation
Explanation with examples
Tu,P
Utilization time
Time allowed for utilization of a production resource for manufacturing
fsp
Production resource
setup time
Setup of productio n resource for completing an entire job
- clamping equipment on a machine
• PR basic setup time tbsp
• u nproduct ive setup time tusP - optimization of CNC program
tpp
Production resource
production time
Time allowed for t he production t ime of a lot size (without setup)
tuP
Production resource
interruption time
Time in w hich t he production resource is not utilized or additionally utilized;
power outage, un-planned repair work, etc.
tmp
M ain
productive time
Times in w hich the work object is processed according to plan
• variable times ftv
- manual drilling
• fixed t imes ttf
- cycle of CNC program
t•p
Auxiliary
productive t ime
Production resources are prep., loaded or emptied for t he main productive time
• variable times fav
- manual clamping
• fixed times t8 ,
- automatic workpiece change
tid
Id le t ime
Process or recovery related down time, e.g. filling of a magazine
q
Job volume
Number of unit s to be produced for a job (lot size)
a lot size
Example: Milling a contact surface on 20 base plates using a vertical milling machine
min
Production times:
Milling " main productive time tmp
Clamp workpiece " aux. productive time tap
Transport workpiece "' idle time t;d
=
3.52
4.00
1.20
Production resources basic setup time tbsP
Prod. res. floor-to-floor t ime tffP = tmp + tap + t;,,
Prod. res. unproductive time tuP = 10% of tffP
=
=
8.72
0.87
Production resources setup time t sP = t bsP + t usP = 15.54
Prod. resource time per unit fuwP = ftw + fup
Production resource prod. time fpp = q • fuwP
= 9.59
= 191.80
Setup times:
Read t he job order and drawing
Set up and store the surface cutter
Clamp and uncl amp t he cutter
Set up t he machine
=
=
=
=
min
4.54
3.65
3.10
2.84
= 14.13
Prod. res. unproductive s. time tusP = 10% of tbsp = 1.41
=
Utilization time TUtP = tsP + fpp ~ 16 min + 192 m i n = 208 min (= 3.47 hr)
' ' According to REFA (Verband fur A rbeitsgestaltung, Betriebsorganisation und Unternehmensentwicklung e.V.)
International Association for Work Design, Industrial Organization and Corporate Development
284
Production engineering: 6.2 Production planning
Cost accounting
Simple calculation (numerical example)
Overhead 11
Not directly
Surcharge in percent of wage
costs
attributable to a specific product
Direct costs"
directly attributable
to a specific product
Types
of
costs 11
Material costs
Labor cost s
$ 80 000.00 Depreciation
$ 120 000.00 Salaries (incl.
management salaries)
Interest
Other costs
:!: Overhead
Cost calculatio n
$ 50000.00
$ 80000.00
$ 220 000.00 • 100%
- 183.33%
$ 120 000.00
$ 40000.00
$ 50000.00
A surcharge rounded off to
185% is applied to each wage
hour to cover overhead costs.
$ 220000.00
Rate per hour= $/hr 12.00 + 185% = $/hr 34.20
(for independent contracto r invoices; management salaries • profit)
Material costs
of order
Working time 5 hr
X $/hr 34.20
$ 171 .00
11 Costs must be determined periodically for every operation.
Price w itho ut VAT
$ 295.75
Wage hours - 10000 hrs
Labor costs/hr= $/hr 12.00
$ 124.75
Expanded calculation (schematic)
Material costs
+
r-
Material direct costs
Procurement costs
+
Material overhead
Percent of material direct costs,
e.g. purchasing costs, storage
Direct production costs
Production wages attributable to
one product
Design costs
Salaries etc.
+
Equipment costs
Drilling equipment molds etc.
costs, etc.
i
+
~
Production overhead11
Machine costs
Depreciation, interest, occupancy, energy and maint enance
costs
Remaining overhead
Percent of production wages,
e.g. fringe benefits, occupancy,
operating materials, etc.
Material costs
11 If no machine hourly rates are
calculated, these are included
in the production overhead
and increase the surcharge
rate. The overhead surcharge
rates are taken from the operational accounting sheet.
!
+
Special tools
Special drills etc.
+
Out-of-house processing
Heat treatment etc.
!
Special direct costs of
production
Production costs
+
Special direct costs of
production
i
Example:
Manufacturing costs
+
Management and
sales overhead
Percent of manufacturing costs
!
Prime cost
+
Profit
Percent of prime cost
-
i
:t
Raw price
+
Commissions, discounts, rebates
Percent of sales price
!
Sales price without VAT
I
Material direct costs
Material overhead 5%
Production wages 10 hr x $/hr 15.Machine costs 8 hr x $/hr 30.Residual overhead 200% of production wages
Special tools
$ 1225.00
$ 61.25
$150.00
$ 240.00
$300.00
$125.00
Manufacturing costs
Management and sales overhead
12% of manufacturing costs
$ 2101 .25
Prime cost
Profit addition 10% of the prime cost
$ 2353.40
Raw price
Commissions 5% of sales price
S2588.74
$ 136.25
Sales price before VAT
$2724.99
$ 252.15
$ 235.34
1j
285
Production engineering: 6.2 Production planning
Machine hourly rate calculation
Machine hourly rate calculation
Average production overhead does not take into consideration various machine costs attributable to a specific
product. This type of cost aocounting would be misleading.
If machine costs are taken out of production overhead and converted t o hours the machine was utilized, this yields
the machine hourly rate.
Compilation of machine costs
Machine costs are:
• Calculated depreciation
Linear loss of value over the service l ife of the
machine relative to replacement cost
Energy costs
Costs incurred by electricity, natural gas, steam or
gasoline consumption
• Calculated interest
Average interest for capital invested for
the machine
Maintenance costs
Costs for repairs and regular service
• Other types of costs
Costs for tool wear, insurance premiums, disposal of
coolants and lubricants etc.
• Occupancy costs
Cost s incurred by floor and traffic
space of the machine
Machine running time, Machine hourly rates
TRr
Tr
Tsr
TsM
according to VDI Directive 3258
Machine running time
machine running time in hours/period
total theoretical machine time in hours/period
down times, e.g. work free days, work interruptions
etc., usually in% of Tr
times for service and maintenance, usually in% of Tr
I
TRT = h - TsT - TsM
I
Machine hourly rates
sum of machine costs per period (usually per year)
machine costs per hour; machine hourly rate
CMhr
machine fixed costs per year; e.g . depreciation
Ct
C.,/hr machine variable costs per hour; e.g. electrical consumption
c,
CM
CMhr = - + Cv/ hr
TRT
Calculation of machine hourly rate (example)
Tool machine:
Procurement value$ 160 000.00
Power consumption 8 kW
Occupancy costs $/m2 10.00 x mo nth
Additional maintenance $/hr 5.00
Service life 10 years
Cost per kWh $ 0.15
Space req. 15 m2
Normal utilization
TRr = 1200 hr/year (100%)
Assumed interest rate 8%
Base charge $/month 20.00
Maintenance $/year 8 000.00
Actual utilization 80%
What would be the machine hourly rate for normal utilization and 80% utilization?
Type of cost
Calculation
Fixed costs
$/year
Calculated
depreciation
procurement value
$ 160 000.00
=
service life in years
10 years
$ 16 000.00
Calculated
1
interest
'2 procurement value in$ x interest
100%
$ 80 000.- X 8%
100%
=
$ 6400.00
Maintenance
costs
maintenance factor x depreciation - e.g. 0.5 x $ 16 000.00
maintenance is dependent upon utilization.
$ 8000.00
Energy
base charge for power supply $/month 20.00 x 12 mon.
power consumption x energy costs 8 kW x $/kWh 0.15
$ 240.00
costs
Proportional
occupancy costs
Variable
costs
$/hr
$ 5.00
$1.20
$1 800.00
space cost rate x space requirement
= $/m2 10.00 x month x 15 m 2 x 12 months
Total machine costs (CM)
Machine hourly rate (C,.,h,) at 100% utilization =
Machine hourly rate (C,.,1v) at 80% utilization -
ft
TR/ C.,/hr =
S 32 440.00
$ 32 440.00
hr + $/hr 6.20 = $/hr 33.23
1200
___g_
_ $ 32 440.00
_
0.8. TR/ C.,/hr - 0.8 . 1 200 hr + $/hr 6.20 - S/hr 40.00
The machine hourly rate does not include costs for operator.
$6.20
286
Production engineeri ng: 6.2 Production p lanning
Direct costing 11
Marginal costing (wit h numerical example)
Marginal costing takes the market price of a product into consideration. The market
price must at least cover variable costs (lower price limit ). The remainder is the contribution margin. Contribution margins of all products carry the costs of operational
readiness.
R/piece
R
CM
CM/piece
market price; revenue per piece
revenue (sales) of product
contribution margin of product
contribution marg in per piece
C,
Cv
p
Bp
Variable costs (C,,) 21
depends on production
volume
Material costs
</)
1ii
0
0"
Cl.
~
CM = _!!__ _ ~
piece
fixed costs
variable costs
profit or gain
breakeven point
piece
piece
CM = CM • volume
piece
Profit
Fixed costs (Gl
independent of prod uction
volume
Contribution margin (CM)
CM= R/piece - Cv/piece
Labor costs
Energy costs
$/piece 30.00 Depreciation
$/piece 20.00 Wages
$/piece 10.00 Interest
$ 50 000.00
$80 000.00
$40 000.00
r Variable costs
Others C
$/piece 60.00 L Fixed cost s
$ 200 000.00
No. of pieces
produced
Contribution margin
5 000 pieces $ 110.00 - $ 60.00
</)
Q)
Contribution m argin
Revenue of $/piece 110.00
must cover all variable costs
fi rst. The remainder is used to
cover tot al fixed costs and
includes profit.
$30 000.00
= $/piece 50.00
Total contribution margin 5 000 pieces . $/piece 50.00 = $ 250 000.00
Fixed costs
$ 200 000.00
r
Profit
$ 50 000.00
___g__
$ 200 000.00
OOO .
.
Brea keven point 8P =CM/piece= $/piece 50.00 = 4
pieces
t
800000
400000
,,
1:::~
~~~~~s
o
~ 200 000
8
9 /
.
breakeven
$
"""' ~
0
0 "'-- - - ' - - - - - - ' - - - - ' - - 0
2000
4000 piec. 6000
volume
1
~
---J
fixed costs
';_0,,.,
costs or oontribufion margin
0
1
i =.
fi:/~~
2000
~
4000 piec. 6000
volume -
Cost comparison method
In the cost comparison method, t he machine o r facility that
incurs the lowest costs for a g iven production vol ume
should be selected.
Example for 5 000 pieces
M achine 1: C11 = $/year 100 000.- ; Cv, = $/piece 75.00
$/year 100 000.- + $/piece 75 x 5 000 pieces =$ 475 000
M achine 2: C12 = $/year 200 000.00; Cv2 = $/piece 50.00
$/year 200 000.- + $/piece 50.00 x 5000 pieces=$ 450 000
M achine 1 costs > machine 2 costs
p·
r . M
c,,-Cn
iece count 1m1t Hm = Cv1/piece - Cv,/piece
M
$ 200 000.00 - $ 100 000.00
4000 .
lim = $/piece 75.00 - $/piece 50.00 =
pieces
Machine 2 is more economical at volumes above 4000 pieces.
Cost comparison
t
madline 1 costs
$475000.-
$
~
.,8 400000
C
:i,
piece count limit M,;,,,
600000
"'E 200000
I
i
! machine 1
I/ ~
machme2
Z i--!
i i
0 ,____.____._ __,__ _.__ ......_ _..__ __
0
2000
4000
volume -
6000 pieces
11 Direct costing separates costs into fixed costs (costs of operating readiness) and variable costs (dir~t costs).
21 Variable costs are calculated for each job and compared to revenue.
287
Production engineering: 6.3 Machining processes, Productive time
Turning, Thread cutting
Straight cylindrical turning and facing at constant rotational speed
lo; overrun idle travel
L travel
feed per revolution
n rotational speed
number of cuts
Ve cutting speed
productive time
out side diameter
d, inside diameter
fp
d
dm mean diameter11
I
fsi
workpiece length
starting idle
Productive time
L •i
t =P
n •f
Calculating travel L. mean diameter ~ and rotetional speed n
Facing
Straight cylindrical turning
Solid cylinder
with shoulder
without shoulder
with shoulder
without shoulder
L
Hollow cylinder
L
L = I+ lsi + Joi
L =d-d'+l ·
2
SI
L = ':!.
2 + 1.,·
L =I+ lsi
d
n =~
rr -d
m
=d+d,_ n = ~
2 '
n•dm
1 > Use of mean diameter dm leads to higher cutting speeds. This ensures acceptable cutting conditions for small
diameters (inside area}.
Example:
Straight cylindrical turning without shoulder, /= 1240 mm;
L = I +Is;+ lo; = 1240 mm+ 2 mm +2 mm= 1244 mm
ls, = 10 , = 2 mm; f= 0.6 mm; Ve= 120 m/min;
V
120 ~
t
rr-0.16m
min
n = _ e_ = ----1!l!!L ::t: 239 -
i= 2; d = 160 mm;
n-d
L = ?; n = ? (for infinitely variable speed adjustment}
t =!::..:...!.._=
fp =?
P
n. f
1244mm- 2
~ ,7.4min
1
239 --:- • 0.6 mm
m,n
Thread cutting
Productive time
P thread pitch
n rot ational speed
s no . of starts
h thread depth
a0 cutting depth
Ve cutting speed
t0 productive t ime
total t ravel of t hread cutting tool
thread length
Is, starting idle
/ 0 i overrun idle travel
number of cuts
L
L •i •s
t = --p
P-n
Number of cuts
Example:
.
h
t=-
Threads M 24;/ - 76 mm; is; = lo; = 2 mm;
L= I+ Is,+ 1,. = 76 mm +2 mm + 2 mm = 80 mm
f = 0.6 mm; Ve = 6 m/min; i= 2; Bp= 0.15 mm;
h = 1.84mm;P=3mm;s=1;
n
Ve
n -d
6~
m in
1
n-0.024m~ aomin
L•i ·s
tp = P - n =
80 mm • 13 • 1
1
3mm -80 min
4.3min
8p
288
Production eng ineering: 6.3 Machining processes, Productive time
Turning
Straight cylindrical turning and facing at constant cutting speed
If the rotational speed must be l imited for safety reasons by inputting a rotational speed lim it ni;m, a turning diameter of d < transition diameter d1 is turned at
constant rotational speed (page 287).
Transition diameter
di
Ve
transition diameter
cutting speed
d
number of cuts
outside diameter
n1im
rotational speed limit
d,
inside diamet er
t = n • d8 • L • i
Ip
productive time
ap
cutting dept h
p
de
L
effective diameter
ls1
starting idle
travel
101
overrun idle t ravel
f
feed
Productive time
••,,.;:::•
I
Number of cuts for
_
-
Calculating travel L and effective diameter d,,
Straight cylindrical turning
Ve· f
Nm<"•
2 • Bp
Facing
"'
"'t dd1.. ,_,...,.._.....,_
~ de
.,
t-1t---><.~
~
E
~ d1 >------.
dg t - - - -+-1
~ dt 0--1-----+---"<
'ii
n t1m
num
rotational speed n without shoulder
with shoulder
J--i
J--i
~o'"'
~o"'
J
rotational speed nSolid cylinder with
Hollow cylinder
shoulder
)
I
I oi
I,;
L
L = I+ lsi + Joi
L=d - d,+1 ·
L =I+ fsi
Example:
2
"
Facing; 15; = 1.5 mm; Ve= 220 m/min; f = 0.2 mm;
i • 2; num = 3000/min; di=?; L = ?; de = ?; Ip = ?
220000 mm
min
" • "im n · 3000 ..2._
d, = ~=
23.3 mm(d1 > d,)
min
L = d-d, +I,;= 120 mm -65mm + l .5 mm = 2Smm
2
2
d = d+d, / . 120mm+65mm 1 5
•
+ sr
+ • mm== 9 4mm
2
n •de• L • i
Ve • f
2
n -94mm • 29mm • 2
220000 m'."' • 0.2 mm
min
0. 39min
289
Production engineering: 6.3 Machining processes, Productive time
Drilling, Reaming, Counterboring, Planing, Shaping
Drilling, reaming, countersinking
Cut ,.
0
le
so·
0.6, d
11s·
130°
0.3 • d
0.23 • d
140°
0.18- d
Productive time
tp
productive time
L
t ravel
d
tool diameter
f
feed per revolution
bore depth
n
rotational speed
Ve
cutting speed
lo;
st arting idle
overrun idle travel
le
lead
0
number of cut s
drill point angle
lsi
l
~n -2.
n-d
Calculating travel L
for drilHng and reaming
for counterborlng
T hrough hole
d
Blind hole
d
d
d
d
L = 1+le+ ls;
L = 1 + le + 15 ; + lo;
L = 1+ ls;
Example:
Blind hole of d= 30 mm;
I= 90 mm; f= 0.15 mm;
n = 450/m in; i = 15; I,; = 1 mm;
o =130°; L =?; t0 = ?
l =I+ le+ I,; = 90 mm + 0.23 • 30 mm + 1 mm s 98 mm
L -i
tP
n.f
98mm-15
1
450 -,- - 0.15mm
21.78min
min
Planing and shaping
fp
productive time
w0
overrun width
I
workpiece length
n
no. of do uble strokes per minute
fsi
starting idle
overrun idle travel
Ve
cutting speed. approach speed
Vr
return speed
stroke length
width of workpiece
W
f
planing, shaping w idth
f eed per double stroke
le,;
L
w
w.
approach width
Productive time
number of cuts
Calculating stroke length l and planing width W
Workpieces without shoulder
Workpieces with shoulder
L =1 + ls; + 10 ;
L = 1 + ls; + 10 ;
W = w+ Wa
290
Production engineering: 6.3 Mac hining processes, Productive time
Milling
Ip
productive t ime
I
workpiece length
Productive time
ap cutting depth
a. engagement (milling width)
approach
1.
Feed per revolution of milling cutter
I
lc,; overrun idle travel
lsi starting travel
L
total travel
d
cutter diameter
f= ft. N
Feed rate
rotational speed
n
feed per revolution
ft
feed per tooth
Rotational speed
N number of teeth
Ve
cutting speed
Vt
feed rate
number of cuts
Total travel L and starting travel lst in relation to the mHling process
Face milling
Peripheral
face milling
eccentric
centric
a. >0.5 • d
a.,< 0.5 . d
I,
I,
t,
L = I + la + /0 i + /51
L = I + 0.5 • d + 18 + 10 ;
1,, = 0.5 • f d2 -
a.2
Example:
Face m illing (see left illustration): N = 10, f1 = 0.08 mm,
Ve= 30 m/min, /8 = /0 ; = 1.5 mm, i = 1 cut
Sought after: n; vt; L; Ip
30 _m_
n
Solution: n
Vt
- ~-~
- 119_!_
" . d :r • 0.08 m
min
-
n • f, • N - 119
.2_
•0.08 mm . 10 • 95.2 m'."
mm
mm
~ - 30 m m • 0.375, it follows that a0 < 0.5 • d
d
L
80mm
=I+ 1a +/oi +/st
1., • .Ja. • d- a~ • b omm. 80 mm - (30 mm)2 • 38.7 mm
260
L
=260mm + 1.5 mm+ 1.5 mm + 38.7 mm - 301.7mm
fp • t,_-j_ . 301.7 mm • 1 • 32 min
Vt
95.2mm
mon
291
Production engineering: 6.3 Machining processes, Productive time
Grinding
Straight cylindrical grinding
t0
L
n
f
v,
d1
d
a0
/
w0
/0 i
r
r
Workpiece rotational
productive time
t ravel
number of cuts
workpiece rotational speed
workpiece feed per revolution
feed rate
initial diameter of workpiece
final diameter of workpiece
cutting depth
workpiece length
grinding wheel width
overrun idle travel
grinding allowance
Pr
,.__o_d_u_c_t::
_e_
= t_in
_
~ -~-~_ _.....,I
n = _l,'.L_
rr . d,
Number of cuts
for external straight
for internal straight
grinding
grinding
i = d- d, + 21>
2 • Bp
11 2 cuts to spark out. for lower t olerance grades addi•
t ional cuts are necessary
Calculating travel L
Workpieces w itho ut shoulder
Workpi eces
w ith shoulder
L
2·Wg
l-.-
-"----
--1---'4- ~
3
3
"'g
---=--- - - - - - - - --i~-1,; =3
L = l -~- w.
3
g
Feed for roughing f s 2/ 3 • w9 to¾. w9 ;
feed for finishing f = ¼ • w9 to ½ • w 9
Surface grinding
rP
productive time
I
workpiece length
transverse feed per stroke Number of cuts
no. of strokes per minute
n
i = .!.+ 21>
start. idle, overrun idle travel v, feed rate
Bp
L travel
number of cuts
w width of workpiece
grinding allowance
w0 overrun width
w9 grinding wheel width
W grinding width
aP
cutting depth
No. of strokes
I
I
v,
n=L
Productive time
11
; (w
,+1)
f p = 7; •
2 cuts to
spark out
Calculating travel L and grinding width W
Workpieces w ithout shoulder
,,
L=I + 2 • I;
Workpieces with shoulder
I,
I;
l; • 0.04 · I
h•
Transverse feed for roughing f = 2
I;
W = w-~-w.
3
g
L =I + 2 • I;
l;-0.04 . /
w9 to 4/ 5 • w9 ;
feed for finishing f = ½ ·
w9 to 2/ 3 • w9
W = w - ~ • Wg
3
292
Production engineering 6.3 Machining processes, Machining coolants
Machining coolants for cutting metals
Terminology and applications for machining coolants
tfype of machining
Effect
Group
coolant
SESW
machining
coolants
1)
Grinding
Organic or synthetic
materials in water
Machining at high
cutting speed
Emulsions
2%- 20% emulsive
(soluble) machining
coolant in water
Good cooling effect, but
low lubrication,
e.g. machining (turning, m illing,
drilling) of easy-to-machi ne
m aterials, at high cutting speed;
for hig h working temperatures;
susceptible to bacterial or fungal
attack
Cutting oil
M ineral oils wit h polar
additives (greases or
synthetic esters) or EP
additives 21 t o increase
lubricating performance
For lower cutting speed,
higher surface quality, for difficult-to-machine materials;
very good lubrication and
corrosion protection
¥
"'
i
C
-~
.!!
0
.a
""'
C
"iii
iii
.5
"
.E
0
.a
..! !.."'
SN
machining
coolants
insoluble in
water
2)
Inorganic mat eri als
in water
Solutions/
dispersions
SEMW
machining
coolants
(oil in water)
Applications
Composition
-
¥
i
"'
.E
cf. DIN 51385 (1991-06)
Explanation
C
"
·v '
Machining coolants may be hazardous to health (page 198) and are therefore only used in small quantities.
EP = Extreme Pressure; additives to increase accept ance of high surface pressure between chip and tool
Guidelines for selecting coolants
Manufacturing process
Steal
Cu,
Cu alloys
Al,
Al aHoys
Mg alloys
maleable cast iron
Cast iron,
Roughing
emulsion,
solution
dry
dry
emulsion,
cutting oil
dry,
cutting oil
Finishing
emulsion,
cutting oil
emulsion,
cutting oil
dry,
emulsion
dry,
cutting oil
dry,
cutting oil
emulsion,
solution,
cutting o il
dry,
emulsion
dry,
emulsion,
cutting oil
cutting oil,
emulsion
dry,
cutting oil
emulsion,
cutting oil
dry,
emulsion
dry,
cutting o il,
emulsion
cutting oil,
emulsion
dry,
cutting o il
cutting oil,
emulsion
dry,
cutting oil
dry,
cutting oil
cutting oil
cutting oil
emulsion
dry,
emulsion,
dry,
cutting oil
cutting oil,
emulsion
dry,
cutting o il
cutting oil,
emulsion
emulsion
cutting oil
cutting oil
cutting oil
Hobbing,
gear shaping
cutting oil
cutting oil,
emulsion
-
-
-
Thread cutting
cutting oil
cutting oil,
emulsion
cutting oil
cutting oil
cutting o il,
dry
Grinding
emulsion,
solution,
cutting oil
solution,
emulsion
emulsion,
solution
emulsion
. -
Honing, lapping
cutting oil
cutting oil
-
-
Turni ng
Milling
Drilling
.
1 ~:.
l
-,.
►
Reaming
Sawing
Broaching
ii.
~
-
293
Production engineering 6.3 M achining processes, M achining coolants
Hard and dry machining. High-speed milling, MQCL
Hard turning with cubic boron nitride (CBN)
Mat erial
hardened st eel
HRC
Turning process
$
External turning
Cutting
speed
45-58
Internal t urning
Exlernal t urning
> 58-65
Internal turning
Feed f
mm/revolution
Cutting depth
lip
mm
60-220
0.05-0.3
0.05-0.5
60- 180
0.05- 0.2
0.05- 0.2
50- 190
0.05- 0.25
0.05- 0.4
50- 150
0.05-0.2
0.05-0.2
Ve m/min
Hard milling w ith coated solid carbide (VHM) tools
Material
hardened steel
Cutting
speed
HRC
m/min
working
engagement
Bemex
mm
t o 35
80-90
0.05 • d
36- 45
60- 70
0.05 • d
46-54
50- 60
0.05 • d
~ib
Ve
Feed per tooth ft in mm
for lathe diameter d in mm
2- 8
>8-12
> 12-20
0.04
0.05
0.06
0.03
0.04
0.05
High-speed cutting (HSC) w ith PCD
Cutting
speed
Material group
10
Ve
Cutter diameter d in mm
20
,.
a.
,.
a.
m/min
mm
mm
mm
mm
280- 360
210-270
0.25
0.09-0.13
0.40
0. 13- 0.18
r-;;;,
> 1100- 1400
-:.v7
Hardened st eel
48- 55 HRC
> 55-67 HRC
90- 240
75-120
0.25
0.20
0.09- 0.13
0.40
0.35
0. 13 - 0.18
EN-GJS > 180HB
300- 360
0.25
0.09- 0.13
0.40
0. 13 - 0.18
Titanium alloy
90- 270
0.20- 0.25
0.09- 0.13
0.35- 0.40
0.13- 0.18
Cu alloy
90-140
0.20
0.09-0.13
0.35
0. 13-0.18
Quenched and
tempered steels
Cutting tool material and machining coolant for:
Al materials
Iron materials
High-alloy steels
Cast i ron
Cast alloy
Wrought alloy
Drilling
ToN, dry
ToAIN11, MQCL
ToN, dry
ToAIN, MQCL
ToAIN, M CCL
Reaming
PCD, MQCL
_ 2)
PCD, MCCL
ToAIN, PCD,
MQCL
ToAIN, MQCL
Milling
ToN, dry
ToAIN, MCCL
ToN, dry
ToAIN, dry
ToAIN, MQCL
Sawing
MQCL
MCCL
_ 2)
ToAIN, MQCL
ToAIN, MQCL
-~
U
-
Steel Rm
850- 1100
o/
;4.:1-4~
-
Dry machining
Process
Minimum quantity of machining coolant (MQCL or MOL)3
Dependency of MQCL volume on
machining method
milling
drilling
turning
grinding
reaming
lapping
honing
Increasing lubrication requirement
11
-
-
Titanium alum inum nitride (super hard coat ing)
Suitability of minimum quantity lubrication
for the material t o be machined
Al alloy castings
Ferritic steel
Cu alloys
Pear1ilic steel
Mg alloys
Al wrought alloys
Cast iron materials
Stainless steels
-=:::::::::::
I
Increasing material suitability
21 Not normally done
3 1 Generally 0.01- 3 I/hr
294
Production engineering: 6.3 Machining processes, Tools
Cutting tool materials
Designation of hard cutting tool materials
Example:
Code letter (see the t able below)
cf. DIN ISO 513 (2005-1 1)
1 - - - - - HC
-
K
20 - - ----<
Application group
Cutting main group
M (yellow)
Cutting tool
material group
K 11
Components
H (gray)
Properties
Applications
Uncoated hard metal, main component High hot hardness up to
1000 •c, high wear resistis tungsten carbide (WC)
ance, high compression
HW Grain size> 1 µm
strength, v ibrat ion
HF
Grain size< 1 µm
damping
Indexable inserts for
drilling. turning and
milling tools, also for
solid hard metal tools
HT
Indexable inserts for
lathe and milling tools
for finishing at high
cutting speeds
Uncoated hard metal of titanium Like HW, but with high
carbide (TiC), titanium nitride
cutting edge stability,
(TiN) or of both. also called
chemical resistance
cermet.
HC
Hard metals
HW and HT, but coated with
titanium carbonitride (TiCN)
Increase of wear resistance
without reducing toughness
CA
Cutting ceramics, primarily of
aluminum oxide (Al2 0 3 )
High hardness and hot
hardness up to 1 200 •c
sensitive to severe tempe-
Inc reasingly replacing
the uncoated hard
metals
Cutting of cast iron,
usually without cooling
lubricant
rature changes
CM
Mixed ceramics with aluminum
oxide (Al 20 3 ) base, as well as
other oxides
CN
Silicon nitride ceramics, primari- High toughness, high
Tougher than pure ceramics, Precision hard turning
better resistance to
of hardened steel,
temperature variations
cutting at high cutting
speed
ly of silicon nitride (Si3 N4 )
cutting edge stability
Cutting of cast iron at
high cutting speed
CR
Cutting ceramics with aluminum oxide (Al 20 3), as a main
component, reinforced
Tougher t han pure ceramics
due to reinforcement, improved resistance against
Hard turning of hardened steel, cutting
at high cutting speed
cc
Cutting ceramics such as CA,
CM and CN, but coated with
titanium carbonitride (TiCN)
temperature variations
Cutting ceramics
w ithout reducing tough-
Increasingly replacing
the uncoated cutting
ness
ceramics
Increase of wear resistance
Cubic crystalline boron nitride (BN),
Very high hardness and
also designated CBN or PCB or ·super- hot hardness up to
hard cutting tool material"
2000°c, high wear
Boron nitride
BL
With low boron nitride content
BH
With high boron nitride content
BC
BL and BH, but coated
Cutting tool material of carbon (C),
also designated CBN, PCB or "superhard cutting tool material"
Diamond
DI
Tool steel2 '
DP
Polycrystalline diamond (PCD)
OM
Monocrystalline diamond
HS
High-performance high-speed
steel with alloying elements
tungsten (W), molybdenum (Mo),
vanadium (V) and cobalt (Co),
usually coated with titanium
nitride (TiN)
11 Code letters according to DIN ISO 513
21 Tool steels are not included in DIN ISO 513 but in ISO 4957
Dressing of hard materials (HRC > 48) with
high surface quality
resistance, chemical
resistance
High wear resistance,
very brittle, temperature
resistance up to 600 •c.
reacts with alloying elements
Cutting of non-ferrous
metals and Al alloys with
high silicon content
High toughness, high
bending strength, low
hardness, temperature
resistant up to 600 •c
For severe alternating
cutting forces, machining
of plastics, for the
cutting of Al and Cu
alloys
295
Productio n eng ineering: 6.3 Machining processes, Tools
Cutting tool materials
Classification and application of hard cutting tool materials
Code letter
Application
group
color code
cf. DIN ISO 513 (2005-11)
Cutting tool material
properties11
Possible cutting
parameters11
Workpiece - material
Wear
resistance
Toughness
Cutting
speed
Feed
Steel
P01
P10
P20
P30
P40
P50
P05
P15
P25
P35
All types of steels and cast
steels, w ith the exception
of stainless steel w ith
austenitic structure
P45
Stainless steel
M01
M
yellow
M 10
M20
M30
M40
M05
M1 5
M25
Austenitic and austenitic
ferritic stainless steels and
cast steels
M35
Cast iron
K01
K10
K20
K30
K40
N01
N10
N20
N30
S01
S10
S20
S30
K05
K15
K25
Cast iron with flake
and spheroidal graphite
malleable cast iron
K35
N05
N 15
N25
S05
S15
S25
Aluminum and other
non-ferrous metals
(e. g. Cu, Mg).
non-ferrous materials
te. g. GPR, CFRPI
High-temperature special
alloy on the basis of iron.
nickel and cobalt,
titanium and titanium
alloys
Hard materials
H01
H
H10
gray
H20
H30
H05
H15
H25
Hardened st eel,
hardened cast iron
materials, cast iron
for ingot casting
11 Increasing in direction of th e arrow
~ w~ w
LJ ~ LJ u
~ w~ i
~ ~ ~ w
~ ij ~ ~
~ w~ i
296
Production engineering: 6.3. Machining processes, Tools
cf DIN ISO 1832
12005 111
Designations for indexable inserts for cutting tools
<
60°
l;os
Designation examples:
Indexable carbide insert with rounded corners (DIN 4968) without mounting hole
;,.<
<
s
~
wA
-~
'· I /
-~.,..
Insert DIN
Equilateral and
non-equiangular
an to the insert
® Tolerance class
Standard number
16
03
08
T
I
I
I
I
I
oO
Ho
s
E
N
15
04
~ ~~~ ~ ~
_J
po
-
P20
Ui ~
sD
Vf
Ro
I
- P10
TD
0
c<;;r
E { : }5°
0 750
M{!;o
A E] Bso
we;•
B E] B2•
K ~5°
Lo
Many company specific shapes are used in addition to standardizied shapes.
A
B
C I D I E I F I G I N I p I
0
7
30
I
l
50
I rl
I 20° I 25° I 30° I
15°
I
Allow. dev. for
A
Control dim. d
± 0.025
C
H
I • 0.013
± 0.025
± 0.01 3
Contro l dim. m
± 0.005
± 0.013
± 0.025
± 0.025
J
Control dim. m
l
L
K
I ± 0.013
± 0.025
± 0.025
F
A
0:00:0
Q
M
O!D DIJ
u
acJ
K
w
T
± 0.025
± 0.025
± 0.09
u
N
± 0. 16
± 0.08 ... ± 0.20
± 0.25
± 0.09
± 0.13
on
D:DD:D
ODDID
DD
R
G
± 0.025
± 0.05 ... ± 0.15
c=JC=::J
~ i:==:J
i:==::i
N
E
M
± 0.05 ... ± 0.15
"0.005
I 11 ° I special data
0°
F
Insert thickness s
Insert thickness s
@ Insert size
N
I
I I I I I I
p
-
6590
Control dim. d
clamping
features
G
I
I
Insert DIN
Allow. dev. for
© Facesand
N
I
Indexable carbide insert w ith wiper edges (DIN 6590) without mounting hole
Non-equilateral and
L
equiangular
A, B, K non-equiangular
@ Normal clearance angle
T
I
Q) Basic shape
Equilateral, equiangular
and round
-
4968
± 0.025
aoao
B
H
J
0::00:D
DD
!:JD
X
Special data
C
The cutting length is the lo nger cutting edge for non-equilateral inserts, for round
inserts it is the diameter.
@ Insert thickness
Insert thickness is given in mm w ithout decimal places.
(J) Cutting point
Code number multiplied by fact or 0.1 = corner radius re
configuration
A
1. Letter symbol for cutting edge angle x,
of main cutting edge
D
E
F
p
45° 60° 75° 85° 90°
l A IBIC ID E F G N p
a'n on w iper edge (corner c hamfer) I 3° I 5° I 7° I 15° 20° 25° 30° oo 11°
2. Letter symbol for clearance angle
® Cutting point
F sharp
I
E rounded
T chamfered
l
S chamfered
rounded
K double
chamfered
® Cutting direction
R right hand cutting
@) Cutting tool material
Carbide with machining applicat ion group or cutting ceramic
L left hand cutting
I
p doub. chamfered
and rounded
N right and left hand Cutting (neutral)
297
Production engineering: 6.3 Machining processes, To ols
cf DIN 4983
12004 07)
Designation of indexable and short indexable insert holders
2lJ
Designation example:
Holder DIN 4984
/1
~t~ l lilil■•u J 1
Ill
T
- C
w N
R
32 25
M 16
of
holder - ~ ~
standard
holding method
insert
shape11
design of holder
~~
normal clear. angle of insert 11an -
]~1
-·•·
type of holder
height of cutting edge h 1 = h2 in mm shank width w in mm
length of holder / 1 in mm
indexable insert size11
1) For indexable inserts, see page 296
Designation
Insert
hold ing
Configurations
Letter symbol
C
s
p
M
~ ~ ~ ~~
Holding of
indexable insert
Design of holder
straight
~
offset
ct]
Type of holder
Length
of holder
=>
clamped
from above
clamped from
above and
from hole
clamped from
hole
Letter symbol
A
B
D
E
M
N
V
Side cutting
edge angle K,
90°
75°
45°
&0·
so·
53•
72.5°
Type of holder
J
R
T
90° 107.5° 93°
75°
&0·
G
H
countersink hole
and screw
straight
offset
Letter symbol
C
F
K
s
u
w
Side cutti ng
edge angle K,
90°
90°
75°
45°
93°
so· as·
Type of holder
straight
Letter symbol
R
right ho lder L
Letter symbol
A
B
C
D
E
F
G
H
J
K
L
M
11 in mm
32
40
50
60
70
80
90
100
110
125
140
150
Letter symbol
N
p
Q
R
s
T
u
V
w
X
y
/ 1 in mm
160
170
180
200
250
300
350
400
450 Cust lengths 500
y
Fo rms D and S also
available w it h round
indexable inserts
of basic form R
offset
neutral
(bot h sides)
left holder N
Holder DIN 4984 - CTWNR 3225 M 16: holder w ith square shank. clamped above (C), triangular
indexable insert (T), K, = 60° (W), a 0 = 0° (N), right hand (R), h 1 = h, = 32 mm, b = 25 mm, / 1 =
150 mm (M), /3 = 16 .5 mm (16).
298
Production engineering: 6.3 Machining processes, Forces and power
Forces and power in turning and drilling
I
Turning
Fe cutting force in N
chip section in m m 2
a0 cutting depth in m m
f feed per revolution in mm
h chip thickness in mm
0
" cutting edge angle in degrees ( )
C correction fact or for the cutting
speed
Ve cutting speed in m/min
kc specific cutting force in N/mm2
(page 299)
P, cutting power in kW
P1 drive power of the machine tool in kW
'I efficiency of t he machine t ool
Correction factor C for
the cutting speed
A
Cutting speed
Ve in m/min
C
10-30
1.3
31-80
1.1
81- 400
1.0
Chip section
Cutting force
Example:
A shaft of 16MnCr5, a0 = 5 mm, f = 0.32 mm, v, = 110 m/min, " = 75°
Sought after: h; k, ; C; A; F, ; P1 w ith q = 0.75
Solution: h - f • sin x = 0.32mm - sin 75° -0.31mm
kc = 3735N/mm2 (see table on page 299),
C - 1.0 (see correction fact or t able)
A - a0 - f - 5 mm - 0.32 mm - 1.6mm2
N
F, • A - k, - C - 1.6mm2 • 3735 mm2 - 1.0 - 5976N
P, = ~ =F, • v,
'1
'1
Chip thickness
I
h = f- sinx
Cutting power
5976N-110m = 14608 W= 14.6kW
0.75 - 60s
Drilling
F,
z
A
d
f
f,
o
h
C
Ve
kc
P,
P1
'I
cutting force per edge in N
num ber of cutting edges (twist drill z = 2)
chi p section in mm2
drill diameter i n mm
feed per revolution in mm
feed per cutting edge in mm
drill po int angle in degrees (0 )
chip thickness in m m
correction factor fo r t he cutting speed
cutting speed in m/min
specific cutting force in N/mm 2 (page 299)
cutting power in kW
d rive power of the machine tool in kW
efficiency of the machine tool
Example:
Material 42CrMo4, d = 16 mm, v, = 28 m/min, f = 0.18 m m, o = 118°
Sought after: h; k, ; C; A; F, ; P,
0 8
Solution: h - ~ - sin ':!. - •1 mm - sin 59° - 0.08 mm
2
2
2
kc - 6265 N/mm2 (see table o n page 299)
A - ~ . 16mm-0.18 mm _ 0_nmm 2
4
4
C • 13 (see correction factor t able)
N
Fe - 1.2 - A - k, - C - 1.2 -0.nmm 2 -6265mm2 -1.3 - 7037N
Pc - ~
. 2. 7037 N. 28m - 3284 N. m - 3284W - 3.3WI
2
60s - 2
s
11 The specific c utting force values ke are assessed in t urning t ests.
The conversion to drilling is realized v ia the f actor 1.2 in the formula.
Correction factor C for
the cutting speed
Cutting speed
Ve in m/min
C
10- 30
1.3
31 - 80
1.1
i~
Chip section per cutting
d •f
A=4
Cutting force per cutting edge11
I
Fc= 1.2 - A- kc · C
Chip thickness
h = !_·Sin~
2
2
Production engineering: 6.3 Machining processes, Forces and power
299
Specific cutting force
l
-
~ - - - - ~~---A =1mm2
'\_-
,,.
ke
h
..!...
/2
The specific cutting force ke is the the force that is required to separate a chip
w ith a cross section of A= 1 mm' from a workpiece. The values are assessed in
t urning t ests and form the basis of the calculation of the cutting fo rces and the
d rive power in chip-removing machining processes.
'()
"'""'
specific c utting force N/mm 2
chip thickness in mm
f
feed in mm
ap
cutting depth i n mm
X
angle of incidence in degrees (0 )
The chip thickness h depends on the applied machining process.
Calculat ion of chip thicknesses: pages 298 and 300.
c:::;::::::::::
Standard values for the specific cutting force 1>
Mat erial
Specific cutting force ke in N/mm2 for the chip thickness h in mm
0.05
0.08
0.10
0.15
0.20
0.25
0.30
0.40
0.50
0.80
1.00
1.50
2.00
S235
E295
E355
3850
5635
4565
3555
4990
4215
3425
4705
4055
3195
4235
3785
3040
3930
3605
2930
3710
3470
2840
3535
3365
2705
3285
3205
2605
3100
3085
2405
2740
2850
2315
2585
2745
2160
2330
2560
2055
2160
2340
C15,C15E
C35, C35E
C45,C45E
4575
4425
4760
4125
3895
4210
3925
3670
3975
3590
3290
3575
3370
3045
3320
3210
2865
3130
3085
2725
2985
2895
2525
2770
2755
2375
2615
2485
2095
2315
2365
1970
2185
2165
1765
1965
2030
1635
1825
C60, C60E
11SMnPb30
16MnCr5
4750
2675
5950
4365
2460
5265
4190
2360
4965
3895
2195
4470
3700
2085
4150
3555
2000
3915
3440
1935
3735
3265
1840
3465
3135
1765
3270
2880
1625
2895
2770
1560
2730
2575
1450
2455
2445
1375
2280
20MnCr5
18CrMo4
34CrAIMo5
5775
4955
4930
5135
4575
4360
4855
4405
4115
4385
4110
3705
4085
3915
3435
3860
3770
3245
3690
3655
3095
3435
3480
2870
3245
3350
2710
2885
3095
2395
2730
2975
2260
2475
2780
2035
2295
2645
1890
42CrMo4
50CrV4
102Cr6
7080
6290
5895
6265
5565
4910
59 15
5250
4500
5320
4725
3840
4940
4385
3435
4660
4140
3145
4445
3945
2930
4125
3660
2620
3890
3455
2400
3445
3060
2000
3250
2885
1835
2925
2595
1565
2715
2410
1400
90MnCrV8
X210CrW12
X5CrNi18-10
5610
5155
5730
5080
4565
5190
4850
4305
4955
4455
3875
4550
4195
3595
4285
4000
3395
4085
3850
3235
3935
3625
3005
3705
3460
2835
3535
3135
2510
3200
2990
2365
3055
2745
2130
2805
2585
1975
2640
X30Cr13
TiA16V4
5155
3340
4565
3025
4305
2890
3875
2655
3595
2495
3395
2385
3235
2295
3005
2160
2835
2060
2510
1985
2365
1780
2130
1635
1975
1540
GJL-150
GJL-200
GJL-400
2315
2805
4165
2100
2495
3685
2005
2360
3480
1840
2130
3130
1730
1985
2905
1650
1875
2740
1590
1790
2615
1500
1670
2425
1430
1575
2290
1295
1405
2025
1235
1325
1910
11 35
1200
1720
1065
1115
1595
GJS-400
GJS-600
GJS-800
2765
3200
5500
2455
2955
4470
2325
2845
4055
2100
2655
3390
1955
2530
2985
1845
2435
2710
1765
2360
2500
1645
2250
2200
1555
2165
1995
1380
2000
1625
1305
1925
1470
1180
1795
1230
1100
1710
1085
AICuMgl
AIMg3
AC-AISi 12
2150
2020
2150
1930
1810
1930
1835
1725
1835
1670
1570
1670
1565
1470
1565
1485
1395
1485
1425
1340
1425
1335
1250
1335
1265
1190
1265
1135
1065
1135
1080
1015
1080
985
925
985
920
865
920
MgAl8Zn
CuZn40Pb2
CuSn7ZnPb
895
1740
1760
820
1600
1565
785
1535
1480
725
1425
1335
690
1355
1245
660
1300
1175
635
1260
1125
605
1195
1045
580
11 50
990
530
1055
880
505
1015
830
470
945
750
445
895
700
11 The st andard values apply to tools w ith hard metal edges. Tool wear increases the specific cutting force by
approximately 30 %. The values specified in the table include this addition. For turning, drilling (page 298) and
milling processes (page 300), the effect of the cutting speed on the standard val ues for the specific cutting force
is considered via correction factors C in the upper table.
300
Production engineering: 6.3 Machining processes, Fo rces and power
Forces and power in milling
Face milling
Fe cutting force per tooth in N
A chip section per tooth in mm2
ap cutting depth in mm
a. engagement (milling width) in mm
h chip thickness in mm
feed per revo lution in mm
f, feed per t oot h in mm
d cutter d iameter in mm
Ve cutting speed in m/min
v, feed rate i n mm/min
N number of teeth
Ne number of teeth engaged
,p angle of engagement in degrees (0 )
kc specific cutting force in N/mm 2
(page 299)
C correction factor for the
cutting speed
Pc cutting power in kW
P1 d rive power in kW
1/ effective power of the machine
t ool
Example:
Feed rate
Chip cross section
per tooth
Cutting force per tooth 11
I
Fe = 1.2 • A • kc • C
Chip thickness
ford= (1.2-1.6)· a.21
Material 16MnCr5; d • 180 mm; N • 12; a0 = 120 mm; ap = 6 mm;
f, a 0.10 mm; Ve = 85 m/min; ~ = 0.8.
Sought after: A; h; kc; Fe; ,p; N0 ; Pc; P1
A - ap• f,- 6mm • 0.1 mm- 0.6mm 2
h -f, - 0.lmm
N
k 0 - 4965 mm• (table on page 299)
Solution:
Fe • 1.2 ·A· k0 • C; C = 1.0(table of correction factors C)
N
F0 - 1.2-0.6mm2-4965mm2 • 1.0 m m - 3575N
Number of teeth
180
mm - 1.5; ,p . 113° (angle of engagement ,p table)
!!.. .
120mm
a0
N • N, L a 12. 83" -2.8
•
360°
360"
p_c • N • F. • v • 2.8 · 3575N · S5m - 14181 N -m-14.2kW
e c c
60s
s
P, . fl. . 14.2kW • 17.8 kW
'I
Cutting power
0.8
Angle of engagement ,p
d/a0
ip in °
d/a0
1/J in °
d/a0
,pin °
83
1.20
113
1.35
96
1.50
1.25
106
1.40
91
1.55
80
1.30
100
1.45
87
1.60
77
diameter
-a.d -cutter
engagement
Correction factor C
for the cutting speed
Cutting speed
Ve in m/min
C
30-80
1. 1
81-400
1.0
11 The values of the specific cutting force kc (page 299) are assessed in turning tests. The conversion to milling is
achieved via the factor 1.2 in the formula.
21 In o rder t o ensure favo rable cutting conditions, the cutter diameter should be selected in the range
d = (1.2-1.6) · a0 •
301
Production engineering: 6.3 M achining processes, Standard values
Drilling
Twist drills of high-speed steel IHSSI
Type11
Helix angle
cf. DIN 14 14-1 (2006-11)
Application
/.
Point angle 31
Helix
angle 21
I
N
Universal application for materials
up to Rm~ 1000 N/mm2, e. g. structural, casehardened, quenched and tempered steels
30°-40°
, ,so
H
Drilling of brittle, short-chipping
non-ferrous metals and plastics, e. g.
CuZn alloys and PMMA (Plexiglas)
13°-19°
, ,s·
w
Drilling of soft, long-chipping non-ferrous
metals and plastics, e.g . Al and Mg alloys, PA
(polyamide) and PVC
400-470
130°
I
1l Tool application groups for HSS tools acco rding to DIN 1835
2> Depends on drill diameter and pitch
3> Standard version
Po int angle
Standard values for drilling with HSS twist drills1>
Material group
Drill d iameter d in mm
Cutting
speed2>
Workpiece material
Tensile strength
Rm in N/mm 2
or
Hardness HB
2-3
Ve
m/min
I
>3--6
I
> 6-12
I
>12- 25
I
>25-50
Feed fin mm/revolut ion
Steels, low strength
Rm s 800
40
0.05
0.10
0.15
0.25
0.35
Steels, high strength
Rm >800
20
0.04
0.08
0.10
0.15
0.20
Stainless steels
Rm ,;800
12
0.03
0.06
0.08
0.12
0.18
Cast iron, malleable cast i ron
s 250 HB
20
0.10
0.20
0.30
0.40
0.60
A l alloys
Rm s 350
45
0.10
0.20
0.30
0.40
0.60
Cu alloy s
Rm ,.500
60
0.10
0.15
0.30
0.40
0.60
Thermoplastics
-
50
0.10
0. 15
0.30
0.40
0.60
Thermoset plastics
-
25
0.05
0.10
0.18
0.27
0.35
Standard values for drilling with carbide drills1>
Workpiece material
Material group
Cutti ng
speed 2>
Tensile strength
Rm in N/mm2
or
Hardness HB
Ve
Drill diameter din mm
2-3
m/min
I
>3--6
I
>6-12
I
>12-25
I
>25-50
Feed f in mm/revolution
Steels, low strength
Rm ,;800
90
0.05
0.10
0.15
0.25
0.40
Steels, high strength
Rm> 800
80
0.08
0.13
0.20
0.30
0.40
St ainless steels
Rms B00
40
0.08
0.13
0.20
0.30
0.40
Cast iron, malleable cast iron
s 250 HB
100
0.10
0.15
0.30
0.45
0.70
Al alloys
Rm s 350
180
0.15
0.25
0.40
0.60
0.80
Rm s 500
200
0.12
0.16
0.30
0.45
0.60
-
80
0.05
0. 10
0.20
0 .30
0.40
80
0.05
0. 10
0.20
0.30
0.40
Cu alloys
Thermoplastics
Thermoset plastics
I
.
Standard values for modified conditions
St andard values for cutting speed and feed are valid for moderate usage conditions:
• sho rt drill
• t ool life approx. 30 m in • average strength of material
• hole dept h < 5 • d
Standard values are • increased for more favorable conditions,
• decreased fo r unfavorable conditions
11 Fo r cooling lubricants, see pages 292 and 293
2> Values for coated drills
302
Production engineering : 6.3 Machining processes, Standard va lues
Reaming and tapping
'
Standard values for reaming with HSS reamers11
Workpiece material
Material group
Cutting speed
Tens. strength
Rm in N/mm 2
or
Hardness HB
Tool diameter d in mm
Ve
Reaming allow.
for d i n mm
2-3 1 >:Hl 1>6--121 >12-251 >25--50
m/min
1020
>20-50
0.20
0.30
0.30
0.60
Feed fin mm/revolution
Steels, low strength
Rms 800
15
0.06
0.12
0.18
0.32
0.50
Steels, high strength
Rm > 800
10
0.05
0.10
0.15
0.25
0.40
Stainless st eels
Rm ,;800
8
0.05
0.10
0.15
0.25
0.40
Cast iron, malleable cast iron
" 250 HB
15
0.06
0.12
0.18
0.32
0.50
Al alloys
Rm " 350
26
0.10
0.18
0.30
0.50
0.80
Cu alloys
Rm " 500
26
0.10
0. 18
0.30
0.50
0.80
Thermoplastics
-
14
0.12
0.20
0.35
0.60
1.00
Thermoset plast ics
-
14
0.12
0.20
0.35
0.60
1.00
Standard values for reaming with carbide tooling1>
Workpiece material
Material group
Cutting speed
Tool d iameter d in mm
Reaming allow.
ford in mm
>:Hl 1>6--12 1 > 12-25 1 >25--50
to 20
>20-50
0.20
0.30
0.30
0.60
I
Tens. strength
Rm in N/mm2
or
Hardness HB
m/min
Steels, low strength
Rm " 800
15
0.06
0.12
0.18
0.32
Steels, high strength
Rm> 800
10
0.05
0.10
0.15
0.25
0.40
Stainless steels
Rm ae 800
10
0.05
0.10
0.15
0.25
0.40
Cast iron, malleable cast iron
s 250 HB
25
0.10
0.18
0.28
0.50
0.80
Al alloys
Rm" 350
30
0.12
0.20
0.35
0.50
1.00
Cu alloys
Rm s 500
30
0.12
0.20
0.35
0.50
1.00
Thermoplastics
-
20
0.12
0.20
0.35
0.50
1.00
Thermoset plastics
-
30
0.12
0.20
0.35
0.50
1.00
Ve
2-3
Feed fin mm/revolution
0.50
Standard values for tapping and thread forming 11
Workpiece material
Material g roup
HSS tool
Tens. strength
Fl,,, in N/mm2
or
Hardness HB
Tapping 21
I
Carbide tool
Thread
forming21
Cutting speed Ve m/min
Tapping21
I
Thread
forming21
Cutting speed Ve m/min
S1eels, low strength
Rm s 800
40- 50
40- 50
-
40- 60
Steels, high strength
Rm>800
20-30
15- 20
-
20-30
20- 30
S1ainless steels
Rmae 800
8 - 12
10- 20
-
Cast iron, malleable cast iron
s 250 HB
15-20
-
25- 35
-
A l alloys
Rm " 350
20- 40
30- 50
60- 80
60- 80
Cu alloys
50- 70
Rm s 500
30- 40
25- 35
30- 40
Thermoplastics
-
20- 30
-
50- 70
-
Thermoset plastics
-
10-15
-
25- 35
-
'' For cooling lubricants, see pages 292 and 293
21 Upper limit values:
for material groups with lower strengths; sho rt threads
Lower limit values: for material groups w i1h higher streng1hs; long threads
303
Production engineering: 6.3 M achining processes, St andard values
Turning
Roughness depth depending on tool nose radius and feed
R,h theoretical
roughness depth
r tool nose radius
f feed
ap cutting depth
Ex ample:
R,h = 25 µm; r = 1.2 mm; f =?
, ,,~
Theor. rough-
~
= ✓8 - 1.2 mm • 0.025 mm " 0.5mm
Roughn. depth
R,h
0.4
inµm
0.07
0. 11
0. 18
0.23
0.28
1.6
4
10
16
25
I
Nose radius r in mm
0.8
1.2
I
Feed fi n mm
0.10
0. 12
0.20
0.16
0.31
0.25
0.39
0.32
0.49
0.40
I
1.6
0.14
0.23
0.36
0.45
0.57
Standard values for turning with HSS tools1121
Material group
Workpiece mat erial
Tensile strength
Rm in N/m m 2 or
Hardness HB
Cutting
speed Ve
in
m/min
Steels, low strength
Rm s 800
40-80
Steels, high strength
Rm >800
30- 60
30- 60
Stainless st eels
Rm ~ 800
Cast iron, malleable cast iron
s 250 HB
20- 35
A l alloys
Rm ,;350
120- 180
Cu alloys
Rm s 500
100- 125
Thermoplastics
-
100- 500
Therm oset plastics
-
80- 400
Feed
f
in
mm
Cutting depth
0. 1-0.5
0.5- 4.0
Feed
in
mm
Cutting depth
Bp
in
mm
0. 1- 0.5
0.3-5.0
a,,
in
mm
Standard values for turning using coated carbide tools21
Material group
Workpiece material
Tensile strength
Rm in N/mm 2 or
Hardness HB
Cutting
speed v0
in
m/min
Steels, low st rength
Rm s 800
200- 350
Steels, high strength
Rm >800
100- 200
Stainless steels
Rm~ 800
80- 200
Cast iron, malleable cast iron
s 250 HB
100 - 300
Al alloys
Rm ,.350
400 - 800
Cu alloys
Rm s 500
Thermoset plastics
Application of the cutting data range
Thermoplastics
f
150-300
500- 2000
400- 1000
Example: Standard values for turning of steels w ith lower strengths using carbide tools
Upper values
Application
Lower values
Application
Ve = 350 m/min
• finish machining (finishing)
• stable tool and workpiece
Ve= 200 m/min
• premachining (roughing)
• unstable tool or workpiece
f = 0.5 mm,
ap = 5.0 mm
• premachining (roughing)
• stable tool and workpiece
f = 0.1 mm,
Bp ~ 0.3 mm
• finish machining (finishing)
• unstable tool or workpiece
11
HSS lathe tools have for t he most part been replaced by lat he tools
w ith carbide indexable inserts.
21 Machining coolant, see pages 292
and 293
304
Productio n eng ineering: 6.3 M achinin g p rocesses, Tap er t urning
Taper turning
Terminology for tapers
cf. DIN ISO 3040 (1991-()9)
f
D large t aper diameter
d small taper diameter
L taper length
a taper angle
a taper-generating angle
2 (setting angle)
C taper ratio
c:,
taper incline
1: x taper:
on a taper length of x mm
the taper diameter
changes by 1 mm.
Taper turning on CNC lathes
CNC program accord ing t o DIN 66025 1' to produce a
workpiece wit h a taper (see fig ure):
0
,..._
'Q
N 10
N20
GOO
G01
XO
XO
N30
G01
X50
N40
N50
G01
G01
X60
N60
G01
X72
N70
GOO
X100
Z2
zo
Approach at rapid speed
F0.15
Traversing motion to P1
Traversing motion to P2
Z-25
Z-40
Traversing motion to P3
Z150
Tool change point
Traversing motion to P4
Traversing motion over P5
11 Compare to page 387
Taper turning by setting the compound rest
Example:
Setting angle
a
0= 225 mm, d = 150 mm, L = 100 mm;
a
a
0-d
tan- = - 2 2-L
(225- 150) mm
_
0 375
2 - 100mm
a
2
C
C
tan- = 2 2
~=
2 1·C
·• = 1•
D-d
tan- = - 2
2- L
= 20. 556" = 20" 33 ' 22 •
D- d
L
!225 - l 50)mm 0.75 = 1: 1.33
100mm
Taper turning by offsetting the tailstock
tailstock offset
lat he axis
Tailstock offset
maximum allowable
tailstock offset
Lw
C
V-T = - · L
2
workpiece lengt h
w
Example:
D ~ 20 mm; d = 18 mm;
L = BO mm; Lw = 100 mm
Vr = ?; Vrmax = ?
D - d 1.,,
Vr = -2- .
M aximum allowable
tailstock offset11
T
= (20- 18)mm. 100mm = l .2S mm
2
80mm
I.,, 100mm
Vr max $
=~
= 2mm
50
11 If the tailstock offset is too large the workpiece cannot be secured between the lat he cent ers.
V-
< Lw
Tmax -
50
305
Production engineerin g: 6.3 Machining processes, Standard va lues
Milling
Standard values for milling with HSS milling cutters
Material group
Workpiece material
Te nsile strength
Rm in N/mm 2 or
Hardness HB
Cutting
speed
Ve
in m/min
Steels, low strength
Rm s 800
50-100
Steels, high strength
Rm>800
30-60
Stainless steels
Rm" 800
15-30
Cast iron, malleable cast iron
s 250 HB
25---40
Rm s 350
50-150
Al alloys
~rrln
Cu alloys
,.,
-
Thermoplastics
Thermoset plastics
M illing cutter
(except for
end mill)
Rm :5 500
50-100
-
100-400
-
100-400
Feed f, in m m
End m ill d in m m
6
12
20
0.05-0.15
0.06
0.08
0.10
0.10-0.20
0.10
0.15
0.20
Standard values for milling with coated carbide
Material group
Workpiece mat erial
Tensile strength
Rm in N/mm2 or
Hardness HB
Steels, low strength
Rm s 800
J
Steels, high st rength
Cutting
speed
Ve
in m/min
Rm> 800
150-300
Rm " 800
150-300
Cast iron, malleable cast iron
:s 250 HB
150-300
Rm ,;350
400-SOO
Rm" 500
200-400
Thermoplastics
-
500-1500
Thermoset plastics
-
400-1000
Cu alloys
.
.
Feed f, inmm
End mill d in mm
6
12
20
0.05-0.15
0.06
0.08
0.10
0.10-0.20
0.10
0.15
0.20
200-400
Stainless steels
Al alloys
M illing cutter
(except f or
end m ill)
Increasing the recommended feed per cutting edge ~ for slotting with side milling cutters
Cutting depth a,,, based on the m illing cutter 0 d
Feed
per toot h
1/6 • d
1/3 • d
1/ 10 • d
1/20 • d
increase
1 • f,
1.15 • f,
1.45 • f,
2 • f,
to be adjusted
0.25 mm
0.29 mm
0.36 mm
0.50 mm
Meanings of cutting data ranges
Example: Standard values for m illing of low-strength steels using HSS milling cutters
Upper val&MS
Application
Lower val&MS
Application
Ve = 100 m/min
• finish machining (finishing)
• rigid tool and workpiece
Ve = 50m/min
• premachining (roughing)
• low rigidity of tool or workpiece
f,=0. 15mm
• premachining (roughing)
• rigid tool and workpiece
fi = 0.05 mm
• finish machining (finishing)
• low rigidity of tool or workpiece
Calculation of feed rate
v, feed rate in mm/min
f, feed per tooth in mm
n
N
rotational speed of milling cutter in 1/m in
number of t eeth
Example:
Ve = 100 m/min; d = 40 mm; fi = 0.12 mm; N= 10
Ve
100 m/min
n = ~ = n. 0.04m =795 1/min; v1 = n •fi • N= 796/min • 0.12 mm• 10 = 955 mm/ min
Feed rate
I
v1=n•fi•N
I
306
6.3 Machining processes, Standard va lues
Processes and problems"
Possible COff8Ctive measures
Drilling
,,'iii.,
c,,.,
·0
:: E
'o
Cl,:,
u
"'
:,
0
-0
0,.,
C: .,
B
0,
~
:t:.!!!
.,
.;
-., .,
~E ., ., ., - =., ., ·g
C:.;
o-
.. 3::., ..
0,
Q. . .
~
s0
o..=!
::i
!:!
· - 0,
C:
'O
4)
6£ ~o
~]
-2!
o=
-
t:
,:; 0
B
U)
.g
l
>
Check cutting geomet ry
Increase supply of lubricant
u
u
ft
.
Decrease feed f
Increase cutting speed Ve
.
Decrease projection length
Check cutting parameters
Check type of carbide
Turning
,,
.,
.,..:"'
o.,
C:
~~
., 't
~ i;l
--~.,, _,,.,
.;
]~
·-
~
0,
0. C
E Cl
C:
0 11)
o, Cl
C: C:
., u
:,
:,
., 0,
ai .E
Q.:,
., .,O·- =·= .,_
.. <.> .<::
Cl <.>
Cl u
,::;
Cl..:
:f f
-=
~
u
-o,:,
0,
0,.,
0.,
., ., .,
.,
"O
0
C: .,
0 0,
., .,
,::;
.,
..
,,.,
:0
-
c: Cl
"'11)
:.= C
0
Q.:,
(I) (.)
~
u-
ft
m·E
X
.,
.!:
Q.
:c
0:5 t:
.,
"'.,C:
~
"- ·-
(.)
c,"iij
c.:
0 Q.
....I.,
.,
C:
0
·.:;
E
.0
>
u
ft
u
u
ft
Change cutting speed Ve
ft
Change feed f
u
Decrease cutting depth
.
Choose a more wear-resistant carbide type
Choose tougher carbide type
Choose a positive cutting geometry
Milling
,,
B
-- ,,8> .,
.,
., ~.,
8. g' £ .,
C:
..:
"'
~g
:: 't
~ i;l
,::;
.,
.;
....
.,
c,.,,
::c ~
0
C:.,
0 Cl
·.:; "O
"'"'
E
Cl
C:
Cl
-0 .
"O
,
Cl Cl
C: C:
~B ='E
~
O•-
"':,
Cl <.>
u
ft
Q)"i:
-0,:,
Cl
Q.:,
Cl a,
C: Cl
C:
.,
"'.,
<.>.<::
"' 0
u_
u
(.)
~
ft
...,
:0
X
Q.:,
(I) (.)
i!:
:, t:
0.,
.,
~
..
(.)
0
- = ..
c6 "E
.,
"O
.!:
C:
u. ·-
't
i;l~
r..:.::
0"'
0 :,
0.. O'
.,
C:
0
.::
E
.0
>
Change cutting speed Ve
u
.
u
ft
Change feed ft
Choose a more wear-resistant carbide type
.
Choose tougher carbide type
Use milling cutter with wider spacing
Change milling cutter position
,, • problem to be solved
Dry milling
ft increase value of cutting parameter
u decrease value of cutting parameter
307
Production engineering: 6.3 Machining processes, Indexing
Indexing with a dividing head
Direct indexing
In direct indexing the dividing head spindle, along with
the indexing plate and workpiece, is turned by the
desired indexing step. The worm is disengaged from the
worm wheel.
D no. of divisions
a angular division
nh no. of holes in the indexing plate
n; indexing step; no. of hole spacings to be indexed
dividing head
spindle
Indexing step
f}.
'
= l1t,
D
Example:
Worm disengaged
Indirect indexing
worm gear
dividing head
spindle
workpiece
In indirect indexing the dividing head spindle is driven
by the worm and worm wheel.
D no. of divisions
a angular d ivision
gear ratio of dividing head
nc indexing st ep; no. of indexing crank revolutions
for one division
Indexing step
;
nc = -D
i -a
n = -c
360°
Example 1:
i 40 = -10
O68 17
n 0 = - :; -
D = 68; i = 40; nc = ?
15 16 17 18 19 20
21 23 27 29 31 33
37 39 41 43 47 49
Example 2:
a = 37 .2°; i = 40; nc = ?
n _ i • a _ 40 • 37.2" _ 37.2 _ 186 _
indexing
crank
indexing
plate
•
360"
Circles of holes on
indexing plates
360"
9
9 •5
or
4
2
17 19 23 24 26 27
15
28 29 30 31 33 37
39 41 42 43 47 49
51 53 57 59 61 63
Differential indexing
dividing head
worm gear
spindle
In differential indexing the dividing head spindle is
driven with worm and worm wheel like indirect indexing. Simultaneously the dividing head spindle drives
the indexing plate using change gears.
a angular division
D
no. of divisions
D'
auxiliary no. of divisions
gear ratio of dividing head
nc
indexing step; no. of indexing crank revolutions
for one division
N dg
no. of teeth of driving gears (N1, N3 )
Ndn
no. of teeth of driven gears (N2, N4 )
For selecting O' the following applies:
D'> D : Indexing crank and indexing plate must rotate
in the same direction.
D' < D: Indexing crank and indexing plate must rot ate
in opposite directions
If necessary the required direction of rotation is
achieved by means of an idle gear.
No. of teeth on
change gears
Example:
i=40; 0=97; nc = ?; IV,ig = ?; O'selected = 100
Ndn
indexing
crank
indexing
plate
(Indexing crank and indexing plate must rotate in
the same direction).
i 40 8
0
• = LY = 100 = 20
N.,g =_!_ .(O'-~ = 40 ·(100- 97) = 3. · 3 = ~ = ~
Ndn 0 '
100
5
5 40
No. of teeth on
change gears
24
24
28
36
40
44
56
64
72
84
86
96
32
48
80
100
308
Production engineering: 6.3 Machining processes, Standard values
Grinding
cutting speed
Ve
Surface grinding
rinding wheel
Cutting speed
dg diameter of grinding wheel
l
j Ji ~'•"·
feed rat e
L
t ravel
..
workpiece
v,
Cylindrical
grinding
Speed ratio
Ve = 30 rn/s; v 1 = 20 m/min; q = ?
v,
d,
q =~ =
v,
n
30 rn/s • 60 s/min
20rn/min
1800rn/min
20rn/min
I
90
Standard values for cutting speed Ve, feed rate v,, speed ratio q
Material
Surface grinding
Peripheral grinding
Side wheeling
Ve
Steel
Cast iron
Carbide
Al allovs
Cu alloys
Vf=1t·d,-n
Example:
~.:
grinding
wheel
q
I
Vt= L • n s
Surface grinding
workpiece rotational speed
speed ratio
n
Vc=n- d 9 -n9
Feed rate
"• no. of strokes
d, diameter of workpiece
Cylindrical grinding
I
ng rot ational speed of grinding wheel
v,
m/s
30
30
10
18
25
"'
m/min
10-35
10-35
4
15-40
15-40
"'
Ve
q
80
65
115
30
50
I
Cylindrical grinding
External cyl. grinding
Internal cyl. grinding
Ve
m/min
6-25
6-30
4
24-45
20-45
m/s
25
25
8
18
18
q = Ve
Vt
q
50
40
115
20
30
m/s
35
25
8
18
30
"'
m/min
10
11
4
24-30
16
"'
"e
q
125
100
100
50
80
m/s
25
25
8
16
25
m/min
19-23
23
8
30-40
25
q
80
65
60
30
50
Grinding data for steel and cast iron with corundum or silicon carbide grinding wheels
Processes
Grain size
30-46
46-80
80-120
Rough grind
Finishing
Precision grinding
Grinding allowance
0.5--0.2
0.02-0.1
0.005--0.02
Depth of cut in mm
0.02-0.1
0.005--0.05
0.002-0.008
Maximum speed of grinding wheels
Shape of grinding wheel
Rz inJJm
3- 10
1- 5
1.6-3
cf. DIN EN 12413 (2007-09)
Type of grincing machine
Guide1l
Maximum speed Ve in m/s for bond type2l
B
BF
E
M
R
RF
Pl
V
Straight grinding wheel
stationary
pd or ho
50
63 40
25
50
50
40
hand-held grinder
free-hand
50
80
- - 50 80 50 Straight cutting wheel
stationary
pd or ho
80 100 63
63
80
hand-held grinder
free-hand
80
11 pd positively driven: feed by mechanical means; ho hand operated: feed by operator;
21 Type of bond, see page 309
free-hand grinding: g rinding machine is guided entirely by hand;
Restrictions for use of grinding tools31*
cf. BGV D12•1 (2001-101
-
VE
VE1
Meaning
Not allowed for free-hand or hand operated
grinding
VE
VE6
VE7
VE8
VE10
VE11
-
-
Meaning
Not allowed fo r side wheeling
Not allowed for free-hand grinding
Not allowed w ith backing pad
Not allowed for dry g rinding
Not allowed for free-hand or hand operated abrasive cutting
VE2 Not allowed for free-hand abrasive cutting
VE3 Not allowed for wet grinding
VE4 Not allowed in enclosed work area
VE5 Not allowed without vacuum exhaust
31 If no restriction is given, the grinding tool is suitable fo r all applications.
Color stripes for maximum allowable peripheral speeds "' 50 m/s*
cf. BGV D124 1(2001-10)
Color stripe
blue
yellow
red
green
blue & yellow
blue & red
Ve max in m/s
50
63
80
100
125
140
160
red&red
green&grNr
320
360
Color stripe
Ve max in m/s
41
yellow& red yel. &green
180
200
red&green
225
blue& blue yellow & yell.
250
280
BGV Berufsgenossenschaftliche Vorschrift (Employers' Liability Insurance A ssociation Provisions)
*I According to European Standards
blue& green
309
Production engineering: 6.3 Machining processes, Abrasives
!.111r. ..., ••,~... ;filiTj
Abrasives
cf. DIN ISO 525 (2000-08)
Symbol Abrasive
Chemical composition
KnoopArees of application
harc!Mss
Norm. corundum Al2O3 + additions
A
z
white fused alu- A l2O3 in crystalline
mina
form
18000
Carb. steel, unhardened steel, cast steel, malleable cast iron
21000
High and low alloyed steel, hardened steel, case hardened
steel, tool steel, titanium
-
zircon corundum Al2O3 + ZrO2
Stainless steels
Hard materials: carbide, cast iron, HSS, ceramic, glass;
soft materials: copper, aluminum, plastics
C
silicon carbide
SiC + additions
24800
BK
boron carbide
B4C in crystalline form
47000
Lapping, polishing of carbide and hardened steel
CBN
boron nitride
BN in crystalline form
60000
High-speed steels, cold and hot work steels
D
diamond
C in cryst alline fo rm
70000
Carbide, cast iron, glass, ceramic, stone, non-f errous metals. not for steel; dressing of grinding w heels
Hardness grade
cf. DIN ISO 525 (2000-08)
Hardn. grede Application
Designation
extremely soft ABCD
E F G
very soft
Deep and side w heeling of
hard materials
soft
H I J K
medium
LM NO
Conventional metal
grinding
Designation
Hardn. grade Application
hard
P QR S
very hard
TU V W
External cylindrical g rinding; soft materials
extremely hard XY Z
Grain size
cf. DIN ISO 525 (2000-08)
Grain designation for bonded abrasives
coarse
medium
fine
very fine
Grain desig nation
F4, F5, F6 t o F24
F30, F36, F46 to F60
F70, F80, F90 to F220
F230 to Fl 200
Attainable Rz in µm
"' 10-5
"' !',---2.5
"' 2.!',---1,0
"' 1.0-0.4
Grain ranges
Structure
cf. DIN ISO 525 (2000-08)
0 1 2 3 4 5 6 7 8 9 10 11
Code
<
Structure
Bond
dense (nonporous)
I
12 13 14, etc. up to30
I
open (porous)
>
cf. DIN ISO 525 (2000-008) and VOi 3411 (2000-08)
Properties
Areas of application
Code
Type of bond
B
BF
synthetic resin bond,
fiber reinforced
Nonporous o r porous, elastic,
resistant t o oil, cool grinding
Rough or cut-off grinding, form grinding with
diam. and boron nitride, high pressure grinding
E
shellac bond
Sensitive t o temperature, tough
elastic, impact resistant
Saw t ooth grinding, fo rm grinding, control
wheel for centerless g rinding
G
galvanic bond
Tight grip due t o protruding
grains
Internal grinding of carbide,
hand grinding
M
met al bond
Nonporous or porous, tough,
insensitive to pressure and heat
Form and tool g rinding using d iamond
o r boron nitride, wet grinding
MG
magnesite bond
Soft, elastic, sensitive to
water
Dry grinding, knife grinding
PL
plastic bond
Soft, elastic depending upon
plastic and degree of hardening
Plastic abrasive material for finishing,
precision fin ishing and polishing
R
RF
rubber bond,
fiber reinforced
Elastic, cold grinding,
sensitive to oil and heat
Cut-off grinding
V
Porous, brittle, insensitive
vitrified (ceramic) bond to water, oil, heat
=>
Rough and finish grinding of steels using
corundum and si licon carbide
Grinding wheel ISO 603-1 1 N-300 x 50 x 76.2 -A/F 36 L 5 V - 50: Form 1 (straight grinding w heel), w heel
face N, outside diameter 300 mm, width 50 mm, hole diameter 76.2 mm, abrasive A (normal corun dum or
whit e fused alumina), grain size F36 (medium), hardness grade L (medium), structure 5 vitrified (ceramic)
bond (V). maximum peripheral speed 50 m/s.
310
Production engineering: 6.3 Machining processes, Grinding wheels
Selecting grinding wheels
Standard values for selecting grinding wheels lexduding diamond and boron nitridel
Cylindrical grinding
Material
Abrasive
Roughing
Finishing with wheel diameter
over500mm
upto500mm
Fine finishing
Grain size Hardness Grain size Hardness Grain size Hardness Grain size Hardness
Steel, unhardened
Steel, hard., unalloy. and alloy.
Steel, hardened, high alloyed
Carbide, ceramic
Cast iron
Non-terr. met., e.g. Al, Cu, CuZn
A
A
A,C
C
A, C
C
54
46
80
60
60
46
M- N
L-M
M-N
80
K
L
K
80
80
80
80
60
M-N
K- L
N- O
K
60
L- M
180
L- M
60
240-500
240-500
H-N
H-N
H- N
L
K
60
J-K
M- N
K
L
100
M
60
K
-
-
60
60
240-500
Internal cylindrical grinding
Material
St eel, unhardened
Steel, hard., unalloy. and alloy.
Steel. hardened, high alloyed
Carbide, ceramic
Cast i ron
Non-terr. met., e.g. Al, Cu, CuZn
Abrasive
A
A
A,C
C
A
C
upto 20
Grinding wheel diameter in mm
from 20to40
from 40to 80
over 80
Grain size Hardness Grain size Hardness Grain size Hardness Grain size Hardness
L-M
L- M
46
K
M
54
80
60
80
80
80
80
80
K-L
J- K
120
G
L- M
120
1-J
100
80
120
M-N
K
H
K-L
K
80
M- N
80
L
80
60
80
60
K
H
M
46
J
G
M
60
J- K
54
J
120
Peripheral face grinding
Material
Abrasive
Cup wheel
D<300mm
Straight grinding wheels
D s 300mm
O > 300mm
Abrasive
segments
Grain size Hardness Grain size Hardness Grain size Hardness Grain size Hardness
Steel, unhardened
Steel, hard., unalloy. and alloy.
Steel, hardened, high alloyed
Carbide, ceramic
Cast iron
Non-terr. met .. e.g. Al, Cu, CuZn
A
A
A
C
A
C
46
J
46
46
J
46
H✓
60
60
46
J
J
J
46
46
60
46
60
J
J
1-J
J
J
J
36
J
24
46
J
1- J
J
J
J
36
J
J
36
I✓
46
J
J
J
46
60
46
60
24
36
Tool grinding
Cutting tool material
Tool steel
High-speed steel
Carbide
Abrasive
A
A
C
Straight grinding wheels
Dish wheels
Cup
wheels
O s 100 0>100
0 "225 0>225
Grain size Grain size Hardness Grain size Grain size Hardness Grain size Hardness
80
60
M
80
60
60
46
K
60
46
M
K
80
54
K
80
54
K
46
46
46
K
H
H
Cutting on stationary machines
Material
Abrasive
Straight cut-off WMels v, up to 80 m /s Straight cut-off wheels v, up to 100m/s
O " 200mm
O>200mm
D s 500mm
D>500mm
Grain size Hardness Grain size Hardness Grain size Hardness Grain size Hardness
Steel, unhardened
Cast iron
Non-terr. met., e.g. Al, Cu, CuZn
A
A
A
80
60
60
0-R
0-R
0-R
46
46
46
0-R
0-R
0-R
24
u
20
24
U-V
20
0-R
U-V
30
s
24
s
Grinding and cutting with hand tools
Material
Abrasive
Cut-off wheels
Ye up t o 80 m/s
Rough grinding wheels
Ye up to 80 m/s
Ye up to 45 m/s
Mounted points
Grain size Hardness Grain size Hardness Grain size Hardness Grain size Hardness
Steel, unhardened
Steel, corrosion resistant
Cast iron
Non-terr. met., e.g. Al, Cu, CuZn
A
A
A,C
30
T
24
30
R
16
30
T
20
A,C
30
R
20
M
M
R
R
24
R
36
24
R
36
s
24
R
30
T
-
-
-
-
Q-R
Productio n eng ineering: 6.3 Machining p rocesses, Grindin g w heels
311
Grinding with diamond and boron nitride
Grain designation ranges
Areas of application
Grain
diamond
designation1) boron nitride
Attainable Ra in µm
cf. DIN ISO 848 (1998-03)
Rough grind
D251- D151
B251- B 151
Finishing
D126--D76
B126--B76
~ 0.55---0.50
~ 0.45---0.33
Precision grinding
lapping
064. D54. D46
B64. B54, B46
,. 0.18--0. 15
D20. D15. D7
B30, BG
,. 0.05---0.025
'' Mes h size of test sieve in µm
Standard values for cutting speeds
Process
Abrasive
Cutting speed v. in m/s by bond type11
M
G
dry
wet
dry
w et
dry
wet
30--50
30-60
30-60
22- 50
22- 27
20--30
22- 50
30-50
30-60
30-60
22--40
22--40
20--30
20--30
27- 35
30-60
30-60
24--40
30-50
8--15
18--27
12- 20
18--40
12- 18
15-30
27- 35
30-50
22- 30
27- 35
30--50
30--40
22- 50
15-22
15-22
15-27
15-30
22-35
27-35
30--50
30-60
27--40
30-60
12- 18
22- 35
22- 27
18--30
22--40
21 Approx. four times t he value for high speed g rinding (HSG)
B
Surface grinding
CBN
D
External cylindrical
CBN
grinding 21
D
Internal cylindrical
CBN
grinding
D
Tool
CBN
grinding
D
Cut-off
CBN
grinding
D
11 Bond types, see page 309
V
dry
wet
30-60
25-50
30-60
25-50
30--50
25-50
30-50
-
-
-
-
-
-
-
-
Standard values for depth of cut and feed of diamond grinding wheels
Process
Face grinding11
External cyl. grindi ng11
Depth per stroke in mm for grain size
Crossfeed relative to wheel
width w
Feed
D181
D126
064
m /m in
0.02--0.04
0.01--0.03
0.01--0.02
0.0--0.02
0.005---0.01
0.005---0.01
0.3-2.0
0.01-2.0
¼-½• w
-
Crossfeedrel•
t ive to wheel
width w
10--15
Internal cyi. grinding
0.002--0.007
0.002--0.005
0.001--0.003
Tool grinding
0.01--0.03
0.005---0.015
0.002--0.005
Groove g rinding
1.0--5.0
0.5-3.0
11 Approx. t hree times the value for high speed grinding (HSG)
0.5-2.0
0.3-4.0
Standard values for depth of cut and feed of CBN grinding wheels
Depth per stroke in mm for grain size
Process
Surface orindina
External cvl. o rindino
Internal cyl. arindina
Tool a rindino
Groove g rinding
8252/B181
B151/B126
B91/B76
Feed
m/min
0.03--0.05
0.02--0.04
0.005---0.015
0.002--0.1
1.0--10
0 .02--0.04
0 .02--0.03
0.005---0.01
0.01--0.005
1.0--5.0
0.01--0.015
0.015---0.02
0.002--0.005
0.005---0.015
0.5-3.0
20--30
0.5-2.0
0.5-2.0
0.5--4.0
0.01- 2.0
High-performance grinding with CBN grinding wheels
1
1
/4- /-j•W
-
-
-
cf. VDI 3411 (2000-08)
Grinding processes achieving extremely high material removal rat es by utilization of special machines and tools with
increased cutting speeds(> 80 m/s) and appropriate machine coolant. Predominantly used for side and external cylindrical grinding of metallic materials.
.
Grinding wheel preparation (conditioning)
Processing step
Dressing
Cleaning
Truing
Sharpening
Action
Removal of grain and
bond
Reduction of t he
bond
No effect on abrasive
layer
Goal
Establishing concentricity
and wheel profile
Creating t he grinding
w heel surface structure
Remove c hips from pores
Maximum allowable peripheral speeds in high-performance grinding
Bond type11
B
V
M
G
Highest allowable
peripheral speed in m/s
140
200
180
280
11 Bond types, see page 309
312
Production engineering: 6.3 Machining processes, Standard values
'
Honing
•8
Ve cuning speed
v. axial speed
J
Vp
~v.
v,
A
Vp
peripheral speed
a
angle of i ntersection
betw. abrading tracks
cont act pressure
p
Cutting
contact area of
honing stone
speed
F, radial infeed force
n number of honing stones
w w idth of honing st ones
length of honing stones
I
I
I
vC = J va2 + v p2
I
Angle of
intersection
Example:
Hardened steel, finish honing, v 0 = ?; v. = ?; Ve= ?; a = ?
read from table: v 0 = 25 m/min; v. = 12 m/min
2
Ve =
v
v,
Vp
~
a
I
~~ ~
2
tan !:. = v.
2
Vp
I
Contact pressure
) +(25~ ) ~ 28~
.Jv/ +vl = ( 12~
mm
mm
m,n
Fr
p =-
A
tan~=.':'.!.= 12 m/min = 0.48 ; a = 51.3"
2 vP 25 m/m1n
I
F.
p = - -rn • w- 1
v,
Cutting speed and machining allowances
Peripheral speed
vpin m/min
Material
Axial speed
Va in m/min
Machining allowances in mm
for hole diameter in mm
2- 15
15-100
100-500
10-20
0.02-0.05
0.03-0.15
0.06-0.3
5--20
6-20
0.01-0.03
0.02-0.05
0.03-0.1
10-20
11- 20
0.02-0.05
0.03-0.15
0.06-0.3
Rough honing Finish honing Rough honing Finish honing
9-20
Steel, unhardened
18-40
20-40
Steel, hardened
14-40
15-40
Alloy steels
23-40
25-40
Cast iron
23-40
25-40
10-20
11-20
9- 20
10-20
A luminum alloys
22-40
24-40
Honing with diamond grit v0 up t o 40 m/min and v. up to 60 m/min; a= 60°- 90°
Contact pressure of honing tools
Contact pressure pin N/cm 2
Diamond
Plastic bonded
honing stick
honing stone
Boron nitride
honing stick
Honing process
Ceramic
honing stone
Rough honing
50-250
20D-400
300-700
200-400
Finish honing
20-100
40-250
100-300
100-200
Selection of corundum, silicon carbide, C8N and diamond honing stones
Tensile
strength
N/mm2
Material
Steel
Process
rough honing
<500
(unhardened) intermed. h oning
finish honing
Honing stone made of
Roughness
depth
corundum and silicon carbide21
Rz
Honing Grain Hard- Bond Strucµm
ture
abrasive size
ness
700
R
1
8-12
A
R
2-5
400
B
5
0.5--1.5
1200
M
2
500-700
(hardened)
rough honing
intermed. honing
finish honing
5--10
2- 3
0.5--2
A
Cast
iron
-
rough honing
finish honing
plateau honing11
C
Nonferrous
metals
-
5--8
2- 3
3-6
6-10
2-3
0.5--1
rough honing
intermed. honing
finish honing
A
A
C
80
400
700
R
0
M
80
400
1000
0
0
K
H
N
D126
D54
D15
B
3
5
3
876
854
830
V
3
7
8
D91
046
D25
V
3
1
5
D64
D35
D15
N
80
120
900
CBN or diamond
Grain size
21 see page 309
11 In plateau honing the peaks of the material surface are removed.
Selection of honing stone made of diamond and cubic boron nitride (CBN)
Abrasive
I Natural diamond I
Material
I
Steel, carbide
Synthetic diamond
J Cast iron, nitrided steel. non-ferrous metals, glass, ceramic
I
CBN
\ Hardened steel
313
Production engineering: 6.4 Material remova l
Productive time and standard values for material removal
Electric discharge machining (wire EDM)
productive time in m in
f eed rat e in mm/min
travel, cutting length in mm
cutti ng height in mm
geometric t olerance in µm
fp
wire electrode
Vt
~
v, I
/
/ cf?., / y
~1
~
L
H
T
Productive t ime
I
L
fp = v,
I
Example:
V
Material: Steel, H - 30 m m; L = 320 mm;
T = 30 µm; v1 = ?; tp = ?
vt = 1.8 mm/min (from table)
L
320 mm
fp = ~ = 1. 8 mm/min
I
178 min
I
Feed rate vt (standard values) 11
Feed rate v1 in mm/min
Cutting
height H
inmm
10
St eel eroding
I
60
9.0
40
8.5
30
4.0
Copper eroding
Desired geometric tolerance T in µm
20
10
40
20
10
7.5
3.9
2.1
3.5
2.0
I Carbide eroding
80
20
10
0.7
0.6
0.3
0.3
20
5.1
5.5
2.5
2.5
1.5
4.7
2.4
1.5
4.5
3.1
30
3.7
4.0
1.8
1.8
1.1
4.0
1.9
1.1
2.3
0.2
0.2
50
2.5
2.5
1.2
1.2
0.8
2.6
1.4
0.7
1.4
0.2
0.2
11 These standard values are average values from the main cut and all subsequent cuts required to reach geometric tolerance.
With unfavorable flushing conditions the achievable feed rate drops considerably.
Characteristics and application of common wire electrodes
W ire
material
CuZn alloy
El. conducti vity
in m/(Q • m m 2)
13.5
Tensile st rength
i n N/mm2
Typical w ire
diameter in mm
18.5
400-900
1900
0.2--0.33
0.025--0.125
Universal
Cuts w ith very t ight geometric tolerance
Molybdenum
Tungsten
18.2
2500
0.025--0.125
Narrow slots, small cor ner radii
Application
Electric discharge machining (sink EDM)
s
electrode
I
A ~'
_ v
/
~~
productive t ime in min
removal area
of electrode in mm2
V removal volume in mm3
Vw removal rate in mm3/min
fp
Productive time
s
I
V
tp = Vw
Example:
Roughing of steel; graphite elect rode,
5 = 150 mm 2; V = 3060 mm3; Vw = ?; tp = ?
Vw = 31 mm3/ min (from table)
I/
V
3060 mm3
fp = Vw = 31 mm3 /min
99 min
Removal rate Vw (standard values) 11
Workpiece
material
Steel
Carbide
Electrode
Graphite
Copper
Copper
10
to
50
7.0
13.3
6.0
Removal rate Vw in mm3/min
Finishing
Roughing
desired roughness depth Rz in µm
removal area S in mm2
50
100
200
300
400
2
3
4
6
8
to
to
to
to
to
to
to
to
to
to
100
200
300
400
600
3
4
6
8
10
18
62
2
81
105
5
31
22
28
51
85
105
0.1
0.5
1.9
3.8
5
15
18
28
30
33
0.1
0.5
2.2
5.2
-
11 Actual values w ill vary widely d ue to t he effects of different processing methods. Ref er to page 314.
I
314
Prod uction eng ineering: 6.4 M aterial remova l
Process parameters in EDM erosion
t
.,_
off
time
Vw
V
removal rate in mm3/min
Ve
absolute tool wear in
mm3
Vrel
relative tool wear in %
0,
~~
,v C
.c .,
u
V,
~
~
·-,::, ::,
u
time t - on
t ime
Parameter
Graphite
in various grain
Electrode sizes
Material
Pulse
duration
Relative t ool wear
Vre1 = Ve · 100%
V
Universal application; low wear behavior; high removal rate;
for finish and rough machining; difficult to manufacture electrode by machining;
high thermal expansion; no cracked edges;
tendency to warp
Universal application; very low wear; greater current density than Cu;
low electrode weight; easy to manufacture electrode by machining;
non-warping; low thermal expansion; more detailed electrodes are made by
selecting a finer graphit e grain; unsuitable for carbide machining
Detailed electrodes; very low wear; very high material removal rate with relatively
low d ischarge currents even wit h large current densities;
only manufactured in limit ed sizes, high electrode weight
Copper-graphite
Special applications involving small elect rode dimensions with simultaneous high
electrode strength; wear and material removal rate play a subordinate role in t hese
special applications
Requirements for dielectric fluids:
low and constant conductiv ity f or stable sparking
low v iscosity for filtrability and penetrating ability in narrow gaps
low evaporation t o reduce hazardous vapors
high flash point t o avoid fire hazard
high heat conductance value for good cooling
extremely low health hazard for operators
Depending on requirements and available options, d ifferent flushing methods can
Replacement of
be used to maintain stable erosion performance:
dielectric fluid
at t he erosion site • flooding (most commonly used met hod, simultaneous heat rejection)
pressure flushing through hollow electrodes or next to electrode
Remove eroded
• vacuum flushing through hollow electrode or next to electrode
partides from
• interval flushing caused by retracting electrode
gap
• movement flushing by relative movement between workpiece and electrode,
w ithout interrupting erosion cycle
positive
Electrode is positively polarized; for low electrode burn rate during roughing w ith
long pulse duration and low frequency
negative
Electrode is negatively polarized; for erosion with short pulse duration and high
frequency
,_ '
Kept constant during feed (controlled by discharge voltage).
Control sensit ivity set too high: Electrode continually pulses on and off, controlled
discharge impossible.
Control sensitivit y set too low: Abnormal d ischarges increase or gap remains too
large for discharge.
Polarity
Discharge
current
t
Tungsten-copper
Synthetic oils,
filtered and
cooled; according
Dielectric
to machine
fluid
manuf acturer
Gap
V
Vw= -
Explanations, characteristics and applications
Electrolytic
copper
R ushing
Removal rate
removal volume in mm3
removal t ime in min
side
Determined primarily by duration and size of discharge pulse, depends on material
matching and no-load voltage
low
Low removal performance, low tool wear on copper electrodes, high wear on
g raphite electrodes
high
~
High removal performance, high tool wear on copper electrodes, low wear on
graphite electrodes
short
Electrode wear with posit ive polarity is larger, lower removal rate
long
Electrode wear with positive polarity is smaller, higher removal rate
315
Production engineering: 6.5 Separation by cutting
'
Cutting force, Operating conditions for presses
Cutting force, cutting work
F
cutting force
calculat ed cutting force
s
shear area
R m max maximum tensile strength
rse max maximum shear strength
w
cutting work
sheet metal thickness
s
Fm
force- stroke curve
t
"-
Cutting force
I
F=S·TsBmax
Max. shear strength
Example:
~ FfCf-'-'-"!=-
S = 236 m m2 ; s = 2.5 mm; Rm max = 510 N/mm 2
.E I+---+-->-
£"' a--+---+-
Wanted : fse max; F; W
3 1--....L.-'--....L.-'--''----'--+'- - ' - L
Solution: r semax= 0.8 • Rm max
C
= 0.8. 510 N/mm2 = 408 N/mm2
working stroke h - - -
F = S • r,a max = 236 mm2 • 408 N/mm2
sheet metal
thickness s
= 96 288 N = 96.288 kN
W =
~
2
2
3 . F- s- 3 -96.288 kN. 2.5 mm
160 kN • mm = 160 N . m
Operating conditions for eccentric and crank presses
Press drives are usually designed such that the
nominal pressing force is applied at crank angle
a = 30°.
crank
Work capacity in
continuous mode
W. = F" • S
Machines operate without int erruption in continuous mode or can be stopped after each cycle in
single-stroke mode. Fo r presses with adjust able
strokes, the allowable pressing force is less than
the nominal p ressing force.
15
C
Work capacity in
single-stroke mode
F
cutting force, shaping fo rce
Fn
nominal pressing force
Fanow allow. pressing force for adjustable stroke
S
stroke, maximum stroke for adjustable
stroke
Sa
h
adjusted stroke
working dist ance(= sheet metal thickness s)
a
crank angle
W
cutting work, shaping work
We
W,
work capacity in continuous mode
work capacity in single-stroke mode
ram
metal
strip
Operating conditions
Fixed stroke
Example:
F
Eccentric press with fixed stroke Fn = 250 kN; S = 30 mm;
F=207kN;s=4mm
Find: W; We, Can the press be put into continuous mode?
Solution: W =3. · F • s =3. • 207 kN -4 mm = 552 kN • mm = 552 N • m
3
3
W. = Fn • S
e
15
250 kN • 30 mm
15
500 kN . mm= 500 N . m
If F < Fn, but W> We, the press cannot be used in continuous mode for
this workpiece.
" Fn
w " We o r
Ws w,
Adjustable stroke
F
s Fallow
Fn·S
Fallow 4- J Sa · h - h2
w We or
w "" w,
316
Production engineering: 6.5 Separation by cutting
Tool and workpiece dimensions
Punch and cutting die dimensions
-
u
punch
~
m d
d
punch
dimension
Process
D cutting d ie
dimension
u d ie clearance
'
0
i--=--
"'
~
cutting die
cf. VDI 3368 (1982-05)
Piercing
Blanking
a
Shape of
w o rkpiece
~
s
sheet metal
thickness
Governing
specified size is:
dimension of
punch d
dimension of
cutting d ie D
a
clearance angle
Dimension of
opposite tool
cutting die
D= d+2· u
punch
d=D-2-u
Die clearance u as a function of material and sheet metal thickness
Cutting die opening
with clearance angle a
sheet metal
Cutting die opening
without clearance angle a
shear strength r 08 in N/mm 2
I 251-400 I 401-600 I over600
die c learance u in mm
0.015
0.02
0.025
0.02
0.03
0.04
shear strength r,8 in N/mm 2
upto 250 I 251--400 I 401-600 I over 600
die clearance u in mm
0.015
0.02
0.025
0.03
0.025
0.03
0.04
0.05
thickness s
mm
upto 250
0.4-0.6
0.7-0.8
0.0,
0.015
0.9-1
1.5--2
0.02
0.03
0.03
0.05
0.04
0.06
0.05
0.08
0.03
0.05
0.04
0.07
0.05
0.09
0.05
0.11
2.5--3
3.5--4
0.04
0.06
0.07
0.09
0.10
0.12
0.12
0.16
0.08
0.1 1
o.11
0.15
0.14
0.19
0.17
0.23
Web width, edge width, trim stop waste for metallic materials
a
e
Cl:)
~
edge width
web width
edge length
web length
B strip width
i trim stop waste
(trench stop waste)
,.,.
) ~,
-·-l
.,,
-
1.
Polygonal workpieces:
The web or edge length, whichever is larger,
is used to determine web and edge widths.
Round workpieces:
Fo r all diameters values g iven for /8 = /8 =
10 mm of polygonal workpieces app ly to
web and edge widths.
Polygonal workpieces
Strip
width 8
mm
upto
100mm
-
I C
~M
!
Web length /0
Edge length ,.
mm
Web
width e
Edge
width a
0.1
0.3
0.5
0.75
1.0
1.25
1.5
1.75
2.0
2.5
3.0
up to 10
e
a
0.8
1.0
0.8
0.9
0.8
0.9
0.9
1.0
1.2
1.3
1.5
1.6
1.9
2.1
11-50
e
a
1.6
1.9
1.2
1.5
0.9
1.0
1.0
1.1
1.4
1.4
1.6
1.7
2.0
2.3
51-100
e
a
1.8
2.2
1.4
1.7
1.0
1.2
1.2
1.3
1.6
1.6
1.8
1.9
2.2
2.5
over 100
e
a
2.0
2.4
1.6
1.9
1.2
1.5
1.4
1.5
1.8
1.8
2.0
2.1
2.4
2.7
1.8
2.2
2.5
3.0
3.5
4.5
e
a
0.9
1.2
1.0
1.1
1.0
1.1
1.0
1. 1
1.3
1.4
1.6
1.7
2.0
2.3
11-50
e
a
1.8
2.2
1.4
1.7
1.0
1.2
1.2
1.3
1.6
1.6
1.8
1.9
2.2
2.5
51- 100
e
a
2.0
2.4
1.6
1.9
1.2
1.5
1.4
1.5
1.8
1.8
2.0
2.1
2.4
2.7
101- 200
e
a
2.2
2.7
1.8
2.2
1.4
1.7
1.6
1.7
2.0
2.0
2.2
2.3
2.6
2.9
~~
1.8
2.0
2.5
3.0
3.5
4.0
5.0
1.5
trim stop waste i
up to 10
over
100mm
to
200mm
Sheet metal thickness sin mm
trim stop waste i
1.5
317
Production engineering: 6.5 Separation by cutting
Location of punch holder shank, Utilization of strip stock
Location of punch holder shank for punch geometry with known center of gravity
Punch layout
prepunching
Distance of the center of forces
Workpiece
blanking out
Example:
0
N
a,= 31
Based on the figu re at left, calculate the distance x of
center of forces S.
Solution:
The outer perimeter of the cutting punch is chosen as
reference edge.
10
20
Blanking punch: C1 = 4 . 20 mm= BO mm; a1 = 10 mm
selected reference edge
Piercing punch: C, • " • 10 mm= 31.4 mm; a2 = 31 mm
C1, C2, C., ...
a,, a2 , "3 ...
circumferences of individual punches
distances from punch centers of gravity
to selected reference edge
c, + c2
x _ 80 mm • 10 mm+ 31.4 mm • 31 mm"
mm
16
80 mm+ 31.4 mm
distance of center of forces S
from chosen reference edge
x
C,·a,+C,·82
X
Location of punch holder shank for punch geometry with unknown center of gravity
Center of forces corresponds to centroid of the line11 of
all cutting edges.
Punch layout
Workpiece
Distance of the center of forces
x = 1, • a, + 12 • a2 + 13 • a3 + ...
,, + /2 +/3 + ...
X
Example:
Calculate the location of the punch holder shank on
the progressive die for the workpiece shown in the
figure at the left.
20
Solution:
a3 = 21
refer.
edge
a,= 41
cutting edge lengths
a1 , a2, a3 to an distance from line centroids
to selected reference edges
X
distance from center of forces
to selected reference edge
n
number of indiv idual cutting edge
lnin mm
an in mm
1
15
5
75
2
23.6
9.8
231.28
3
4
20
2 -20
21
420
1240
5
20
31
41
:!:
118.6
-
/0 •
820
2786.28
2
x =:[In• an= 2786.28 mm
:[In
118.6 mm
11 For line centroids, see page 32
Bn in mm 2
n
23_5 mm
Utilization of strip stock for single row stamping
"'
•
0/./
I
V
workpiece w idth
__J_
w
strip width
a
edge width
):
e
V
web width
strip feed
A
area of workpiece
(including holes)
R
number of rows
T/
degree of utilization
---r
e
workpiece length
w
"'
Strip width
I
I
W = w+2 • a
Strip feed
V= I+ e
Utilizatio n factor
R-A
IJ= V · W
318
Production engineering: 6.6 Forming
fTfJ:11 ;F.fililF.h11
.1~11111111 ■,.
•~,11 ... :.•,....,11t;1ro,1uf:Hf1l1•11l 11,........,r.. •
Smallest allowable bending radius for bent parts of non-ferrous metals
Material
Material condition
AIMa3-01
AIMa3-H14
A1Mg3-H111
soheroidized
cold work hardened
cold work hardened
cf. DIN 5520 12002-07)
Thickness sin mm
o.8 I 1 I 1.5 I 2 I 3 I 4 I 5 I 6
Smallest allowable bendina radius , 11 in mm
0.6
1
2
3
4
6
8
10
1.6
2.5
4
6
10
14
18
6
8
10
1
5
3
45
_5
6
8
10
14
AIMg4.5Mn-H112 spheroidized
1 -+1
2 _5
4 -+--+---+---l-l-- - -----+-"a.c.n.=.dc.accn"'n""ea""
l""
ed'----+-l ._
-+-1---~
straiahtened
~s
AIMg4.5Mn-H111
cold work hardened
1_6
2_5
4
and annealed
solution annealed
AIMgSi1-T6
4
5
8
and artificiallv aaed
CuZn37-R600
hard
4
5
2.5
11 For bending angle a= 90°, regardless of rolling direction
6
l0
16
20
25
12
16
23
28
36
8
10
12
18
24
Smallest allowable bending racius for cold bencing steel
cf. DIN 693511975-10)
Minimum bending radius 11 , for sheet metal thickness s in mm
M inimum tensile
strength Rm
in N/mm2 over-to
1
1.5
2.5
3
4
5
6
7
8
10
12
14
16
18
up to 390
1
1.6
2.5
3
5
6
8
10
12
16
20
25
28
36
40
390-490
1.2
2
3
4
5
8
10
12
16
20
25
28
32
40
45
490-640
1.6
2.5
4
5
6
8
10
12
16
20
25
32
36
45
50
20
11 Values apply to bending angle as 120° and bending transverse to rolling direction. Value of the next larger sheet
metal thickness should be selected for bending longitudinal to ro lling direction and bending angle a > 120°.
Bend allowances v for bending angle a =90°
Bending
radius r
inmm
cf. Supplement 2 to DIN 6935 !withdrawn)
Bend allowance v per bend in mm for sheet metal thickness s i n mm
0.4
0.6
0.8
1
1.5
2
1
1.6
2.5
4
1.0
1.3
1.6
1.7
1.8
2.2
2.8
1.9
2.1
2.4
3.0
-
-
2.9
3.2
3.7
-
-
-
1.3
1.6
2.0
2.5
4.0
4.5
4.8
5.2
6.0
6
10
16
20
-
-
3.4
3.8
5.5
8.1
9.8
4.5
6.1
8.7
10.4
5.2
6.7
9.3
11.0
5.9
7.4
9.9
11.6
6.7
8.1
10.5
12.2
25
32
40
50
-
-
-
11.9
15.0
18.4
22.7
12.6
15.6
19.0
23.3
13.2
16.2
19.6
23.9
13.8
16.8
20.2
24.5
14.4
17.4
20.8
25. 1
-
-
-
-
2.5
3
3.5
4
4.5
5
6
8
10
-
-
-
-
6.9
-
-
-
-
-
-
7.5
8.9
11.2
12.8
8.3
9.6
11.9
13.4
9.0
10.4
12.6
14.1
9.9
11.2
13.3
14.9
12.7
14.8
16.3
-
-
17.8
19.3
21.0
22.3
15.0
18.0
21.4
25.7
15.6
18.6
22.0
26.3
16.2
19.2
22.6
26.9
16.8
19.8
23.2
27.5
18.2
21.0
24.5
28.8
21.1
23.8
26.9
31.2
24.1
26.7
29.7
33.6
-
Calculation of blank size for 90° bent parts
L
a, b, c length of leg
s thickness
, bending radius
n number of bends
v bend allowance
r
v
..
r--
..
--
"'('
/
a
L
developed length 11
♦
-
cf. DIN 693511975--10)
Developed length21
I
L=a+b+c+ ... -n•v l
21 Calculated developed length
should be rounded off to a
whole mm value.
Example lsee illus.):
a = 25 mm; b = 20 mm; C= 15 mm; n = 2; t = 2 mm;
r = 4 mm; material S235JR; v = ?; L = ?
v = 4.5 mm !from table above)
L = a + b + c- n - v = (25 + 20 + 15 - 2 - 4.5) mm = 51 mm
-
11 If the ratio r/s > 5, the formula for developed length I page 24) can be
used.
319
Production engineering: 6.6 Forming
Calculation of blank size, Springback in bending
Calculation of blank size for parts with any selected bending angle
L developed length
a, b length of leg
v
bend allowance
k
correction factor
cf. DIN 6935 (1975-10)
s sheet met. thickness
r bending radius
{3 aperture angle
Developed length11
I
L =a +b - v
Bend allowance for /J = 0° to 90°
180"-P) · ( r + s -k)
v=2-(r+s) -n • ( ~
2
a
Bend allowance for /J over 90° to 165°
180°--/3 - n • ( 180°-P)
s • k)
v = 2 • (r +s) -tan - - • ( r +2
180°
2
fJ > 90° t o 166°
Bending allowance for {3 over 166° to 180°
v ~ 0 (negligible)
Correction factor
I k= 0.65 + 0.5 • log ~
V)
Example:
Bent part with {3 = 60°, a = 16 mm, b = 21 mm, r = 6 mm,
S= 5 mm; k= ?; V= ?; L = ?;
Correction factor
t
-'<
10
!.. = 6 mm = 1.2; k = 0.7 (from diagram);
~
0.8
/
~
.g 0.6
~
... --
s 5mm
k = 0.689 (calculated by formula)
I
0.4
:s 0.2 II
C:
0
= 2 - (6 +5)mm - ><.
t
8
(1~~6()") .(6 + ; -o.1) mm = 5.nmm
L = a+b - v = 16 mm+ 21 mm - 5.n mm ae 32 mm
0
3 4
5 6
ratio rls - -
11 For r/s > 5 the developed length (page 24) is sufficiently accurat e
for calculations.
Springback in bending
s
tool
Radius on tool
a 1 angle of bend before
springback (on tool)
a 2 angle of bend after
springback (on workpiece)
r1
radius on tool
r2
bending radius on workpiece
ka
springback factor
sheet metal thickness
s
Angle of bend before springback
I
Springback factor -"fl for the ratio r2/ s
Material of
bent part
1.6
2.5
4
6.3
10
16
25
40
63
100
DC04
DC01
X12CrNi1 8-8
0.99
0.99
0.99
0.99
0.99
0.98
0.99
0.99
0.97
0.98
0.97
0.95
0.97
0.96
0.93
0.97
0.96
0.89
0.96
0.93
0.84
0.94
0.90
0.76
0.91
0.85
0.63
0.87
0.77
0.83
0.66
E-Cu-R20
CuZn33-R29
CuNi18Zn20
0.98
0.97
0.97
0.97
0.97
0.96
0.96
0.95
0.97
0.95
0.94
0.96
0.93
0.93
0.95
0.90
0.89
0.92
0.85
0.86
0.87
0.79
0.83
0.82
0.72
0.77
0.72
0.6
0.73
EN AW-Al99.0
EN AW-AICuMgl
EN AW-AISiMgMn
0.99
0.92
0.98
0.99
0.90
0.98
0.99
0.87
0.97
0.99
0.84
0.96
0.98
0.77
0.95
0.98
0.67
0.93
0.97
0.54
0.90
0.97
0.96
0.95
0.93
0.86
0.82
0.76
0.72
320
Production engineering: 6.6 Forming
Deep drawing
Calculation of blank diameter
Drawn part
without flange d2
~
W3
D=Jd,2 +4 • d 1 • h
with flange d 2
D = Jd,2+4-d1 -h
without flange da
di
D = Jd,2 + 4 • (d, • h, + d2 • h,)
-
with flange d 3
~
D = Jd,2 +4 • (d, • h, +d2 • h,)
d<
~
2
without flange d 4
e
with flange d 2
D = J 2 • d,2 +4 • d 1 • h+(d,2 - d,2)
without flange d 2
D = Jd,2 + 4 • h,2 + 4 • d 1 • h,
with flange d i
D = Jd,2 +4. h,2 +4 . d, . h, +(d,2 - d 12)
D = J2 . d 12 = 1.414. d
1
with flange d 2
with flange d 4
D =Jd,2 + 4 • d 2 - l+(d/ - d/l
1
without flange d 2
D = J2 • d 12 + 4 • d 1 • h
without flange d 2
d2
D = Jd,2 + 4 • d2 • I
'
'
Blank diameter D
Drawn part
Blank diameter D
~
D = Jd,2+d,2
Example:
Cylindrical drawn part with flange d 2 (see figure, upper left) with d 1 = 50 mm, h = 30 mm; D =?
D = Jd12 +4. d 1 • h = J502 mm2 +4 . 50 mm. 30 mm = 92.2 mm
Drawing gap and radii on draw ring and draw punch
draw punch
d
blank holder
w
drawing gap
s
sheet met al thickness
k
material factor
r,
radius on draw ring
'st
radius of draw punch
D
blank diameter
d
punch diameter
d,
draw ring diameter
I
Radius of draw ring in mm
'r = 0.035- [50 + (D-d)) •
✓s
For each redraw the radius of the draw
ring should be reduced by 20 to 40%.
I
Radius of draw punch in mm
D
' st = (4 to 5) • s
Example:
Steel sheet; 0 = 51 mm; d= 25 mm; S= 2 m m; w = ?; r,= ?; r,. = ?
k
Material factor k
Steel
0.07
Aluminum
0.02
Other non-ferrous metals
0.04
w
= 0.07 (from table)
= s + k. ~ = 2 + 0.07 . {1o.2 = 2.3 mm
r, = 0.035. [50 + (0- d)] •
fs = 0.035 • [50 + (51 - 25)] • f2 = 3.8 mm
r., = 4.5 • s = 4.5 . 2 mm = 9 mm
321
Production engineering: 6.6 Forming
Deep drawing
Drawing steps and drawing ratios
0
d
d1
d2
dn
p,
P2
P,0 1
s
blank d iameter
inside diameter of finished draw n part
punch d iamet er for 1st draw
punch diamet er for 2nd draw
punch diameter for nth draw
drawing ratio for 1st draw
drawing ratio for 2nd draw
tot al drawing ratio
sheet metal thickness
Drawing ratio
1st draw
2nd draw
Example:
draw ring
Cup w ithout flange made of DC04 (St 14) wit h d 50 mm; h= 60 mm; D= ?; P, = ?; P2 = 7; d1 = ?; d:i = ?
D =Jd 2 +4 - d-h
= J (50 mm >2 + 4 • 50 m m• 60 m m = 120 mm
fJ, =2.0; fJ-i = 1.3 (acco rd ing to table below)
Tot al
drawing ratio
d, = _[)__ = 120 mm = 60 mm
fJ,
2.0
Redraw
Material
f3,ot = f3, • /32 • •• •
d, = :!J. = 60 m m =46 mm
{J,.
1.3
Two draws sufficient since d2 < d
Max. drawing
ratios11
Rm2I
Material
Max. drawing
ratios1>
P,
Material
P2
DCO1 (St 12)
1.8
1.2
410
CuZn30-R270
2.1
1.3
270
DCO3(St1 3)
1.9
1.3
370
CuZn37-R300
2.1
1.4
300
DCO4 (St1 4)
2.0
1.3
350
CuZn37-R410
1.9
1.2
410
X10CrNi18-8
1.8
1.2
750
CuSn6--R350
1.5
1.2
350
P2
n
Rm21
P,
N/mm2
D
f3,o, - c1
Max. drawing
rat ios11
Rm21
P,
P2
Al99.5 H111
2.1
1.6
95
A1Mg1 H111
1.9
1.3
145
A1Cu4Mg1 T4
2.0
1.5
425
AISi1 MgMn T6
2.1
1.4
310
N/mm2
N/m m 2
11 Values apply up t o d
1 : s • 300; they w ere determi ned for d 1 • 100 mm and s • 1 mm. Values change neglig ibly
21 maximum tensile strength
for other sheet metal thicknesses and punch diameters.
Tearing force, deep drawing force, blank holding force
F,
tearing force
F dd
deep drawing force
d,
punch diam et er
s
sheet metal t hickness
Rm
tensile st rengt h
p
draw ing ratio
Pmax m ax. possible
draw ing ratio
Ft,
blank holding fo rce
0
blank diameter
cit,
support diameter
of blank holding force
Blank holding pressure pin N/mm2
Steel
2.5
Cu alloys
2.0-2.4
A l alloys
1.2-1 .5
p
blank holding pressure
'r
w
radius on draw ring
draw ing gap
Deep drawing force
/3- 1
fcJd = 1t • (d1 + s) • s • Rm· 1.2 • - --
/Jmax - 1
Support diameter of blank holding force
Example:
D = 210 mm; d, • 140 mm; s = 1 mm; Rm = 380 N/mm2; P= 1.5; Pmax = 1.9; Fdd = ?
5
- 1.2 • 1. - l = 112218 N
Fdd= n • (d 1 + s) • s • Rm - 1.2 • ~ =n • (140mm + 1 mm) - 1 mm - 380 ~
Pn,., - 1
mm2
1.9 - 1
322
Production engineering: 6.7 Joining, Welding
•1•i:.lllllll I 111 1N;l,.'1,..J!!I'_. 1J...'IIU
,1,.h:.Jll:.Jr.1■fill;,u;
Welding, cutting, soldering and related processes
N11
1
101
111
cf. DIN EN ISO 4063 (2000-04)
Method, process
NII
Method, process
N1l
Arc welding
24
25
flash butt welding
upset welding
7
Other welding methods
metal arc welding
shielded metal arc welding
3
Gas welding
73
74
electrogas welding
induction welding
oxyacetylene welding
75
753
light beam welding
infrared welding
gas welding w ith oxygen/
propane flame
78
788
stud welding
friction stud welding
Method, process
11
metal arc welding
w ithout shielding gas
311
12
13
submerged arc welding
gas shielded metal arc welding
312
131
135
gas metal arc welding
metal active gas welding (MAGI
4
Pressure welding
B Cutting
flux cored arc welding
136 w ith active gas shield
41
42
ultrasonic welding
friction welding
81
82
oxygen cutting
arc cutting
137
flux cored arc welding
w ith inert gas shield
45
47
diffusion welding
pressure gas welding
83
84
plasma cutting
laser beam cutting
14
141
tungsten gas shield. arc welding
gas tungsten arc welding
5
Beam welding
9
Brazing, soldering
15
151
plasma arc welding
plasma TIG welding
51
52
electron beam welding
laser beam welding
91
912
brazing
torch brazing
2
Resistance welding
512
electron beam
welding, nonvacuum
914
924
metal bath brazing
vacuum brazing
21
22
resistance spot welding
seam welding
521
solid-state laser beam
in atmosphere
94
944
soldering
metal bath soldering
225
23
foil butt seam welding
projection welding
522
gas laser beam welding
946
952
induction soldering
iron soldering
-
Process ISO 4063-111: Specified welding process- manual arc welding (111)
1> N Reference number for designating methods and processes in drawings, operating procedures and data pro-
cessing
Welding positions
cf. DIN EN ISO 6947 (1997-05)
-
PE
-
PO
PC----.._
~~fi1
g §~
PA
Main position, description
PA
flat welding position
weld axis vertical, horizontal work, final pass
at t op
PB
horizontal position
horizontal work, final pass at top
~r,
1--
PF
PC
transverse position
weld axis horizontal, horizontal work
r---
PG
PD
horizontal
overhead position
PE
overhead position
horizontal work direction, overhead,
final pass at bottom
horizontal work direction, weld axis vertical,
final pass at bottom
PF
vertical up position
upward work direction
PG
vertic. down position
downward work direction
)))))))))))))~
e~
---
PB ,
Name
Code
direction
General tolerances for weldments
cf. DIN EN ISO 13920 (1996-11)
Allowable deviations
~
..
-/,IX
11 /
,-..
shorter leg
..
..
for length dimensions
t,,Jinmm
nominal size range / 11
..,
Degree
of accuracy
to
30
for angle dimensions
ll.a in ° and·
nominal size range 11>
over
30
to
120
over
120
to
400
over
400
to
1000
over
1000
to
2000
over
2000
to
4000
400
over
400
to
1000
over
1000
±10'
to
A
±1
±1
±1
±2
±3
± 4
±20'
±15'
B
±1
±2
±2
±3
±4
± 6
±45'
±30'
±20'
C
±1
±3
±4
±6
±8
±11
± 1·
±45'
±30'
323
Production engineering : 6.7 Joining, Welding
cf DIN EN ISO 9692 1 12004 051
replaces DIN EN 29692
Weld preparation
Weld preparation
WorkName,
weld symbol piece
weld
thickness 01>
t
Edge form
pages 93-95
mm
Flare-V
groove
weld
0-2
s
0-4
s
II
0-8
V groove
weld
V
Y-buttweld
y
d
3-10
s
3-40
d
5-40
s
> 10
d
> 10
bevel
groove
weld
V
d
3-10
s
3-30
d
> 10
d
>2
s
double
bevel weld
K
Fillet weld
~
VI
..._
~
~
~
Preferred
welding
method21
Remarks
Thin sheet
welding,
usually w ithout
filler material
gap b
mm
webc
mm
angle a
in °
-
-
-
3, 111, 141,
512
t
-
-
3, 111, 141
~ t /2
-
-
111,141
" t /2
-
-
13
s4
s 2
40°-60°
3
""" 60°
111, 141
s3
s2
400---60°
13
~
1-4
2-4
1-3
2-4
Little filler
material,
no weld
preparation
With backing run
so·
111,
13, 141
~ 60°
111, 141
~
40°-60°
With root and
backing run
13
(X
double
V-weld
X
~
~
.::_
.I\..
butt weld
Dimension
·
¥
~ 60°
1-3
~
6fr
~
111,141
"2
400-600
13
Symmetrical
edge form,
h = t/2
2-4
1-2
35°---60°
111 ,
13, 141
-
1-4
s 2
35°---60°
111 ,
13, 141
With backing run
1-4
s 2
35°---60°
111,
13, 141
Symmetrical
edge form,
h = t/2 or t/3
" 2
-
70°- 100°
3, 111 ,
13, 141
s 2
-
70°-110°
3, 111,
13, 141
T-joint
b
>3
d
.::~
,:,
f2
1> D Design: s single-V weld; d double-V weld
21 For welding methods, see page 322
Double fillet weld,
corner joint
324
Production engineering: 6.7 Joining, Welding
Compressed gas cylinders, Gas welding rods
Compressed gas cylinders*
cf. DIN EN 1089-3 (2004-06)
Color coding 11
as per DIN EN 1089-3
body
shoulder
Volume
Filling
Filling
V
pressure Pr- quantity
I
bar
40
150
6m3
Oxygen
blue
white
blue
R3/4
50
200
10m3
chestnut- chestnut40
19
8kg
Acetylene
yellow Quick connect
19
10 kg
brown
brown
50
10
200
2 m3
Hydrogen
red
red
red
W21.80x1/14
200
10m3
50
dark10
200
2 m3
A rgon
gray
gray
W21.80x1/14
green
10 m 3
50
200
10
200
2 m3
Helium
gray
brown
gray
W21.80x1/14
50
200
10 m 3
20
200
4 m3
Argon-carbon
fluorescent
gray
W21.80x1/14
dioxide mixture gray
green
50
200
10 m 3
10
58
7.5 kg
Carbon dioxide gray
gray
gray
W21.80x1/14
50
58
20 kg
dark40
150
6 m3
Nitrogen
gray
black
W24.32x1/14
green
50
200
10 m 3
11 Changeover to the new color coding should be completed by July 1, 2006. During the t ransition
period the hazardous substance label (page 331) is the only legally valid designation.
*) According to European Standards
Type of gas
shoulder
N
, body
previous
Connection
threads
Gas welding rods for steel joint welding
cf. DIN EN 12536 (2000-08),
replaces DIN 8554-1
Classification, weld metal analysis, weld behavior
Designation
new
Weld met al analysis in % (standard values)
prev.
C
Si
Mn
Mo
01
GI
<0.1
011
GIi
<0.2
0111
G Iii
<0.15
< 0.25
O IV
G IV
<0.15
<0.25
ov
GV
<0.10
<0.25
Ni
<0.20
<0.65
-
-
< 0.25
< 1.20
-
-
< 1.25
-
<0.80
< 1.20
<0.65
<1.20
<0.65
Weld behavior
Cr
Flow behavior
Spatter
Tendency
for pores
-
highly fluid
high
yes
-
less highly fluid
low
yes
-
semifluid
none
no
-
< 1.20
semifluid
none
no
-
< 1.20
semifluid
none
no
Areas of application, mechanical properties
N/mm2
Tensile
strength
Rm
N/mm2
Elongation
at fracture
A
%
u
> 260
360-410
> 20
> 30
0 11
u
> 300
390- 440
> 20
> 47
S235, S275
P235GH, P265GH
0 111
u
>310
400-460
> 22
>47
Boilers, pipes,
t emperature resistant up to 530 °C
S235, S355, S275, P235,
P235GH, P265GH,
P295GH, 16Mo3
O IV
u
> 260
440-490
> 22
> 47
Boilers, pipes,
temperature resistant up to 570 °C
13CrMo4-5, 16CrMo3
ov
T
> 315
490- 590
> 18
> 47
•
Welding
rod,
code
A reas of
application
Steel type
Sheet, tube
S235, S275
0 1
S235, S275,
P235GH, P265GH
Vessels,
pipes
=
1
..
T"
'-~·
I
Yield
strength
Re
Rod EN 12536 - 0 IV: Gas welding rod of Class IV
11 T Treatment condition of the weld: U untreated (weld condition); T tempered
2 > NI notch impact energy at +20°C, determined using an ISO-V test specimen
Nl 21
Kv
J
325
Production engineering: 6.7 Joining, Welding
Shielding gases, Wire electrodes*
Shielding gases for arc welding of steel
cf. DIN EN 439 (1995-05)
1
Composition >
Gas type,
effect
Welding
methods
Materials;
Applications
Rl
H2 < 15%, balance Ar or He
R2
(15-35)% H2, balance Ar o r He
reduction
gases
TIG, plasmawelding
high-alloy steels,
Ni, Ni alloys
inert gases
(neutral
behavior)
MIG,TIG,
plasmawelding
Al, Al alloys,
Cu, Cu alloys
gas mixtures,
weak
oxidizing
MAG welding
alloyed Cr-Ni steels;
mainly stainless and
acid-resistant steels
Codes
11
100%Ar
12
100%He
13
He< 95%, balance Ar
M11
CO2 s 5%, H2 s 5%, balance Ar or He
M1 2
(3- 10)% CO 2, balance Ar or He
M13
0 2 < 3%, balance Ar
M21
(5-251% CO 2, balance Ar or He
M22
(3-10)% CO 2, balance Ar or He
M23
CO2 s 5%, (3-10)% 0 2 , balance Ar or He
M31
(25-50)% CO2 , balance Ar or He
M32
( 10- 15)% 0 2 , balance Ar or He
M33
(5-50)% CO 2, (8-15)% 0 2, balance Ar or He
mixed gases,
more strongly MAG welding
oxidizing
low-alloyed and
medium-alloyed steels
mixed gases,
medium
oxidizing
MAG w elding
unalloyed and low
alloyed steels; heavy
plate
strongly oxidizing gases
MAG welding
unalloyed steels
C1
100% co,
C2
0 2 s 30%, balance CO2
=
Shielding gas EN 439-13: Inert gas with up to 95% Helium, balance Argon
11
Ar argon
He helium
o,oxygen
CO 2 carbon dioxide
H2 hydrogen
Wire electrodes and deposits for gas-shielded metal arc
welding of non-alloy and fine grain structural steels
Designation example (weld metal):
EN440
T
I Standard number!
I
I
Designation for
gas shielded metal
arc welding
Code digit for
the mechanical
properties of the
weld metal
(page 3271
- G
46
3
M
TT ~T
Code digit for
notch impact
energy of the
weld metal
(page 3271
cf. DIN EN 440(1994-11)
G3Si1
--.-Designation
for shielding gases
Code
Jetter
Shielding gases
DIN439
M
M21, M22,
M23, M24
C
C1
Chemical composition of the wire electrodes (examples)
Designation
Main alloying elements
Designation
Main alloying elements
GO
A ll compositions agreed upon
G2TI
0.5-0.8% Si, 0.S-1.4% Mn, 0.05-0.25% li
G3Si1
0.7- 1.0% Si, 1.3 - 1.6% Mn
G2Ni2
0.4--0.8% Si, 0.8-1.4% Mn, 2.1- 2.7% Ni
=
EN 440-G 464 M G3Si1: Properties of weld metal: Minimum yield strength R0 = 460 N/mm2 ,
notch impact energy at - 40°C = 47 J; mixed gas M21-M24, electrode w ith 0.7- 1.0% Si, 1.3- 1.6% Mn
Wire electrodes (selection)
Designation as per
DIN EN 440
Welding
methods
Shielding
gases
Usable on steels,
examples
G464MG3Si1
MAG
M21- M24, Cl
S185-S355, E295, E335,
Applications, properties,
examples
joint and build-up welding
P235-P355, GP240R,
G 504 M G4Si1
MAG
M21- M24, Cl
l 210-l360
like G3Si1, but higher mechanical
strength properties
G46M G2Ni2
MAG
M21
12Ni14, 13MnNi6-3,
S(P)275-S(P)420
fine grain struct ural steels and
steels with low-temp. toughness
*) According to European Standards
326
Production engineering: 6.7 Joining, Welding
Standard values for gas shielded metal arc welding, Filler metals for aluminum
Weld seam type
Weld design
Weld
W ire
Number
thickness diameter of passes
a
mm
mm
Settings
Voltage
V
Efficiency values
Current W ire feed
A
rate 11
m/min
Shielding gas
Filler
metal
I /min
g/m
Productive
time
minim
MAG welding, standard values for unalloyed structural steel
Wire electrode DIN EN 440 - G 46 4 M G3Si1
Welding position: PB
'I>
Shielding gas DIN EN 439 - M21
1
20
22
23
105
215
220
7
11
11
10
45
90
140
1.5
1.4
2.1
1.0
1.0
1.2
1
1
3
30
300
10
15
215
300
390
2.6
3.5
4.6
1.2
3
4
30
300
10
15
545
805
6.4
9.5
2
3
4
0.8
1.0
1.0
5
6
7
~
,
8
10
4
5
6
1.2
1.6
1.6
10°-
5
6
8
1.6
MIG welding. standard values for aluminum alloys
Welding position: PA
Filler metal DIN 1732 - SG - A1Mg5
I
~,
Shielding gas DIN EN 439 - 11
1
23
25
26
180
200
230
3
4
7
12
18
18
30
77
147
2.9
3.3
3.9
1
2
2
22
22
26
160
170
220
6
6
7
18
126
147
183
4.2
4.6
5.0
11 For MIG welding: welding t ravel speed
TIG welding, standard values for aluminum alloys
Welding position: PA
~t I
Filler metal DIN 1732 - SG -A1Mg5
1
1.5
3.0
1
2
3
3.0
4
5
6
-
0.3
0.2
5
19
22
3.8
4.3
1
-
110
125
0.2
6
28
1.8
5.9
3.0
1
-
160
185
210
0.2
0.1
0.1
8
10
10
38
47
47
6.7
7.1
12
5
4.0
1st layer
2nd layer
-
165
0.1
0.2
12
105
13
6
4.0
1st layer
2nd layer
-
165
0.1
0.2
12
190
16
-~
,
70°
Shielding gas DIN EN 439 - 11
75
90
Welding fillers for aluminum
Designations11
Material
number
cf. DIN 1732 (1988-06)
Application for base metals
(Designation without adding EN AW)
SG-Al99.8
(EL-Al99.8)
3.0286
A l99.7, Al99.5
SG·A199.5Ti
(EL-Al99.5Ti)
3.0805
Al99.0, Al99.5
SG-A1Mn1
(EL-AIMnl)
3.0516
AIMn1, AIMn1Cu
SG-AIMg3
3.3536
AIMgl(C), A1Mg3
SG-AIMg5
3.3556
AIMg3, A1Mg4, AIMg5, AISi1MgMn, AIMg1SiCu, AIZn4.5Mg1,
G-AIMg5, G-AIMgSi, G-AIMg3, G-A1Mg3Si
SG-AIMg4.5Mn
3.3548
AIMg4, AIMg5, AISi1MgMn, AIMg1SiCu, AIZn4.5Mg1, G-AIMg5,
G-AIMgSi
SG-AISi5
(EL-AISi5)
3.2245
AIMgSi 1Cu, A1Zn4.5Mg1
SG-A1Si12
(EL-AISi12)
3.2585
G-AISi1, G-AISi9Mg, G-AISi7Mg, G-AISi5Mg
1> SG metal fillers with bare surfaces; EL coated rod electrodes
327
Productio n engineering : 6.7 Jo ining, Welding
Rod electrodes for arc welding
cf. DIN EN ISO 2560 (2006-03)
replaces DIN EN 499
Coated rod electrodes for unalloyed steels and fine grain steels
I Classification of rod electrodes
I
I
• Yield strength
• Notch impact energy 47 J
I
I • Tensile strength
I • Notch impact energy 27 J
according to
Designation example
I
ISO 2560-A - E 46 3 1NiB 54 HS
~
-
Standard number
A classification according to
yield strength and notch
impact energy 47 J
-
H hydrogen content
5 -> 5 m l/100 g weld metal
I
~
E coated rod electrode
Code numbers for the welding position
Code numbers for the mechanical properties
of weld metal
Code Minimum
number
y ield
strength
N/mm2
Tensile
strength
N/mm2
Minimum
elo ngation
at fracture
E4, in%
35
355
440- 570
22
38
380
470- 600
20
42
420
500-640
20
46
460
530-680
20
50
500
560- 720
18
Welding position
Code
number
1
all positions
2
all positions, except vertical down welds
3
butt weld in flat position, fillet weld
in flat and horizontal position
4
butt and fillet weld in flat position
5
for vertical down weld and as in number 3
Code number for the efficiency and the type of current
Code
number
Code letter for the notch impact energy
of weld metal
Efficiency
%
Type of current
Code letter/
code number
Minimum notch impact energy
47 J at °C
1
> 105
AC and DC
2
> 105
DC
z
no requirement s
3
> 105 s 125
AC and DC
A
+ 20
4
>105s125
DC
0
0
5
> 125 s 160
AC and DC
2
- 20
6
> 125s160
DC
3
- 30
7
> 160
AC and DC
4
- 40
8
> 160
DC
Code letters for the chemical
composition
1--
Code
letters
Maximum content in %
Mn
Mo
Ni
None
2.0
-
-
-
Code letters for the type of coat ing
Code
letters
Type of coating
A
acid coating
B
basic coating
Mo
1.4
0.3- 0.6
-
C
cellulose coating
MnMo
1.4- 2.0
0.3- 0.6
-
R
rut ile coating
0.6-1.2
RA
rut ile acid coating
1.8-2.6
RB
rutile basic coating
0.6- 1.2
RC
rutile cellulose coating
0.6- 1.2
RR
thick rutile coating
1Ni
1.4
2Ni
1.4
M n1Ni
1.4- 2.0
-
1NiMo
1.4
0.3- 0.6
2560-A 2
12: A rod electrode wi th guaranteed yield strength and notch impact energy, 42 y ield
= ISO
strengt h Re= 420 N/mm', 2 notch impact energy 47 J at - 20°C, RB rutile basic coating, 1 efficiency> 105%, 2 all
E 42
RB
welding positions except for vertical down welds.
328
Production Engineering: 6.7 J oining, Welding
Coating of rod electrodes, Weld design
Coating of rod electrodes used for arc welding
The coating of rod electrodes has a decisive influence on the welding properties and t he mechanical properties of
the weld metal.
The coating consists of a homogeneous mixt ure of the following components:
• slag formers
• deoxidizers
• inert gas fonmers
• arc st abilizers
binders
alloy contents, if applicable
The addition of iron powder increases the efficiency of the weld metal.
Properties, application and welding position according to the type of coating11
Type of coating
Properties, application
Welding position (page 322)
acid coating
With thick coat ed rod electrodes, fine drip
transition w ith flat, smooth welds, risk of
solidification cracking
Limited application in
constrained positions
basic coating
High notch impact energy, particularly at
low temperatures, low crack sensitivity
PA,PB,PC,PD, PE, PF
cellulose coating
Intense arc w ith particular suitabil ity for
vertical down welding
PG
rutile coating
Good drip transition, suitable for the
welding of thin sheets
PA,PB,PC,PD, PE,PF
rutile acid coating
Typically t hick coated rod electrodes,
same properties as electrodes with acid coating
PA, PB, PC, PD,PE, PF
rutil e basic coating
Good welding and mechanical properties
PA, PB,PC,PD, PE, PF
rutile cellulose coating
Good drip transition, suitable for welding
of thin sheets, also in vertical down position
PA,PB,PC,PD,PE,P~ PG
11 The specifications apply to rod electrodes designated according to the yield strength and the notch impact
energy (page 327).
Weld design for arc welded V joints
Weld
t hickness
60°
"'
filler pass
root pass
Spec. electrade consump.
Weld weight
per pass
total
Zs
ms
m
piece/m
g/m
g/m
4
1
1R
1 FP
3.2 X 450
4 x450
3
2
75
80
155
1.5
1R
1 FP
3.2 X 450
4 x450
4
2.9
100
110
210
1R
2 FP
1R
1F
1 FP
1R
1F
1 FP
3.2 X 450
4 x450
3.2 X 450
4 x450
5 x450
3.2 X 450
4 x450
5 x450
4
4.7
4
3.7
3.5
4
4
6.2
100
185
100
145
215
100
195
380
1
1
3.2 X 450
4 x450
3.2
3.6
80
140
80
140
8.6
8
215
310
215
310
5
s
Electrode
dimensions
d xi
mm
mm
a
final pass
Number
and
type of
pass1I
Gap
s
mm
6
2
8
2
10
2
285
460
675
Weld design for arc welded fiUet welds
3
4
-
final pass
5
6
-
3
3
3.2 X 450
4 x450
root pass
8
-
1R
2 FP
4
5
X 450
x 450
3
7
120
430
550
10
-
1R
4 FP
4
5
x450
x450
3
12.3
120
745
865
3
18.5
120
1125
1245
12
'b
11
-
R root pass;
1R
4FP
F filler pass;
4
5
x 450
x450
FP final pass
329
Production engineering: 6.7 Joining, Welding
Areas of application and standard values for beam cutting
Areas of application for cutting processes
Sheet metal thickness sin mm
Materials
6
4
2
8 10
20
100
40
Struct ural steel,
unalloyed and alloyed
Chrome-nickel steels
Aluminum,
aluminum alloys
Titanium, glass, ceramic,
stone, plastics, rubber,
foam materials, etc.
Standard values for oxyacetylene cutting
Material: unalloyed structural steel;
Sheet met.
thickn.
Widt h of
cut
Cutting
nozzle
mm
Acetylene
pressure
Oxygen pressure
s
mm
fuel gas: acetylene
cutting
heating
mm
bar
bar
Total
oxygen
Acetylene
Cutting rate
consumption
quality
cut
standard
cut
consumption
bar
m 3/hr
m 3/hr
m/min
m/min
2.0
0.2
1.67
1.92
2. 14
0.27
0.32
0.34
0.69
0.64
0.60
0.84
0.78
0.74
2.5
3.0
3.5
2.5
0.2
2.46
2.67
2.98
0.36
0.37
0.38
0.62
0.52
0.45
0.75
0.69
0.64
4.0
4.3
4.5
2.5
0.2
3.20
3.42
3.54
0.40
0.42
0.44
0.41
0.38
0.36
0.60
0.57
0.55
5
8
10
3- 10
1.5
2.0
2.5
3.0
10
15
20
10-25
1.8
25
30
35
25-40
2.0
Standard values for plasma cutting11
Sheet met.
thickn.
s
mm
Material: high-alloyed structural steels
Cutting method: argon-hydrogen
Material: aluminum
Cutting method: argon-hydrogen
Electrical
Cutting
current
rate
Electrical current
qua!.
cut
A
stand.
cut
A
4
5
70
120
10
15
20
25
70
120
quality
cut
Consumption values
stand.
cut
argon
hydrogen
nitro·
m/min
m/min
3
m /hr
3
m 3/hr
1.4
1.1
2.4
2.0
0.6
0.65
0.95
1.2
0.24
0.35
0.25
0.35
0.6
0.45
0.35
1.2
1.2
1.5
0.24
m /hr
gen
quality
cut
A
1.2
0.24
0.48
70
70
Consumption
values
rate
quality
cut
stand.
argon
cut
hydrogen
A
m/min
m/min
m3/hr
m 3/hr
3.6
6.0
5.0
1.2
0.5
1.2
0.5
stand.
1.2
0.6
Cutting
120
120
1.9
1.1
0.6
0.35
0.2
11 Values apply to an arc power of approx. 12 kW and 1.2 mm cutting noozle diamet er.
cut
1.6
1.3
0.75
0.5
330
Production engineering: 6.7 Joining, Welding
Standard values, Quality and dimensional tolerances for beam cutting
Standard values for laser cutting11
Sheet met.
M21 thickness
s
mm
Cutting
speed
Cutting
gas
V
m/min
Cutting
gas press.
p
bar
Laser power 1 kW
Cutting
speed
Cutting
gas
V
m/min
Cutting
gas press.
p
bar
Cutting
speed
V
m/min
Laser power 1.5 kW
5.0- 8.0
4.0- 7.0
2
2.5
4.0- 6.0
3.5-5.0
3
4
3.5- 4.0
2.5- 3.0
3.5- 4.2
2.8-3.3
3.6-2.8
2.8-3.4
5
6
1.8-2.3
1.3-1.6
2.3- 2.7
1.9-2.2
2.5- 3.0
2.1 -2.5
-.;
1
1.5
4.0- 5.5
2.8- 3.6
"'"'
2
2.5
2.2 - 2.8
1.6- 2.0
3
4
1.3-1.4
Q)
ti
-0
Q)
>-;;;
E
C
::,
~
Q)
C:
·.;
iii
7.0- 10
5.5- 7.5
02
N2
1.5- 3.5
5.0- 7.0
3.5-5.2
14
2.0- 4.0
1.9-3.2
15
-
-
7.0- 10
5.6- 7.4
4.8-6.2
4.2- 5.0
8
10
Cutting
gas press.
p
bar
Laser power 2 kW
1
1.5
-.;
Cutting
gas
02
1.5- 3.5
N2
1.8-.2.4
1.0- 1.1
4.8- 6.1
4.2-5.0
6
10
4.5- 9.0
3.8-6.6
10
14
3.4- 5.3
2.7-3.8
14
15
2.2- 2.7
1.4-1.8
02
1.5- 3.5
12
13
14
N2
14
16
11 The table values apply a the focal length off= 127 mm (5") and a cutting gap width of w = 0.15 mm.
21 M material group
Cutting quality and dimensional tolerances for thermal cuts
Quality of cut surfaces
The specification s apply to
• oxy-fuel gas cutting,
• plasma cutting,
• laser beam cutting.
Range
The quality of the cut surfaces
is determined by
• the perpendicularity tolerance u,
• the average surface roughness R,s.
nominal length
workpiece thickness
perpendicularity tolerance
average surface roughness
limit deviations from the
nominal length I
I
s
u
R,s
t,.{
"'
:
-
M
u
r--
I
ISO 9013-~
standard number~
Qua~ty of cut
Jj
perpendicularity tolerance u
according to row 3
average surface roughness R,s
according to row 4
tolerance class 2
cf. DIN EN ISO 9013 (2003-07)
Perpendicularity
tolerance u
inmm
Average surface
roughness R,s
inµm
1
u < 0.05 + 0.03 • s
R,s < 10 + 0.6 • s
2
u < 0.15 + 0.07 • s
R,s < 40 + 0.8 • s
3
u < 0.4 + 0.01 • s
R,s < 70 + 1.2 • s
4
u < 1.2 + 0.035 • s
R,5 <110+1.8-s
Comments
Put in workpiece
thickness
inmm
Limit deviations from the nominal length
Limit deviat ions t,./ from nominal lengths/ in mm
Workpiece
thickness s
inmm
Tolerance class 1
Tolerance class 2
>35
> 125
> 315
>35
> 125
> 315
s 1000
s 125
s 315
s 1000
" 125
,s315
> 1 ,s3.15
± 0.3
± 0.3
±0.4
± 0.5
± 0.7
± 0.8
>3.15 s 6.3
± 0.4
± 0.4
± 0.5
± 0.8
±0.9
± 1.1
> 6.3 s 10
± 0.6
±0.7
± 0.7
± 1.3
± 1.4
± 1.5
> 10 s 50
± 0.7
± 0.7
± 0.8
± 1.8
± 1.9
± 2.3
> 50 s 100
± 1.3
± 1.4
± 1.7
± 2.5
± 2.6
± 3.0
> 100 s 150
± 1.9
±2.0
± 2.1
±3.3
±3.4
± 3.7
Example: oxy-fuel gas cutting according to tolerance class 2, / = 450 mm,
s = 12 mm, cutting quality according to range 4
Sought after: t,./; u; R,s
Solution:
t,./ =±2.3 mm
u = 1.2 + 0.035 · S= 1.2 mm+ 0.035 • 12 mm = 1.62 mm
R,s= 110+ 1.8 . S = 110µm+ 1.8 -12 µm = 131.6 µm
331
Production engineering: 6.7 Joining, Welding
Gas cylinders - Identification*
Hazardous substance labels
cf. DIN EN ISO 7225 (2008-02)
A hazardous substance label must be applied t o individual gas cylinders t o identify their contents and any possible hazards from these contents. Up to t hree hazard labels warn of the main hazards.
Example:
supplemental information on
hazards and safety
precautions
product name,
i.e. oxygen
gas
composition
EWG no. for pure substances
or the words
complete
name of the gas,
e.g. oxygen, compressed
manufacturer's name,
address, phone number
Hazard label
non-combustible,
combustible
toxic
fl ammable
corrosive
non-toxic
Color coding
cf. DIN EN 1089-3 (2004-06)
Color coding of the cylinder shoulder is used as additional information about the properties of the gases.
It is readily recognized when the hazardous substance label is illegible from a distance.
This color coding does not apply to liquid gases.
General color coding
>
. . . . . . . . rtallpotandal
toxic and/or corrosice
flammable
inert21
oxidizing
Color coding for special gases
Oxygen
11 N = new
Acetylene
21
Argon
i
Nitrogen
Non-toxic, non-corrosive, non-flammable, non-oxidizing
•1 Accordin to Euro ean Standards
Carbon dioxide
Helium
332
Production engineering: 6.7 Joining, Welding
Gas cylinders - Identification*
Pure gases and gas mixtures for industrial use
Color coding (examples)
cf. Information sheet from Industrial Gases Associat ion
Coding
Coding
new11 2)
old
Xenon, Krypton, Neon
Oxygen
N
blue
blue
white
gray
fl ourescent
green
blue
gray
(black)
gray
Acetylene
0
new1l2l
old
Hydrogen
yellow
chestnut brown
red
red
yellow
(black)
chestnut brown
red
red
Argon
Forming gas (mixture of nitrogen/hydrogen)
gray
dark green
red
red
gray
gray
red
(dark green)
gray
Nitrogen
Mixture of argon/carbon dioxide
dark green
black
gray
flourescent
green
dark green
gray
gray
gray
Carbon dioxide
Compressed air
gray
gray
gray
flourescent
green
gray
gray
Helium
gray
brown
gray
gray
gray
gray
11 For gas cylinders color coded as per DIN EN 1089, the
letter "N" (= new) must be put on t he shoulder of the
cylinder two times (opposite sides). The "N" is not
required on cylinders whose color coding has not
changed.
21 The cylinder body may be another color. However, this
must not lead to confusion regarding the hazardous
nature of the cylinder contents.
*) According to European Standards
333
Production engineering : 6.7 Joining, So ldering and Brazing
Brazing
Brazing heavy non-ferrous metals
cf. DIN EN 1044 (1999-071
Silver containing brazing materials
Brazing mat erial
Material
Group Oesig- number
11
nation
Alloy
designation
as per
ISO 367721
AG301
2.5143
B-Ag50CdZnCu-620/640
640
G
f, I
AG 302 2.51 46
B-Ag45CdZnCu-605/620
620
G
f, I
C
N
"O
u::,
u
2.5141
B-Ag45ZnCdCu-595/630
610
G
f, I
AG309
2.1215
B-Cu40ZnAgCd-605/765
750
G,V
f, I
c
c
N
AG 104
2.5158
B-Ag45CuZnSn-640/680
670
G
f, I
AG 106
2.5157
B-Cu36AgZnSn-630/730
710
G
f, I
u
AG203
2.5147
B-Ag44CuZn-675/735
730
G
f, I
AG 205
2.1 216
B-Cu40ZnAg-700/790
780
G
f, I
AG 207
2.1207
B-Cu48ZnAg(Sil-800/830
830
G
f, I
860
G,V
f, I
1/)
::,
O>
<(
g~
- o AG 208 2.1205 B-Cu55ZnAg(Sil-820/870
8i
., _ CP 102 2.1210 B-Cu80AgP-645/800
Materials
·c
AG304
O>
<(
Information for use
Wor1<ing
tempera- Brazing Solder
ture
joint31 f eed41
precious metals, st eels,
copper alloys
st eels, malleable cast i ron, copper,
copper alloys, nickel, nickel alloys
steels, malleable cast iron, copper,
copper alloys, nickel,
nickel alloys
steels, malleable cast iron, copper,
copper alloys, nickel, nickel alloys
710
G, V
f, I
CP 104
2.1 466
B-Cu89PAg-645/815
710
G,V
f, I
CP 105
2.1467
B-Cu92PAg-645/825
710
G,V
f, I
B-Ag50CdZnCuNi-635/655
660
G
f, I
~.S AG403 2.5162 B-Ag56CulnNi-600/710
730
G
f, I
chrome, chrome-nickel steels
G
f, I
carbide onto steel,
tungsten and molybdenum mate ri als
steels
~
0
> Q)
== .0
1/)
AG351 2.5160
Q)
copper and nickel-free copper alloys.
Unsuitable for materials containing
Fe o r Ni
Cu alloys
N
0. ~
1/) .J:l
AG 502
2.5156
B-Ag49ZnCuMnNi-680/705
690
Copper based brazing materials
cu 104
cu 201
cu 202
cu 301
2.0091
B-Cu100(Pl-1085
11 00
G
I
2.1021
B-Cu94Sn(P)-910/1040
1040
G
I
2.1055
B-CuBBSn(Pl-825/990
990
G
I
2.0367
L-CuZn40
900
G,V
f, I
G,V
f, I
steels, malleable iron, Ni, Ni alloys
V
f
cast iron
G
f, I
Cu, Fe-free and Ni-free Cu alloys
5)
5)
51
nickel, cobalt,
nickel and cobalt a lloys,
unalloyed and alloyed steels
cu 305
2.0711
B-Cu48ZnNi(Sil-890/920
910
CP 202
2.1463
B-Cu93P-7 10/820
720
iron and nickel materials
steels, malleab. iron, Cu, Ni, Cu & Ni alloys
Nickel based brazing materials for high-temperature brazing
NI 101
2.4140
B-Ni73CrFeSiB(C)-960/1060
NI 103
2.4143
B-Ni92SiB-980/1040
NI 105
2.4148
B-Ni7 1CrSi-1080/1 135
NI 107
2.41 50
B-Ni76CrP-890
Aluminum based brazing materials
AL 102
3.2280
B-Al92Si-575/615
610
G
f, I
AL 103
3.2282
B-A190Si-575/590
600
G
f, I
AL 104
3.2285
B-AIBBSi-575/585
595
G
f, I
11 The two letters indicate the alloy group, while t he three dig it numbers
are purely numbers increasing sequentially.
21 Numbers at the end indicate the melting range. Alloy components,
see pages 116 and 117.
31 G suitable for gap brazing; V suitable fo r V-joint brazing
41 ffilled brazing; I lapped brazing
51 Refer to manufacturer's data.
aluminum and A l alloy types
AIMn, AIMgMn, G-AISi;
especially for A l alloy types
AIMg, AIMgSi up to 2% Mg content
Brazing joint
Gap brazing:
w < 0.25mm
V-joi nt b razing:
w > 0.3mm
ff
334
Product ion engineeri ng: 6.7 Joining, Soldering and Brazing
Solders and flux
Solders
Alloy
group 11
cf. DIN EN ISO 9453 (2006-12)
Working
temperature
Application examples
L-Sn63Pb
L-Sn63Pb
L-Sn60Pb
183
183
183-190
elect ronics, printed circuit board s
printed circuit boards, high-grade steel
L-Sn50Pb
L-PbSn40
183-215
183-235
183-255
320--325
electronics industry, t in plating
thin-sheet packaging, metal goods
183
183-190
precision mechanics
L-Sn60Pb(Sb)
S-Pb58Sn40Sb2
S-Pb74Sn25Sb1
L-PbSn40Sb
L-PbSn25Sb
185-231
185-263
radiat or manufacturing, wiping solder
w iping so lder, lead solders
141
142
S-Sn60Pb38Bi2
S-Pb49Sn48Bi3
-
180--185
138
precision solders
low-tem perat ure solder, safety fuses
151
S-Sn50Pb32Cd18
L-SnPbCd18
145
161
162
S-Sn60Pb39Cu1
S-Sn50Pb49Cu1
L-SnPbCu3
L-Sn50PbCu
230--250
183-2 15
electronic devices, precision mechanics
17 1
S-Sn60PbAg
L-Sn60PbAg
178-180
electrical devices, printed circuit boards
182
191
S-Pb95Ag5
S-Pb93Sn5Ag2
L-PbAg5
-
304--365
296-301
for high operating temperat ures
electric motors, electrical equipment
A lloy designation
as per ISO 36773 1
Previous
designation
DIN 1707
102
103
S-Sn63Pb37
S-Sn63Pb37E
S-Sn60Pb40
111
114
116
124
S-Pb50Sn50
S-Pb60Sn40
S-Pb70Sn30
S-Pb98Sn2
131
132
S-Sn63Pb37Sb
S-Sn60Pb40Sb
-
134
136
Alloy
no. 2)
101
tin-lead
lead-tin
t in-leadanti mony
tin-leadb ismuth
ti n-leadcadmium
t i n-leadcopper
tin-leadsilver
lead-tinsilver
1)
2)
3)
-L-PbSn2
·c
precision mechanics
plumbing work, zinc, zinc alloys
radiat or manufacturing
precision mechanics, electrical industry
t hermal fuses, cable joints
Filler metals fo r alum inium are no longer in EN ISO 9453.
The alloy num bers replace t he material numbers as per DI N 1707.
With traces (<0.5%) of Sb, Bi, Cd, Au, In, A l, Fe. Ni, Zn: see pages 116 and 117.
Flux for soldering
cf. DIN EN 29454-1 (1994-02)
Designation by main constituents
Flux
type
1 rosin
2 organic
Flux basis
1 colophonium
2 without colophonium 1 without activat or
2 act ivated by halogens
1 water soluble
3 act ivated w ithout halogens
2 not water soluble
A liquid
1 salts
1 w ith ammonium chloride
2 w ithout ammonium chloride
B solid
2 acids
1 phosphoric acid
2 ot her acids
C paste
3 alkali ne
1 amine and/or ammonia
3 inorganic
=:>
Classification by effect
Flux
form
Flux activator
Designations
Effect of
DIN EN DIN 851 1 residues
3.2.2 ...
3.1.1...
F-SW11
F-SW12
3.2. 1...
3.1.1...
2.1.3...
2.1.2...
1.2.2...
F-SW13
F-SW21
F-SW23
F-SW25
F-SW28
1.1.1...
1.2.3...
F-SW31
F-SW33
Aux
Activation temper.
FH10
FH11
FH12
FL10
Fl20
somewhat
corrosive
noncorrosive
Flux ISO 9454 -1.2.2.C: Flux of type rosin (1), base w ithout colophoni um (2).
activat ed by halogens (2), available in paste form (C)
Flux for brazing
FH20
FH21
FH30
FH40
very
corrosive
cf. DIN EN 1045 (1997-08)
Instructions for use
550--800
550--800
550--850
·c
·c
·c
100-1000 ·c
150--1100 •c
Multi-purpose flux; residues rinsed off o r chemically st ripped.
Cu-Al alloys; residues rinsed off or chemically st ripped.
Stai nless and high-alloy steels, carbide; residues chemically stripped.
over 1000 ·c
550--1 ooo ·c
Multi-purpose flux; residues rinsed off or chemically stri pped.
M ult i-purpose flux; residues removed mechanically or chemically stripped.
For copper and nickel solder; residues removed mechanically.
Boron-free flux; residues rinsed off or chemically stripped.
400--100 ·c
Light alloys; residues are rinsed off or chemically st ripped.
Light alloys; residues are non-corrosive, but should be protected from moisture.
400--100 •c
335
Production engineering: 6.7 Joining, Soldering and Brazing
Soldered and brazed joints
Classification of soldering and brazing processes
Soldering and brazing processes
High t emperature brazing
Brazing
Differentiating
characteristics
Soldering
Working t emperature
< 450 · c
> 450 • c
> 900 · c
Energy source
soldering iron, soldering
bath, electrical resistance
flame, furnace
flame, laser beam,
electric induction
Base material
Cu.Ag,
Al alloys,
stainless steel,
steel, Cu,
Ni alloys
steel,
carbide inserts
steel, carbide
Soldering or filler
material
Sn, Pb alloys
Cu, Ag alloys
Ni-Cr alloys,
Ag-Au-Pd alloys
Auxiliary materials
Flux
flux, vacuum
vacuum, shielding gas
Standard values for soldering gap widths
Base material
for solders
Soldering gap width in mm
for brazi ng materials primarily of
copper
brass
silver
unalloyed steel
0.05----0.2
0.05----0.15
0. 1-0.3
0.05----0.2
Alloy steel
0.1-0.25
0.1-0.2
0.1-0.35
0.1-0.25
Cu, Cu alloys
0.05----0.2
-
-
0.05----0.25
-
0.3-0.5
-
0.3-0.5
Carbide
Design rules for soldered joints
~
4...
1
.,, t -
~
dmax:::::: 5. s
Soldered j oint under shearing load
~
:
+
Production process simplification
s
Soldered pipe fitting
• Soldering gap should be large enough so that flux and solder adequately fi ll the gap by capillary action (t able above)
• The two surfaces to be soldered should be parallel.
• Surface roughness due to machining can remain for
Cu soldering Rz = 10-16 µm, for Ag soldering at Rz =
25 µm.
Load transfer
Load on solder jo int reduced by folded seam
stop +
position
Preconditions
knurled
pr ess fit
• The load on the soldered joint should be in shear (transverse forces) if at all possible. In particular, solder seams
should not be loaded with tensile or peeling stress.
Soldering gap depths /d > 5 • s do not fill with solder reliably. Therefore load capacity cannot be increased by a
larger gap depth.
Load capacity can be increased by design features such as
folds
Production process simplification
• In solderi ng there should be a means for assuring proper
positioning of the parts to be joined, e.g. by part shape
or by knurled press fit.
Application examples
• pipes and fittings
• sheet metal parts
• tools with brazed carbide cutters
336
Production engineering: 6.7 J oining, Ad hesive bonding
Adhesives, Preparation of joint surfaces
Properties and conditions of use for adhesives11
Curing conditions
max.
Comb. tensile
operating
and shear
temperastrength
lure
•e
·c
N/mm2
Trade name
Adhesive
Temperat ure Tome
"C
Acrylic
resins
AgometM.
Acronal,
StabilitExpress
Epoxy resins Araldi!,
(EP)
Metallon,
Uhu-Plus
Elasticity
20
24 hr
120
6--30
low
20-200
1 hr to
12 hr
50-200
10-35
low
Phenolic
resins (PF)
Porodur,
Pertinax,
Bakelit e
120-200
60s
140
20
low
Polyvinyl
chlo ride
(PVC)
Hostalit,
lsodur,
Macroplast
20
> 24 hr
60
60
low
Polyurethane Desmocoll,
(PUR)
Delopur,
Baydur
50
24 hr
40
50
present
Applications,
special characteristics
metals, thermosets,
ceramics. g lass
metals. thermosets. glass.
ceramics, concrete, wood;
long curing time
metals, thermosets,
glass, e lastomers, wood,
ceramics
met als, thermosets,
glass, elastomers, wood,
ceramics
metals, elastomers,
glass, wood,
some t hermoplastics
Polyester
resins (UP)
Fibron,
Leguval,
Verstopal
25
1 hr
170
60
low
Polychloroprene
(CR)
Baypren,
Contitec,
Fast bond
50
1 hr
110
5
present
Cyanoacrylate
Permabond,
Sicomet 77
20
40 s
85
20-25
low
fast-curing adhesive for
metals, plastics, elastomers
Hot glue
Jet-Melt,
Ecomelt,
Vesta-Melt
20
>30s
50
2- 5
present
all types of mat erials;
adhesive action through
cooling
1)
metals, thermosets,
ceramics, glass
contact glue for metals
and plast ics
Due to varying chemical compositions of adhesives, the values given are only approximate values. For detailed
information please refer t o information from t he manufacturer.
Preparation of parts for bonded joints
Treat ment sequence 1l
for load severity 2 >
Material
low
Al alloys
Mg alloys
1-2-3-4
To alloys
Cu alloys
cf. VOi 2229 (1979-061
1-2-3-4
Treatment sequence11
for load severity21
Material
medium
high
1-6-5-3-4
1-2-7-8-3-4
Steel, bright
1-6-2-3-4
1-7-2-9-3-4
1-6-2-3-4
1-2-10-3-4
Steel, galvanized
Steel, phosphatized
1-6-2-3-4
1-7-2-3-4
Other metals
low
medium
high
1-6-2-3-4
1-7-2-3-4
1-2-3-4
1-2-3-4
1-2-3-4
1-2-3-4
1-6-2-3-4
1-2-3-4
1-6-2-3-4
1-7-2-3-4
1)
Code numb8'S for type of t reatment
1 Cleaning of dirt, scale, rust
6 M echanical roughing by grinding or brushing
2 Removing grease with organic solvent
7 M echanical roughing by shot blast ing
or aqueous cleaning agent
8 Etching 30 min, at 60°C in 27.5% sulfuric acid solution
3 Rinsing w ith clear water
9 Etching 1 min, at 20 °c in 20% nitric acid solution
4 Drying in hot air up to 65 •c
10 Etching 3 min, at 20 •c in 15 % hydrofluoric acid solution
5 Removing grease with simultaneous etching
2)
Load severity for bonded joints
low:
Tensile shear strength up t o 5 N/mm 2; dry environment; for precision mechanics, electrical equipment
Medium: Tensile shear strength up to 10 N/mm 2; humid air; contact with oil; for machine and vehicule manufacturing
High:
Tensile shear strength up to 10 N/mm2; direct contact w ith liquids; for aircraft, ship, and container
manufacturing
337
Production engineering: 6.7 Joining, Adhesive bonding
Design of adhesive bonded joints, Test methods
Design examples
Bonded joints should be loaded in compression or shearing if possible.
Tensile, peeling or bending loads should be avoided.
Butt joint/overlap joint
Tube joint
i!J,h
,Mr
good, since the bonding surfaces
only have a shear load
good, since the bonding surfaces
only have a shear and
compression load
good, since sufficiently large
bonding surfaces can withstand
shear load
1JD1.h
not as good, since small
Mr
bonding surfaces cannot
withstand tensile and shear load
not as good,
since peeling forces act due to
off-center application of force
Test methods
Test method
standard
Contents
Bending peel test
DIN 54461
Tests resistance of bonded joints against peeling forces
Tensile shear test
DIN EN 1465
Tests tensile shear strength of high-strength bonded lap joints
Fatigue tast
DIN EN ISO 9664
Tests fatigue properties of structural adhesives under tensile-shear loads
Tensile test
DIN EN 26922
Tests tensile strength of bonded butt joints perpendicular to bonded surface
Roller peel test
DIN EN 1464
Tests resistance to peeling forces
Compression shear tast
DIN EN 15337
Tests shear strength, primarily of anaerobic11 adhesives
11 Sets with exclusion of air
Adhesive behavior as a function of temperature and size of bonding surface
increasing
width w
t
t
.r:
C> 30
C
e
1n
:;;a,
20
.r:
"'
~
10
'iii
C
e
test t emperature 8 Tensile shear strength of
overlap bonded joints
bonded surface area Effect of adhesive joint surface
area on breaking load
338 Production engineering: 6.8 Workplace safety and environmental protection
Safety colors, Prohibitive signs*
Safety colors
cf. DIN 4844-1 12005-05) and BGV A811 (2002-04)
Color
red
yellow
Meaning
stop,
prohibited
caution!
potential danger
safety,
first aid
Contrast color w hite
black
w hit e
w hite
Color of graph- black
icsymbol
b lack
whit e
w hit e
Notice of hazards (e. g.
fire, explosion, radiation);
notice of obstructions (e. g. speed
bumps, holes)
Identification of am bulances and emergency
exits;
fi rst aid an d
emergency aid st ations
Requirement t o
wear personal protective equipment (PPE);
location of a
telephone
Application
examples
(see pages 340
and 341)
St op signs,
em ergency st op
prohibitive signs,
fire fighting
equipment
Prohibitive signs
Prohibited
mandatory signs,
notices
cf. DIN 4844-2 (2001-02) and BGV AB11 12002-04)
No smoking
No fires, open
flame or
smoking
Pedestrian access Do not extinguish
prohibited
with water
Non-potable
water
Access prohibited Access by forklifts
for unauthorized
prohibited
persons
Do not touch
Do not t ouch live voltage
Do not
connect
No access for
persons w ith
pacem aker
Placement or stor- Transport of pasage prohibited sengers prohibited
Walking in this
area prohibited
No spraying with
water
No cell phones
No food or drink
allowed
Do not use this
device in the
bathtub, shower
or sink
Do not reach in
Operating w ith
long hair
prohibited
Hand-held or
manually operated grinding not
allowed
No magnetic or
electronic data
media allowed
Clim bing
prohibited fo r
unauthorized
persons
German Employer's Liability Insurance Association - Accident Prevention Regulations (Berufsgenossenschaftliche Unfallverhiitungsvorschrift) BGV AB (replaces VGB 125)
• ) According to European Standards
11
Production engineering: 6.8 Workplace safety and environmental protection
339
Warning signs*
cf. DIN 4844-2 (2001-02) and BGV A811 (2002-04)
Warning signs
Warning:
Hazardous area
Warning:
Warning:
Combustible
materials
Explosive
substances
Warning:
Suspended
load
Warning:
Forklift traffic
Danger:
High voltage
Warning:
Non-ionic,
electromagnetic
radiation
Warning:
Strong magnetic
field
Warning:
Substances
hazardous to
health or irritants
Warning:
Danger of tipping
when rolling
11
Warning:
Toxic substances
Warning:
Warning:
Corrosive substances
Radioactive
materials or
ionizing radiation
Warning:
Optical radiation
Warning:
Laser beam
radiation
Warning:
Oxidizing
substances
Warning:
Danger of
tripping
Warning:
Danger of falling
Warning:
Biological hazard
Warning:
Extreme cold
Warning:
Gas cylinders
Warning:
Hazards due to
batteries
Warning:
Explosive
atmosphere
Warning:
Milling shaft
Warning:
Crushing hazard
Warning:
Automatic
start-up
Warning:
Hot surface
Warning:
Risk of hand
injury
Warning:
Danger of slipping
Warning:
Moving
conveyor
on track
German Employer's liability Insurance Association - Accident Prevention Regulations (Berufsgenossenschaftliche Unfallverhutungsvorschrift) BGV AB (replaces VGB 125)
*) According to European Standards
340 Production engineering: 6.8 Workplace safety and environmental protection
•
Sa f ety SIQnS
*
cf DIN 484-l 2 12001 021
and BGV A8 ' 12002 041
Mandatory signs
General
mandatory sign
Wear safety
glasses
Wear hard hat
Wear ear
protection
Wear respirator
Wear protective
gloves
Wear protective
clothing
Wear face
protection
Use safety belt
For pedestrians
Use crosswalk
Disc. plug from
power bef. opening
Disconnect
before working
Wear life
preserver
Sound horn
Follow
instructions
Emergency
shower
Eye rinsing
equipment
Escape route mergency exit
Meeting point
Wear safety shoes
•
Use safety
harness
Escape and rescue signs for escape routes and emergency exits
Direction arrows f or First aid stations,
escape routes and emergency exits2 1
Emergency
telephone
Doctor
First aid
Medical stretcher
Defibrillator
Fire protection symbols and additional symbols
Directio nal arrows
Wall hydrant and
fire hose
Ladder
Fire extinguisher
Work area!
High Voltage
Danger to life
Locatton:
Date:
Sign may only be
removed by:
Fire fighting
equipment
Manual fire alarm
Extra sign which
gives more information to
supplement the safety sign
1l German Employer's Liability Insurance Association
-Accident Prevention Regulations (Berufsgenossenschaftliche
Unfallverhutungsvorschrift) BGV Af3
Fire alarm
telephone
Extra sign which
gives more information to
supplement the safety sign
21 only in combination with other escape route
and rescue signs
*) According to European Standards
Production engineering: 6.8 Workplace safety and environmental protection 341
·
Sa f ety Signs
*
cf DIN 4844 2 12001 02<
and BGV AR <2002 04<
Information signs
I
Discharge time
longer than
1 minute
In case of
failure part can
have live voltage
Before touching
- discharge
- ground
- short c1rcu1t
5 Safety rules
Befo•e rJeg,r,n 1ng wo,k
£ nploy safety disconnec t
Le>< k oul to prt vent iesfil'1
Check for rm voll dqi
Ground an d s'lor1 u r cu•t
Cover or enl use ,1d1,Kl'< !
pc1rt'> wh ich t1 1ve I• ,e vol rnge
Combination signs
®
Workarea!
Location:
High Voltage
Hazardous
Date:
~~~b~lybe
Do not connect
Combination signs for escape
routes or emergency exits with
corresponding direction indicat ed
by arrows
Warning of high voltage
l~ ffll lffll~ I
lffllHI ffl
First aid station
First aid
station
11
Walking on roof
is prohibited
Prohibited! Walking on
roof is prohibited.
Fire blanket
Fire blanket for fighting fire
Lh
Tum off engine.
Risk of poisoning.
Danger of t oxic
gases
German Employer's Liability Insurance Association - Accident Prevention Regulations (Berufsgenossenschaftliche Unfallverhiitungsvorschrift) BGV A S (replaces VGB 125)
*) According to European Standards
342 Production engineering: 6.8 Workplace safety and environmental protection
Danger symbols and description of hazards*
Code letter, danger symbol, haza rd description
T+
Danger criteria of
materials
When consumed
in very small
amounts leads to
death or may
cause acut e
or chronic damage to health.
Very toxic
T
Code letter,
Danger criteria of Code letter,
Danger criteria of
danger symbol,
materials
danger symbol,
materials
hazard description
hazard description
Contact w ith skin
Xi
E
Xn
When ingested
may result in
death or cause
Solid material
can be easily
ignited by a
source of ignition.
X = St. Andrew's
cross
i = irritating
Flammable
Risk of explosion
by shock, friction,
fire o r other
N
sources of
ignition.
Danger of
explosion
T = t oxic
branes can cause
inflammation.
F
F = flammable
may cause acute
or chronic damage to health.
Toxic
or mucus mem-
Liquid material
w ith flash point
< 21 •c.
Irritant
T = toxic
When consumed
in small amounts
leads to death or
6
RL \~:: E:,~
0
0
acute or chronic
harm t o health.
E = explosive
Substances that
substantially
increase the risk
and severity of a
fire, because they
produce oxygen.
Environmentally
dangerous
Twith R 45
Substances
change water,
ground, air, climate, animals,
plants, etc. in
such a way that
the environment
is endangered.
N = noxious
(harmful)
Substance may
cause cancer fro
inhaling, swallowi ng or from contact with the skin.
R 45: M ay cause
Harmful to
health
C
X = St. Andrew's
cross
n = noxious
living tissue can
be damageci by
contact.
cancer
Oxidizing
F+
Carcinogenic
0 = oxidizing
T = t oxic
Liquid substances
with flash point
< O°C and boiling
point < 35 °C;
gaseous sub-
Subst ances
which can have a
mut agenic effect
on humans.
Twith R46
R 46: May cause
heritable genetic
damage.
stances, which
are flammable in
contact with air.
Corrosive
Highly
flammable
C = corrosive
XnwithR40
Limited
evidence of
mutagenic
eflect
Mutagenic
substances
F - flammable
Substance which
can cause concern T with R 60, R 61
due to possible
mutagenic effect
on humans. However, there is not
yet sufficient
inform ation available to give conDanger to
elusive proof.
fertility
Substances which
X = St. Andrew's
T = toxic
R 60 = may impair
fertility
R 61 = may cause
harm to the
unborn child
cross
n = noxious
R 40 = irreversible
damage possible
(page 199)
11 EU-Directive, Appendix II
are known to
T = t oxic
Xn with
R 62, R63
impair fertility or
reproduction.
Substances
which cause concern due to possi-
ble impairment of
fertility of
humans.
•) According to European Standards
Limited
evidence of
influence on
fertility
X = St. Andrew's
cross
n = noxious
R 62 = possible
risk of impaired
fertility
R 63 = possible
risk of harm to
unborn child
Production engineering: 6.8 Workplace safety and environmental protection
Identification of pipe lines*
c1
343
°
1 2403
N
(2007 051
Area of application and requirements
Area of application: A precise identification marking of pipe lines, indicating the substance being conveyed, is necessary for reasons of safety, fire fighting and proper maintenance and repairs. The identification marking is intended to
indicat e possible hazards and help t o prevent accidents and damage to health.
Requirements concerning identification marking
Identification marking must be clearly visible and longlasting.
Identification can be established by painting, lettering
(e.g. via self-adhesive foil strips) or signs.
Particularly operation-critical and hazardous places
should be marked (e.g. beginning and end of branch
pipes, wall penetrations, linings).
Marking must be repeated at least every 10 m of pipe
length.
Indication of the group and supplemental color (see
table below).
Indication of the flow direction by means of an arrow.
• Indication of the conveyed substance by specifying the
name (e.g. water) or the chemical formula (e. g. H2 0).
• With hazardous mat erials, additional indication of
hazard signs (page 342) or warning signs (page 339) if
general hazards are implied.
Color assignment according to conveyed substances
Conveyed substance
Group
RAL
Supplem.
color
RAL
Color of
lettering
RAL
Water
1
white
Steam
Air
2
3
white
black
9003
9003
9004
Flammable gases
Non-flammable gases
4
5
black
black
9004
9004
Acids
Lyes
7
white
w hite
9003
3001
9004
6
9003
Flammable liquids
and solid materials
8
3001
white
9003
Non-flammable liquids
and solid materials
9
9004
white
9003
Oxygen
0
white
9003
Identification of special pipe lines
Fire extinguishing lines must be fitted w ith a red/White/red color marking. The white field contains the graphical symbol of the safety sign "Fire fighting equipment and materials" (cf. page 340) in the color of the extinguishing agent.
Potable water lines must be fitted w ith a green/white/green color marking. Non-potable water lines have a
green/blue/green marking. The code letters and their colors are listed in the table below.
Description
Code
Description
Code
Potable water line
Potable water line, cold
PW
PWC
Potable wat er line,
hot, circulating
PWH-C
Potable water line, hot
PWH
Non-potable water line
NPW
Potable water
Compressed air
Examples of identification marking
Heating oil
Fire extinguishing unit
(water)
Oxygen (fire-promoting, 0)
Oxygen
◄~------------~
*) According t o European Standards
Acetylene (highly flammable, F+)
Acetylene
344 Production engineer ing: 6.8 Workplace saf ety and env ironmental prot ection
Sound and noise*
Sonic terms
Term
Explanation
Sound
Sound comes from mechanical vibrations. It propagates in gaseous, liquid and solid bodies.
Frequency
Number of oscillations per second. Unit: 1 Hertz = 1 Hz = 1/s. Pitch increases w it h frequency.
Frequency range of human hearing: 16 Hz- 20.000 Hz.
Sound level
Measure of the sound st rength (sound energy).
Noise
Undesirable, annoying o r painful sound waves; damage depends on strengt h, duration,
frequency and regularity of exposure. For a noise level of 85 dB (A) and higher there is danger
of permanent hearing loss.
Decibel (dBi
Standardized unit for sound level.
dB(AI
Since the h uman ear perceives tones of d ifferent heights (frequencies) to have different
st rengths when t hey are actually at the same sound levels, noise must be appropriat ely
dampened with filters for certain frequencies. Frequency weighting curve w ith Filter A
compensates for this and indicat es the subjective auditory impression. A difference of 3 dB (A)
corresponds approximately to a doubling (or halving) of the sound int ensity.
Sound level
Type of sound
dB(AI
Threshold of
auditory sensitivity
4
Breathing at d istance
of 30cm
10
Type of sound
normal speech
at d istance of 1 m
Type of sound
dB (Al
heavy st amping
95--110
angle grinder
95--115
dB(AI
70
machine tools
75--90
85
car horn at
distance of 5 m
disco music
hammer drill, mot orcycle
90
hammer and anvil
110
engine test st and, walkman
90--110
jet engine
120--130
Soft rustling of leaves
20
Whispering
30
loud talking
at distance of 1 m
welding torch, lathe
Tearing paper
40
Quiet conversation
50-60
Noise protection regulations
80
100
100--1 15
cf. Accident Prevention Regulations on "Noise• BGV 83 (1997-01)
Accident prevention regulations
for noise naon,4ucino ona.ations
115 Workplace regulation
Requirem. to post signage for noise ranges 90 dB (A) and above.
Above 85 dB (A) sound prot ection devices must be available, and they must be used above 90 dB (A).
If t he ri sk of accidents increases due t o noise, appropriate
measures m ust be taken.
Regular preventative medical checkups are compulsory.
New operat ional equipment must conform to t he most
advanced level of noise reduct ion.
max.dB (A)
55
No ise limit value for:
oredominantly mental activities
simple, predominantly mechanized
activities
all other activities (value may
be exceeded by 5 dB I
break rooms, ready rooms and
fi rst-aid rooms
70
85
55
Noise harmful to health
I
I
I
Psychological reactions
I I I
I I I-I
I I I
I
I
I
I III
Vegetative reactions
II
II I
I
Damage to hearing
I I
I I
I
I
I
I
I
10
20
-I
1
1
I
I-I
30
40
50
60 65 10
80 85 90
danger limit
for hearing
•1 Accord ing t o European Standards
100
-
inc:unlllle--
I
Physical damage
0
2JJI
,, =--.
:--....
110
120
I
I
I
I
130
140
150
pain
thr eshold
~
160 dB(A)
sound level - - - -
Table of Contents
345
7 Automation and Information Technology
7 .1
Basic terminology for control engineering
Basic terminology, Code letters, Symbols .. ... . 346
Analog controllers ........... . .. .... .. ..... 348
Discontinuous and digital controllers ....... .. 349
Binary logic ................. . . ..... . . .. ... 350
7.2
Electrical circuits
Circuit symbols ........ ... ......... . . . ..... 351
Designations in circuit diagrams ........ .. ... 353
Circuit diagrams ... . ... ..... .............. . 354
Sensors ................ .. ................ 355
Protective precautions .. .......... .. ... .... . 356
7 .3
Function charts and function diagrams
Function charts ............................ 358
Function diagrams . ... .. .... ......... ... .. . 361
7.4
Pneumatics and hydraulics
Circuit symbols . ... ..... .. ... .. .. .. ... ..... 363
Layout of circuit diagrams .. ..... . .... . ...... 365
Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
Hydraulic fluids ....... .......... . .......... 368
Pneumatic cylinders ... ..... . ............... 369
Forces, Speeds, Power . . . . . . . . . . . . . . . . . . . . . . 370
Precision steel t ube ........................ 372
7 .5
Programmable logic control
PLC programming languages .... .. .. . ....... 373
Ladder diagram (LD) .. ..................... 374
Function block language (FBL) . . .. .... . . ... .. 374
Structured text (ST) ... ........... . ..... . ... 374
Instruction list ........ .. ...... . .... .. ..... 375
Simple functions ....... ...... . .. ... .. ... . .. 376
7.6
Handling and robot systems
Coordinate systems and axes ................ 378
Robot designs ....................... .. ... . 379
Grippers, job safety ... ... .... . ........... .. 380
7.7
Numerical Control (NC) technology
Coordinate systems ............... .. ... ... . 381
Program structure according to DIN ... .... ... 382
Tool offset and Cutter compensation ...... .. .. 383
Machining motions as per DIN ............... 384
Machining motions as per PAL ... ..... . .. ... 386
PAL programming system for lathes .......... 388
PAL programming system for milling machines . 392
7 .8
Information technology
Numbering systems ........ . ............... 401
ASCII code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
Symbols for program flow charts ... .. ... ..... 403
Program flow chart, Structograms ....... .. ... 404
WORD commands ....... .. .......... ... ... 405
EXCEL commands ........ ......... .... .. .. 406
w
l+
OFF I - - ~
ON;-~
L-
I k1 rsJ
~--
~
NO
346
Autom ation: 7 .1 Basic terminology
Basic terminology of open loop and closed loop control systems
Basic terminology
cf. DIN 19226-1 to -5 ( 1994-02)
Open loop control
Closed loop control
For open loop control the output variable, such as the temperature in a hardening furnace, is influenced by the input
variable, such as the current in the heating coil. The output
variable does not have an effect on t he input variable.
Open loop control has an open action flow.
For closed loop control the controlled variable, such as t he
actual temp. in an annealing furnace, is continuously monitored and com pared to the target temp. (reference variable) and, if there are deviations, adjusted to the reference
input variable. Closed loop control has a closed action flow.
Example: Annealing furnace
Schemat ic
presentation
Schematic
presentation
disturbance
heat losses
disturbance
heat losses
manipulated
variable
controller
button
controlled system
annealing furnace
Functional diagram of
open loop control syst em
Simplified functional diagram of closed loop
control system ·- - - - -·
z
r;;;:;;;-n I
I;.;-~i rol
w
y
final
control
controller
element
button
relay
1:.:::1
t emperat ure
setpoint
.
I
1ustment •
ewcontact
annealing furnace
fzciis-7
xcontrol.
variable
heat loss
actual
temperature
current
controlled
ring '
sysl8rn
~
X
X
con1rolad
xanr.
vaiatJle
current
temperature
setpoint
Application-based code letters
cf. DIN 19227-1 (1993-10)
Designation example:
POIC
T T
I
First letters
density
electrical parameters
F flow, throughput
G d istance, position, length
H manual input/int ervention
K time
L status (e. g. level)
M humidity
p pressure
Q quality parameters
R radiation parameters
s speed, rotational speed
T temperature
w weight, mass
D
E
actual
temperal
I
Supplementary letters
D
difference
F
ratio
J
control p oint query
Q
sum,int egral
Succeeding letters
error indication
automat ic closed loop control
upper lim it value
display
lower lim it value
R registration
A
C
H
I
L
Example: Differential pressure closed loop control
p1
t
Explanation: P
D
PDIC
I
312
C
p2
t
pressure
difference
display
auto matic closed loop cont rol
In plain language: Pressure d ifferential closed
loop control with display of pressure difference
347
Automation: 7 .1 Basic terminology
Symbols
location of output & uur control
C)
0(
0
Local,
general
Process control
room
0
Measuring point, control point
Effect on the controlled system
0
B
D
cf OIN 19227 1 11993 101
Servo motor,
general
Reference line
Servo motor; the
setting for minimal
mass flow or flow of
energy is set during
loss of auxiliary
power.
Measuring point,
sensor
Example
Servo mot or; the
setting for maxim um mass flow or
flow of energy is set
during loss of aux iliary power.
Local control console
Local, implemented
by process control
system
Final cont rol element, control point
T
R
Servo motor; the
final control device
remains in the most
recently acquired
setting d uring loss
of auxiliary power.
Local, implemented
by process
computer
C
Temperature oontrol
and registration at local
control stand measuring
point 310
Solution based symbols for devices
Symbol
Explanation
Sensors
D
0(
~
D
Symbol
cf. DIN 19227-2 (1991-02)
Explanation
Sym bol
Final controlling & user control
elements
Controllers
Sensor for
temperature,
general
D
Explanation
Controller, general
Valve actuator with
motor drive
Two-point controller
wit h switching o utput and PIO behavior
Valve actuator w ith
solenoid drive
T hree-point cont roller wi th switching output
Adjuster for electric
signal
Sensor for pressure
Sensor for level with f-- - - - - - - - - - - - - - f -- -- - - - -- - -Signal designators
float
Adapters
Pressure transducer
w ith pneumat ic
signal o utput
Sensor for weight.
scales; indicating
:j::j:
Signal, electrical
Signal, pneumatic
A nalog signal
Digital signal
Example: Temperature controler
Output devices
[SJ
-f
A
n
- ---1
signal amplifier for
actuating signal
Basic symbol,
general display
Printer, analog, no.
of channels as a
numeral
temperature
transducer
with electrical
signal output
temperature
sensor
Monitor
signal adjuster for electrical
signal to adjust reference
input variable w
water bath
valve
actuator,
motor
driven
M
steam
348
Automation: 7.1 Basic terminology
Analog controllers
Analog (continuous) controllers
cf. DIN 19225 (1981-12} and DIN 19226-2 (1994-02}
In analog controllers the manipulated variable y may assume any desired value within the control range.
Controller design
P-<:0ntrollers
Proportional
controllers
Level control example, description
Transition function
x
inflow valve
controlled variable
Symbol''
Block~2l
- - step funct ion 31
y manipulated variable - - step response41
e error
Output variable is
proportional to
input variable.
P-controllers
have steady-state
errors.
I-controllers
Integral contro llers
~t
I-controllers a re
slower than
P-controllers, but
they eliminate all
errors.
~t
~
t-
PI-controllers
Proportional
integral controllers
~t
In Pl-controllers a
P-controller and a
I-controller are
connected in parallel.
~t
D-controllers
Derivative con•
!rollers
.,
PD-<:0ntrollers
Proportional
derivative controllers
~
~
t-
~
D-controller systems only occur w ith P- or Plcontroller systems, since pure D-controller
behavior with constant error does not provide
any manipulated variable and therefore no
closed loop control.
PD-controllers are created when a P controller
and a D element are connected in parallel.
The D part changes the output variable at a rate
proportional t o the rate of change of the input
variable. The P part changes the output variable
so that it is proportional to the input variable
itself.
PD-controllers act quickly.
PID-<:Ontrollers
Proportional
integral
derivative controllers
PIO-controllers are created by connecting P, I
and D-controllers in parallel.
Initially the D part reacts with a large change to
the control signal, afterwards this change is
reduced to approximately the magnitude of the
P element, and finally the effect of the I element
causes the response to rise linearly.
11 Symbol as per DIN 19227-2
JI Signal curve at controlled system input
21
Block representation as per DIN 19226-2
41 Signal curve at controlled system output
349
Automation: 7.1 Basic terminology
Discontinuous and digital controllers
Switching (discontinuous) controllers
cf. DIN 19225 (1981-12> and DIN 19226-2 (1994-021
Switching controllers change the manipulated variable y discontinuously by switching in several steps.
Example, description
Controller design
Transition function,
Symbol
switching behavior
Block representation
Two-point controller
heat radiation
___:;;::.·-:?2 contacts
I!T':~:
set-point potentiometer
Three-point controller
switch pos. 1
Air conditioning system
0
2
erro,
switch pos 3
In an air conditioning system three temperature ranges are assigned t hree
switch positions:
- heating ON
- heating/cooling OFF
- cooling ON
·£
O error
switch ~s. 1
Digital controllers (software controllers)
cf. DIN 19225 (1981-12) and DIN 19226-2 (1994-02)
The operating mode of the digital cont roller is implemented as a computer program.
Controller design
Example (simplified)
Transient function
Explanation
tI
Computers
error step
., . I I I I I 1 1 1 1
Enter
reference input
variable w
Programmable
Logic Controllers
(PLC)
Microcontrollers
Aquire
controlled variable x
Microprocessors
Generate error
time t
t;
~
individual parls
'"'4
3
~ l:.+"T""~ ~.:;:;.;__
e= w-x
time f ~
H
PIO
,._4
control algorithm
3
2
1
Output manipulated
variable y
step response
The computer program
has the following tasks:
- generate error e
- calculate the manipulated variable y based
on programmed control algorithms
At the step response all
P. D and I-parts are
summed.
Sampling of analog sig·
nals and their conversion to digital values
and internal program
flow causes a time delay
of t he controlled variable x (similar to a
T-controlled system>.
time f ~
P-controlled systems with time delay IT part)
Controller design
Example
P=ntrolled
system with delay
1st order
(P-T1 controlled
system)
Filling a gas vessel
P=ntrolled
system with delay
2nd order
(P-T2 controlled
system)
cf. DIN 19226-2 (1994-021
p ~ P,
P:L._
P,l _
P;
:&,
f
Explanation
~t~
If the pressure vessel is
filled by a How of gas,
pressure p 1 in the vessel gradually reaches
the pressure of the gas
flow.
,._t ~
Po ~
f
Filling two gas vessels
Transient function
time t ........
~t~
,.,tuZ
time f ~
If two vessels are connected in series, pressure f>2 increases in the
second vessel slower
than pressure p 1 in the
first vessel.
350
Automation: 7.1 Basic terminology
Binary logic
Circuit symbols
Function
~
AND
(NANO)
(NOR)
~
~
0
1
0
1
1
OR
~
(XOR)
0 = (11 A 12) V
-(11 A 12)
1
12
0
0
1
1
0
1
1
0
11
12
0
0
0
1
1
0
0
1
0
0
11
12
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
I = inputs
0
1
0
1
1
~
1
11 12 0 1 02
0 0
0 1 0 1
1 0 1 0
1 1 D D
~
S set
R reset
0
0
0
Exclusive
flop)
11 12
11
1
(RS flip-
0
1
p-.imatic
elec:tric
state unchanged
condition
D indeterminate
state
0 = outputs, e.g. lamps
'
T
~-$
~::1
O
12
~
(1
12
~
~
0 C>¢
(1
0 C>¢
I ~-J
(1
c1 9
o C>¢
~-1
(1
(1
0 C>¢
.T
~
~
11
~-$
12
~
11
~-~-12_.J
(1
c19
oO
11
1
12
•
1-- ~ ---
~
~ ?~ ?
11 ___i
(1
~
~11 - ~
12 '' (1 '
0
j
(1
~
C = relays, contacts
,1
~-□
O(~
c1 y
']
12
• •
•
~-1
11
0
~
0 = i"i""vi2
Memory
0
1
1
0 = i"i""A"i2
NOT-OR
0
0
1
o =T
NOT
AND
0
0
1
1
~
'
12
0
1
0 = 11 V 12
NOT
11
0
0 = 11 A 12
OR
Technical implem-.tlon
Function table
logical equation
ct 0 IN EN 50517 12 11999 041
11 l
l
l 12 l
l
l
~- - j 1(1 ~ - -2J[2
(2
[1
[1
9
[2
01 c
> 9 02¢->
351
Automation: 7.2 Elect rica l circuits
Circuit symbols
cf DIN EN 60617 1 to 1211999 041
General circuit symbols
Resistor,
-c::::::J-- general
[=:I
Fuse
-H-
Capacitor
~
..
-
Inductor, coil
~---@
representation
w
Permanent
0::::::,.
Nonstandard
magnet
Lamps,
general,
optional representation
Buzzer
Horn
~~ component
Electrolytic
-{Z}-
transducer
m
Connection
to ground,
optional representation
Converter,
Conductors, connectors and terminals
Conductor,
general
tr.
Grounded
conductor,
PE
Conductor,
~
moveable
!
t
Neutral conductor, PN
r
Neutral conductor with
protective
function PEN
-
Conductor,
insulated
t
Devices and machines
Measuring
device,
machine
$H
-0-
Measuring
device,
recording
--R
Transformer,
optional representation
Valve
Designations
J_
*
* /;,
Semiconductor diode,
general
LED light
emitting
diode
Types of current
Adjustability
Function
r'
stepped
general
/
continuous
adjustable
?
Effect
thermal
~
radiation
regulated
1rt
Double
junction,
optional representation
1
Ground
@
Ground connectar connection
Semiconductor components
-0-
~
/
TT
Junction,
optional representation
--
DC
~
AC with low
frequency
~
AC with high
frequency
I
~
¥
PNP
transistor
¥
NPN
transistor
Types of connections
y
Y connection
b..
Delta
connection
Yb.
Y-delta connection
Three-pole
switch, protective systern IP44
~
Motor circuit
breaker
I
Automatic
breaker
..-\
Ground-fault
circuit interrupter
Circuit symbols in wiring system drawings
switch
(j cf Circuit
a) single-pole
a)
bl double-pole
b)
j'
Three-way
switch, illuminated
Grounding-
~
Sensor switch
~
type
¥
Series switch
@
Key bunon
@
DC-AC
converter,
regulated
~
DC or AC
(universal)
receptacle
' IP44
~
Application examples
+
Inductor,
continuously
adjustable
--Lr
5
-?
Resistor,
5 step
variable
~
Three-core
cable w ith
junction
Cable with
3 conductors,
w ith ground
conductor (G)
and 1.5 mm2
cross section
®
DC motor
~
Three-phase
motor
352
Automation: 7.2 Electrica l circuits
Circuit symbols
Relay contacts
\
cf DINEN606171tu 1211999011
Actuation types
NO contact,
normally open
1---
Manual,
general
"F---
By tilting
(
NC contact,
normally
closed
~--
By
pressing
fr--
By key
}---
J---
By pedal
\
By
pulling
Single pole
double throw
_f---
By
turning
G---
By coil
Electromech. relays
Switch behavior
Q
-v-
Lock,
prevents
automatic
return
Q
Q
Timer on
delay
a)
Delayed
action (parachute effect)
for movement
a) to the right
b)to the left
bl
Timer off
delay
~
)=
Timer on off
delay
Symbol for
"actuated
state"
11'
By pressure
energy
~-~--
By proximity
By touching
By bi metal
(thermal)
~--
Sensors (Block representation)
Relay coil,
general
F
rn--
I! I
Capacitive
sensor,
reacts to
proximity of
all substances
~
Inductive
sensor,
reacts to
proximity of
metals
~
Magnetic
sensor,
reacts to close
proxim ity of a
magnet (reed
switch)
l'/~I
Optical
sensor,
reacts to
reflection of
infrared beam
E~-\
Magnetic
proximity
switch with
NO contact,
reacts to
proximity of
magnetic
material.
*~r
Capacitive
proximity
switch with
NC contact,
reacts to proximity of all
materials.
Examples of switch applications
a)
I
~-\
NO contact
manually
~~~--1
~--1
Double pole
single throw
NC contact
wit h roller
actuation
bl
it~
it(
al
bl
a) NC contact
bl NO contact
Representation in actuated condition
~~
NO contact
a) closes
bl delayed
opening when
actuated
(}-~t
Emergency
palm button
~
Limit switch,
NO contact
r
Limit switch,
NC contact
¢--X
Valve w ith
electromagnetic
actuation
Flip-flop elements
Delay elements
RS flip-flop
set dominant
RS11 flip-flop
11 12 01 02
11
0
01
2
Function
t able21
0
0
0
1
1 0
1 0
1
DO
1
n
•• l
1 0
I
1
RSflip-flop
reset dominant
11 12 01 02
01
2
Function
table
0
0
••
0 1 0 1
1 0
11 12 01 02
11
12
s 1 01 0 0 • •
Rl 1
02
1 0
1 1 1 0
Wrth rise-delay time
0 1 0
1 0
Function
table
1
9
1 0
1 1 0
1
When a signal is applied
to input I, outputO
assumes
value 1 after
time r, elapses.
With turn-off delay
Flip-flops are integrated
circui ts which store signal
conditions.
1> R = reset
s z set
unchanged state
D indeterminate state
21 •
The numeral 1 after an R or S input indicates that the
logical state of this input is dominant.
If a signal simultaneously lies at inputs 11 and 12 (11 = 1
and 12 = 1) the following applies:
Input w ithout the numeral 1 (R for set dominant, S for
reset dominant RS flip-flop) is always set to logical
state O.
~
With loss of a
signal at
input I, output
O takes the
value O after
completion of
t ime r2.
353
Automation: 7.2 Electrical circuits
Designations in circuit plans*
Designation of devices in circuit diagrams
Example:
cf. DIN EN 61346-212000-12)
rp
S2E
I
Type of device
I
Sequential number
I I
I
Device function
I
I
Code letters for function
(not standardized)
Code letters
for type (selection)
B
F
K
Q
M
p
Sensor, proximity switch
Fuse
Switch relay, timed relay
Circuit breaker, contactor
Solenoid valve, solenoid
Indicator light, horn
R Resistor
s Control switch, push-button
switch
A
Function OFF
B
Direction of movement
E
Function ON
Example of circuit diagram
K
Jog operation
::-[
s
Save, set
S§
E E-- _
Kl
R
Clear, reset
Kl
s
G Test
Kl
Designation of wires and connections
Pl
Ml
X
cf. DIN EN 60446 (1999-10) and DIN EN 6044512000-081
Insulated wires
Designation
Type of wire
DC network
AC network
Code
letters
Symbols
positive
L+
+
negative
L-
neutral wire
M
Phase co nducto r 2
L2
Phase conducto r 3
L3
neutral wire
N
Ground
black
L2
L1
PEN wire !neutral wire with
ground function, PE + N)
Rectifier circuit
L1
Phase conducto r 1
Ground wire
Example
} ,.
brown
L3
N
PE
black
0
~
light blue
u
<{
L-
--- /:--~-
E
black
l • black
½
Device connections
Connections for
Designation
Phase conductor 1
u
Phase conductor 2
V
Phase conductor 3
w
1> Color is unspecified. Black is recommended,
brown to differentiate. Green-y ellow may not be
used.
2 > PEN-wires have a continuous green-yellow
conductor color. To avoid confusion with PE
w ires, PEN w ires are additionally marked with
light blue on the ends of the wires,
e.g. with a wire clip or adhesive tape.
*) According to European Standards
j
C
.><
-- T---@
PEN
.,
- green-yellow
J
PE
.><
Example
Star-connected (squirrel) cage motor
Terminal board
0
~
.,
C
u
C
354
Automation: 7.2 Electrica l circuits
Circuit diagrams
ct OIN EN 6108211998 091
Connector markings on relays
Example:
Relay with 2 NOs
and2NCs
2nd~
·
II Fuiction runber
conlacls
I
~-t-~r~t:1:::1
(1
I
~
4
4
N
N
-
N
m
l...:t
-
1stdgt
Consecutive numbering of contact sels
NC
NC
NO
NO
delayed
~1
I
SPOT
dela)<ed
SPOT
delayed
~1 ~\I ~~I
J1 ~ ~
Designing circuit diagrams
Current sections and distribution of electric circuits
• Every electrical device is shown with a
vertical current section regardless of the
actual spatial arrangement of the elements.
• Current sections are numbered sequentially from left to right.
Main circuit
Control circuit
2
L+
4
3
(1
(1
• The control circuit contains devices for
signal input and signal processing.
S31--
• The main circuit contains the necessary
final control element s for the working
elements.
• The spatially shared devices, e.g. relay
coil and relay contact, are not represented.
(1
R
Ml
(1
L-
Designation of devices
• Contacts and the associated relay coils
are marked w ith the same code numeral.
Example: Current sections 1, 2 and 3
• 2 NO contacts belong t o relay coil Cl ,
both marked as Cl. They are used to
lat ch the relay coil.
• All contaCls of a relay are entered as a
complete contact set or as a table under
the current path of the relay. Both representations ind icate the current section
on which a contaCl is located.
2
L+
;!
,,,
N
~
;!
S21--
S31)' ~-
:=
~
0
(3
(2
13
14
13
L-
14
523~ 6 23-"f24
33"";34
nh
-,..J---
-..J,---
Representation as contact set
0
Contacts
(1
13-14
23-24
Section
2
3
Contacts Section
Contacts
5
13 - 14
(2
13 -14
~
~
M1
(3
N
(3
;!
0
0
;! r
(2
S4
(2
N
6
;!r
N
(1
SH·-
[1
(1
5
4
~
(3
Representation as table
Section
6
R
M3
R
355
Automation: 7.2 Electrical circuits
Sensors
I
Sensors (selection)
Sensors that are _sensitive I
to proxIm Ity
I
I
I
I
I
I
I
Sensors
I
I
Tactile sensors
I
I
I
Inductive
sensors
Capacitive
sensors
I
Photoelectric
sensors
11
11
I
I
Ultrasound
sensors
Magnetic sen-I
sors
11
I
~
Limit
I switches I
Characteristics of sensors
Sensor
type
Inductive
Capacitive
Photoelectric
Ultrasound
Magnetic
Mechanical
Princ:iple
Advantages
Disadvantages
Object
distance
Triggers if an object interferes with the alternating
magnetic leakage field of
the sensor
High degree of protection
UP67), very high switch
point precision, dirt
tolerant
Only objects with high electrical conductivity, unsuit·
able where there is greater
accumulation of metal chips
1 mmto
150mm
Triggers if an object interferes with the alternating
electric leakage field of
the sensor
Small object distances,
High degree of protection
larger design than
(IP67), detects all materials;
comparable inductive sendin tolerant
sors
20mmto
40mm
Triggers if an object
returns the infrared field
of the sensor
Detects all materials,
large distances
Symbol
~
l!I
l'/~I
l!I
~
~
Sensitive to dirt, smoke and
secondary light, auxiliary
power necessary
Evaluates transit times of
Tolerant t o dust, dirt and
reflected ultrasonic pulses
light; detects very small
to determine the distance
objects at large d istances
to an object
Slow, use only with standard
60mmto
pressure, not in areas sub6m
ject to explosion hazards and
no high-frequency noise
A permanent magnet
actuates a proximity
switch (reed contact)
using two cont act springs
Risk of contact welding;
suppresses the current
peaks of RC modules
Triggered by manual
actuation or lever system
Suitable in rough environment, high service life,
suitable for switches in
high frequency circuits
low price, robust, small,
unaffected by interference
fields, no auxiliary power
necessary
I
¥tjrnr,
I
Type of
detection
Mechanical_ mount··1
mg conditions
II
1 flush
mounting
possible
2 flush
mounting
not possible
3 unspecilied
I
-
cf. DIN EN 60947-5-2 (2004-11 )
Example:
I
-
Contact chatter, not
allowed in food and
chemical industries
Designation of proximity sensors
I inductive
C capacitive
u ultrasound
D photoelectric diffuse
reflected
luminous
beam
M magnetic
R photoelectric reflected
luminous
beam
T photoelectric d irect
luminous
beam
approx.
2m
I
,I I
Design
and size
FORM
A cylindrical
threaded
sleeve
B smooth cylindrical sleeve
C rectangular
with square
cross-section
D square, with
rectangular
cross-section
SIZE
(2 digits)
for diameter
or side length
Circuit element function
11
A NO contact
B NC contact
C single pole
double
throw
p programmable by
user
s other
1)
I
I
Type of
output
11
Type of 11
connection
p PNP output, 3
1 integrated
or 4 DC conneclions
N NPN output, 3
or 4 DC connect ions
D 2 DC connections1'
F 2 AC connections21
U 2ACorDC
connections
S other
connection
line
2 plug
connection
3 screw
connection
4
unused
8
9 other
NAMUR
function
I
N NAMUR3l
function
Note:
NAMUR
sensors
are 2 w ire
sensors that
are connected
t o an external
switching
amplifier
type of
connection
DC = Direct Current
21 AC = A lternating Current
3> NAMUR = Normenarbeitsgemeinschaft fur Mess- und Regelungstechnik (Standardization Association for Measurement and Control)
356
Automation: 7.2 El ectrical circuits
Safety precautions*
Safety precautions against electrical shock
Protection
against direct
and
indirect contact
Protection by:
- Safety Extra Low Voltage (SELV)
- Protective Extra Low
Voltage (PELV)
- Functional Extra Low Voltage
FELV
cf. DIN VDE 0 100-410 (2003-061
Protection
against electric shock
under normal conditions:
against direct contact
Protection
against electric: shock
under fault conditions:
for indirect contact
Protection by:
- protective insulation of active
parts, e.g. cable
- coating as insulation, e.g. housings on electr. devices
- distance, e.g. protective hoods,
housings of machine screen
- barriers, e.g. protective screen,
enclosure
Protection by:
- automatic disconnect or warning,
e.g. residual current protective
device
- potential equalization
- non-conductive areas;
e.g. by insulating coverings
- protective insulation, e.g. housings
encapsulated with insulating material
fl
fl
Additional protection by residual current circuit breaker GFl's:
Ground Fault Interrupter
Effects of alternating current
vgl. lEC 60479-1 (1994)
Zone
Safety curves for AC 50 Hz from hand lo hand or
from hand to foot for adults
10 000
Physical effects
AC-1
normally no effect
AC-2
normally no damaging physlcal ell'8ds
AC-3
usually no organic damage, difficulty
breathing (> 2 s), muscle cramps
AC-1
AC-2
200 l=+=:J.-=+%'1---1-+.-l= = ~
1oo HH;=t=:t:±±t~f\7-t-tt-
C
i
50
-5
20
leakage current -
Automatic fuses and wire cross-sectional areas
cf. DIN VDE 0 1000-430 (1991-11 )
Minimum c:ross-,sectionaf ..,. in mm2 for
Rated current of
fuse
I,,inA
Color
code
of
fuse
Cu wires by method of installation
A1
82
C
and oo-ofk>Nedstrancls
2
10 (13)
81
3
3
3
2
3
2
Rated cur-
Color
rent of
fuse
I,,inA
code
of
fuse
25
yellow
3
1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
Minimum cross-sectional area in mm2 for
Cu wires by method of installation
A1
82
81
C
andnuo.-ofk>Nedstrands
2
3
3
3
2
3
2
4
4
2.5
4
4
4
2.5 2.5
3
16
1.5 2.5 1.5 1.5 1.5 1.5 1.5 1.5
35
6
6
6
6
6
6
4
4
20
2.5 2.5 2.5 2.5 2.5 2.5 1.5 2.5
50
10
16
10
10
10
10
10
10
Method of installation of cables and insulated wires
cf. DIN VDE 0 298-4 (2003-081
A1
Installation in thermally
insulated walls, in electrical conduit
82
Installation in elect rical conduit or in the wall, in cable
channels or behind base
boards
81
Inst allation in electr ical
conduit or in the wall or in
cable channels
C
Installation directly on or in
the wall
*I According to European Standards
357
Automation: 7.2 Electrical circuits
Safety precautions*
Protective systems for electrical devices
Example:
I
Protective system
designation IP
(International Protection>
1st code numeral
for protection of
device11against
penetration of
solid foreign
objects
cf. DIN EN 60529 (2000-09!
~ill:
I
2nd code number
for protection of
the device1I
against water w ith
damaging effect
Additional
code letters2I
Supplementary letters
I
no
1st code no.
Protection from
Protection against
foreign objects
accidental contact
0
No protection
No protection
1
Protected against
contact by back of
the hand
Protected against
penetration by foreign
objects d ~ 50 mm
2
Protected against
contact with finger
d = 12mm
Protected against
penetration by foreign
objects d ~ 12.5 mm
3
Protected against
contact w ith a
tool d = 2.5 mm
Prot ected against
penetration by foreign
objects d ~ 2.5 mm
4
Protect ed against
contact w ith a wire
d = 1 mm
Protected against
penetration by foreign
objects d ~ 1 mm
Symbol
5
Protected against
contact with a wire
d=1mm
Protected
from dust
6
Protected against
contact with a wire
d= 1 mm
Dust
proof
*
1t If a code number is not given, the letter X is
used in its place, e.g. IP X6 or IP 3X
2 1 Is only given if the protection is greater than
the 1st code number.
Code
no
2nd code number
Water protection
None
0
No protection
1
Protected against
ver1ical drips
2
Protected against
drips if device is
inclined 15°
I
0
p
q
d
e
i
Protected against
contact by back of the
hand
B
Protected against
contact with finger
d = 12 mm, 80 mm long
Protected against
contact with a tool
d = 2.5 mm,
100mm long
Protected against
contact with a wire
d= 1 mm, 100 mm long
3
Protected against
water spray impacting device at 60°
[I]
&
D
4
Protected against
water spray from all
directions
5
Protected against
water jets from all
directions
6
Protected against
strong water jets
from all directions
7
Protected against
temporary submersion in water
8
Protected against
continual submersion in water
Supplementary letters
&&
••••
••
H
Equipment for high
voltage
M
Tested on water intake
in running machine
s
Tested on water intake
on idle machine
w
Suitable for specific
weather conditions
...kPa
cf. DIN EN 13237 (2003-01)
~TT¥
Example:
Code
••
A
C
Electric equipment for explosive areas
Symbol for
explosion protection
Additional
letters
Symbol
I
Type of protection
I
I
Electrical
devices group
I
I I
Temperature class
GroupR
Type of protection
A
oil immersion
pressurized
enclosure
sand filling
flameproof
enclosure
increased
safety
inherent safety
methane, propane, butane,
propylene, benzene, toluol,
naphthalene, turpentine,
petroleum, gasoline, fuel oil,
diesel oil, carbon monoxide,
methanol, metaldehyde,
acetone, acids, chloride
B
ethylene, acryl
nitrite, hydrogen
cyanide,
dimethylether,
propylene oxide,
coke oven gas,
tetrafluoroethylene
hydrogen,
acetylene,
carbon bisulphide,
ethyl nitrite
&.face
temperature
C
Risk of explosion by occurrence of the following gases:
*l According to European Standards
I
Code
T1
45o•c
T2
3oo•c
T3
200°c
T4
135°c
T5
100°c
T6
B5°C
358
Automation: 7.3 Function charts and Function diagrams
Function charts for sequential controls (GRAFCET) 11
ct 01N EN 60848'2002 12 1
The function chart in accordance with GRAFCET is a graphical design language for sequential control. However, it
does not make any statement about the type of devices used, the direction of lines and the installation of electrical
equipment. Only the general representation via symbols is obligatory; dimensions and other details are left to the
user.
Example: hydraulic press with sequential control
The ram of a hydraulic
press forces bushings into
a plate. When the cylinder
is in its end position (B1 l
and a bushing is available
164), the cylinder eX1ends
in fast motion. The sensor
B2 switches to feed mode.
As soon as the bushing is
forced in (B3) the cylinder
retracts in fast motion.
- Start step Start cycle (S1) and
cylinder in basic position (B1) and
bushing available (B4)
Cylinder A 1 exiends in fast motion
Cylinder A 1 extended (B2)
Cylinder A 1 in feed mode
Cylinder A 1 extended (63)
Cylinder A 1 retracts in fast motion
Cylinder Al retracted (B1)
Symbol
Examples
Explanation
Explanation
Closed cycle (step chain)
Steps
This action is only valid as
Continuous action
t
i
as the corresponding
!Cylinder A 1 retracts in fast motion ! long
step is active.
Stored with rising edge
Solenoid valve M2 ON M2:=1
St ored with falling edge
S ignal light M5 ON M5:=1
When the step is activated,
the value 1 is assigned to the
solenoid valve M2. This action
remains active also after the
reset of the step.
When the step is activated,
the value 1 is assigned to the
signal light P5 only after the
reset of the step.
□
The number must be in
the upper center of the
step field
~
Step
[]
Start st ep
[]
Start step w ith step number 1
[J
Set step
It displays which steps
are set for a definit e
condition of the process
[J
Steps that are active at a
particular time can be
marked with a dot.
~
Macro step
Individual representation
of a detailed part of a
sequential control
□
Inclusive step
This step contains several
steps that are referred to
as included steps.
a
Inclusive start step
This step contains several
steps that are referred to
as included steps.
,
®
I
I
I
I
I
5
g I
Macro step M5, shown in its
detailed structure:
- The release of transition a
activates the access step
E5 of the macro step M5.
- The activation of the exit
step S5 releases transition g.
- The release of transition g
deactivates step S5.
11 GRAFCET French: GRAphe Fonctionnel de Commande Etape Transition.
English: specification language for function charts of sequential controls
Automation: 7.3 Function charts and Function diagrams
359
Sequential chart
A sequential chart consists of a series of steps
placed one after another. Steps and transitions alternate.
- Start step e.g. system "ON"
Start-up push button Sl
Pump motor ON
Tank FULL
Agitator motor ON
15s delay time
OPEN drain valve
1. Sequential charts enforce a step structure
developed from top to
bottom.
2. Within the sequence,
only one step can be
active at a time.
3. The start step describes
the initial condition of
the system.
4. After execution of the
last step and release of
the transition, a feedback loop returns the
system to the start step.
Tank empty
Transistions
The transition is com-
posed of
• a dash and
• a text describing the
Agitator motor ON
transition
Transitions can be
represented by:
• text statements
• Boolean algebra
(equation)
• graphical symbols
15s delay time
1. Step 3 is active, i. e. the
agitator motor is ON.
2. If the condition for the
release of the transition
(the agitator runs for
15 sec.) is satisfied,
step 4 is set.
3. Step 4 resets step 3, i.e.
the ON signal for the agitator motor is no longer
OPEN drain valve
active. The motor is shut
down.
4. The drain valve opens.
Sequence selection (alternative branch)
Sequence branch:
The sequence occurs if
step 5 is set
a) branching to step 6 if the
condition for the release
A sequence branches to
several sequences starting at a single or several
steps.
A difference is made
between:
of transition •e• is satis•
tied, (e= 1) or
• sequence branch
• sequence junction
b) branching to step 8 if
the condition for the
release of transition "f"
is satisfied (f= 1).
Example:
sequence
branch
Simultaneous sequences (parallel branch)
A sequence branches to
multiple sequences that
are simultaneously activated but run independently of each other.
The next individual step is
carried out only after all
branches are processed.
_Q_
A sequence from step 2 t o
steps 22, 24 et c. only
occurs if,
a) step 2 is set
00
b) the condi tion for the
release of the common
transition "a" is satisfied
(a=1).
0
and
360
Automation: 7.3 Function charts and Function diagrams
Function charts for sequential controls, Examples
er 0IN EN 6084812002 121
Example: Lifting device
Workpieces are lifted by a lifting cylinder and pushed onto a roller conveyor by a transfer cylinder.
Actuating the main valve and start button S1 causes the lifting cylinder 1A1 to extend, lifting the workpiece and activating the l imit switch 1B2 in the end position. This causes transfer cylinder 2A1 to extend, pushing the workpiece
onto the roller conveyor and activating limit switch 2B2. Cylinder 1A1 returns to its initial position, actuates 1B1 thereby causing cyl inder 2A1 to be retracted.
s1@
start
System "ON".
Cylinders 1A1 and 2A1
in initial position
Start button S1
Extend cylinder 1A1
182 (Cylinder 1A1 is extended)
Extend cylinder 2A 1
282 (Cylinder 2A 1 is extended)
Retract cylinder 1A1
181 (Cylinder 1A1 is retracted)
Retract cylinder 2A 1
lifting cylinder 1A 1
2B1 (Cylinder 2A1 is retracted)
Example: Stirring machine control
Paint flows into a mixing tank, is stirred there and then
pumped back out. Opening valve 01 causes the paint to
fill to a level mark. Afterwards motor M1 is turned on and
the paint is stirred 2 minutes. After shutoff of stirring
motor M1 and activation of pump motor M2 (running
time at least 10 sec), the container is pumped empty.
Shutoff criteri on for pump motor M2 is drop of motor
power below 1 kW (container is empty).
Start button S1
Valve 01 OPEN
p > 0.4 bar (Fill level mark reached)
Valve 01 CLOSED
01
stirring
motor Ml
M
--0-
s1@
Stirring motor Ml ON
start
I
Stirring m otor Ml OFF
Pump motor M2 ON
pressure
sensor for
fill level
P < 1 kW (container empty)
&t>= 10s
Pump motor M2 OFF
361
Automation: 7.3 Function charts and Functi on diagrams
..........,
Function diagrams
I
Path diagram
I
I
Simple motion sequences
so
S1
S2
---•-----------53
~
I
I
State diagram
Description of a working sequence by 2 coordinates
SO: signal element ON
S1: fast motion up to Sl
S2: feed up to S2
S3: fast reverse motion
up to S3
I [):::=::p
Step 1: idle position
Step 2: fast forward
motion
Step 3: feed
Pneumatic
cylinder
time ins
0
1
4 10 11
step
1
2
3
Step 4: end position
Step 5: fast reverse motion
0
4
5
ua---1 tsJ
Symbols of a function diagram
Movements and functions
Paths and movements
Function lines
-
Straight line
working movement
---
Idle and initial position
of subassemblies
---~
Straight line
idle movement
---
For all conditions deviating from the idle or
initial posit ion
Path and movement limits
-
Path limits
general
---
Path limits using
signal elements
Signal elements
cp
9
'Il
ON
9'
OFF
'f>
ON/
OFF
Hydraulic or pneumatic
actuation
Mechanical actuation
Manual actuation
JOG
MODE
AUTOMATIC
MODE
ON
-T
Limit swit ch actuated in
end position
If]
r1
Limit switch actuated
over longer path length
~2s
6bar
Pressure switch set to
6 bar
lime element set to
2sec.
Signal combinations
The signal line begins at
the signal output and
ends at the point where a
change of state is introduced.
~
The signal branch is
marked with a dot.
Execution of a function diagram (state diagram)
Cylinder
0 1 2 3 4
Jffl
Step 1: move from
initial position 1 to
position 2
Step 2: remain in
position
Step 3: move
from position 2 to
initial position 1
Valve with two switch positions
0 1 2 3 4 5
:Im
Step 1: switch
from initial position b to posilion a
St ep 2 and 3:
remain in position
Step 4: switch
from position a to
initial position a
~
AND state:
marked w ith a slash
OR state:
marked with a dot
Signal element activated manually
0 1 2 3 4 5
:H
Step 2: switch on;
control element
switches from b
to a
Example: Final control element mechanically activated
1A1
2l
~
0 1 23456step
Step 1: Final control element switches directional control valve from b to
a and causes extension of cylinder 1A 1.
1. s
t
1
2s
Step 2: Cylinder actuates signal element 1S1
Signal element 1S1 controls timer element
limer runs out (2 sec).
a
b
Step 3: lime, element controls directional control valve from a to b
Cylinder 1A1 retracts to initial state.
2
362
Aut omation: 7.3 Function charts and Function diagrams
Function diagrams, Example
Example: Pneumatically controlled lifting device
Layout
Function diagram
Step
Components
transfer cylinder 2A 1
Name
PosijJ
No. condij,
Main
pneumatic
valve
OVl
a
b
Cylinder
(vertic. stroke)
1A1
512 directional
control valve
1V2
Cylinder
(hofiz. stroke)
2A1
5/2 directional
control valve
(DCV)
2V1
X 1 X2
1
X3
2
3
5
4
I
~
1S3
I
I
l
2
1
2S1
I
I'-.
a
1S2
I~ ..... 1S1
..,..1'7
I)
"
b
2
1
a
I i
( /
2s2\
..... ,
,
"
b
~ i,,tS1
' I
v
Pneumat ic circuit diagram
Ifill
[m:]
I
I
Om
lliTI r-- --t>-
r-4 I, ,i l-7
I
[fil] I
[fill I
Parts list
Designations Name
1A1
2A1
Cylinder, double acting
Cylinder, double act ing
OVl
1V 1
1V2
2V1
3/2 DCV with detent, manually activated
Two pressure valve
5/2 DCV, pressure activated
5/2 DCV, pressure activat ed
Designations Name
1S1
1S2
1S3
2S1
2S2
[ill]
3/2 DCV, roller act ivated
3/2 DCV, roller activated
3/2 DCV, activated by push button
3/2 DCV, roller activated
3/2 DCV, roller activated
363
Automation: 7.4 Hydraulics, Pneumatics
Circuit symbols
cf DIN ISO 1219 1 11996 031
Function elements
►
Hydraulic
fluid flow
t>
Compressed
airflow
tiJ
Direction of
flow
++
Line junction
( (
/
Direction of
rotation
Adjustability
'VVv
Spring
---------
Flow restric•
tion
Power transmission
►-
I>- -- -
Hydraulic
pressure
source
Pneumatic
press. source
Working line
-t-
Line crossing
[233
Quick
coupling
----
Control line
Leakage cur·
rent line
y
Exhaust
without
connection
-----
Enclosure
around
subassemblies
y
Exhaust with
connection
-c:;:J>
Muffler
4
Filter or
screen
L_J
Tank
--C)-
Air
y
Water
separator
-¢-
Air dryer
Service unit
(FRL)
v-
Lubricator
Variable dis•
placement
hydraulic
motor, bidi•
rectional
=f}
Hydraulic
oscillating
drive
=D=
Pneumatic
oscillating
drive
@=
Electric motor
0
-qID-
receiver
Hydraulic
accumulator
Pumps, compressors, motors
0€'
Fixed displace-ment hydraulic
pump, unidirectional
~
Variable dis•
0€'
tional
placement
hydraulic
pump, bidirec·
Compressor,
unidirectional
0€'
0€'
Fixed dis•
placement
hydraulic
motor, unidi-
rectional
Fixed dis·
placement
pneumatic·
motor, unidi•
rectional
simplified:
~
Single-acting
cylinder,
return stroke
by undefined
power source
~
simplified:
~
Single-acting
cylinder,
return stroke
by integrated
spring
Check, and/or valves
---¢--
Check valve,
unloaded
Check valve,
spring loaded
pneumatic
motor, bidi·
rectional
pq
simplified:
~
Double-acting
cylinder w ith
one-sided
piston rod
Pressure valves
$
--¢w-
~
Variable dis•
placement
Double-acting cylinders
Single-acting cylinders
pq
~
__
Pilot operated
check valve
~
~ ~
~
L!J
r·- ·- ·-,
~
Shuttle valve
(OR function)
~
One-way flow
control valve
fil
Quick exhaust
valve
-B-
Dual-pressure
valve(AND
function)
:.._ ______ J
c9t
--Er
Pressure
relief valves
Sequence
valve
2-way pres•
sure regulator, direct·
acting
Pressure
switch, emits
electrical signal
for a preset
pressure
~
~
-+
-EB
Double-acting
cylinder with
one-sided
piston rod
and two·
sided
adjustable
end cushion
Flow control valves
~
Adjustable
throttle valve
Adjustable
2-wayflowcontrol valve
Adjustable
3-wayflow·
control valve,
relief open•
ing to tank
364
Autom atio n: 7.4 Hyd raulics, Pneu matics
Circuit symbols
cf. DIN ISO 1219-1 (1996-03)
DIN ISO 5599 (2005-12)
Connection designations and codes for directional control valves
Example:
5/2 directional control valve
with connection designation
.-----l--l
6V1
~
M
l'-_D_e_si_g_n_a_to_r_ _,
I
Code designation
Connection designations for
pneumatic and hydraulic equipment
Connection
jT'"-~w-....jF'--------------1
I n~~~r
lc~~~!~;'o~:11 sw~i;~:it~ !ns
Part
Part
11 designation 11 number
I
I
Switch positions11
~
Part designation
Valve with 2
positions
P
pumps and
compressors
A drives
M drive motors
S signal pick-up
V valves
Z all other parts
Val~~ with 3
I a I I b I pos1
t1ons
O
11 Number of rectangles a
Number of positions
as per DIN
with
numbers
obsolete:
with
letters112l
1
p
2,4,6
A. B,C
3, 5, 7
R,
Inflow,
pressure
port
Working
ports
Vent,
drain
Leakage
oil port
Control
ports31
s. T
-
L
10, 11,
12, 14
x. Y, z
11 Leners are still frequently used in
hydraulic circuit diagrams.
21 The sequence of the letters does not
necessarily correspond to the number
sequence.
JI A pulse at control port 12, for example,
connects ports 1and 2.
7
Designs of directional control valves
2 / directional control valves 3/ cirectional control valves 4/ directional control valves 5/ directional control valves
rn!J
CJtJ
2/2 DCV, normallyclosed
2/2 DCV,
normally
open
Flow paths
rn
CJ
Two closed
ports
[1] 00
Two flow
paths
[I]
Two flow
paths and
one closed
port
18]
m
0
3/2 DCV, normallyclosed
3/2 DCV. normally open
3/3 DCV, NC
in middle
posilion
Two interconnect ed flow
paths
One flow path
in bypass
switch and
two closed
ports
an
®
11IISIZI
4/2 directional
control valve
413 DCV. NC in
middle pos.
413 DCV, with
float in middle
position
lXIIt/41
~
5/2 directional
control valve
5/3 DCV,
NC in middle
position
Actuation of directional control valves
Manually activated
One flow palh
[B]
~
~
General, no
type of actuation indicated
M echanical actuation
=[
Push button
~
Lever
D=[
Pull button
(!F=[
Push and pull
button
I=[
Foot pedal
---[
Direct
hydraulic
--E[
f[
(Fe[
Plunger
Pressure actuation
Plunger with
adjustable
stroke limit
pneumatic
--iL[
Indirect using
pilot valve
Electrical actuation
M[
®=[
Spring
Roller
plunger
~
By solenoid
®«=
By electric
motor
Combined actuat ion
By solenoid
re
Roller lever,
one direction
of actuation
pilot
~ and
valve
M echanical com ponents
!
Notch
365
Automation: 7.4 Hydraulics, Pneumatics
Circuit diagrams
er 0 IN Is012192I1996 111
Designing a circuit plan
circuit 1
circuit 2
The circuit is subdivided into subcircuits
with related control
If the circuit diagram
is made of several
units, the unit number
must be given, beginning w ith numeral 1.
functions.
The actual spatial
arrangement of the
components is not
considered.
Components are
arranged from bottom
to top in the direction
of power flow and
from left to right.
Subassemblies such
as throttle c heck
valves or service units
(FRL) are enclosed by
a dash-dot line.
~
Hydraulic components
are shown in their ini·
tial positions in the
equipment before
pressure is applied.
Simi lar components
or subassemblies are
shown at the same
height within a circuit.
Devices actuated by
drives, e.g. limit
switches, are represented at their point of
activation by a dash
and their designator.
[ill]
1
I Il:=:==:=
[ill] [ill]
I
I t==:::II
-I
For roller plunger
valves operating on
one side only, a directional arrow is also
placed at the dash.
Components of a circuit
Pneumatic compo-
Drive elements
Actuators
nents are shown in
their initial positions
in the equipment
before pressure is
applied.
Control elements
Signal elements
Supply elements
Motors, cylinders, valves
Valves f or controlling drive elements
Valves for signal combination
Components used to trigger
a switching action
Service unit (FRL), main valve
Example: Pneumatic circuit diagram with two cylinders (lifting device)
circuit 1
~
[ill] [fill
circuit 2
[ml
drive elements
[RI] r_J4
r- l;----;i
14
r
final control
elements
control
element
signal
elements
supply elements
[fill
I
I
12
[ill] [ill]
366
Automation: 7.4 Hydraulics, Pneumatics
Electropneumatic controls
Function diagram
Layout
transfer cylinder 2A1
4
B3
lifting cylinder 1A1 up
down 1---"l''-f--+-f-+-
-
5=1
---,~
forward f--t--+--+-- i l -"l<------,1--
transf er
cylinder 2A1
Pneumatic circuit diagram
Lifting
Pushing
[m}B3 B4
B5
~~2
[fil]~~~·
','
a b
1M1
1M2
Circuit diagram
5
6
1
8
i
i
i
i
4
+24 V
C4P-- ft C4P-
(1
B2
B4
B1
(2
(3
(4
(1
(2
(3
(4
1M1
2M1
1M2
2M2
~
ov
switching
N(INO
element table11 - 5
~
6
~
1
~
NO
~- 8
~
~
N( = normally closed
NO= n or mally opened
Circuit diagram with the additional functions - magazine query and continuous operation
10
+24 V
3
11
continuous
operation
4
T
E~
ON
B2
B4
61
(2
(3
(4
continuous
operation
OFF
6
(1
1M1
(5
ov
switching
element table1>
~
=ll¥
~
T
(2
2M1
~
T
(3
1M2
~
T
(4
2M2
~
~
N( = normally closed
NO= normally opened
Example for relay K5: Relay K5 has a normally open switch in section 10 and a normally open switch in section 11.
11 The switching element table is similar to the contact table (pg. 354) and is often used in practice. However it is not
standardized. The table indicates the section in which a NC or NO relay contact can be found.
367
Automation: 7.4 Hydraulics, Pneumatics
Sequence control of a feed unit via PLC according to GRAFCET
Description
Technological scheme
fast
m oto r
reverse
+
motion
feed unit
auto-
I I
Description
single
m a t ( l )ep
I
B1 B2
The hyd raulic cylinder extends in fast motion and
is switched i nt o feed mode by switch B2. In t he
fully extended position, the proximity switch B3
switches to f ast reverse after a t ime delay of
2 seconds.
operating
panel
83
lift cylinder A 1
0
0
• •
START
Function chart and GRAFCET
STOP
Allocation list
Component
designation
Address
Remarks
Mode switch
AUTOMATIC/STEP
S0/51
E0.0/E0.1
NO contact/
NC contact
NO contact
Components and action
- Start step Cylinder i n basic position (B1}
Workpiece available (84}
Start button ON (S2}
Cylinder A 1 ext ends i n fast motion
Cylinder A 1 in posit ion of
proximity swit ch B2
Cylinder A 1 in feed mode
Cylinder A 1 is extended to B3
and dwell time is 2 sec.
Cyli nder A 1 ret racts in fast motion
Cylinder Al retracted (B 1}
Push button START
S2
E0.2
Push button STOP
S3
E0.3
NC contact
Proximity switch
B1-B4
E0.4-E0.7
NO contact
Solenoid valve Q 11
Cylinder in feed mode
1M 1
A l.0
Solenoid valve Q 12
Extend cylinder
2M 1
A l.1
2M2
A l .2
Solenoid valve Q 14
Retract cylinder
Function block language FBL
!Operating modes I
Instruction list IL
Network 4: Step 2
Extend in f ast motion
M0 1
Network 1: Function block FB1
Network 2
FUNCTION BLOCK
Basic position
Operating modes
ON
U E0.4
U E0.7
SM0.3
IController I
OFF
E0.0
E0.1
E0.2
E0.3
10pen,,;ng _,.i I
Automatic mode
Single
step
M0.1
Release
START
Network 1
CALL FB1
Reset
STOP
Network 2: Basic posit ion
~
~
! Step chain
Network 3: Step 1
Start step
M02
Colo r marking: step fl ag in red
Transition in blue
MO l
E06
M3.0
Network 6: Step 4
Fast reverse w ith dwell t ime
Tl
2 0
I--<
Network 3
Step 1:
Start step
U E0.2
UN E0.3
U M0.1
U E0.4
UM4.0
OM0.2
S M l .0
UM2.0
R M l .0
Network4
Step 2:
Fast extension
UM0.1
UM0.3
UM1.0
SM2.0
O M0.2
OM3.0
RM2.0
Network 5
Step 3:
Feed mode
U M0.1
U E0.5
U M2.0
SM3.0
U M0.2
OM4.0
RM3.0
Network 6
Step 4:
Fast reverse
U M0.1
U E0.6
UM3.0
= Tl
UT1
SM4.0
UM0.2
OM1.0
RM4.0
Network 7 to 9
Steps 5 to 7:
Command output
UM2.0
= A l.1
U M3.0
= A l.0
U M4.0
= A 1.2
PE
368
Automation: 7.4 Hydraulics, Pneumatics
Hydraulic fluids
Mineral oil based hydraulic oils
Type
Standard
HL
DIN 51524- 1
HLP
HVLP
cf. DIN 51524-1 to -3 (2006-04)
Effect of the ingredients
Applications
Hydraulic units up to 200 bar, w it h
high temperature requirements
-
Inc rease in
corrosion
DIN 51524-2) resistance
+
Increase in
aging
DIN 51524-3
resistance
+ Reduction of wear due to scoring
in mixed friction area
Hydraulic units with hydro pumps
and hydro motors above 200 bar
+ Reduction of wear due to scoring
operating pressure and w ith high
in mixed friction area
+ Improvement of v iscosity-tempera- temperature requirements
ture behavio r
Hl.10
HLP10
Properties
HL22
HLP22
HL32
HLP32
HL46
HLP46
HL68
HLP68
HL 100
HLP 100
at - 20°c
600
-
-
-
-
-
at o· c
90
300
420
780
1400
2560
at 4o•c
9- 11
19.8-24.2
61.2-74.8
90-110
2.4
4.1
28.8-35.2
5.0
41.4- 50.6
at 100°c
6.1
7.8
9.9
Pour point 11 equal to or lower than
3o•c
-21°c
- 10•c
- 15°c
- 12· c
- 12·c
Flash point above
125•c
165°c
115•c
1s5•c
195•c
205•c
~
Kinematic
v iscosity in mm2/s
11 The pour point is the t emperature at which hydraulic oil still flows under the force of gravity.
=> Hydraulic oil DIN 51524 - HLP 46: Hydraulic oil of type HLP, kinematic viscosity= 46 mm2/s at 40°C
Viscosity-temperature behavior of HL and HLP hydraulic oils
200
HL 100/HLP 100
mm2
HL 68/HLP 68
s
10~
HL 46/HLP 46
z, 100 68
'\. '\. I'\..'\..'\.
HL 32/HLP 32
·.;
HL 22/HLP 22
8
50 46
u,
32
·s:
~
LP10
u
22
r-.. "~
20
E
~~
t
" " ""
.,
C
:ii:
~
" ' '~
...
~~
I~
10
10
-20
0
20
40
temperature
Non-flammable hydraulic fluids
ISO
Type
VISCOSity
dasses
HFC
HFO
15, 22, 32,
46, 68, 100
~~
---
60
80
Example of reading from diagram:
A gear pump operates at an average
operating temperature of 40°C.
During operation the allowable
kinematic viscosity of the hydraulic
oil is allowed to fluctuate between
20 to 50 mm2/sec.
According to the diagram there are
6 hydraulic oils that would be suitable:
• HL 22/HLP 22
• HL 32/HLP 32
• HL 46/HLP 46
·c 100
Suitability for
temperatures Characteristics
Applications
·c
- 20 to +60
Aqueous monomer and/or polymer
solutions, good wear protection
M ining, printing machines, welding
machines, forging presses
- 20 to+ 150
Water free synthetic liquids, good
resistance to aging, lubricating property through w ide temperature range
Hydraulic equipment with high operating temperatures
Biodegradable hydraulic fluids
cf. VDMA 24569 ( 1994-03)
Suitability and properties
Hydraulic
fluid
Unsaturated
esters
Saturated
esters
Polyglycol
oils
Suitability: •
Lowtempe- High temperarature
tu re oxidation
flowability
stability
f)
f)
•
•
•
•
very good
'- good
Rust
protection
•
•
~
C) average
Compatibility
Seal compatiCost
with inner
bility
effectiveness
coatings
~
._
._
._
~
limited/poor
~
._
f)
~
f)
Fluid life
._
•._
Dimensions and piston forces
Piston diameter
12
16
20
25
32
40
50
63
80
100
125
160
Piston rod diameter (mm)
6
8
8
10
12
16
20
20
25
25
32
40
40
Coupling thread
MS MS G'fa G'fa G' fa G'fa
G¼ G¾ G¾ G½ G½ G¾
G¾
single-act. cyI.2I
Pushing force 11
at Pe = 6 bar in N double-act. cyl.
50
96
151
58
106
164 259 422 665
1040 1650 2660 4150 6480 10600 16600
54
79
137 216 364 560
870 1480 2400 3890 6060
Pulling force11 at
Pe= 6 bar in N
double-act. cyl.
375 644
968
10, 25, so
single-act. cyl.
Stroke
in mm
241
1560 2530 4010
9960 15900
25, so. 80, 100
to
to
to
160 200 320
double-act. cyl.
200
10, 25, 50, 80, 100, 160, 200, 250,320, 400,500
21 The return fo rce of the spring is considered.
11 For a cylinder efficiency ~ = 0.88
Calculating air consumption
Single-acting cylinder
A
air consumption
gage pressure in
cylinder
Pamb ambient air pressure
n
number of strokes
Q
piston surface
Air consumption1I
Single-acting cylinder
area
specific air consumption per cm
Q = A. 5 . n. Pe + Pamb
piston stroke
Pamb
piston stroke
Pe
q
s
Example:
Single-acting cylinder with d = 50 mm;
S= 100 mm; Pe • 6 bar; n = 120/min;
Pamb = 1 bar; air consumption O in I/min?
Double-acting cylinder
Q = A · s - n-Pe + Pamb
Air consumption11
Double-acting cylinder
Q "' 2 ·A-s-n-Pe + Pamb
Pamb
P amb
2
= n • (5 cm) . 10 cm. 120 _2._ . _(6_+_1_) b_a_r
4
min
1 bar
= 164934 c m3 ~ 166- min
min
1
Pe or Pamb
P amb or Pe
(on return)
(on return)
Air consumption taken from diagram
t
t,C:
V>
,,
·u
"'
/
/
0.02
r=0.01 2 ~
0.0125
/
/ / / v.,,
Q)
C.
V>
..,,,, /
/
'//
L~
V
10.76 13.49
Air consumption11
Double-acting cylinder
I
Q ,., 2.q,s-n
diagram for Pe = 6 bar.
25 32 35 40
50 63 70mm 100
pislon diameler d
4UM6
O=q -s -n
der of d = 50 mm, S• 100 mm
and n = 120/min from the
~
V ,,V
//.
,, ,,0 ,,
O.Ol 10 12 14 16 20
I
Calculate the air consumption of a single-acting cylin-
/
./
/
Air consumption1I
Single-acting cylinder
Example:
,, ,,
II
l/
0.05
0.04
0.03
0
~ //1/ / ~ '):_
-:cl
-~
<'19 /
I
"iij
'l-
,<;~~.
0
"
',,§J <
,o'o~ , jo'i:>'Q#
C:
8
0.864
0.707
0.55
II
0.14
0.1
::,
/
~½, '// 0.39
0.2
lE
1.256
I
1.0
_L
cm
0.5
0.4
0.3
----
According to the diagram
t he piston stroke is
q = 0.14 I/cm.
O = q-s-n =
= 0.14 I/cm -10cm - 120/min
= 1681/min
11 When it fills dead space, actual air consumption may be up to 25% greater. Dead spaces include compressed air
lines between t he directional control valve and the cylinder and unused space in the end position of the piston. The
cross-sectional area of the piston rod is not t aken into consideration.
370
Automation: 7.4 Hydraulics, Pneumatics
Force calculation
Piston forces
A
Extending
1
lli~
Pe
gage pressure
A 1, A2 piston areas
F1
piston force when
extending
F2
piston force when
retracting
d 1 piston
diameter
d2 piston rod
diameter
11 efficiency
Effective piston force
I
F =Pe·A·1]
Example:
Pressure units
Hydraulic cylinder w ith d1 = 100 mm; d, = 70 mm;
~ = 0.85 and Pe = 60 bar.
What are the effecti ve piston forces?
N
1 Pa = 1 m2 =10-5 bar
1 bar = 10...!:!_= 0.1 __!::!_
cm2
mm2
1 mbar = 100 Pa = 1 hPa
Extending:
N
n . (10 cml2
• 0.85
F, = Pe • A, •'1 = 600 cm2 •
4
= 40056 N
Retracting:
F2 = Po· Az • ry
2
...!:!_ . n • ((10 cml - (7 cml2] . 0.8S
cm2
4
= 20428 N
=
600
Hydraulic press
In confined liquids o r gases, pressure is distributed Displaced volume
uniformly in all directions.
A1 • S1 = A2 • S2
F1 force on pressure piston
Work
on both pistons
F2 force on working piston
A 1 area of pressure piston
F1 • S1 = F2 • S2
A 2 area of working pist on
s1 travel of pressure piston
Ratios:
5:, travel of working piston
forces, areas, travel
hydraulic transmission ratio
I
I
Example:
Transmission ratio
p.
F1 = 200 N; A 1 = 5 cm2; A 2 = 500 cm 2;
5:, = 30 mm; F2 = ?; s 1 = ?; i = ?
F _ F, ·A2 _ 200 N • 500 cm2
i- ~
5cm2
52 • A,_
s, = ~ =
30 mm· 500cm2
5 cm2
i = F1
F2
20000 N = 20 kN
i = 52
51
3000 mm
i = Ai
A:1
Pressure intensifier
A 1, A 2 piston surface areas
Pe,
gage pressure at piston area A 1
A,1
gage pressure at piston area A 2
~
efficiency of pressure intensifier
Example:
~
A 1 = 200 cm2 ; A 2 = 5 cm2; = 0.88;
Pel = 7 bar = 70 N/cm 2; Pe2 = ?
A,
~
Circuit symbols
accord. to DIN ISO 1219-1
:-7
p.-, = P , . A, . ry = 70 ...!:!_ . 200 cm2 . 0.88
e A,_
cm2
5cm2
= 2464 N/cm2 = 246. 4 bar
I
I
371
Automation: 7.4 Hydraulics, Pneumatics
Speeds, Power
Row rates
Q, 0 1, 0 2 volume flow rates
A, A 1, A2 cross·sectional areas
A
(~
-_ -_ -~-.- - - - ---~-==>- --==>
--·
------
v, v1, v2
Volume flow rate
flow rates
Continuity equation
In a pipeline of variable cross-section the volume
flow rat e O is constant throughout all cross-sections over time t.
Ratio of flow rates
Example:
A,
~
~
Pipeline w ith A 1 = 19.6 cm2; A 2 = 8.04 cm2 and
Q = 120 I/min; v1 = ?; v2 =?
v = E_ = 120000 cm3/min
1
A,
19.6 cm 2
v 1 -A,
v2 = ~
6122 cm = 102 ~
min •
s
1.02m/s - 19.6cm2
8.04cm2
249
~
s
Piston speeds
A
Extending
EE ~
A
Q
volume flow rate
A 1, A 2 effective piston areas
v,. v2 piston speeds
Example:
Hydraulic cylinder w ith pist on diameter
d 1 = 50 mm; piston rod diameter
cl, = 32 mm and Q = 12 1/min.
How high are the pist on speeds?
Extending:
Q 12000cm3/min
cm = 6. ~
611
11
v, = -;;;;; = rr . (5cm)2
min
min
Retracting
,~
4
Retracting:
Q
12000 cm3 /min
v 2 = A, = rr • (5cm)" _ rr • (3.2cmr'
4
4
= 1035 cm = 10.35 ~
min
min
Power of pumps and cylinders
input power on pump drive shaft
output power on pump outlet
Q
volume flow rate
Pe
gage pressure
1/
efficiency of t he pump
M
torque
n
rotational speed
9550 conversion fact or
600 conversion factor
P,
P2
Example:
Pump with Q = 40 I/min; Pe= 125 bar; 1/ = 0.84;
P, = ?; P2 = 1
Pz = Q. Pe = 40. 125 kW = 8.333 kW
600
600
8 333
P, = ~ = •
kW = 9.920 kW
1/
0.84
Formulae for input and
output power with:
Pin kW, Min N · m,
n in 1/min, Q in I/min,
Pe in bar
372
Automation: 7.4 Hydraulics, Pneumatics
Tubes
Seamless precision steel tubes for hydrauric and pneumatic lines (selection)
Materials
~
_o
cf. DIN EN 10305-1 (2003-02)
E235 (St37.4), E355 (St52.4) according to DIN 1630
Material
Mechanical
properties
Tensile strengt h
Rm
N/mm2
Yield strength
N/mm2
Elongation at
fracture EL
%
R,,
E235
340 to 480
235
25
E355
490 to 630
355
22
Good cold workability, surface phosphatized or electroplated and
chromed
-
Applications
For lines in hydraulic or pneumatic systems at maximal rated pressures up to 500 bar
Delivery type: Normal manufactured length: 6 m , normalized. Tubes have a surface quality of Ra s 4 µm.
Seamless precision steel tube for hydraulic and pneumatic applications, made of
= E235, normalized, bright-drawn,
outside diameter 20 mm, wall thickness 2 mm
Tube HPL-E235-NBK-20 x 2:
Row sectional area
A
cm2
Outside
diameter
mm
Wall
thickness
s
mm
4
4
5
5
6
6
8
8
8
10
10
10
12
12
12
14
14
14
15
15
15
16
16
16
16
18
18
18
18
0.8
1.0
0.8
1.0
1.0
1.5
1.0
1.5
2.0
1.0
1.5
2.0
1.0
1.5
2.0
1.0
1.5
2.0
1.0
1.5
2.5
1.0
2.0
3.0
3.5
1.0
1.5
2.0
3.0
0.05
0.0,
0.10
0.07
0.13
0.07
0.28
0.20
0.13
0.50
0.39
0.28
0.79
0.64
0.50
1.13
0.95
0.79
1.33
1.13
0.79
1.54
1.13
0.79
0.64
2.01
1.77
1.54
1.13
20
20
20
20
22
Outside
diameter
D
D
mm
22
22
22
25
25
25
25
25
25
28
28
28
28
28
30
30
30
30
30
35
35
35
35
35
Wall
thickness
s
mm
Flow sectlonal area
A
cm2
Outside
diameter
mm
Wall
thickness
s
mm
Flow sectional area
A
crn2
2.0
2.5
3.0
4.0
1.0
2.0
3.0
3.5
1.5
2.5
3.0
3.5
4.5
6.0
1.5
2.0
3.0
3.5
4.0
2.0
2.5
3.0
5.0
6.0
2.5
3.5
4.0
5.0
6.0
2.01
1.77
1.54
1.13
3.14
2.54
2.01
1.77
3.80
3.14
2.84
2.55
2.01
1.33
4.91
4.52
3.80
3.46
3.14
5.31
4.91
4.52
3.1 4
2.55
7.07
6.1 6
5.73
4.91
4.16
38
38
38
38
38
42
42
42
50
50
50
50
50
55
55
55
55
60
60
60
60
70
70
70
70
80
80
80
80
2.5
4.0
5.0
7.0
10.0
2.0
5.0
8.0
4.0
5.0
8.0
10.0
13.0
4.0
6.0
8.0
10.0
5.0
8.0
10.0
12.5
5.0
8.0
10.0
12.5
6.0
8.0
10.0
12.5
8.55
7.07
6.16
4.52
2.55
11.34
8.04
5.31
13.85
12.57
9.08
7.07
4.52
17.35
14.52
11.95
9.62
19.64
15.21
12.57
9.62
28.27
22.90
19.64
15.90
36.32
32.17
28.27
23.76
D
Rated pressure depending on wall thickness
Rated pressure p in bar
Outside
diameter
Din mm
64
6
8
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.5
1.0
1.5
1.5
2.0
10
12
1.0
1.0
1.0
1.0
1.0
1.5
1.5
2.0
1.5
2.0
2.0
2.5
16
20
1.5
1.5
1.5
1.5
1.5
2.0
2.0
2.5
2.5
3.0
3.0
4.0
25
30
2.0
2.5
2.0
2.5
2.5
3.0
3.0
4.0
4.0
5.0
5.0
6.0
38
50
3.0
4.0
3.0
4.0
4.0
5.0
5.0
6.0
6.0
8.0
8.0
10.0
I
100
I
160
250
I
Wall thickness sin mm
I
320
I
400
373
Automation : 7.5 Programmable logic control
Programming languages
PLC programming languages (overview)
I
I
cf. DIN EN 6113 1 (2003-12)
I
Text languages
I
I
Graphic languages
I
I
I
I
Instruction List IL
Function block
language FBL
II
Structured text ST
I I
Ladder diagram LAD
II
I
Common elements of all PLC languages (selection)
Delimiters (selection)
cf. DIN EN 61131 (2003-12)
Symbol Use
Symbol Use
(**)
At beginning and end of comment
+
Leading prefix for decimal numbers
Addition operator (ST)
-
Leading prefix for decimal numbers
Year-month-day separator
Subtraction, negative operator (ST)
Horizontal line (LAO and FBL)
:=
Initialization operator
Assignment operator (ST)
#
Base number and t ime literal separator
$
Beginning of special characters in strings
:
Step names and variable/type separators
Statement label separators (ST)
Network label separators (LAD and FBL)
()
Instruction lists modifier/operator (ST)
Function arguments (ST)
Delimiter for FBL input lists (ST)
;
Separator for type declaration
Separator for statements (ST)
"
Beginning and end of character strings
e orE
Separator for areas
Separator for CASE areas (ST)
Bulleted lists, initial values and field index
separators, operand lists, function argument
lists and CASE value lists separators (ST)
Whole number/fraction separator
Separat or for hierarchal addresses and struclured elements
%
Direct representation prefix11
Real-exponent delimiter
I or!
Vertical lines (LO)
Individual element variables for storage locations
Variable Meaning
I
Q
M
X
Variable Meaning
storage location input
storage location output
storage location t ag
(individual) bit size
B
w
D
L
Operators
Name
ADD
SUB
MUL
DIV
AND
OR
XOR
NOT
s
R
GT
GE
EQ
NE
LE
LT
Example (AWL)
byte size (8 bill
word size (16 bit)
double word size (32 bit)
long word size (64 bill
.
ST %QB5 11:
Stores current result in byte size in
output storage location 5
Elementary data types
Symbol Meaning
+
.
-
I
&
;;, 1
=1
:J,
.... 31
___ 31
>
>=
=
addition
subtraction
multiplication
division
Boolean AND
Boolean OR
Boolean exclusive OR
negation
sets Boolean operator to • 1"
sets Boolean operator to "0"
comparison: gre ater than
comparison: greater than or equal to
comparison: equal to
comparison: not equal to
comparison: less than or equal to
comparison: less than
Data type
Bits
BOOL
SINT
INT
DINT
LINT
REAL
LREAL
STRING
TIME
DATE
Key word
Boolean
short whole number
whole number
do uble whole number
long whole number
real number
long real number
variable long number sequence
duration
date
1
8
16
32
64
32
64
BYTE
WORD
DWORD
LWORD
bit sequence of length 8
bit sequence of lengt h 16
bit sequence of lengt h 32
bit sequence of length 64
<>
<=
<
11 Directly represented individual element variables have a leading %symbol.
21 This symbol is not allowed as operator in text language.
31 Nosymbol
4 1 Manufacturer specific
_41
_ 41
_41
8
16
32
64
374
Automation: 7.5 Programmable logic control
Programming languages
Ladder diagram (LOI
cf. DIN EN 61131 (2003-12)
A ladder diagram represents the flow in an electromechanical relay system.
Symbol
Symbol
I Description
Lines and blocks
Symbol
Coils
-·· 1)
Vertical line
-j f-
NO contact
logic condition " 1"
Line junction
-r~
Coil output energize
--0~
Coil output deenergize
••• 1)
••• 1)
Crossing w ithout
connection
--{s}-
NC contact
-!If- logic
condition "0"
... 1)
D
I Description
Contacts
Horizontal line
I
I
-1-:-
I Description
... 1)
Blocks w ith
connection lines
-jPf-
f-- Left power rail
--l Right power rail
••• 1)
-jNf-
Latching coil,
stores an operation
---{R~ Unlatching coil
Contact for sensing
rising edge,
signal from "0" to • 1•
••• 1)
--{P}... 1)
Contact for sensing
falling edge,
sig nal from • 1• t o "0"
--{N}-
Coil for sensing
positive slopes,
signal from ·o· to • 1•
Coil for sensing
negative slopes,
signal from "0" to • 1•
11 component designator
Function block language (FBLI
cf. DIN EN 6113112003-12)
Functio n block language consists of indiv idual function blocks with statistical data. They are useful in implementing
frequently recurring functions.
Symbol
0
Symbol
I Description
g5
Elements are rectangular or square.
Input parameters are placed on the left side
and out put parameters on the ri ght side.
FB 1.2
~
1 Description
-D-D-
The block's funct ionality is entered as a
name or symbol w ithin the block.
The block designator is located above the
block.
Elements must be interconnected by horizontal and vertical signal flow lines.
Negation of Boolean signals is shown by a
circle on the input or output.
Structured text ISTI
cf. DIN EN 61131 (2003-12)
Structured text is a high level language and builds on the syntax of ISO-PASCAL.
A : = A+ B • (B- C)
a-:L~:~.
I
I I
Operand
I
Statement
Type
.-
assignment
condit ional statement
selection statement
repeat statement
repeat statement
repeat statement
leaving a repeated statement
IF
CASE
FOR
WHILE
REPEAT
EXIT
Comparison of Function Block Language (FBL) and Structured text ISTI
Function blocks (examples)
Structured text (examples)
B
~
~
B
or
F
~
~
F
or
A:~ ADD (B, C, D)
or
A:=B+C+D
E:= AND IF, G, H)
or
E:= F & G & H
375
Automation: 7.5 Programmable logic control
Programming languages
Instruction list (IL)
cf. DIN EN 6 1131 (2003-12)
Instruction list is a machine-oriented textual programming language. similar to assembly language.
Structure of an instruction
Operator modifiers
~!l~:~-1
Boolean negation of the operand.
C
Statement is o nly executed if the evaluated result
is a Boolean 1.
(
Evaluation of the operato r is deferred until
")" appears.
~ ~
Standard
operator
>
N
Separates multiple.
Modifier
11
Standard operators
Operator
Moditier
Meaning
Operator
Moditier
LD
N
setting an operand
DIV
(
division
ST
N
storing on operand addresses
GT
(
comparison: >
s
-
sets Boolean operator to 1
GE
(
comparison: >=
R
sets Boolean operator back to 0
EO
(
comparison: =
AND
N.(
Boolean AND
NE
(
comparison: <>
&
N,(
Boolean AND
LE
(
comparison: <-=
OR
N,(
Boolean OR
LT
(
comparison: <
XOR
N.(
Boolean exclusive OR
JMP
C,N
jump to label
ADD
(
addition
CAL
C,N
call of a function block
SUB
(
subtraction
RET
C,N
jump back
MUL
(
multiplication
)
-
processing of deferred operations
Meaning
Information list (Ill according to VDl1>
cf. VDI 2880 ( 1985-09)
Structure of an instruction
Label 1: R Al.2
I
I
Label
"Sat solenoid Y2 back"
jITI
I
Operator
I
I
I
I Operand I
I
Comment
Operators for
signal processing
Oparetors for
program organization
I
Operators
L
load
u
AND operation
zv
count forwards
(
open parenthesis
0
OR operation
ZR
count backwards
)
closed parenthesis
N
negation
XO
exclusive OR
UN
NANO operation
ON
NOR operation
E
input
NOP null operation
Operand
SP
unconditional jump
SPB
conditional jump
=
assignment
A
output
BA
call of a block
ADO
addition
M
tag
BAB conditional call of a block
constant
SUB
subtraction
K
BE
.
block end
MUL
multiplication
T
timer
.
comment beginning
DIV
division
z
counter
comment end
s
set
p
program block
PE
program end
R
reset
F
function block
11 In practice, many more PLC cont rols exist which are programmed according to the VDI guidelines.
376
Automation: 7.5 Programmable logic control
Programming languages
Comparison of the most commonly used PLC programming languages
Functions as
com~ts of
programs
Instruction Ust CIU
Function block language
Ladder diagram
accordng to VDI
(FBL)
(W)
AND
w ith 3 inputs
U
U
UN
E11
E12
E13
A10
OR
w ith 3 inputs
U
0
E11
E12
E13
A10
0
: : ~>--i
E13
AND before OR
,
OR before AND
w ith intermediate
t ag
U
U
0
U
U
E11
E12
U
0
E11
E12
Ml
E13
E14
Ml
A10
U
0
U
Exclusive OR
(XOR)
RS flip-flop
Set dominant
RS flip-flop
Reset dominant
Turn on
delay
E11
E12
(UN E11
U E12)
A10
U
R
U
S
E1211
A11
E11
A11
Latch.
ON (E 12)
dominating
E11
~
u e,,,,
S
U
R
A11
E12
A11
U
E11
T1
T1
A10
u
U
0
UN
I
E13
E14
A10
0
U
UN
~
E12
A10
E11
A10
~ ~~
~
~~
I
Tl
E11
It -?I
=
A10
~
A10
E11
E12
Ar>--4
~
11 The following applies to fli p-flops: If S = 1 and R = 1, the last function programmed in the IL dominates.
I
377
Auto mation: 7.5 Programmable logic control
PLC controlled embossing machine tool
Technological scheme
Description
auto•
single
ma1;(1)ep
0
0
START
STOP
• •
operati ng
panel
Workpieces are to be fitted w ith a workpiece number on an embossing machine
tool. The sensor 87 detects whether w orkpieces are still available in the stacker. The
pneumatic cylinder A 1 pushes the workpiece out of t he stacker into the working
position. After t his, the embossing cylinder
A2 extends and embosses t he workpiece.
After a delay t ime of 1 sec., fi rst t he
embossing cylinder A2 and then the
pushing cylinder A 1 are retracted. Cylinder
"3 serves as an ejector of the embossed
workpiece. Sensor 88 detects w hether the
workpiece was actually ejected.
Allocation list
Component and action
- St art step -
Extend cylinder A 1
Cylind er A 1 extended (821
and workpiece at stop (881
Extend cylinder A2
Cylinder A2 extended (841
and dwell time of 1 sec.
Retract cylinder A2
Mode switch
AUTOMATIC/STEP
Push button START
Push button STOP
Proximity switch
Solenoid valve (with c I. A 1)
Solenoid valve (with c I. A2)
Solenoid valve (with c I. "3)
Cy linder A2 retracted (83)
IStep chain I
Retract cy linder A 1
Network 3: Step 1
Start step
M0.2
E0.2
E0.3
M0.1
&
E0.4
M7.0
Cylinder A1 retracted (8 1)
Extend cylinder A3
Cylind er A3 extracted (86)
and workpiece ejected (88)
Retract cylinder A3
Component
desi nation
Address
S0/S 1
E0.0/E0. 1
S2
S3
8 1-84
85-88
1M 1 und 1M2
2M 1 und 2M2
3M1 und 3M2
E0.2
E0.3
E0.4-E0.7
E1 .0-E1.3
A0.0/A0. 1
A0.2/A0.3
A0.4/A0.5
Remarks
NO contact/
NC contact
NO contact
NC contact
NO contact
Network 8: Step 6
Extend cylinder A3
Cylinder A3 ret racted (851
Function block language (FBLI
IOperating modes I
Network 9: Step 7
Retract cylinder A3
M0.1
Network 1: Function block F81
FUNCTION BLOCK
Operating modes
IController I
ON
OFF
EO.O
E0.1
E0.2
E0.3
IOperating panel I
Automatic mode
Single
M0.1
Release
step
START
Reset
STOP
Network 6: Step 4
Retract cyl inder A2
Tl
1 0
1----1
Colo r marking: step flag in red
T ransition in blue
378
Automation: 7.6 Handling and robot systems
Coordinate systems and axes
c1 01N EN 1s0 97s7 120~~;
Robot main ax• for positioning
Robot auxiliary axes
for orientation
Robot axes
CoordlnMe system
+Z
To manipulate workpieces
To reach a desired point in space, 3 robot main axes are 3 robot auxiliary axes for
or tools in space, the follow - necessary.
spatial o ri entation
ing are necessary:
1--- - -- - - - - - ~ -- - - - - - -- - - i . R (roll)
• 3 degrees of freedom for
Cartesian robots
Articulated arm robot s
positioning and
3 translation axes
3 rotat ional axes
• p (pitch)
• 3 degrees of freedom for
(T axes) designated
(R-axes) designated
• Y (yaw)
o rientation
X, Y and Z
A, Band C
Coordinate systems
cf. DIN EN ISO 9787 (2000-07)
acoordnate system
T he base coo rdinate
syst em references
• t he level mounting surface f or the X-Y plane
• t he cen ter of the robot for
t he Z axis
.,..
11nzt
..-.
The flange coordinate system references t he end
surface of the terminating
main axis of the robot.
Tool
-----~
The origin of t he t ool coordinate system lies at t he
tool center point TCP ( Tool
Center Point).
The speed of the tool center point is referred to as
the robot speed and the
path of tool travel as the
robot traject ory.
Symbols for representing robots (selection)
Designation
Symbol
Designation
~;.::~on axis
Translation aligned
(telescopin g)
-E
~~::~,axis
Rotation
aligned
cf. VOi 2861 (1988-06)
Example RRR robots
Symbol
-<J (>--
~A
A ,i
~ .-.·~
0
-<!-
Translation out of
__c-Rotation out of
___ffi_
1-a_li_g_n_
m_e_n_t - - ---1- - - - -- -+a_lig_n_m_e_nt_ _ _ __ , 1 - - - - -___ 7µ
_ __ --i
Gripper
-<:
11 Translation = straight line moti on
Auxiliary axis
(e.g. for roll, pitch
and yaw)
21 Rotation = rot ational motion
rI
•
L
7
______J•
'f'- 3 arm
A/ joints
l.
3 hand
Jotnts
)ijl
•
-
379
Automation: 7.6 Handling and robot systems
Robot designs
Mechanical structuretl
Klnematics21 and working
Cartesian robots
TTT-Kinematics
space
Examples of
design types
ct ::i1N EN 1s0 9787 12000
071
Characteristics, areas of
application
Main axes:
• 3 translational
Areas of application:
• large working space, therefore often in overhead
gantry
• tool and workpiece feed in
production cells
sheet processing with laser
Gantry robot
Cylindrical robots
RTT-Kinematics
Polar robot 1
RRT-Kinematics
beam and water jet cutting
palletizing
Main axes:
• 1 rotati onal
• 2 translational
Areas of application:
• suitable for heavy masses
• handling of heavy forged
and cast parts
• transport of pallets
and tool cartridges
• pick and place
Base robot
Vertical
swivel arm robot
Polar robot 2
Type: SCARA3> robot
Main axes:
• 2 rotational
• 1 translational
Areas of application:
• telescoping type axis 3,
consequently deeper
working space
• point and simple path
welding, e.g. on car bodies
• pick and place with die
casting machines
Main axes:
2 rotational as horizontal
revolute joint
1 translational
RRT-Kinematics
Areas of application:
primarily in vertical
assembly area
point and simple path
welding
• pick and place work
Horizontal
swivel arm robot
Articulated arm robots
RRR-Kinematics
Main axes:
• 3 rotational
Areas of application:
• handling and
assembly area
• complex path welding
painting work
• adhesive bonding
• low space requirement
Vertical
swivel arm robot
yet large working space
1l Axes are designated with numbers, where axis 1 is the axis of the first motion.
= rotational axis; T = translational axis (Designations "R" and "T" are not standardized.)
3) SCARA = Selective Compliance Assembly Robot Arm
2> R
380
Automation: 7.6 Hand ling and robot systems
Grippers, Job safety
Gripper
cf. DIN EN ISO 14539 (2002-12) and VOi 2740 (1995-04)
Gripper
mechanical
pneumatic
magnetic
• suction g ripper
• articulated finger gripper
Finger grippers
Jaw grippers
Linear
Scissors
grippers
~
Characteristics
grippers
Clamp grippers
Needle grippers
Spring
loaded
Characteristics
Clamping
force is created by a
spring.
Opening of
the gripper
by pressure.
Frequently
used
grippers.
3 degrees of
movement
Parallel
gripper
Weight
loaded
t - - - --
-< Clamping
force created
by the own
weight of the
gripping
object.
Both gripper
Spatial
gripper
~
• velcro fastener
gripper
Both g ripper
fingers turn
about an axis
fixed in the
frame.
1 degree of
movement
Flat
gripper
~
Characteristics
adhesive
• electromagnets
• permanent magnets
fi ngers are
6 degrees of
movement
pushed
parallel to
each other
opposite to
the gripper
housing.
Work safety for handling and robot systems*
protective curtain with sensors t hat can
distinguish between human and robot
because of w orkpiece change
Opening of
the gripper
by pressure.
Used in textile industry.
Four nail
plates are.
extended by a
tapered plug
and grip the
f abric.
cf. DIN EN ISO 10218-1 (2007-02) & VOi 2854 (1991-061
Concepts
Explanations
Maximum
space
Area encompassing:
• moving parts of robot
• tool flange
• workpiece
Restricted
space
A portion of the maximum space which should
not be entered in case of an event ual breakdown of the robot system
Separating
safeguards
Containment fences, coverings, permanent
encasements, locking devices
(DIN EN 1088)
Protective
systems with
contactless
activation
Hazardous area security: light curtains and
light barriers
Area monitoring: laser scanners
Access security: light grills and light barriers
Important safety relevant standards
DIN EN 292
DIN EN 61496
DIN EN418
area bordered by
protective fence
*) According to European Standards
DIN EN 294
DIN EN 457
CSA Z 434-03
ANSI R 15.06
Safety stand. for machines, basic terminology
Safety standards for machines, contactless
activation of safety systems
Safety standards for machines, emergency
OFF systems
Safety around machines, safe dist ances
Acoustical hazard signals
Industri al Robots and Robot systems
American Standard f or Industrial Robots
Automation: 7.7 NC t echnology
Coordinate axes
381
c1 DIN 6621111915 121
Coordinate system
Right hand rule
Cartesian coordinate system
+Y
+Y
Coordinate axes X, Y and Z are
perpendicular to each other.
This a rrangement can be represented by thumb, index finger
and middle finger of the right
hand.
Axes of rotation A, B and C are
assigned to coordinate axes X, Y
andZ.
When looking down one axis in
the positive direction, the positive
direction of rotation is clockwise.
+C
I I ,
+Z
ZX plane (G18)
Coordinate axes in programming
Coordinate axes and the resulting
directions of motion are aligned
to the main slideways of t he CNC
machine and are essentially rela•
tive to the clamped workpiece
w ith its workpiece zero point.
Positive directions of motion always result in greater coordinate
values on the workpiece.
The Z axis always runs in the
direction of the main spindle.
Lathe
Horizontal milling machine
To simplify programming it is
assumed that the workpiece
remains motionless and only t he
tool moves.
Example:
2-carriage lathe with programmable
main spindle
Reference points
Machine zero point M
Origin of the machine coordinate system and is set by the
machine manufacturer.
Program zero point PO
Indicates the coordinates of the point at w hich the tool is located
before start of the program.
Reference point R
Origin of incremental position measurement system w ith a distance to the machine zero point set by the machine manufacturer.
Tool holder reference point T
Lies central to the limiting face of the tool holder. On milling
machines this is the abutting surface of the tool spindle, on lathes
the abutting f ace of the tool holder on revolver.
11 not standardized
Workpiece zero reference point W
Origin of the workpiece coordinate system and is set by the programmer based on engineering principles.
382
Automation: 7.7 NC technology
Program structure
Tasks of the control program
Block structure
Explanation of words:
- N10 G01 X30 Y40 F150 S900 T01 M03
-.--- -.--- -.--- - . - - . - - - T
Positional 11 . Technic_
al
data
mformat,on
N10 block number 10
G0l feed. linear interpolation
X30 coordinate of target point in X di rection
Prep.
function
(G function)
I
Block
number
I
Miscellaneous
function
(M function!
II Coordinates of IIr;.ee:i1I s edlll Tool I
t arget point
Y40 coordina te of target point in Y direction
F150 feed 150 mm/min
S900 speed of main spindle 900/min
T01 tool no. 1
M03 spindle clockwise
pe
Program structure
Example:
CNCprogram
I%
Program start
N1 GSO
N2 G88
.........
F0.2
M04
S180
H
NC blocks
M30
H
Program end
I
I
.........
N70
I
& ~·~
15
CNC program
%01
N1 G90
M04
N2 G96
F0.2
S180
N3 GOO
X20
Z2
N4 G0l
X30
Z-3
N5
Z-15
N6 GOO
X200 Z200
N7
M 30
Preparatory functions
Prep.
Effective- Meaning
functions
ness
•
•
•
•
•
•
•
•
•
•
•
•
•
GOO
G0l
G02
G03
G04
G09
G17
G18
G19
G33
G40
G41
G42
Effective- Meaning
Prep.
ness
functions
Positioning at rapid rate
Linear interpolation
G53
Circle interpolation clockwise
G54G59
Circle interpol. counterclockwise
G74
Dwell time predetermined
GB0
Exact stop
G81G89
Plane selection XV
Plane selection ZX
G90
Plane selection YZ
G91
Thread cutting. constant
pitch
G94
Cancel tool offset
G95
Cutter compensation, left
G96
Cutter compensat ion, right
G97
•
•
•
•
•
•
•
•
•
•
•
Cancel shift
Shift 1- Shift 6
Approach reference point
Cancel fixed cycle
Fixed cycle 1-Fixed cycle 9
Absolute dimensional notation
Incremental dimensional not ation
Feed rate
in mm/min
Feed in mm
Constant cutting speed
Spindle speed in 1/min
•
modal:
Preparatory functions that remain effective until they are overwritten by a similar type of
condition.
•
non-modal:
Preparatory functions that are only effective in the block in which they are programmed.
Universal miscellaneous functions Im-functions, selection)
MOO
Programmed stop
M04
M02
Program end
M03
Spindle clockwise
cf. DIN 66025-2 (1988-09)
Spindle counterclockwise
M07
Cooling lubricant ON
M05
Spindle stop
M09
Cooling lubricant OFF
M06
Tool change
M30
Program end wit h reset
383
Automation: 7.7 NC technology
Turning
Milling
Tool offset
Positional codes1I for cutting tool
point P in relation to center M of
cutting radius r.
T: E
2
crosshairs of w·---:::--,,,,......,
the presetting •
device at
1
point P
op ~--L
L
Q
L
r,
1-8
T
transverse offset of X axis
longitudinal correction of Z axis
cutting radius
positional code digits
tool holder reference point
E tool reference point
M center of cutting radius f r,
p
Offset memory
tool cutting point
11 not standardized
72
Q
14
L
53
L
112
r,
0.8
r,
0.4
3
Positional
digit
2
digit
R
T
E
p
tool length
tool radius
tool holder reference point
tool reference point
tool cutting point
Offset memory
Q
Positional
z
Offset memory
z
j 126
R
J
Cutter compensation
G42
Lathe tool forward of spindle axis
Lathe tool right
g
¢::::::,
•
For layout of lathe tool in front of center acco rding to DIN 66217:
Because of the different perspective in the X-Z plane, the cutter compensation would be opposite for the user looking down on the workpiece
and for programming.
Cutter compensations G41 and G42 may be canceled with function G40.
G41
Milling cutter left
10
384
G01
Automation: 7.7 NC technology
Linear motion
Designation and machining example:
N30
n
linear interpolation,
machining motion in
programmed feed
f ".
in X d irection
in Y direction
li:+18
3
19~
1~~
in Z direction
CNC program
N ...
N1O
N2O
GOO
GO1
IN30
X2O
Y1O
21
zo
X60
Y19
!
(Pl )
(P2)
Z-8 (P31
N ...
0
G02
0
N
0
"'
Clockwise circular movement
Designation and machining example:
N40
CNC program
(Pl)
Y4
Y2O.39
10
IN40 G02 )(32 Y38
0-+-1-'-t----- t - '
N50 GO1 X40
N...
4-l+H,,...,_,.....
G03
N...
N1O G41
N20 GO1 X6
N30
(P2)
126 J -1o.»i (P3)
(P4)
Counterclockwise circular movement
Designation and machining example:
N40
Counterclockwise
circle interpolation,
machining motion in
programmed feed
CNC program
N...
N1O G41
N2O GO1 X6
N30
Y4
Y21.88
IN40 G03 )(32 Y38 1a J111.12 I
N50 GO1 X40
N ...
(Pl)
(P2)
(P3)
(P4)
385
Automation: 7.7 NC technology
G01
Linear movement
Designation and
machining example:
N20
Linear interpolation, machining
motion in programmed feed
in Z direction
CNC program
N ...
NlO
GOO
IN20
G01
z-sol
(P11
(P2)
2-61
(P4)
22
X 80
X102
N30
N40
N ...
G02
X60
(P3)
Clockwise circular movement
Designation and machining example:
N30
Clockwise circular
interpolation,
machining motion in
programmed feed
CNCp<ogram
G03
N...
NlO
N20
GOO
GOl
IN30
G02 X100 Z-«> l20
N40
N ...
GOl
X60
(Pl)
(P2)
22
2-40
KO
I (P3)
(P4)
XllO
Counterclockwise circular movement
Designation and machining example:
N40
Counterclockwise
circle interpolation,
machining motion in
programmed feed
CNCprogram
N ...
NlO GOl XO
20
N20 G03 X60 2-11.46
N30 GOl
2-40
IN40 G03 X90 Z-611
N ...
(Pl)
)0
K-45
(P2)
(P3)
NI K-11;J (P4)
386
Automation: 7.7 NC technology
Program structure of CNC machines according to PAL1 l
Linear interpolation with G1 for lathes and milling machines
Turning
Milling
Incremental programming with XI, YI end ZI coordinates in NC programs with G90
NC program
0
=
'ii
10
16 0
N10 ...
N15G90
N20 ...
N25G1 X68Z-16 ;P2
N30 G 1 ! Xl31 Zl-54 !;P3
N35 ...
P3
75
NC program
up
P2
XI
+Y
+X
N10...
N15 G42
N20GO x ...
N25G1 X72
;P2
N30 G1 ! Xl-17 Yl57 ! ;P3
N35...
55 72
Absolute programming with XA. YA end ZA coordinates in NC programs with G91
10
16 0
NC p,-ogram
NC program
N10 ...
N15G91
N20 ...
N25 G1 X68 Z-16
;P2
N30 G1 !XA 130 ZA-70!;P3
N35...
N10...
N15 G42 GO X-16 Y18
N20 G91
N25 G1 X88
;P2
N30 G1 !XASS YA78 ! ;P3
N35...
Start angle AS with coordinate value X
16 0
NC program
NC program
N10...
N15
N20...
N25 G1 X60 Z-16 ;P2
N30 !AS150 X130 ! ;P3
N35...
N10...
N15G42
N20 GO X ... Y18
N25 G 1 X72
;P2
N30 G1 !AS120 X38! ;P3
N35...
38
12
Start angle AS with coordinate value Z
80
NC program
NC program
N10...
N15 G90
N20...
N25G1 X60Z-16 ;P2
N30 G1 !AS140 Z-80! ;P3
N35...
N10...
N15G42
N20 GO X ... Y18
N25 G 1 XSO
;P2
N30 G1 ! AS65 Y66 ! ;P3
N35...
16 0
50
Transition elemMrts radius RN+ end phase RNThe radius AN+ and the phase RN- are transition elements between two contour elements (circles, straight lines)
NC program
90 74
30
N10...
N15G90
N20 GO X48 ZO
;P1
N25G1 Z-30 !RN-10i ;P2
N30 G 1 X82
;P3
N35 G1 Z-74!RN+30! ;P4
N40 G1 X140 Z-90 ;PS
NC program
N10...
N15G42
N20GOX... Y18
N25 G 1 X75 lRN-2l
N30 G1 X60 ~
N35...
;P2
;P3
and testin material)
387
Automation: 7.7. NC technology
Program structure of CNC machines according to PAL
Circular interpolation for lathes and milling machines
Milling
Turning
Circular interpolation with absolute center point coordinatas
Block structure:
G90
Gl X.. Z..
;P2
G2 X.. Z.. IA.. JA.. ;P3
Block structure:
G90
g1 ~:: ~:: IA.. KA.. :~~
NC program
NC program
70
40
NlO ...
N15 G90
N20 GO X38 24
;Pl
N25 Gl Z-40
;P2
N30 G2 X98 Z-70~~P3
N35 ...
04
':,-l~-
N10 ...
N15 G90
N20 GO X... Y9
;Pl
-1..w.+1'-'9c., N25 G1 X40
;P2
N30 G3 X60 Y29 §glJA29 P3
f
40
60
~N_3_5_··- · - - - - - - - ~
Selection criteria for multiple solutions
When using the radius R or th e aperture ang le AO. several arc solutions may result. The programmer can select
the desired arc by defining an arc or a start angle w ith t he help o f the two addresses O and/or Rand H.
Selection of the arc length using the address O or R
Block structure:
G1 X.. Z..
;P2
G2 X.. Z.. R.. 0 .. ;P3
Ifill
shorter arc
70
Block structure:
G1 X.. Z..
;P2
G2 X .. Z.. R+.. ;P3
or:
NC program
Block structure:
G1 X.. Z..
;P2
G2 X.. Z.. R.. 0 .. ;P3
;P2
;P3
NC program
longer arc
N10 ...
N15 G90
N20...
N25 G1 X70 Z-25
;P2
N30 G2 X100 Z-70 R26 ~ ;P3
o r:
N30 G2 X100 Z-70 R026
;P3
25
Block structure:
G1 X.. Z..
G2 X.. Z .. R- ..
or:
12
N10 ...
N15 G90
N20 ...
;P2
N25 G1 X12 Y15
N30 G2 X66 Y15 R26 ~ ;P3
or:
;P3
N30 G2 X66 Y15 RE]26
66
Selection of the start angle using the address H
Block structure:
Block structure:
G90
g1 ~:.· t AO.. H.. :~~
55
18
g~ ~:: t AO.. H.. :~~
ffi1J
smaller start angle
P3
NC program
NC program
N10 ...
N15 G90
N20...
;P2
N25 G1 X50 Z-18
N30 G2 Z-55 R26 A011 s lili] ;P3
N10 ...
N15 G90
N20...
N25 G 1 X30 Y26
;P2
N30 G2 262 R26A0115 l!g};P3
30
0
62
Contour routing for lathes (selection)
W here open contour routing is concerned, the starting point as well as the target point may still be undefined. The
control system calculat es the starting and end point of the open element on the basis o f the specified addresses.
G61 Open line section
G62/G63 Open arc
Block structure:.------- - - , Block structure: ~ - - - - - - ~
Gl X .. Z..
N15 G1 X50 Z-30 ;Pl
G1 x .. Z..
G62 AS .. R..
G61 AS..
N20 G61 AS160
Three-point routing
N15 ...
N20 G 1 X40 Z-20 ;Pl
N20 G61 AS210
;P2
N30 G62 Z-72 R+26 ;P3
0
"'....
30
30
+Z
72
20
388
Automation: 7.7 NC technology
Program structure of CNC machines according to PAL
PAL functions for lathes and milling machines
Programming coordinates and interpolation parameters
XA,YA,ZA
A bsolute input of coordinate values relative to the workpiece zero point
XI, Yl,ZI
Incremental input of coordinate values relative to the current tool position
IA,KA
Absolute input of the interpolation parameters relative to the workpiece zero point
T-addresses for tool change
T
Too l storage place in the tool revolver or holder
TC
Selection of the number of the offset memory
TR
Incremental tool radius or cutting edge offset in the selected offset memory
Tl
Incremental tool length offset in the selected offset memory (milling)
TZ
Incremental tool length offset in Z direction in the selected offset memory (turning)
TX
Incremental diameter offset in X direction in the selected offset memory (turning>
Additional M-functions1> according to PAL
M13
Clockwise spindle rotation, coolant ON
M 17
End of sub program
M14
Counter clockwise spindle rotation, coolant ON
M60
Constant feed
M15
Spindle and coolant OFF
M61
M60 + corner shaping
PAL functions for lathes
G-functions
Types of interpolation
Cutter compensation
GO
Rapid travel/motion
G40
Cancel tool radius offset TRO
G1
l inear interpolation w ith feed rate
G41
G2
Circular interpolation, clockwise
Circular interpolation, counter clockwise
Tool radius offset TRO to t he left of the
programmed contour
G42
Tool radius offset TRO to t he right of the
programmed contour
G3
G4
G9
Dwell time
Feeds and speeds
Exact stop
Travel to configured tool change point
G92
Rotational speed limitation
Linear interpolation for contour routing
G94
G62
Circular interpolation for contour routing,
clockwise
Feed in mm per minute
Feed in mm per revolution
G63
Circular interpo lation for cont our routing,
counter clockwise
G95
G96
G14
G61
G97
Constant cutting speed
Constant rot at ional speed
Reference points
Program features
G50
G22
Call sub program
G23
Repeat program section
Cancellation of all zero point shifts and
rotations
G29
Co nditional jumps
G54G57
Adjust able absolut e zero points
Cycles
G59
Incremental Cartesian zero point shift and
rotation
G53
Cancellation of incremental zero point
shift and rotations
G31
G32
Thread cycle
Tapping cycle
G33
Thread chasing cycle
Machining planes and rechucking
G80
G18
G17
Selection of the plane of rotation
Face machining planes
G81
Completion of a machining cycle contour
description
Longitudinal rough-turning cycle
G19
Shell surface/segment surface machining
planes
Rechucking/opposed spi ndle takeover
G82
Rough facing cycle
G83
G84
Drilling cycle
G30
Dimensions
G70
G71
Inch input confirmation
Metric input confirmat ion (mm)
G90
Absolute dimensions
Input of incremental dimensions
G91
Rough-turning cycle parallel to the contour
G85
Underc ut cycle
G86
G87
Radial g rooving cycle
Radial contour cutting cycle
G88
Axial grooving cycle
G89
Axial contour cutting cycle
G-functions for lathes
G22
Call sub program
Structure of NC block
G22 L I HI 1/1
Obligatory addresses:
L
number of the
sub program
Main program %900
Sub program L911
N10G90..
N15F.. S.. M4
N20 GO X42 Z6 ;Pl
N25 G22 L911 H2
N30..
N35..
N150 M30
N10 G91
N15 GO Z-16
N20 G1 X-6
N25 G1 X6
N30 GOZ-6
N35G1 X-6
N40 G1 X6
N45 M17
Optional addresses:
H
number of
repetitions
extract level
G23
return
Machining example
•
start block number of the program section to
be repeated
end block number of the program section to
be repeated
Optional addresses:
H
number of repetitions
G14
22
10
0
Machining example
G23 N N (HJ
Obligatory addresses:
N
.,.
N
Repeat program section
Structure of NC block
N
Q~
6
Pl
NlO..
N15 GO X58 Z-15 M4
N20 G91
N25G1X-11
N30 Gl Xll
N35 GOZ-16
N40 G23 N20 N35 H2
N45 G90
NSO ...
Travel to tool change point
Structure of NC block
G14 IHI
Optional addresses:
HO travel to tool change point simultaneously in all axes
Hl fi rst X axis, then Z axis H2 first Z axis, then X axis
PAL cycles for lathes
G84
Drilling cycle
Structure of NC block
G84 ZI/ZA [DJ [VI [VB] [DR] IDMI [RI [DAI [Ul IOI [FR] [El
Obligatory addresses:
ZI depth of hole, incremental depth relative t o the current tool position
ZA depth of hole, absolute depth
Optional addresses (selection):
D
pecking amount
(if D is not specified, pecking depth is
equal to t he final drilling depth)
V
safety distance
VB safety distance to the hole bonom
DR reduction value of the pecking amount
DM minimum infeed
R
retract level/distance
DA spot-drilling depth
U
dwell time at hole bonom
0
dwell time selection
01 in seconds
02 in revoluti ons
FR rapid travel reduction in %
E
spot-drilling feed
G32
Machining example
21
31
H&ti~~~
130
35
20
5
N10 G90
N15 G84 Z-130 030 VS VBl DR4 U0.5
N20 ..
Tapping cycle
Structure of NC block
G32 Z/ZI/ZA F
Obligatory addresses:
Z, ZI, ZA thread end point in
Z direction
I incremental, A absolute
F
pitch of thread
!'Jlachinmg
example
ZI
I
35
__ __
M20•35/45
•
~
N10 G90
N15 G32 Z-35 F2,5 S.. M..
2.5
390
Automation: 7.7 NC technology
PAL cycles for lathes
G31
Thread cycle
Structure of NC block
G31 Z/ZI/ZA X/XI/XA F D (ZS) (XS)
[DA) (DUI [OJ (OJ (HJ
Obligatory addresses:
Z, ZI, ZA thread end point in Z direction
Z controlled by G90/G91;
I incremental, A absolute
X, XI, ZI thread end point in X direction;
X controlled by G90/G91,
I incremental, A absolute
F
thread pitch
D
thread depth
Optional addresses [ ..):
ZS thread starting point, absolute in Z
XS thread starting point, absolute in X
DA approach
DU overrun
0
number of cuts
0
number of idle cycles
H selection of infeed type and residual cuts (RC)
Hl without offset (radial infeed), RC OFF
H2 infeed at left flank, RC OFF
H3 infeed at right flank, RC OFF
H4 alternating infeed, RC OFF
Hl 1 without offset (radial infeed), RC ON
H12 infeed at left flank, RC ON
H13 infeed at right flank, RC ON
H14 alternating infeed, RC ON
Residual cuts 'h. 1/,, 1/e, 'I• x (D/O)
G81
Longitudinal rough-turning cycle
Structure of NC block
G81 (or G82) H4 (AKI [AZ) (AX) IAEI
[AS) [AVI [OJ IOI [VJ [El
or
G81 (or G82) D (H1/H2/H3/H24I
Radial
infeed
Hl/Hll
Flank
infeed
left H2/H12
Flank
infeed
rightH3/H13
Alternating
infeed
H4/H14
••••
Machining example
1
40
10
N10 G90
N15 G31 Z-40 X30 F3.5 D2.15 ZS-10 XS30 Q12 013 H14
N20 ..
G82
Rough facing cycle
Iii
Obligatory addresses:
D infeed
Optional addresses (..J:
H type of machining
Longitudinal rough turning
Rough facing cycle with G82
H 1 rough machining, removal below 45°
cycle with G81
H2 stepwise angle-cutting along the contour
Machining example: longitudinal rough-machining cycle
H3 like H 1 with final contour cut
P9 IJqo
H4 contour finishing
H24 rough-machining with H2 and subsequent
finishing
AK contour allowance parallel to the contour
AZ contour allowance in Z direction
AX contour allowance in X direction
AE immersion angle (final angle of the tool)
77 55
125 110
170
20 0 3
AS emergence angle (lateral adjustment angle of tool)
AV safety angle reduction for AE and AS
0 machining starting point
N10
01: current tool position
N15 G81 03 H3 E0.15 AZ0.1 AX0.5
02: calculated from contour
N20 X44 Z3
:Pl
Q idle step optimization
N25 Gl Z-20
;P2
01: optimization OFF
N30 Gl Z-55 AS135 RN20
;P3
02: optimization ON
N35 Gl Z-77 AS180
;P4
V
safety distance for idle step optimization
;P5
N40 Gl Z-110 X64
G81: in Z direction
N45 AS180
;P6
G82: in X direction
N50 AS110 X88 Z-125
;P7
E immersion feed
N55 AS180
;P8
N60 AS130 X136 Z-170
;P9
N65 G80
391
Automation: 7.7 NC technology
PAL cycles for lathes
G86
G88
Rachi grooving cycle
Axial grooving cycle
Structure NC block
G86 Z/ZI/ZA X/XI/XA ET [EBJ (DI (.. ) (selection)
G88 Z/ZI/ZA X/XI/XA ET [EBJ (OJ [ .. J (selection)
Obligatory addresses:
Z, ZI, ZA grooving position in Z direction;
Z controlled by G90/G91,
ZI incremental, ZA absolute
X, XI, XA grooving position in X direction;
X controlled by G90/G91,
XI incremental, XA absolute
ET G86 absolute diameter of grooving depth
GBB absolute grooving depth
Optional addresses(..):
EB grooving width and position
EB+ grooving in direction Z+ relative to the
programmed grooving position P
EB- grooving in direction Z- relative to the
programmed grooving position P
D pecking amount (if no value is specified, the
pecking depth is equal to the groove depth ET)
AS flank angle of grooving at the starting point
relative to the grooving direction (X or Z)
Radial grooving cycle with G86 Axial grooving cycle with G88
AE flank angle of grooving at the end point
relative to the grooving direction (X or Z)
RO rounding or chamfering of upper corners
RO+ rounding
RO- chamfer w idth
Machining example: radial grooving cycle with G86:
RU rounding or chamfering of lower corners
RU+ rounding
10
RU- chamfer width
AK contour allowance parallel to the contour
AX contour allowance in X direction (contour offset)
EP setpoint definition for groove cutting (position Pl
EP1: setpoint in upper corner of the groove
EP2: setpoint in bottom corner of the groove
H type of processing
H 1 roughing cut H 14 roughing and finishing
H2 plunge turning H24 plunge turning and finishing
H4 finishing
DB infeed in% of the cutting tool width for grooving
N10 GO X82 Z-32
V
safety distance above groove
N35 G86 Z-30 XBO ET48 E820 D4 AS10 AE10 R0-2.5 RU2 H14
E feed rate into solid material
G85
Undercut and thread undercut cycle
Structure of NC block
G85 Z/ZI/ZA X/XI/XA I/II) K[KJ [RN) (SXJ (HJ (El
Thread undercuts acc. to DIN 76
SX
Undercuts acc. to DIN 509
Obligatory addresses:
Z, ZI, ZA undercut position in Z direction;
Z controlled by G90/G91,
ZI incremental, ZA absolute
X, XI, XA undercut position in X direction;
Machining process with DIN 76
X controlled by G90/G91,
0.2
XI incremental, XA absolute
I
undercut depth; obligatory parameter for DIN 76 (H1)
K undercut length; obligatory parameter for DIN 76 (Hl)
Optional addresses [ ..):
RN corner radius
SX grinding allowance
E
feed rate for plunging
H undercut shape
H1 DIN 76 H2 DIN 509 E
G80
NlO GO ..
N15G85 ZA-18 XA16 11 .5 KS RNl SX0.2 Hl E0.15
H2 DIN 509 F
Further information on p. 89 and p. 92
Completion of a contour description in a rough-machining cycle
Structure of NC block Optional addresses(..): ZA absolute Z-coordinate of the machining limit parallel to the X axis
GB0 [ZA) [XAJ
XA absolute Z-coordinate of the machining limit parallel to the Z axis
392
Automation: 7.7 NC technology
Program structure of CNC machines according to PAL
PAL functions for milling machines
G-functions
Types of interpolation, contours
Tool offsets
GO
Rapid motion
G40
Cancel cutter compensation
Gl
linear interpolation with feed rate
G2
Circular interpolation, clockwise
G41 G42
Cutter compensation left
Cutter compensation right
G3
Circular interpolation, counter clockwise
Feeds and speeds
G4
Dwell time
G94
Feed in mm per minute
G9
Exact stop
G95
Feed in mm per revolution
Gl O
Rapid motion in polar coordinates
G96
Constant cutting speed
Gll
linear interpolation with polar coordinates
G97
Constant spindle speed
G12
Circular interpolation with polar coordinates,
clockwise
Program features
G13
Circular interpolation with polar coordinates,
count er clockwise
G45
Linear tangential approach to a contour
G46
linear tangential retraction from a contour
G47
Tangent ial approach to a contour in a
quarter circle
G48
Tangential retraction from a contour in a
quarter circle
G61
linear interpolation for contour routing
G62
Circular interpolation for contour routing,
clockwise
G63
G34
Start-up of t he contour pocket cycle
G35
Rough-machining technology of the contour
pocket cycle
G36
Residual material technology of the contour
pocket cycle
Contour description of the contour pocket cycle
Completion of the G38 cycle
G39
Call contour pocket cycle with material removal
Cancellation of the incremental zero point shift
and rotations
G72
Rectangular pocket milling cycle
Cancellation of all zero point shifts and
G73
Circular pocket and spigot milling cycle
Adjustable absolut zero points
G58
Incremental zero point shift, polar and
either parallel to the contour or in meanders
G74
Slot milling cycle
G75
Circular slot milling cycle
G81
Drilling cycle
rotation
G82
Deep drilling cycle with pecking
Incremental Cartesian zero point shift and
G83
Deep drilling cycle with pecking and full retraction
rotati on
G67
Fixed cycles
G80
G54G57
G66
Conditional jumps
Finishing technology of the contour pocket cycle
rotati ons
G59
Repeat program section
G29
G37
Reference points, rotation, mirror images, scaling
G53
Call sub program
G23
G38
Circular interpolati on for contour routing,
counter clockwise
G50
G22
G84
Tapping cycle
mirror image off
G85
Reaming cycle
Scaling (enlarging or reducing or cancellat ion)
G86
Boring cycle
Mirror image across the X or Y axis,
Plane selection, dimensions
G17G19
Plane selection, 2½ D processing
G70
Inch input confirmation
G71
Metric input confirmation (mm)
G90
Input of absolute dimensions
G91
Input of incremental dimensions
G87
Plunge milling cycle
G88
Internal thread milling cycle
G89
External thread milling cycle
G76
Multiple cycle call on a straight line (line of holes}
G77
Multiple cycle call on a pitch circle (line of holes)
G78
Cycle call at a particular point (polar coordinates)
G79
Cycle call at a particular point (Cartesian
coordinates)
393
Automation: 7.7 NC technology
Program structure of CNC machines according to PAL
PAL cycles for milling machines
G1
Linear interpolation with feed rate
Structure of NC block
Gl [X/XI/XAJ [V/VI/YA] [Z/ZI/ZAJ [DJ [AS] .. (selection)
Machining example
Obligatory addresses:
X. XI. XA X coordinate of the target point
V, YI, VA Y coordinate of the target point
Z. ZI, ZA Z coordinate of the t arget point
Optional addresses [ ..]:
D length of travel distance
AS ascent angle relative to the X axis
RN transition element to the next contour element
RN+ rounding radius RN- chamfer width
H selection among two solutions via angle criterion
Hl small ascent angle H2 greater ascent angle
TC selection of the offset memory number
TR incremental change of the tool radius value
TL incremental change of the tool length offset
G11
74
N10 ...
;P2
N15 G1 X74 Y16 RN-12
N20 G1 065 AS120 RN+14 ;P3
Linear interpolation with polar coordinates
Structure of NC block
G11 RP AP/Al [J/JAJ [Z/ZI/ZAJ [RN] .. (Auswahll
Machining example
Obligatory addresses:
RP polar radius
AP polar angle relative to the positive X axis
Al incremental polar angle
Optional addresses[..]:
I, IA
X coordinate of the polar center
V coordinate of the polar center
J, JA
Z, ZI, ZA infeed in Z direction
RN transition to the next contour element
RN+ rounding radius RN- chamfer width
TC selection of the offset memory number
TR incremental change of the tool radius value
TL incremental change of the tool length offset
G2/G3
IA
N15 G42 G47 A20 X30 YO Z-3
N20 G11 IAO JAO AP30 AP90
N25G11 IAOJAORP30AP180
N30G11 IAOJAOAP30AP270
N35 G11 IAO JAO RP30 APO
Circular interpolation with Cartesian coordinates
Structure of NC block
G2 [X/XI/XAJ [Y/VI/VAJ [Z/ZI/ZAJ Ill/IA [J/JA]J /
1(1/IAJ J/JAI / R / AO [RN] [OJ [Fl [SJ [Ml
G3 [X/XI/XAJ .... ....
Machining example
shorter
arc (01)
Optional addresses[... ):
X, XI, XA X coordinate of the target point
V, VI, YA
Y coordinate of the target point
Z. ZI, ZA Z coordinate of the target point
I, IA, J, JA center point coordinates
A
radius of arc and
selection of solution via arc length criterion
R+ shorter arc R- longer arc
AO aperture angle
RN transition element
RN+ rounding radius RN- chamfer width
0
selection of solution via arc length criterion
01 shorter arc 02 longer arc
G12/G13
;P2
;P3
;P4
;PS
;P2
JA
38
JA
80
N10 ...
;P2
N15G1 X38Y70AN+15
N20 G3 XA80 A30 AO135 AN -8 02 ;P3
Circular interpolation with polar coordinates
Structure of NC block
G12 AP/Al [I/IA] [J/JAJ [Z/ZI/ZAJ [RN) [Fl [SJ [Ml
G13 AP/Al [I/IA) [J/JAJ [Z/ZI/ZAJ [RN] [Fl [SJ [M]
Obligatory addresses:
AP polar angle of target point
Al incremental polar angle
Optional addresses [ ...):
I, IA X coordinate of polar center
J, JA Y coordinate of the polar center
RN+ rounding radius RN- chamfer width
Machining
example
~ -+<>--o-_,_
45
JA
15
0
.y
.x
IA
N15 G1 X60 Y15
;P2
N20 G12 IA45 JA45 APSO ;P3
394
Automation: 7.7 NC technology
PAL functions for milling machines
G45
G46
u,-r tangential approach to the contour
Linear tangential retraction from the contour
Structure of NC block
G41/G42 G45 D [X/XI/XAJ IV/YI/VAi IZ/ZI/ZAJ
[WI [El [Fl [SJ [Ml
G46 G40 D [Z/ZI/ZAJ [WI [Fl [SJ [Ml
Machining example
Obligatory addresses:
with G45: D distance to the first contour point,
unsigned
with G46: D length of the retracting motion,
unsigned
Optional addresses [ ..):
X, XI, XA X coordinate of the first contour point
'> -.
V, YI, YA V coordinate of the first contour point
v·
Z, ZI, ZA with G45: infeed at approach point in the Z axis
with G46: retracting motion at the end point
in the Z axis
w absolute position in fast motion in the infeed axis
E
feed rate for plunging
G47
Tangential llflPIOIICh to the contot.r in a qwrtar circle G48
13
so
N1O ...
N15 G42 G45 XO Y8 D13
N2OG1 X50
N25G1V40AS80
N30 G40 G46 D13
;Pl
;P2
;P3
;P4
Tangential retraction from the contot.r in 1 ~ circle
Structure of NC block
G41/G42 G47 R [X/XI/XAJ [V/YI/VA] [Z/ZI/ZAI
IWJ [El [Fl ISi [Ml
G48 G40 R [Z/ZI/ZA] [WI [Fl [SJ [Ml
Machining
example
Obligatory addresses:
with G47: R radius of the approach motion relative
to the center path of the cutter
with G48: R
radius of the retracting motion relative
to the center path of the cutter
Optional addresses [..]:
X, XI, XA X coordinate of the first contour point
V, YI, YA V coordinate of the first contour point
Z, ZI, ZA infeed at the approach point in the Z axis
W absolute position in fast motion in the infeed axis
E feed rate for plunging
G54-G57
N1O ...
N15 G42 G47 XO V8 R13 ;Pl
N20 Gl X50
;P2
N25 G1 V40 AS80
;P3
N30 G40 G48 R13
;P4
Adjustable absolute zero point shift
Structure of NC block
G54 or G55 orG56 or G57
workpiece
zero point W
Explanatory notes:
The workpiece zero point W is determined by the
commands G54 to G57 and has a defined distance to
the machine zero point. The operator enters the shift
values into the zero point register of the controller
before starting the program. The zero point is always
specified in absolute coordinates (XA, YA, ZA) relative
to the machine zero point.
G59
N10 ...
N15G54;W
N20
Incremental zero point shift and rotation
Structure of NC block
G59 (XAJ [VAi IZAI [ARI
Optional addresses [..J:
XA absolute X coordinate of the new w o rkpiece zero point
YA absolute Y coordinate of the new workpiece zero point
ZA absolute Z coordinate of the new workpiece zero point
AR angle of rotation of the new coordinate system relative
to the X axis
Explanatory notes:
If the coordinate system of the workpiece is rotated in
its current position, only the angle of rotation is specified:
N ... G59ARThe zero point shift launched via G54...G57 is reset by:
N ... G50
XA
N1O ..
N15 G54
N2O G59 X2O Y40 Z30 AR45
395
Automation: 7.7 NC technology
PAL cycles for milling machines
G81
Drilling cyde
Structure of NC block
G81 ZI/ZA V [WI IFI [SJ [Ml
Obligatory addresses:
ZI depth of bore in the feed axis
ZA absolute depth of bore relative to the
coordinate system of the workpiece
safety distance from the top edge of
V
the hole
Optional addresses [ ..J:
W retract level relative to the coordinate
syst em of the workpiece
G82
Machining example
ZA
Deep drilling cycle with pecking and fuH retraction
G83 has the following features:
- the same addresses as G82
- retracts to the safety distance V for chip removal
and in addition
FR rapid motion reduction in %
--Obligatory addresses:
ZVZA depth of bore in the feed axis
ZI incremental depth from the top edge of the holeZA absolute depth in workpiece coordinates
D
pecking amount
V
saf ety distance above the top edge of the hole
Optional addresses [ ..J:
W retract level relative to the coordinate
system of the workpiece
VB retract distance to the current hole bonom
DR reduction value of t he last pecking amount
DM minimum pecking amount (unsigned)
U
dwell time at hole bon om (relative to pecking)
unit of the dwell time
0
01 dwell t ime in seconds
02 dwell t ime in number of revolutions
DA incremental spot-drilling depth of the first infeed
E
spot-drilling feed rate
G84
Tapping cycle
GO rapid
motion
G1 feed
ZA
Machining example
N10 ...
N15 G82 Zl-30 D10 V3 W4 VB1.5 DR3 U1 01 DA6
N20 G79 X .. Y.. Z.. ;cycle call
ft
Structure of NC block
_
G84 ZI/ZA F M V [WI [SJ
G1 feed
Obligatory addresses:
ZI incremental depth from the top edge of the hole ZA
ZA absolut e depth in workpiece coordinates
XA/YA
thread pitch
F
M direction of tool rotation for plunging
M3 right -hand thread M4 left-hand thread
V
safety distance t o the top edge of the hole
Optional addresses [..):
W retract level relative to the coordinate
system of the workpiece
G85
---
N10 ...
N15 G81 Zl-18 V6 W15
N20 G79 X.. Y.. Z.. ;cycle call
Deep drilling cyde with pecking
Structure of NC block
G82 ZI/ZA D V [WI [VBJ [DR) [DMJ
IUI !OJ [DAI [El [Fl [SJ [Ml
G83 ZI/ZA D V (WJ [VB) [DR) [DMJ
IUI IOI [DAI [El [FRI [Fl [SJ [Ml
~
- -
N10 ...
N15 G84 Zl-12 Fl.25 M3 V4 W7 S800
N20 G79 X.. Y.. Z.. ;cycle call
Reaming cycle
Structure of NC block
G85 ZI/ZA [WI [El [Fl [SJ [Ml
Obligatory addresses:
ZI/ZA drilling depth in the inf eed axis
ZI incremental depth from the top edge of the hole
ZA absolute depth in workpiece coordinates
V
safety distance from t he top edge of the hole
Optional addresses [ ..):
W retract level relative t o the coordinate
system of the workpiece
E
feed speed of t he retracting motion
Machining
example
N10 ...
N 15 G85 Zl-17 V3 W8 E260
G79 X.. Y.. Z.. ;cycle call
7.7 NC technology
PAL cydes for milling machines
G86
Boring cycle
Structure of NC block
G86 ZI/ZA V (WI (DR] (Fl (SJ (Ml
Obligatory addresses:
ZI/ZA depth to be bored out
ZI
depth of bore in the infeed axis
ZA
absolute depth of bore relative to the coordinate
system of the workpiece
V
safety distance from the top edge of the hole
Optional addresses ( ..]:
W
retract level relative t o the coordinate system
of the workpiece
DR
radial retract d istance to the contour
G87
Plunge milling cycle
Structure of NC block
G87 Zl/ZA R D V (WI (BG] (Fl (SJ (Ml
Obligatory addresses:
ZI/ZA depth of hole to be bored out
ZI
incremental depth from the top edge
ZA
absolute depth of bore relative to the
coordinate system of the workpiece
R
radiu s of the hole to be milled out
D
infeed per helical line
(pitch of the helical motion)
V
safety distance from the top edge of the hole
Optional addresses(..]:
W
retract level relative to the coordinate
system of the workpiece
BG2 machining, clockwise
BG3 machining, counter clockwise
G88
Machining example
.
M
XII
YI
BG3
.
BG2
N10 ...
N15 G87 21-8,5 Rl0.92 D3 V3 W13 D3 BG2
N20 G79 X.. Y.. 2.. ;cycle call
Internal thread milling cyde
Structure of NC block
G88 ZI/ZA DN D O V [WJ [BG] (Fl (SJ (Ml
Machining example
Obligatory addresses:
ZA ~
ZI
ZI/ZA depth of thread
XA~ t
ZI
incremental depth of thread from the top edge
ZI XI/
ZA
absolute depth of thread relative to the
YI
coordinate system of the workpiece
DN
nominal diameter of the internal thread
D
thread pitch
ON
Q
number of thread grooves of the tool
V
safety distance from the top edge of the hole
Optional addresses (..]:
retract level relative t o the
coordinate system of the workpiece
BG2 machining, clockwise
BG3 machining, counter clockwise
W
G89
N10 ...
N15 G88 ZA-16 DN24 D2 07 Vl .5 W10 BG3 F..
N20 G79 X.. Y.. Z.. ;cycle call
External thread milHng cyde
Structure of NC block
G89 ZI/ZA DN D O V [WJ (BG] [Fl (SJ [Ml
Obligatory addresses:
ZI
incremental depth of thread from the top edge
ZA absolute depth of thread relative to the
coordinate system of the workpiece
DN nominal diameter of the external thread
D
thread pitch
Q
number of thread grooves of the tool
V
safety distance to the top edge of the hole
Optional addresses [ ..]:
W
retract level
BG2 machining, clockwise
BG3 machining, counter clockwise
Ma~
J:r~•
13
ZI
8
ON
N10 ...
N15 G89 21-8 DN18.16 D1.5 07 V5 W13 BG3 F..
N20 G79 X.. Y.. 2.. ;cycle call
397
Automation:
PAL cycles for milling machines
G72
Rectangul• pocket milling cycle
Structure of NC block
G72 ZI/ZA LP BP D V IWI [RN) [AKI [All [EPJ
[DBI [RH) [DH) (OJ [OJ [HJ [El [Fl [SJ [Ml
Machining example
Obligatory addresses:
ZI/ZA depth of the circular pocket in the infeed axis
ZI
i ncremental from the top edge of the pocket
ZA
absolute, relative to the coordinate system of
the workpiece
LP
length of the rectangular pocket in X direction
BP
width of the rectangular pocket in Y direction
maximum depth of cut
D
V
safety distance t o the material surface
ZA
r
Optional addresses [..):
36
pocket edge finish allowance
pocket bottom finish allowance
corner radius
EPO, EP1, EP2. EP3 definition of the setpoint at cycle call
AK
AL
RN
40
W
retract level, in fast motion
H
E
type of machining
H1 rough machining H4 finishing
H2 face roughing of the rectangular surface
H14 rough-machining and finishing with the same tool
feed rate for plunging
G73
Circular pocket and spigot milling cycle
N15 G72 ZA-9 LP47 BP24 D4 V3 AK0.4 AL0.5 WB
N20 G79 X40 Y36 ;cycle call for G72
Structure of NC block
G73 ZI/ZA R D V [WI [RZJ [AK) [ALI [OBJ
IRHJ IDHJ [OJ [OJ IHI [El [Fl [SJ [Ml
Obligatory addresses:
ZI/ZA depth of circular pocket in the feed axis
ZI
incremental from the top edge of the pocket
ZA
absolute. relative to the coordinate system
of the workpiece
D
maximum depth of cut
V
safety distance to the material surface
Optional addresses [..):
AZ
AK
AL
radius of the optional spigot
pocket edge finish allowance
pocket bottom fini sh allowance
DB cutter path overlap in %
W
retract level, in fast motion
H- E as with G72
G74
Machining example
,z~
,z~
~
ZA
~
-----------
!~! "
15
•
.x
46
N15 G73ZA-15 R20 D4 V2 AK0.4 AL0.SWS
N20 G79 X46 Y27 ;cycle call for G73
Slot milling cycle (longitudinal slotl
Structure of NC block
G74 ZI/ZA R D V [WI [RZ) [AK) [Al) IDBI
[RH) [DH) [OJ [OJ [HJ [El [fl [SJ [Ml
Obligatory addresses:
ZI/ZA depth of the slot in the infeed axis
ZI
incremental from the top edge of the slot
ZA
absolute, relative to the coordinate system of
the workpiece
LP
slot length
BP slot width
D
maximum depth of cut
V
safety distance
Machinin.
example
,z
=
r-,
15
44
Optional addresses [..):
W
retract level
AK
pocket edge finish allowance
26
AL
pocket bottom finish allowance
EPO. EP1. EP2, EP3 definition of the setpoint at cycle call
0
inf eed motion
0 1 vertical t ool immersion
N15 G74ZA-15 LP50 BP22 D3 V2 ;definition of longitudinal slot via G74
02 ramping tool immersion
N20 G79 X... Y... ;cycle call at a particular point via G79
H-E as w ith G72
398
Automation: 7.7 NC technology
PAL cycles for milling machines
G75
Slot milling cycle (arc)
Structure of NC block
G75 ZI/ZA BP RP AN/AO AO/AP D V (WI (AK) (ALI
(EPJ (OJ [OJ [HJ [El [Fl [SJ [Ml
Obligatory addresses:
ZA
ZI/ZA slot depth
ZI incremental from the top edge of the slot
ZA absolute depth
BP slot width
RP slot radius
AN polar start angle relative to the positive X axis and the
center point of the slot's first end radius
AO polar aperture angle between the center points of the slot"s
end radii
AP polar final angle relative to the positive X axis and the
center point of the slot's second end radius
(only 2 of the 3 polar angles need to be defined)
Machining example
D
maximum depth of cut
v safety distance
Optional addresses [ ..):
15
EP definition of the calling point for the slot cycle
EPO center of the circular slot
EP1 center of the right or top semicircle at the rear end
EP3 center of the left or bottom semicircle at the rear end
retra ct level, in fast motion
AK slot edge finish allowance
AL slot bottom finish allowance
30
Q
direction of motion
01 climb milling
02 conventional milling
H type of machining
64
H1 rough machining
H4 finishing
N15 G75 ZA-15 BP12 RPBO AN70 AO120 AK0.3AL0.5 EP3 D5 V3 W6
H14 rough machining and finishing
N20 G79 X64 Y30 ;cycle call for G75 at EP3
E feed rate for plunging
w
G76
Cycle call on a straight line (hole line)
Structure of NC block
G76 IX/XI/XAJ (Y/YI/YA) [Z/Zl/ZAJ AS D O [ARI [WI IHI
Obligatory addresses:
AS angle of the straight line relative to the first geometry axis
+ counter clockwise
- clockwise
D spacing of the cycle calls on the line
y
0
number of cycle calls on the line
Optional addresses [ ..):
X, XI, XA X coordinate of the first point
X
absolute or incremental X coordinate (G90, G91)
XI difference in coordinates between the current tool
Machining e,cample
position and the first point on the line
long,tudmat slot with G14
XA absolute coordinate input of the starting point
Y, YI, YA Y coordinate of the first point
y
absolute or incremental Y coordinate (G90, G91)
oo ~
YI
difference in coordinates between the current tool
Z-5 1.1>
position and the first point on the line
YA absolute coordinate input of the starting point
Z,Zl,ZA Z coordinate of the first point
absolute or incremental Z coordinate (G90, G91)
ZI
difference in coordinates between the current tool
,X
position and the first point on the line
ZA absolute coordinate input of the starting point
AR angle of rotation relative to the positive X axis
N15 G74 ZA-5 LP34 BP20 .... ;definition of longitudinal slot with
W retract level, absolute
G74 N20G76X126Y18Z0AS120D42 O3AR-30 ;cyclecall
H
reversing position
H1 tool travels to safety distance between two positions and to
the retract level after the last position
H2 tool travels to the retract level between two positions
f.-
z
399
Automation: 7.7 NC technology
PAL functions for milling machines
G77
Cycle caU on a pitch circle (hole circlet
Structure of NC block
G77 (I/IA) (J/JAJ (Z/ZI/ZAJ RAN/Al Al/APO (AR) (WI (HJ (FP)
Obligatory addresses:
R radius of pitch circle
AN polar angle of first object
.y
Al con stant segment angle
AP polar angle of last object
0 number of objects on the pitch circle
IA
Optional addresses (..):
I
difference in X coordinates between the circle center and the starting point
IA absolute X coordinate of the circle center
Machining example
J
difference in Y coordinates between the circle center and the starting point
JA absolute Y coordinate of the circle center
absolute or incremental input via G90/G91
Z
ZI difference in Z coordinates between the current tool position and the
pitch circle center
ZA absolute coordinate of the target point
60
AR angle of rotation in direction of the positive first geometry axis
Q orientation of the object to be processed
01 forced rotation of the object Q2 fixed orientation of the object
W retract level, absolute
,y
H
retracting motion
H1 the tool travels to the safety distance V after completion
of the machining process
H2 the tool travels to the retract level W
after completion of the machining process
N15 G74 ZA-5 LP34 BP20 .... ;longitudinal slot with G74
H3 like H1, but the tool travels to the next position
N20 G77 R40 AN-65 Al60 AR40 05 IABO JA60 ;cycle call
on the pitch arc
G78
Cyde call at a particular point (with polar coordinatesl
Structure of NC block
G78 [I/IA) (J/JA) RP AP (Z/ZI/ZAJ [ARI (WI
Obligatory addresses:
I, IA X coordinate of the center of rotation
J, JA Y coordinate of the center of rotation
RP radius of the rotation circle
AP angle of rotation relative to the X axis
Optional addresses (..):
Z, ZI, ZA Z coordinate of the top edge
AR angle of rotation of the object
relative to the X axis
W retract level
G79
N15 G72 ZA.. LP.. BR.. ;rectangular pocket with G72
N20 G78 IA45 JA2 RP50 AP60 AR135 ;cycle call G78
Cycle call at a particular point (with Cartesian coordinatesl
Structure of NC block
G79 (X/XI/XAJ IV/YI/YA) (Z/ZI/ZAJ (ARI (WI
.y
Optional addresses (..):
X, XI, XA X coordinate of the first point
Y, YI, YA Y coordinate of the first point
Z, ZI, ZA Z coordinate of the first point
AR angle of rotation of the object relative to the X axis
W retract level, absolute in workpiece coordinates
G61
Machining
example
~
40
450
.y
,X
55
N15 G72 ZA.. LP.. BP.. ;rectangular pocket with Gn
N20 G79 XA55 YA40 AR-45 ;cycle call G79
Line• interpolation for contour routing
Structure of NC block
G61 (XI/XAJ (YI/YA) (Z/ZI/ZAJ (DJ (AT) (AS) (RN) (HJ (OJ
Optional addresses (..):
XI. XA
X coordinate of the target point
YI, YA
Y coordinate of the target point
Z, ZI, ZA infeed in the Z axis
D
travelling distance AT transition angle
AS ascent angle relative to the X axis
RN+ rounding radius
R- chamfer width
H1 small ascent angle H2 larger ascent angle
01 short distance
02 longer distance
N15 Gl X... Y...
;Pl
N20 G61 AT135 RN20
;P2
N25 G61 XA93 YA56 AS30 ;P3
400
Automation: 7.7 NC technology
Program structure of CNC machines according to PAL
PAL cydes for milling machines
G62/G63 Circular interpolation for contour routing
Structure of NC block
G62 or G63 [XI/XA] [YI/VA] [Z/Zl/ZA] [I/IA) [J/JA] [RI [ATI [AS) [AO] ~ - - - ~
IOI [AE/AP] [RN] [HJ [OJ (Fl [SJ (Ml
Optional addresses[..):
XI, XA, YI, YA coordinates of the target point
Z, ZI, ZA infeed in the Z axis
R
radius of the arc
R+ shorter arc R- longer arc
+y
AS angle between tangents AT transition angle (starting point)
AO aperture angle
AE angle between tangents (end point)
AP polar angle of the arc's end point
RN+ rounding radius
RN- chamfer width
H1 smaller AT angle
H2 larger AT angle
01 shorter arc
02 longer arc
G34-G39
G34
I
Machining example
75
+X
N1S G1 X... Y...
;Pl
N20 G63 R+40 AS-4S RN1S ;P2
N2S G61 Y7S AS130
;P3
Circular interpolation for contour routing
Start-up of the contour pocket cycle (CPC)
Structure of NC block GM ZI/ZA (AK] (ALI
Obligatory addresses:
ZI depth of bore from tool position
ZA absolute depth of bore
Optional addresses (..]:
AK pocket edge finish allowance
AL pocket bottom fini sh allowance
G35
I
Rough-machining technology
of the contour pocket cycle
Structure of NC block
G35 T D [VJ (TC] (TR] [n] [OM] [OBJ
[RH) (DH] (OJ [QJ (El [Fl [SJ [Ml
G36
I
Residual material rough-machining
t8chnology of the contour pocket cyde
Structure of NC block
G36 T D [VJ (TC) [TRI (TL] [OM) [OBJ
[RH) [DH) [OJ [QJ [El [Fl ISi (Ml
G37
I
Rnishing technology of the
contour pocket cycle
Structure of NC block
G37 T D (VJ (TC) [TR] In) IDB] (RH)
[DH) 101 [QJ [HJ [El [Fl [SJ [Ml
NS G54
NlO T1 M .. G97 S.. G94 F..
N15 G34 ZA-10 AKO.S ALO.S ;start-up of contour pocket cycle
;rough-machining technology ol the CPC
N20 G3S TOl 06 M3
N25 G37 T02 06 M3 S.. F.. ;finishing technology of the CPC
;contour
description of the pocket
N30 G38 Hl
N35 GO X-40 YO
;Pl
N40 G61 AS90 RN+9
;P2
N4S G63 JA20 R13 RN+9 01 ;P3
;P4
NSO G61 ASS RN+9
N55 G63 IA40 R13 RN+9 01 ;PS
;P6
N60 G1 XSO Y-2S
N65 ...
N70 Gao
;completion of G38
;contour description of the Island
N75 G38 H2
N870 ...
NBS Gao
;completion of G38
;cal the contour pocket cycle
N90 G39 ...
Obligatory addresses for G35, G36, G37:
T
tool number D absolute depth of bore
Optional addresses for G35, G36, G37:
V
safety distance
T... addresses for tool change (p. 388)
OM infeed minimum for island height optimization
DB cutter path overlap at the bottom
RH radius of the center path of the helical infeed
DH infeed per helical turn
01 plunging
02 helical plunging
01 climb milling
02 conventional milling
H4 finishing of edge/bottom H4 finishing of bottom/edge
H6 finishing of edge only H7 finishing of bottom only
E
feed rate for plunging
G38
I Contour dNcription of the contour pocket cycle
Structure of NC block
G38 H [ZI/ZA) (IIA JA R) / (LP BP IA JA [RN] [AR)))
Obligatory addresses:
H1 pocket H2 island H2 pocket in an island
Optional addresses (..): see on page 397
;adjuS1able absolute zero point
I
G39 Call contour pocket cyde with eitta material removal
parallel to the contour or loop-type material removal
Structure of NC block
G39 Z/ZI/ZA V [W] [X/XI/XAJ [V/VI/VAJ [AN) [HJ
Obligatory addresses:
Z, ZI, ZA material surface in Z
V
safety distance to the material surface
Optional addresses [ ..]:
W height of retract level, absolute
X, XI, XA starting point of machining in X
Y, YI, YA starting point of machining in Y
AN angle for loop-type material removal,
if AN is not defined, removal is parallel to the contour
H1 rough-machining H2 iso lating (facing) H4 finishing
HS isolating in finishing mode
H14 rough-machining and finishing
G80
I
Completion of a G38 pocket/island
contour description
Structure of NC block: G39
401
Automation: 7.8 Information technology
Numbering systems
Decimal system
Binary number system
Base 10
Numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Decimal number n10
205
Base 2
Numbers: 0, 1
Binary number "2
J T~
10 2 = 100
1010
P T=,
I
22 . 4
23 - 8
10 1 = 10
10° = 1
Place value
Value
2-100-200 0 • 10 - 0
Total
value n10 =
200
+
0
I
(decimal) I
5- 1 - 5
Value
1 • 8 = 8 0 - 4 = 0 1 ·2 = 2 0 - 1 = 0
Total
value
n 1o =
8
0
2
+
0
= 10
(decimal)
I
I
I
Place value
i
5
20s
1
21 = 2
2° = 1
I
i
I
T
Hexadecimal numbering system
Base 16
Numbers and letters: 0, 1. 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Decimal value: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
Conversion into binary number:
Conversion into decimal number:
A2F
Every digit represents a
g roup of 4 Bits
IT~
Number value
1S2 C 256
161 = 16
16" • 1
4 bit group (tetrad}
Value
10-256= 2560 2-16 = 32 15-1 = 15
Total
I
I
I
I
value n1o =
2560
32
15
2601 Binary number n2
ldecimall
I
Place value
i
i
1
A2F
J T1
10
2
I
15
1010
0010
I
1111
~
,.J__~
10100010 1111
~
Binary numbers "2 and hexadecimal numbers n16 for decimal numbers n10 up to 255
...,
b,;
! : - I>,
0
0
0
0
0
0
0
1
0
0
1
0
0
00
1
n10
01
n1s
n,n
2
02
n10
3
n10
03
n1s
4
n10
n1,
04
5
n10
05
n1s
6
n 10
06
n1s
7
n 10
07
n1s
8
n10
08
n1s
9
n10
09
n10
n,o 10
n,s OA
11
n10
n,s OB
n,o 12
n,s oc
n,o 13
n,s OD
n,o 14
n,s OE
n,o 15
n,s OF
16
10
17
11
18
12
19
13
20
14
21
15
22
16
23
17
24
18
25
19
26
1A
27
1B
28
1C
29
1D
30
lE
31
lF
32
20
33
21
34
22
35
23
36
24
37
25
38
26
39
27
40
28
41
29
42
2A
43
2B
44
2C
45
2D
46
2E
47
2F
"C-
I I I ....--~-ii-----,.
be
1sttetrad
No.
n,o
b,;
lb.11>,lbsl bs b• bs b, b1
2nd tetrad
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1 0
0
1
1 0
1
1
1
1
0
1
1
1
1
-
-
n1,
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
Bit pattern (binary numbers}
Decimal numbers and hexadecimal num ers
48 64 80
96 112 128 144 160 1 6 192
30 40 50
60 70 80 90 AO EO co
49 65 81
97 113 129 145 161 1 7 193
31 41 51
61 71 81 91 A1 E 1 Cl
98 114 130 146 162 1 8 194
50 66 82
32 42 52
62 72 82 92 A2 B2 C2
51
67 83
99 115 131 147 163 179 195
33 43 53
63 73 83 93 A3 B3 C3
52 68 84 100 116 132 148 164 180 196
34 44 54
64 74 84 94 A4 B4 C4
53 69 85 101 117 133 149 165 181 197
35 45 55
65 75 85 95 A5 B5 cs
54 70 86 102 118 134 150 166 182 198
36 46 56
66 76 86 96 A6 B6 C6
55 71 87 103 119 135 151 167 183 199
37 47 57
67 77 87 97 A7 B7 C7
56 72 88 104 120 136 152 168 184 200
38 48 58
68 78 88 98 AB BB ca
57 73 89 105 121 137 153 169 185 201
39 49 59
69 79 89 99 A9 B9 C9
58 74 90 106 122 138 154 170 186 202
3A 4A 5A 6A 7A BA 9A AA BA CA
59 75 91 107 123 139 155 171 187 203
3B 4B 5B 6B 7B 8B 9B AB BB CB
60 76 92 108 124 140 156 172 188 204
3C 4C 5C 6C 7C BC 9C AC BC cc
61 77 93 109 125 141 157 173 189 205
30 40 50 60 70 80 90 AD BO CD
62 78 94 110 126 142 158 174 190 206
3E 4E 5E 6E 7E BE 9E AE BE CE
63 79 95 111 127 143 159 175 191 207
3F 4F 5F 6F 7F BF 9F AF BF CF
1
1
0
1
1
1
1
0
1
1
1
1
208
DO
209
01
210
02
21 1
03
212
04
213
05
214
06
215
07
216
08
217
09
218
DA
219
DB
220
DC
221
DD
222
DE
223
OF
224
EO
225
E1
226
E2
227
E3
228
E4
229
E5
230
E6
231
E7
232
EB
233
E9
234
EA
235
EB
236
EC
237
ED
238
EE
239
EF
240
FO
241
Fl
242
F2
243
F3
244
F4
245
F5
246
F6
247
F7
248
F8
249
F9
250
FA
251
FB
252
FC
253
FD
254
FE
255
FF
Example of reading from table: Binary number ~ "" 10110010 co rresponds to decimal num ber n, 0 • 178 or hexadecimal number n 16 ..- 82.
402
Automation: 7.8 Information techno logy
7-Bit ASCII Code
Dllc Hex Cha,.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Dllc Hex Chat. DIie
Char.
NUL 16 10 DLE 32 20
1 SOH 17 11 DC1 33 21
2 STX 18 12 DC2 34 22
3 ETX 19 13 DC3 35 23
4 EQT 20 14 DC4 36 24
5 ENO 21 15 NAK 37 25
6 ACK 22 16 SYN 38 26
7 BEL 23 17 ETB 39 27
8
BS 24 18 CAN 40 28
9
HT 25 19 EM 41 29
A
LF 26 1A SUB 42 2A
B VT 27 18 ESC 43 28
C FF 28 1C FS 44 2C
D CR 29 1D OS 45 2D
E SO 30 1E RS 46 2E
F
SI 31 1F US 47 2F
SP
0
#
$
%
&
+
DIie Hex Char. DIie Hex Char. DIie Hex Char. DIie Hex Char. DIie Hex Char.
48 30
49 31
50 32
51 33
52 34
53 35
54 36
55 37
56 38
57 39
58 3A
59 38
60 3C
61 3D
62 3E
63 3F
0
1
2
3
4
5
6
7
8
9
<
>
?
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
40
41
42
43
44
45
46
47
48
49
4A
48
4C
4D
@
A
B
4E
N
4F
0
C
D
E
F
G
H
I
J
K
L
M
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
50
51
52
53
54
55
56
57
58
59
SA
58
SC
SD
SE
SF
P
0
R
S
T
U
V
W
X
Y
Z
I
I
I
96 60
97 61
98 62
99 63
100 64
101 65
102 66
103 67
104 68
105 69
106 6A
107 68
108 6C
109 6D
110 6E
111 6F
a
b
C
d
e
f
g
h
j
k
m
n
o
112 70
p
113 71
q
114 72
115 73
S
116 74
t
117 75
u
118 76
V
119 77 w
120 78
x
121 79
y
122 7A
123 78
124 7C
125 7D
126 7E
127 7F DEL
Meanings of control characters
Name
Dec Char.
Dec Char.
Name
0
1
2
3
4
NUL
SOH
STX
ETX
EQT
NULL
START OF HEADING
START OF TEXT
END OF TEXT
END OF TRANSMISSION
17
18
19
20
21
DC1
DC2
DC3
DC4
NAK
DEVICE CONTROL 1
DEVICE CONTROL 2
DEVICE CONTROL 3
DEVICE CONTROL 4
NEGATIVE ACKNOWLEDGE
5
6
7
8
9
ENO
ACK
BEL
BS
HT
ENQUIRY
ACKNOWLEDGE
BELL
BACKSPACE
HORIZONTAL TABULATION
22
23
SYN
ETB
SYNCHRONOUS IDLE
END OF TRANSMISSION BLOCK
10
11
12
13
14
15
16
LF
VT
FF
CR
SO
SI
DLE
LINE FEED
VERTICAL TABULATION
FORM FEED
CARRIAGE RETURN
SHIFT-OUT
SHIFT-IN
DATA LINK ESCAPE
24
25
26
27
28
29
30
CAN
EM
SUB
ESC
FS
GS
RS
CANCEL
END OF MEDIUM
SUBSTITUTE CHARACTER
ESCAPE
FILE SEPERATOR
GROUP SEPERATOR
RECORD SEPERATOR
31
32
127
US
SP
DEL
UNIT SEPERATOR
SPACE
DELETE
Meanings of special characters (Int ernat ional reference version)
Dec Char.
32
33
34
35
36
37
38
39
40
41
42
#
$
%
&
Name
space
exclamation point
quotes
number symbol
dollar symbol
percent
business 'And'
apostrophe
parenthesis open
parenthesis closed
asterisk
Dec Char.
43
44
45
46
47
58
59
60
61
62
63
+
<
>
7
Name
pl us
comma
minus, dash
period, decimal point
forward slash
colon
semicolon
less than
equal to
greater than
question mark
Dec Char.
64
91
92
93
94
95
96
123
124
125
126
@
I
I
J
Name
at
bracket open
back slash
bracket closed
circumflex
underline
accent grave
curly bracket open
vertical line
curly bracket closed
tilde
Control symbols (0-32 and 127 decimal) cannot be seen on monitor or printer; they are fo r transmitting sy stem commands.
Numbers 128-255 (decimal) in expanded ASCII code are either coded like symbols 0-127 or they are used for
special symbols (cursive symbols, graphic symbols, user defined code). For example, number 128 is the EURO
symbol € .
11 ASCII = AMERICAN STANDARD CODE FOR INFORMATION INTERCHANGE
403
Automation: 7.8 Information t echnology
Graphical symbols for data processing
Symbols for program flow charts
Symbol
D
0
0
0
0
II
Name, comments
Process, e.g.
addition, subtraction
Processing unit,
e.g. person, computer
cf. DIN 66001 ( 1983-12)
Symbol
0
CI
Branch, e.g.
decision
Selector device,
e.g. switch
v
Loop end, end of
a repeating program
section
Synchronization in
parallel processing
Synchronization device
I>
II>
l>I
Call with return
~
Control, external
Data storage medium,
general
processed
Data storage medium
for dat a t o be machine
orocessed
Data to be manually
processed
Manual filing,
e.g. card file, archive
CJ
Manual, optical o r
acoustic data
Input device, e.g.
keyboard, microphone
---!-
~
C=>
0
Data on punched tape
-+-
t:=J
0
Data or device:
memory with only
sequential access,
e. g. magnetic tape
CD
Data or device:
memory that is directly
accessed, e.g.
disk or hard drive
Repeating block
with starting condition
--{
Process sequence
Access path
Data transmission pat h
Interface to environment, e.g. start
Connector, connects
graphic displays
Refinement, refers to
magnific. or zooming
Comment for inserting
explanatory text
Representation of connec:tion lines
£
Direction of action
Connection at symbol
Fanning out
cf. DIN 66261 (1985-11)
Repeating block
with end condition
Starting condition:
Repeat, if ...
Instruction 1
Main memory
0
Data on card,
e.g. punch card
Punch card device
reader, puncher
Punch tape device
reader, puncher
Name, comments
Data in main
memory
Optical or acoustic data,
e.g. picture, sound
Optical or acoustic
output device, e.g.
monitor, loudspeaker
[:]
Symbols for Nassi-Shneiderman diagrams
Sequence block
□
Data on paper, e.g. document; input/output
device for paper, e.g.
document reader, printer
Call with no return
Interruption,
external
Data, general
Symbol
Data to be machine
Manual process,
e.g. reading, w riting
Manual processing
location
Loop start,
beginning of a
repeating program
section
Name, comments
Instruction 1
Instruction 2
Instruction 1
Instruction 2
Instruction 3
Instruction 2
Instruction 3
Instruction 4
Instruction 3
End condition:
If ... , then repeat
Alternative
Simple alternative
Alternative
Conditional alternative
,d,/
'tion 4
d
'tion / 4
not
satisfied
~
Instruction
No
instruction
(empty)
Alternative
Multiple alternatives
not
satisfi ed
~
Condition
1
Instruction
----
Condition
Condition - - - 2
Condition
3
Instruction
Instruction
Instruction
Instruction
404
Automation: 7.8 Information technology
Graphical symbols for data processing
Program flow chart and Nassi-Shneiderman diagram
Example: Circle calculations
Program flow chart
Nassi-Shneiderman diagram
Program: circle calculation
Begin
Clear screen
Value assignment Pl= 3.1415927
Clear screen
Initial value assignment W$ = • n•
Repeat, until W$ = "j"
Value assignment Pl
diameter of the
smallest circle
diameter of the
largest circle
increment
Initial value W$
Loop
Output error
Value assignment D • D1
Repeat, until D > D2
Calculation
C • D • Pl
A - D'2•P1/4
Output D, C, A
until W$ - "i"
Input 01, D2, S
Increment value of D by S
lnputW$
Program end
yes
Output error
Value assignment D
BASIC program
Loop
until D > D2
Processing C, A
~----,---~
Output D, C, A
Increment value of D
End of loop
lnputW$
End of loop
End
--·ITA circumference
area
REM
•• • Circle Calculation Program •••
REM
*** for circumference and area of circle ***
CLS
PRINT
CONST Pl = 3.1415927 #
W$ = "n"
REM
••• Input value•••
DO UNTIL W$ = T
PRINT " Diameter i nitial value:•;
INPUTD1
PRINT " Diameter end value:•;
INPUTD2
PRINT "Increment:•;
INPUTS
IF D1 < 0 OR D1 > D2 OR S < = 0
THEN
PRINT " Invalid input"
ENDIF
REM ••• Processing and Output •••
PRINT"D", •c•, "A"
D = D1
DO UNTIL D > D2
C = D • Pl
A = D '2 *Pl/4
PRINTD, C,A
D = D+S
LOOP
REM *** End ***
PRINT " End program? (y/n)";
INPUTW$
LOOP
END
Automation: 7.8 Information technology
Insert Menu
File Menu
New
Creates a new document.
Open
Opens an existing document.
Close
Closes the current document.
Page Numbers
Defines location and layout.
Save
Saves the current document.
AutoText
Inserts predefined text.
Saves the current document
Symbol
Save as
405
Break
under a user-selected name.
Page setup
Sets margins, page orientation, paper
size and paper source.
Configures page break or column
break.
Inserts special characters from available
character sets.
Index and
Tables
Selects text for an index, creates table
of contents.
Print Preview
Displays a print image of the document.
Picture
Inserts graphics.
Print
Configures printer and printout.
Text Box
Inserts a text box.
Exit
Ends MS-Word.
File
Inserts a file.
Object
Inserts a formula, table, etc.
Hyperlink
Inserts a link to an URL.
Edit Menu
Undo
Undoes the last action.
Repeat
Repeats the last action.
Cut
Deletes selected text and saves it to the
clipboard.
Copy
Copies selected text or graphics
to the clipboard.
Paste
Inserts the clipboard contents.
Select All
Selects the entire document.
Find
Searches for text or formatting.
Replace
Searches and replaces text or for-
Goto
Jumps to point in text or specific page.
matting.
View Menu
URL = Uniform Resource Locator
(Internet address)
Window Menu
New Window
Opens a new window with contents of
current window.
Arrange All
Arranges all open documents.
Split
Splits a document into two windows.
1 Document 1
List of opened documents.
Tools Menu
Spelling and
grammar
Checks document for spelling and
grammatical errors.
Language
Sets the language for corrections.
Letters and
Mailings
Links document to data of a control file
(database).
Normal
Normal view for creating documents.
Print layout
Displays print layout of a document.
Outline
Shows outline of a document.
Toolbars
Shows/hides tool bars.
Customize
Configures screen layout.
Ruler
Shows/hides ruler.
Options
Defines settings for MS-Word.
Header and
Footer
Inserts text at top or bottom of page.
Zoom
Magnifies or reduces the screen
display.
Macro
Combines individual commands into
one action.
Table Menu
format Menu
Font
Defines font type and character sets.
Paragraph
Configures paragraph settings.
Bullets and
Numbering
Configures numbering and bullets.
Borders and
Shading
Configures border type and shading.
Tabs
Sets tab stop locations.
Text direction
Changes orientation of text from
horizontal to vertical.
Insert Table
Creates a table.
Insert
Inserts individual cells (rows,
columns).
Delete
Deletes individual cells (rows,
columns).
Select
Selects individual cells (rows,
columns).
Merge Cells
Combines cells into one cell.
Split cells
Splits individual cells into multiple
cells.
Convert
Converts table to text and vice versa.
Table Properties Defines cell height, column width and
table layout.
406
Automation: 7.8 Information t echnology
Insert Menu
File Menu
New
Creates a new workbook, chart or
Cells
macro template. When opening a chart
Rows
the commands on the menu bar
change.
Columns
Opens an existing workbook.
Worksheet
Closes the current workbook.
Open
Close
Inserts individual cells.
Inserts entire rows.
Inserts entire columns.
Inserts a new worksheet in the workbook.
Save
Saves the current workbook.
Chart
Inserts charts in t he workbook.
Save as
Saves t he current workbook under a
newly chosen name and file format.
Page Break
Sets page and/or column breaks.
Page setup
Sets margins, page orientation, paper
s ize and headers/footers.
Function
Inserts mat hematical functions f or cal·
culation.
Print Area
Sets the selected print area.
Picture
Inserts graphics.
Print Preview
Displays a print preview of the workbook.
Object
Inserts a formula, a table, a chart, etc.
Print
Configures printer and printout.
Hyperlink
Exit
Ends Excel.
Edit Menu
Inserts a link to an URL.
URL = Unif orm Resource Locato r
(Internet address)
Window Menu
New W indow
Opens a new window with contents of
current window.
Arrange
Configures window layout for opened
workbooks.
Undo
Undoes the last action.
Repeat
Repeats the last action.
Cut
Deletes selected area of worksheet
and saves it to the clipboard.
Copy
Copies selected text o r g raphics
t o the clipboard.
Split
Splits a workbook into two w indows.
Freeze Panes
Paste
Inserts diagrams or data series from
the clipboard or other applications.
Freezes a worksheet in the screen
view.
1 Workbook 1
List of opened workbooks.
Fill
Copies content s of selected cells
downwards, upwards, to the right or
left.
Delet e Sheet
Deletes worksheet of a workbook.
Move or Copy
Sheet
Moves or copies single worksheets
within a workbook.
Find
Searches for text o r formatting.
Replace
Searches and replaces text or formatting.
Data Menu
Sort
Sorts t able area in alphabetical o rder.
Import External
Data
Enables importing from ext ernal databases, tables or text.
v-
Spelling
Checks table for spelling erro rs.
Share workbook Lets m ultiple users work on t he
workbook simultaneously.
Protection
Protects workbook or individual worksheets from unauthorized access.
Formula
Auditing
Searches for errors within functions
and cross-references.
Macro
Combines individual commands int o
one action.
Customize
Defines screen layout.
Options
Configures settings for EXCEL.
Format Menu
Menu
Page Break
Preview
Tools Menu
Displays expansion of a t able on one
or more pages.
Toolbars
Switches the toolbars on and off.
Ruler
Turns ruler on and off.
Header and
Footer
Zoom
Cells
Sets number format, orientation, font
and frames.
Rows
Sets cell height.
Columns
Sets column width.
Inserts text at t he top and/or
bottom of all pages.
Sheet
Sets name of sheet.
Magnifies or reduces the screen
display.
Conditional
Formatting
A pplies the format of a cell if a specific
condition is true.
407
Standards: 8.1 International standards
International Material Comparison Chart
Chart I
Germany
U.K.
USA
France
Japan
Sweden
AFNOR
JIS
ss
Standard
DIN, DINEN
Mat.No. AISI/SAE
BS
Structural and machine construction steels
S185
1.0035
A283IAI
1449 15 HR; HS
A33
-
1300
S235JR
1.0037
10 15,A283
Fe360 B
E 24-2
STKM 12A;C
1311
S235JRG1
1.0036
A283ICJ
Fe 360 B 4360-40 B
-
-
131 1, 1312
S235JRG2
1.0038
A550.36
E 24-2 NE
Fe360 B;
6323-ERW 3; CEW 3
STKM 12A;C
1312
-
S235JO
1.0114
-
4360-40C
E 24-3, E 24-4
S235J2G3
1.0116
A515I55I
Fe360D lFF
E 24-3, E 24-4
S235J2G4
1.0117
1513
A2
E 36-4
-
SN 400 B; C; SN 490 B; C 14 12
1312, 13 13
-
S275JR
1.0044
1020
Fe 430 B FU
E 28-2
S275JO
1.0143
A572I42I
4360-43 C
E 28-3. E 28-4
-
S275J2G3
1.0144
A 500 (A; B; Di Fe430 01 FF
E 28-3, E 28-4
SM400A;B;C
1411, 1412, 1414
S355JR
1.0045
-
4360-50 B
E 36-2
STK400
2172
S355JO
1.0553
A678ICi
A3
320-560 M
-
1606
S355J2G3
1.0570
1024; 1524
1449 50/35 HR; HS
E 36-3, E 36-4
STK500
2132 to 2134, 2174
-
S355J2G4
1.0577
A 738IA;CJ
Fe 510 02 FF
A52FP
S355K2G3
1.0595
A678ICI
224-430
-
-
1414-01
2174
S355K2G4
1.0596
A678ICI
224-430
-
-
-
E295
1.0050
A570I50)
Fe 490-2 FN
A50-2
SS490
1550, 2172
E335
1.0060
A 5721651
Fe 590-2 FN
A60-2
SM570
1650
E360
1.0070
-
Fe 590-2 FN
SM570
1650
-
Unalloyed quality steels
S275N
1.0490
A516(60J
-
S275M
1.8818
A 7 15171
-
-
S355N
1.0545
A714IIIIJ
4360-50 E
E355R
-
S355M
1.8823
A 715171
-
-
-
2334-01, 2134-01
Alloy high grade steels
-
S420N
1.8902
A633m
S420M
1.8825
-
-
E420R
-
-
-
-
S460N
1.8901
A633m
-
E460R
-
-
S460M
1.8827
A 734IBI
-
-
-
-
Quenched and tempered structural steels with higher yield strength
S4600L
1.8906
S5000L
1.8909
S6200L
1.8927
S9600L
1.8933
-
4360-55 F
S4600,T
SM 520 B,C
2143
-
S500T
-
-
S620T
S960 T
-
-
-
Unalloyed steels - Case hardened steels
C10E
1.1121
1010
040 A 10. 045 M 10 C 10,CX 10
S 9CK. S 10 C
1265
C10R
1.1207
1011
-
-
-
C15E
1.1141
1015
040 A 15. 080 M 15 XC 12
C15R
1.1140
1016
080A 20
E355C
S 15,S 15CK
1370
-
-
-
Alloy steels - Case hardened steels
16MnCr5
1.7131
51 15
527 M 17
16MC5, 16MnC,5
16MnC<S5
1.7139
51 15
620-440
16MC5
-
2127
2523
2173
18CrMo4
1.7243
5120/5120 H
527 M 20
20MC5
Scr420 M
18CrMoS4
1.7244
5120/5120 H
527 M 20
20MC5
Sc,420 M
2523
20MoCr4
1.7321
K 12220
-
20MoCrS4
1.7323
K 12220
-
-
-
15NiCr1 3
1.5752
3310
655 H 13
12NC15
SNC815(HI
-
20NiCrMo2-2
1.6523
8620H
805 H 20
20 NCD 2
SNCM220H
2506
20NiCrMoS2-2
1.6526
8621,'8620 H
-
20 NCD2
SNCM220M
2506
17NiCrMo6-4
1.6566
-
815M 17
18 NCD6
-
2523
408
Standards: 8.1 International standards
International Material Comparison Chart
Chart II
Germany
USA
U.K.
France
Japan
Sweden
AFNOR
JIS
ss
Standard
DIN, DIN EN
Mat.No. AISI/SAE
BS
17NiC,MoS6-4
1.6569
4718/47 18 H
-
-
-
20MnCf5
1.7147
5120
527 M 20
20MC5
SMn C 420 H
-
20MnCrS5
1.7149
5120/5120 H
527 M 20
20MC5
Scr420 M
2523
14NiCrMo13-4
18C,NiMo7-8
1.6657
9310
832M 13
16NCD13
1.6687
-
-
18NCD6
-
1450
Unalloyed steels - 0uenc:hed and tempered steels
C22
1.0402
1020
055M 15
Af42C20
S 20 C. S 22 C
C22E
1.1151
1023
055M 15
2 C 22. XC 18, XC 25
S20C
1450
C25
1.0406
1025
070M 26
1 C25
-
-
C25E
1.1158
1025
(070M 26)
2 C 25, XC 25
S25C,S28C
1450
C35
1.0501
1035
060A35
C35, 1 C35
S35C,S35CM
1572. 1550
C35E
1.1181
1035
080A35
C35
S35C
1550, 1572
C45
1.0503
1045
080A46
C45
S 45 C, S 45 CM
1672, 1650
XC 42 H 1
S 45C
1672
S58C
S 58 C, S 60CM,
565CM
-
C45E
1.1191
1042, 1045
080M46
C60
1.0601
1060
060A62
C60E
1.1221
1064
C60
060 A 62, 070 M 60 2C60
CJ0
1.0528
G 10300
080A30
XC32
SJOC
C35
C40
1.0501
1.0511
1035
-
-
1040
060A35
080M40
AF 60 C40
-
F.1 14A
C50
1.0540
G 10500
080M50
XC50
S50C
-
C55
1.0535
1055
070 M 55, 5770-50
C54; 1 C55
S 55C, S 55CM
1655
-
1665, 1678
Alloy steals - Quenched and tempered steels
38C'2
1.7003
-
120 M 36
38C2,38C,2
-
38Cr52
1.7023
5140
530A40
42C4
Scr440M
2245
46Cr2
1.7006
5045
42 C 2, 46Cr 2
-
-
-
46Cr52
1.7025
A 768 (95)
-
34Cr4
1.7033
5132
530A32
32 C 4, 34 C,4
SNB5
SCr430 (H)
34CrS4
37Cr4
1.7037
1.7034
4340/4340 H
5135
818M40
530A36
35NCD6
37 C,4, 38C 4
SNCM439
Ser 435 (H) (Ml
37CrS4
1.7038
513&5135 H
-
38 Cr4
Scr435 H
-
25CrMo4
1.7218
4118
708M25
25CD4
SCM420
24CrMoS4
41C,4
1.7213
4130/4130 H
CDS 110
30CD4
1.7035
5140
530A40
41 Cr4,42C4
SCM430 M
Ser 440 (H) (M)
-
41Cr54
1.7039
L1
524A 14
-
-
2092
34CrMo4
1.7220
4137
708A37
35CD4
SCM 432
2234
42CrMo4
1.7225
4140
708M40
42CD4
SCM440(H)
2244
50CrMo4
1.7228
4150,4147
708A47
50CrMo4
51CrV4
1.8159
6150
735A50
50CV4
SCM44541Hl
SUP 10
2512
2230
36CrNiMo4
1.6511
9840
817 M37
36 CrNiMo 4, 35 NCD 5,
40NCD3
-
-
34CrNiMoS4
1.6582
4337,4240
816 M 40, 817 M 40 34CrNiMo8
SNCM447
2541
30NiCrMo8
1.6580
823M30
30Cr-NiMo8
SNCM431
36NiCrMo16
1.6773
5135/5135 H
-
38Cr4
Scr435M
-
31CrMo12
1.8515
-
722 M24
JOCD 12
34CrAIMo5-10
1.8507
A355CI.D
-
30CAD6.12
-
-
2225
2223-01
Nitriding steels
2240
40CrAIMo7-10
1.8509
E7140
905M39,En41 B
40CAD6.12
SACM 1, SACM 645
2940
40CrMoV13-9
1.8523
-
897 M39
-
-
-
Steals for flame and induction hardening
Cf45
1.1193
1045
060 A 47,080 M 46 XC42 H 1TS
S45C,S45CM
1672
42Cr4
1.7045
5140
530A40
42C4TS
Scr440
2245
41CrMo4
1.7223
4142
708 M 40, 3111-5/1
42CD4TS
SNB 22, SCM 440
2244
Cf35
1.1183
1035
080A35
XC38H 1TS
S35C,S35CM
1572
409
Standards: 8.1 International standards
International Material Comparison Chart
I
Chart Ill
Germany
USA
U. K.
France
Japan
Sweden
AFNOR
JIS
ss
St andard
DIN, DIN EN
Mat. No. AISI/SAE
Cf53
1.1213
1050
070M 55
XC48H 1TS
S50C,S50CM
1674
Cf70
1.1249
-
-
-
-
-
11SMn30
1.0715
1213
230M07
S250
SUM22
1912
11SMnPb30
1.0718
12 L 13
S 250 Pb
SUM23L
1914
11SMn37
1.0736
1215
S300
SUM25
-
11SMnPb37
1.0737
12 L 14
-
S 300 Pb
10S20
1.0721
1108. 1109
moM151
10 F 2
BS
Free cutting steels
10SPb20
1.0722
-
-
10 Pb F 2
35S20
1.0726
1140
212 M 36
35MF6
-
46520
1.0727
1146
En80M
45MF4
SUM43
-
1926
-
1957
Cold work steels, unalloyed
C80U
1.1525
W 108
-
C80E2U,Y1 80
-
-
C105U
1.1545
W 1
BW1A
Y105
SK3
1880
Cold work steels, alloy
45WCrV7
1.2542
S1
BS 1
45WCrV8
S1
2710
60WCrV8
1.2550
S1
BS 1
55WC20
-
-
100MnCrW4
1.2510
0 1
80 1
90MnWCrV5
SKS3
90MnCrV8
1.2842
02
802
90 Mn V 8, 90 MV8
-
X210Cr12
1.2080
P3
803
Z200C 12
SK012
2710
102Cr6
1.2067
L3
IBL3)
100Cr6,Y 100C6
SUJ 2
45NiCrMo16
1.2767
-
BP30
-
X153CrMoV12
1.2379
02
802
Y35NCO 16
Z 160COV 12
-
SK012
2260
X100CrMoV51
1.2363
A2
BA2
Z100COV5
SK012
2260
X40CrMoV51
1.2344
H 13
BH 13
Z40COV5
2242
X210CrW12
1.2436
04106)
806
Z 210 CW 12-01
SK061
SK02
55NiCrMoV7
1.2714
-
-
-
SKS51
-
X37CrMoV5-1
1.2343
H 11
BH 11
Z38COV5
SKO 6
32CrMoV12-28
1.2365
H 10
BH 10
32COV 12-28
-
-
HS6-5-2C
1.3343
M2
BM2
HS 6-5
SKH 51
2722
HS&-5-2-5
1.3243
M35
BM35
Z 85 WOKCV 06-05-04-02
SKH55
2723
HSl 0-4-3-10
1.3207
-
BT42
HS 104-3-10
SKH 57
-
HS2-9-2
1.3348
M7
-
HS 2-9-2,
Z 100 OCWV 09-04-02-02
-
2782
HS2-9-HI
1.3247
M42
BM42
HS 2-9-1-8
SKH 59
2716
S2-9-2-8
1.3249
M42
BM34
-
-
-
2312
Hot work steels
High speed steels
Stainless steels, austenitic
X10CrNi18-8
1.4310
301
301 S 21/22
Z 12 CN 18-09
SUS301
2331
X2CrNi18-9
1.4307
F 304 L
304 L
-
SUS F 304 L
2332
X5CrNi189
1.4350
304
304S31
Z 5 CN 18.09
SUS304
X2CrNiN19-11
1.4306
304 L
304/305 S 11
Z2CN 18- 10
SCS 19, SUS 304 L
2352
X2CrNi18-10
1.431 1
304 LN
304S61
Z 3 CN 18-07 Az
SUS304LN
2371
2332. 2333
X5CrNi18-10
1.4301
304
304 S 17
Z 5 CN 17-08
SUS304
X8CrNiS18-9
1.4305
303
303 S 22/31
28 CNF 18-09
SUS303
2346
X6CrNiTi1S.10
1.4541
321
321 S 31/51
Z6CNT 18-10
SUS321
2337
X4CrNi18-12
1.4303
305/308
305 S 17, 305 S 19
Z 5 CN 18-11 FF
SUS 305 J 1, SUS 305
-
X5CrNiMo 17-12-2
1.4401
316
3 16 S 13117/19
Z 3 CNO 17-11-01
SUS 316
2347
X6CrNiMoli17-12-2
1.4571
316Ti
320 S 18/31
Z 6 CNOT 17-12
SUS 3161i
2350
X2CrNiMo18-14-3
1.4435
316 L
316 S 11/13/14
Z 3 CNO 17-12-03/
Z3CN0 18-14-03
SUS316 L
2353
410
Standards: 8. 1 International standards
International Material Comparison Chart
Chart IV
Germany
USA
U.K.
France
Japan
Sweden
BS
AFNOR
JIS
ss
Standard
DIN,DINEN
Mat.No.
AISI/SAE
X2CrNiMoN17·13-3
1.4429
316 LN
3265 63
Z3CN017-12Az
{SUS 316LN)
X2CrNiMoN17-13-5
1.4439
316 L
316 5 11
Z 2 CND 17-12
SUSF316L
2348
X1NiCrMoCu25-20-5
1.4539
USN N08904 -
Z 2 NCDU 25-20
-
2562
2375
Stainless steels, ferritic
X2CrNi12
1.4003
A268
-
-
-
-
X6Cr13
1.4000
403
403517
Z8C 12,Z 8C13FF
SUS403
2301
X6Cr17
1.4016
430
4305 15
Z8C 17
SUS430
2320
X2Crli12
1.4512
409
409 5 19
Z3CT 12
SUH409
-
X6CrMo17-1
1.4113
434
4345 17
Z8CO 17.01
SUS434
-
X2CrMoTi18-2
1.4521
443/444
-
-
SU5444
2326
Stainless steels, martensitic
X12Cr513
1.4005
4 16
41652121 10'13 SU5416
-
2380
X 12Cr13
1.4006
4 10
4 10S21
Z10 C13
SU5410
2302
X20Cr13
1.4021
420
4205 37
Z20C 13
SUS420J 1
2303
X30Cr13
1.4028
420 F
4205 45
Z30 C 13
SUS 420J 2
2304
X46Cr13
1.4034
-
1420S 451
Z44C 14,Z38C 13M
SUS 420J2
2304
X39CrMo17-1
1.4122
5925
-
-
-
-
X3CrNi Mo13-4
1.4313
CA6-NM
425C 11
Z4CNO 13.4 M
SC55, SC56
2384
-
Hot rolled steels for springs
38Si7
1.5023
-
-
41 Si7
465i7
1.5024
9255
-
5157, 51 Si 7
-
55Cr3
1.7176
5155
525A 58
55Cr3, 55C3
SUP9 (A){M)
2253
61SiCr7
1.7108
9261. 9262
-
61 SC7
-
-
51CrV4
1.8159
6150
735A 50
55 CrV 4
SUP10
2230
2090
Cold rolled strip and sheet from soft steels
OC03
1.0347
A619
14493CR
E
CR2
1146
0C04
1.0338
A620I1008)
1449 2 CR; 3 CR
ES
SPCE; HR4
1147
G 5501 FC 10
0110-00
Cast iron with flake graphite (gray ironl
EN-GJL-100
EN-JL- 1010 A4820B
1452 Grade 100
Ft 100
EN-GJL-150
EN-JL- 1020 A4825B
1452 Grade 150
A 32-101 FGL 150; FT 15 D G 5501 FC 15
0115-00
EN-GJL-200
EN-JL-1030 A4830B
1452 Grade 220
A 32-101 FGL 200; FT 20 D G 5501 FC 20
0120-00
EN-GJL-250
EN-JL- 1040 A4840B
1452 Grade 250/
260
A 32-101 FGL 250; FT 25 D G 5501 FC25
0125-00
EN-GJL-300
EN-JL-1050 A4845B
1452 Grade 300
A 32-101 FGL 300; FT 30 D G 5501 FC 30
0130-00
EN-GJL-350
EN-JL- 1060 A4850B
1452 G rade 350
A 32-101 FGL 350; FT 35 D G 5501 FC35
0135-00
Cast iron with spheroidal (nodularl graphite
-
EN-GJS-35D-22
EN-JS -1010 -
EN-GJS-S00-7
EN-JS-1050 A 536 6D-45-12 2789 Grade 500f7 A 32-201 FGS S00-7
G 5502 FCD 500
0727-02
EN-GJ=3
EN-JS-1060 A 536 S0-55-06 2789 Grade 600/3 A 32-201 FGS 60D-3
G 5502 FCD 600
0732-03
EN-GJS-700-2
EN-JS-1070 A 536 10070-03
2789 Grade 700-2 A 32-201 FGS 700-2
G 5502 FCO 700
0737-01
-
-
0717-15
Malleable cat iron
EN-GJMW-350-4
EN-JM 1010 -
86681 W 35-04
A 32-701 MB 35-7
G 5703 FCMW 330
EN-GJMW-400-5
EN-JM 1030 -
6681 W40-05
A 32-701 MB 40-05
G 5703 FCMW 370
-
EN-GJMW-450-7
EN-JM 1040 -
6681 45-07
A 32-701 MB 45D-7
G 5703 FCMWP 440
-
EN-GJMB-JSD-10
EN-JM 1130 A47 Grade
310 B 340/12
22010+32510
A 32-702 MN 350-10
G 5703 FCMB 340
0815-00
EN-GJMB-45D-6
EN-J M 1140 -
6681 P 45-06
A 32-703 MP 50-5
-
0854-00
EN-GJMB-55D-4
EN-JM 1160 -
6681 PSS-04
A 32-703 MP 60-3
G 5703 FCMP 540
0856-00
EN-GJMB-65D-2
EN-JM 1180 -
6681 P65-02
-
-
0862-03
EN-GJMB-700-2
EN-JM 1190 A220 Grade
70003
6681 P 70-02
A 32-703 MP 70-2
G 5703 FCMP 690
0862-03
411
Standards: 8.1 International standards
International Material Comparison Chart
ChartV
Germany
USA
U. K.
AISI/SAE
BS
France
Japan
Sweden
AFNOR
JIS
ss
Standard
DIN, DIN EN
Mat. No.
Cast steels for general applications
GS-38
1.0420
-
-
-
Se360
GS-45
1.0446
A27
-
-
Se450
-
Cast steels for pressure vessels
GP240GH
1.0619
A216Grade
wee
1504-1 61 Gr. B
-
-
-
G17erMo5-5
1.7357
A217 Grade
We6
-
-
-
-
Aluminum and wrought aluminum alloys
old
new old
Al99.5
1050A
1050A
1B
1050A A-5
1050A A 1050
4007
AIMn1
3103
3103
N3
-
4054
Al Mnl Cu
3003
5005A
N41
5005 A-G0.6
3003 A3003
5005 A5005
-
AIMg 1
3003
5005A
3103 13103} A-M l
AIMg2
5251
N4
5251 A-G2M
5251
-
-
AIMg3
5754
5251
5754
AIMg 5
5019/5119
5019/5119
-
-
A-G3M
5454 A5454
AIMg3Mn
5454
5454
N51
5454 A-G3Me
5083
5083
NS
AleuPbMgMn
2007
2007
-
5083 A-G4.5Me
A-U4 PB
AJeu4PbMg
2030
2030
-
Al MgSiPb
6012
6012
-
Aleu4SiMg
2014
2014
H 15
AJeu4MgSi
2017
2017
AJeu4Mg1
2024
2024
2 L 97/9
A· U4G
2024 A-U4G1
AIMgSi
6060
6082
AIZn4.5Mg1
7020
AIZn5Mg3Cu
7022
7075
Al Zn5.5Mgeu
5754 -
A-G5
Al Mg4.5Mn0.7
Al Sil MgMn
new
A5083
4106
4125
-
4140
-
4335
-
-
A-SGPB
-
I2014 A} A-U 4 SG
-
-
A 2017
2024 A2024
6060
H9
16063} A· GS
6060 A6063
4103
6082
7020
H30
6082 A-SGM 0.7
4212
H 17
7020 A-Z5G
6082 7020 IA7N01}
7022
-
7075
2 L 95/96
A356
LM25
7075 A 7075
A-S7g
-
-
-
-
7075 A-Z5GU
-
4425
-
A-24 GU
Aluminum casting alloys
Ae-AISi7M g
Ae-42000
Magnesium alloys, Titanium, Trtanium alloys
-
MgM n2
3.3520
MIA
MAG-E-101
G-M2
MgAl3Zn
3.5312
AZ31 B
MAG-E-111
G-A3Z 1
MgAl6Zn
3.5612
AZ61 A
M AG-E-121
G-A6Z 1
-
-
MgAl8Zn
3.5812
AZSOA
-
G-A7Z 1
-
Ti1
3.7025
-
-
3.7035
TA2
-
-
TiAl6V4
3.7165
-
TAI
Ti2
-
T A 10-13. 28, 56
-
-
-
TtAIMo4Sn2
3.71B5
-
T A45·51. 57
-
-
-
The publisher and it s affiliat es have taken care to collect the above data t o the best of their ability. However,