AGMA 908-B
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Ob87575 000302b b y 4
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-.
AGMA 908-B89
(Revision of AGMA 226.01)
April 1989
AMERICAN GEAR MANUFACTURERS ASSOCIATION
~~
D
Geometry Factors for Determining the Pitting Resistance
and Bending Strength of Spur, Helical and Herringbone
Gear Teeth
AGMA INFORMATION SHEET
(This Information Sheet is not an AGMA Standard)
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Copyright American Gear Manufacturers Association
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A G M A 908-B
W Ob87575 0003027 580 W
INFORMATION SHEET
Geometry Factors for Determining the Pitting Resistance and Bending Strength of
Spur, Helical and Herringbone Gear Teeth
AGMA 908-B89
(Revision of AGMA 226.01 1984)
[Tables or other self-supporting sections may be quoted or extracted in their entirety. Credit line
should read: Extracted from AGMA Standard 9084389, INFORMATION SHEET, Geometry Factors
for Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear
Teeth, with the permission of the publisher, American Gear Manufacturers Association, 1500 King Street,
Suite 201, Alexandria, Virginia 22314.1
AGMA standards are subject to constant improvement, revision or withdrawal as dictated by
experience. Any person who refers to any AGMA Technical Publication should determine that it is the
latest information available from the Association on the subject.
Suggestions for the improvement of this Standard will be welcome. They should be sent to the
American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia 223 14.
ABSTRACT
This Information Sheet gives the equations for calculating the pitting resistance geometry factor, I, for
external and internal spur and helical gears, and the bending strength geometry factor, J , for external spur
and helical gears that are generated by rack-type tools (hobs, rack cutters or generating grinding wheels)
or pinion-type tools (shaper cutters). The Information Sheet also includes charts which provide geometry
factors, Z and J , for a range of typical gear sets and tooth forms.
Copyright O, 1989
American Gear Manufacturers Assocation
1500 King Street, Suite 201
Alexandria, Virginia 223 14
April, 1989
ISBN: 1-55589-525-5
AGMA
ii
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908-B89
A G M A 908-B
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Ob87575 0003028 417
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Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
FOREWORD
1
[The foreword, footnotes, and appendices are provided for informational purposes only and should
not be construed as part of American Gear Manufacturers Association Information Sheet 908-B89,
Geometry Factors f o r Determining the Pitting Resistance and Bending Strength of Spur, Helical and
Herringbone Gear Teeth.]
This Information Sheet, AGMA 908-B89, was prepared to assist designers making preliminary design
studies, and to present data that might prove useful for those designers without access to computer
programs. The tables for geometry factors contained in this Information Sheet do not cover all tooth
forms, pressure angles, and pinion and gear modifications, and are not applicable to all gear designs.
However, information is also contained for determining geometry factors for other conditions and
applications. It is hoped that sufficient geometry factor data is included to be of help to the majority of
gear designers.
Geometry factors for strength were first published in Information Sheet AGMA 225.01, March, 1959,
Strength of Spur, Helical, Herringbone and Bevel Gear Teeth. Additional geometry factors were later
published in Standards AGMA 220.02, AGMA 221.02, AGMA 222.02, and AGMA 223.01. AGMA
Technical Paper 229.07, October, 1963, Spur and Helical Gear Geometry Factors, contained many
geometry factors not previously published. Due to the number of requests for this paper, it was decided to
publish the data in the form of an Information Sheet which became AGMA 226.01, Geometry Factors for
Determining the Strength of Spur, Helical, Herringbone and Bevel Gear Teeth.
)
AGMA 218.01, AGMA Standard for Rating the Pitting Resistance and Bending Strength of Spur and
Helical Involute Gear Teeth, was published with the methods for determining the geometry factors. When
AGMA 218.01 was revised as ANWAGMA 2001-B88, the calculation procedures for Geometry Factors,
I and J , were transferred to this revision of the Geometry Factor Information Sheet. The values of I and J
factors obtained using the methods of this Information sheet are the same as those of AGMA 218.01. The
calculation procedure for I was simplified, but the end result is mathematically identical. Also, the
calculation of J was modified to include shaper cutters and an equation was added for the addendum
modification coefficient, x , previously undefined and all too often misunderstood. Appendices have been
added to document the historical derivation of both I and J .
Because an analytical method for calculating the Bending Strength Geometry Factor, J , is now
available, the layout procedure for establishing J has been eliminated from this document. All references
to geometry factors for bevel gears have been removed. This information is now available in AGMA
2003-A86, Rating the Pitting Resistance and Bending Strength of Generated Straight Bevel, ZEROL Bevel
and Spiral Bevel Gear Teeth.
The first draft of this Information Sheet, AGMA 908-B89, was presented to the Gear Rating
Committee in August, 1987. It was approved by the AGMA Gear Rating Committee on February 24,
1989, after several revisions. It was approved for publication by the AGMA Technical Division Executive
Committee on April 2 1,19 89.
I
AGMA
iii
908-B89
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Copyright American Gear Manufacturers Association
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AGHA 908-B
W Ob87575 0003029 3 5 3 W
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
PERSO JNEL of the AGMA Committee for Gear Rating
Chairman: J. Bentley (Peerless-Winsmith)
Vice Chairman: O. LaBath (Cincinnati Gear )
ACTIVE MEMBERS
M. Antosiewicz (Falk)
J. D. Black (General Motors/AGT)
E. J. Bodensieck (Bodensieck Engineering)
W. A. Bradley (AGMA)
R. Calvert (Morgan Construction)
A. S . Cohen (Engranes y Maquinaria)
J. DeMarais (Bison Gear)
R. Donoho (Clark Equipment)
R. J. Drago (Boeing)
D. W. Dudley (Honorary Member)
R. Errichello (Academic Member)
H. Hagan (Nuttall Gear)
N. Hulse (General Electric)
H. Johnson (Browning Co.)
X. D. Kemp (Kymmene-Stromberg Santasalo)
J. C. Leming (Arrow Gear) (Deceased)
L. Lloyd (Lufkin Industries)
J. Maddock (Consultant)
D. McCarthy (Dorris)
D. R. McVittie (Gear Works - Seattle)
M. W. Neesley (Westech)
J. A. Nelson (General Electric)
W. P. Pizzichil (Philadelphia Gear)
J. W. Polder (Maag/NNI Netherlands)
E. E. Shipley (Mechanical Technology)
W. L. Shoulders (Reliance Electric) (Deceased)
F. A. Thoma (Honorary Member)
C. C. Wang (Consultant)
R. Wasilewski (Arrow Gear)
D. L. Manet (Falk)
T. J. Maluri (Gleason)
B. W.McCoy (Marathon Le Tourneau)
D.Moser (Nuttall Gear)
B. L. Mumford (Alten Foundry)
W. Q. Nageli (MAAG)
B. C. Newcomb (Chicago Gear - D. O. James)
G. E. Olson (Cleveland Gear)
J. R. Partridge (Lufkin Industries)
A. E. Phillips (Emerson Electric/Brawning)
B. D. Pyeatt (Amarillo Gear)
T. Riley (NWL Control System)
G. R. Schwartz (Dresser)
A. Seireg (Academic Member)
E. R. Sewall (Sewall Gear)
L. J. Smith (Invincible Gear)
M. Tanaka (Nippon Gear)
H.J. Trapp (Klingelnberg)
T. Urabe (Tsubakimoto Chain)
D. A. Wagner (General Motors/AGT)
R. E. Weider (Clark Equipment)
L. E. Wilcox (Gleason)
H. Winter (Academic Member)
J. Worek (IMO Delaval)
J. Amendola (MAAG/Artec)
K. Beckman (Lufkin)
E. R. Braun (Eaton)
D. L. Borden (Consultant)
A. Brusse (Hamilton)
G. Buziuk (Brad-Foote)
J. Cianci (General Electric)
D. M. Connor (Cummins Engine)
J. T. Cook (Dresser)
E. Danowski (Sumitomo Heavy Industries)
R. DiRusso (Kaman)
A. B. Dodd (NAVSEA System Command)
L. L. Haas (SPEC0 Division)
F. M. Hager (Cummins Engine)
A. C. Hayes (DACA)
W. H. Heller (Peerless-Winsmith)
G. Henriot (Engrenages et Reducteurs)
R. W. Hercus (F. W. Hercus)
M. Hirt (Renk)
W. H.Jogwick (Union Carbide)
T. Kameyama (Seiki-Kogyosho)
D. L. King (Terre11 Gear)
P. Losekamp (Xtek)
K. Mariager (F. L. Smidth)
AGMA
Copyright American Gear Manufacturers Association
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No reproduction or networking permitted without license from IHS
iv
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908-B 89
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ASSOCIATE MEMBERS
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Table of Contents
Section
Title
1. Scope
1.1
1.2
1.3
1.4
1.5
Page
Pitting Resistance Geometry Factor. I .................................
Bending Strength Geometry Factor. J .................................
Tables ..........................................................
Exceptions .......................................................
Bending Stress in Internal Gears .....................................
1
1
1
1
1
2 . Definitions and Symbols
2.1
Definitions .......................................................
2.2
Symbols .........................................................
.
Basic Gear Geometry
3.1
3.2
3.3
3.4
3.5
Contact Ratios ....................................................
Minimum Length of the Lines of Contact .............................
Load Sharing Ratio, m N
.........................................
Operating Helix Angle, qr .........................................
Operating Normal Pressure Angle, +nr
..............................
6
6
6
6
6
4 . Pitting Resistance Geometry Factor. I
4.1
4.2
4.3
4.4
5
.
6
.
Pitting Resistance Geometry Factor Calculation .........................
7
Operating Pitch Diameter of Pinion. d ................................
7
Radii of Curvature of Profiles at Stress Calculation Point . . . . . . . . . . . . . . . . . 7
Helical Overlap Factor. C
,,, .........................................
7
Bending Strength Geometry Factor. J
5.1
Virtual Spur Gear .................................................
5.2
Pressure Angle at the Load Application Point ..........................
5.3
Generating Rack Shift Coefficient ....................................
5.4
Load Angle and Load Radius .......................................
5.5
Tool Geometry ..................................................
5.6
Generating Pressure Angle .........................................
5.7
Algorithm for Determining the Critical Point ..........................
5.8
Iteration Convergence .............................................
5.9
Radius of Curvature of Root Fillet ...................................
.............................................
5.10
Helical Factor. Ch
5.11
Stress Correction Factor. Kf .......................................
5.12
Helix Angle Factor. KQ
........................................
5.13
Tooth Form Factor. Y ............................................
8
8
9
9
10
12
13
14
15
15
16
16
16
Determining Addendum Modification Coefficients
6.1
6.2
6.3
6.4
Generating Rack Shift Coefficients ..................................
Sum of the Addendum Modification Coefficients for Zero Backlash . . . . . . .
Tooth Thinning for Backlash ......................................
Addendum Modification Coefficients ................................
AGMA
Copyright American Gear Manufacturers Association
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No reproduction or networking permitted without license from IHS
16
16
17
17
908-B 89
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3
2
2
AGflA 908-B
Ob87575 0003031 T O 1
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
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Table of Contents (cont)
Section
Title
Page
7. Geometry Factor Tables
Using the Tables .................................................
Whole Depth ....................................................
Outside Diameter ................................................
Type of Gearing .................................................
Center Distance ..................................................
Tooth Thickness Backlash Allowance ................................
Undercutting
Top Land
Cutter Geometry
Axial Contact Ratio ...............................................
7.1
7-2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
Bibliography
17
18
18
18
18
18
19
19
19
19
....................................................
......................................................
.................................................
. . ................................................................
53
Appendices
....
...........
55
61
Appendix D
Appendix E
Original Derivation of AGMA Geometry Factor for Pitting Resistance. I
ANWAGMA 2001-B88 Pitting Resistance Formula Derivation
Explanation of the AGMA Gear Tooth Strength Rating Derivation
For External Gears ...............................................
Selection of Shaper Cutter Geometry ................................
Derivation of Helical Overlap Factor. C,,, .............................
Appendix F
High Transverse Contact Ratio Gears
................................
73
Appendix A
Appendix B
Appendix C
65
69
71
Tables
Table 2-1
Table 5-1
Tables
Symbols Used in Equations .........................................
2
Limiting Variation in Action for Steel Spur Gears for Load Sharing . . . . . . . . 8
I and J FACTORS ...............................................
20
Figures
..........................
5
.......................................
9
10
11
12
12
12
13
13
14
15
15
Fig 3-1
Transverse Plane View of The Line of Action
Fig
Fig
Fig
Fig
Fig
Fig
Fig
Fig
Fig
Fig
Fig
Load Angle and Load Radius
Pressure Angle Where Tooth Comes to Point ..........................
Shaper Cutter with Protuberance ....................................
Involute Drawn Through Point "S"
Pressure Angle Where Cutter Tooth Comes to a Point ..................
Angle to Center. S. of Tool Tip Radius (Effective Cutter) ...............
Critical Point of Maximum Bending Stress ............................
Shaper Cutter Generation ..........................................
Iteration Function
Oblique Contact Line .............................................
Helical Factor. Ch ...............................................
5-1
5-2
5-3
5-4
5-5
5-6
5-7
5-8
5-9
5-10
5-11
Fig 7-1
..................................
................................................
Undercutting Criteria
.............................................
.'t.... . .
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No reproduction or networking permitted without license from IHS
908-B8 9
vi
AGMA
.4 . . .
19
"I
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A G M A 908-B
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Ob87575 0003032 948
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Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
1. Scope
thickness due to protuberance below the active
profile is handled correctly by this method.
The procedures in this Information Sheet describe the methods for determining Geometry
Factors for Pitting Resistance, I, and Bending
Strength, J . These values are then used in conjunction with the rating procedures described in
AGMA 200 1-B88, Fundamental Rating Factors
and Calculation Methods for Involute Spur and
Helical Gear Teeth, for evaluating various spur
and helical gear designs produced using a generating process.
(7) The root profiles are stepped or irregular.
The J factor calculation uses the stress correction
factors developed by Dolan and Broghamer[11.
These factors may not be valid for root forms
which are not smooth curves. For root profiles
which are stepped or irregular, other stress correction factors may be more appropriate.
(8) Where root fillets of the gear teeth are
produced by a process other than generating.
(9) The helix angle at the standard (reference) diameter* is greater than 50 degrees.
1.1 Pitting Resistance Geometry Factor, I. A
mathematical procedure is described to determine
the Geometry Factor, I, for internal and external
gear sets of spur, conventional helical and low axial contact ratio, LACR, helical designs.
In addition to these exceptions, the following
conditions are assumed:
(a) The friction effect on the direction of
force is neglected.
(b) The fillet radius is assumed smooth (it is
actually a series of scallops).
1.2 Bending Strength Geometry Factor, J . A
mathematical procedure is described to determine
the Geometry Factor, J, for external gear sets of
spur, conventional helical and low axial contact
ratio, LACR, helical design. The procedure is
valid for generated root fillets, which are produced by both rack and pinion type tools.
1.5
Bending Stress in Internal Gears. The
Lewis method [2] is an accepted method for calculating the bending stress in external gears, but
there has been much research [3] which shows
that Lewis’ method is not appropriate for internal
gears. The Lewis method models the gear tooth
as a cantilever beam and is most accurate when
applied to slender beams (external gear teeth with
low pressure angles), and inaccurate for short,
stubby beams (internal gear teeth which are wide
at their base). Most industrial internal gears have
thin rims, where if bending failure occurs, the fatigue crack runs radially through the rim rather
than across the root of the tooth. Because of their
thin rims, internal gears have ring-bending
stresses which influence both the magnitude and
the location of the maximum bending stress. Since
the boundary conditions strongly influence the
ring-bending stresses, the method by which the
internal gear is constrained must be considered.
Also, the time history of the bending stress at a
particular point on the internal gear is important
because the stresses alternate from tension to
compression. Because the bending stresses in internal gears are influenced by so many variables,
no simplified model for calculating the bending
stress in internal gears can be offered at this time.
1.3 Tables. Several tables of precalculated Geometry Factors, I and J, are provided for various
combinations of gearsets and tooth forms.
1.4 Exceptions. The formulas of this Information Sheet are not valid when any of the following
conditions exist:
(1) Spur gears with transverse contact ratio
less than one, mp < 1.0.
(2) Spur or helical gears with transverse contact ratio equal to or greater than two, m p 2 2.0.
Additional information on high transverse contact
ratio gears is provided in Appendix F.
(3) Interference exists between the tips of
teeth and root fillets.
(4) The teeth are pointed.
( 5 ) Backlash is zero.
(6) Undercut exists in an area above the theoretical start of active profile. The effect of this undercut is to move the highest point of single tooth
contact, negating the assumption of this calculation method. However, the reduction in tooth root
[
3
Numbers in brackets refer to the bibliography.
* Refer to AGMA 112.05 for further discussion of standard (reference) diameters.
AGMA
1
908-B 89
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Copyright American Gear Manufacturers Association
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A G M A 908-B
m
Ob87575 0003033 884
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Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
2. Definitions and Symbols
resistance and bending strength formulas are
shown in Table 2-1.
NOTE: The symbols, definitions and terminology used in this Standard may differ
from other AGMA standards. The user
should not assume that familiar symbols can
be used without a careful study of these
definitions.
Units of measure are not shown in Table 2-1
because the equations are in terms of unity normal module or unity normal diametral pitch.
2.1 Definitions. The terms used, wherever applicable, conform to the following standards:
ANSI Y10.3-1968, Letter Symbols for Quantities Used in Mechanics of Solids
AGMA 112.05 Gear Nomenclature (Geometry) Terms, Definitions, Symbols, and Abbreviations
AGMA 600.01 Metric Usage
2.2 Symbols. The symbols used in the pitting
Symbols
Bn
C
Cl,C2’
’ 6‘
‘n 1 ‘n 4’ ‘n 6
‘h
Ç
a..
cJI
Da i9Da2
d
F
H
hF
I
J
J1
Js
Kf
KJI
L
min
M
mF
MG
mN
mn
mP
n
ni
“2
AGMA
Terms
normal operating circular backlash
standard center distance
distances along line of action (Fig 3-1)
distances along line of action of virtual spur gear
helical factor
operating center distance
helical overlap factor
addendum diameter, pinion and gear
pinion operating pitch diameter
effective face width
parameter for stress correction factor
nominal tool addendum
height of Lewis parabola
pitting resistance geometry factor
bending strength geometry factor
adjusted geometry factor
geometry factor from table
stress correction factor
helix angle factor
parameter for stress correction factor
minimum length of contact lines
parameter for stress correction factor
axial contact ratio
gear ratio
load sharing ratio
normal module
transverse contact ratio
virtual tooth number
virtual tooth number of tool
pinion tooth number
gear tooth number
2
908-B89
,+
Copyright American Gear Manufacturers Association
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Where First Used
Eq 6.7
Eq 6.4
Eq 3.11-3.16
Eq 5.15-5.17
Eq 5.69
Eq 3.7
Eq 4.1
Eq 7.1-7.2
Eq 4.1
Eq 3.20
Eq 5.72
Eq 5.36
Eq 5.62
Eq 4.1
Eq 5.1
Eq 7.6
Eq 7.6
Eq 5.1
Eq 5.77
Eq 5.72
Eq 3.21
Eq 5.72
Eq 3.20
Eq 3.1
Eq 3.24
Eq 7.9M
Eq 3.18
Eq 5.2
Eq 5.29
Eq 3.1
Eq 3.1
*
’&
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Table 2-1
Symbols Used in Equations
A G H A 908-B
= Ob87575
0003034 7 5 0
=
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Table 2-1 (cont)
Symbols Used in Equations
Symbols
na
nC
nr
‘nd
pb
PN
PX
R2
Rbli Rb2
Rbc
RC
%i
R o l , R02
Roc
‘ n ) ‘n2
r;
‘no
G O
‘i*
‘na, ‘na2
rn b ‘nb2
%bo
nL
‘
SF
’n
’ n i , ‘n2
‘na
‘no
sns
X
xl’
x2
X
g
xO
x g l *x g 2
Y
Y
Y’
Z
AGMA
Terms
Where First Used
fractional part of mF
tool tooth number
fractional part of m
P
normal diametral pitch
transverse base pitch
normal base pitch
axial pitch
standard pitch radii, pinion and gear
base radii, pinion and gear
base radius of tool
standard pitch radius of tool
mean radius of pinion
addendum radii, pinion and gear, internal and external
outside radius of tool
reference pitch radii of virtual spur gear
generating pitch radius of virtual spur gear
reference pitch radius of virtual tool
generating pitch radius of virtual tool
radius to center “S” of tool tip radius
virtual outside radii
virtual base radii
virtual base radii of tool
virtual load radius
tooth thickness at critical section
reference normal circular tooth thickness
reference normal circular tooth thickness, pinion and gear
tooth thickness at outside diameter
reference normal circular tooth thickness of tool
standard tooth thickness, thinned for backlash
stock allowance per side of tooth
addendum modification coefficient at zero backlash
addendum modification coefficient, pinion and gear
generating rack shift coefficient
addendum modification coefficient of tool
generating rack shift coefficient, pinion and gear
tooth form factor
iteration function
derivative of iteration function
active length of line of action
3
908-B89
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Eq 3.22
Eq 5.29
Eq 3.22
Eq 7 . 5
Eq 3.8
Eq 3.9
Eq 3.19
Eq 3.2-3.3
Eq 3.5-3.6
Eq 5.34
Eq 5.33
Eq 4 . 3
Eq 3 . 1 2 , 3.15
Eq 5.36
Eq 5 . 3 , 5.12
Eq 5.51
Eq 5.30
Eq 5.52
Eq 5.39
Eq 5 . 5 , 5.14
Eq 5.4, 5.13
Eq 5.31
Eq 5.28
Eq 5.72
Eq 5.20
Eq 6.1-6.2
Eq 7 . 9
Eq 5.35
Eq 7 . 6
Eq 5.37
Eq 5.19
Eq 6.5
Eq 5.19
Eq 5.35
Eq 6.1-6.2
Eq 5 . 1
Eq 5.63
Eq 5.64
Eq 3.17
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A G H A 908-B
Ob87575 0003035 657
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Table 2-1 (cont)
Symbols Used in Equations
Symbols
ßn
Asn
80
8ao
?n
nF
en
‘no
KFiKS
ns
1i.no
En
E nF
p 1 * p2
Pmí, P m 2
Pa0
PF
PF
Q
Qn
Q;
QnL
+nP
Qnpo
Qnr
Qnns
Qnw
Qr
Jr
%
Jrr
o
Terms
Where First Used
angle of surface, normal
iteration angle
angle between tangent to fillet and tooth center line
amount gear tooth is thinned for backlash
amount of protuberance, tool
amount of effective protuberance, tool
ordinate of gear fillet curve
ordinate of critical point “F”
angular displacement of gear
angular displacement of tool
distance from pitch point to points “F” and “S”
angle to center “S” of tool tip radius
auxiliary angle locating point “S”
abscissa of gear fillet curve
abscissa of critical point “F”
radii of curvature of profiles at point
of contact stress calculation
radii of curvature of profile at mean radius
tool tip radius
radius of curvature of fillet curve
minimum radius of curvature of fillet curve
standard transverse pressure angle
standard normal pressure angle
generating pressure angle
load angle
pressure angle at radius where gear tooth is pointed
pressure angle at radius where tool tooth is pointed
operating normal pressure angle
pressure angle at point “S” on tool
pressure angle at load application point
operating transverse pressure angle
standard helix angle
base helix angle
operating helix angle
angle of inclination of helical contact line
Eq
Eq
Eq
Eq
Eq
Eq
5.53
5.65
5.59
5.19
5.38
5.38
Fig 5-8
Eq 5.61
Eq 5.57
Eq 5.56
Eq 5.54, 5.55
Eq 5.47
Eq 5.53
Fig 5-8
Eq 5.60
Eq 4.1
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
Eq
4.8
5.39
5.66
5.68
3.4
3.4
5.48
5.22
5.22
5.43
3.28
5.40
5.10
3.7
3.2
3.10
3.27
5.70
SUBSCRIPTS
o tool
1 pinion
2 gear
n normal or virtual spur gear
r operating or running
- absence of a subscript indicates transverse
90 8-B89
AGMA
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A G M A 908-6
W 0687575 000303b 593
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
3. Basic Gear Geometry
The following equations apply to spur and
helical gears where spur gearing is a particular
case with zero helix angle. Where double signs
are used (e.&, t ) ,the upper sign applies to external gears and the lower sign applies to internal
gears. The equations are derived in terms of unity
normal module (mn = 1.0) or unity normal
diametral pitch and are valid for any consistent set
of units. All angles are given in terms of radians,
unless otherwise specified.
where
Cr
= operating center distance
Transverse base pitch, p b
Pb =
IT
nl
Normal base pitch, p N
p N = 7T cos +n
Base helix angle, Qb
The following variables must be made dimensionless by dividing with the normal module, m,,
or multiplying with the normal diametral pitch,
P n d , (See AGMA 112.05 for definitions of mn
or Pnd ). The variables to be adjusted are Cr ,
F , Ro 1, Ro 2, Roc Rc, ha0 80 Pa,* and AS,.
Qb = cos-’
(Eq 3.9)
(%)
PN
(Eq 3.10)
Figure 3-1 is a view of the line of action in the
transverse plane. The lengths, c1 through c6,
are derived from Fig 3-1. See 1.4 item ( 6 ) . referencing exceptions regarding gear tooth undercut.
y
Gear ratio, mG
/
n
I
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
n2
mG = nl
where
n 2 = gear tooth number
\
= pinion tooth number
Standard (reference) pitch radius, R
where
Q
= standard helix angle
Standard (reference) pitch radius, R
R2 = R 1 m G
Standard transverse pressure angle,
+
where
+n
= standard normal pressure angle*
Pinion base radius, R b l
Rbl = R i
COS
+
(Eq 3.5)
Gear base radius, Rb2
Fig 3-1 Transverse Plane View of The
Line of Action
R b 2 = R b l mG
Operating transverse pressure angle, +r
* For a complete discussion, see 9.01 of AGMA 112.05 Gear Nomenclature (Geometry) Terms,
Definitions, Symbols, and Abbreviations
AGMA
I
Copyright American Gear Manufacturers Association
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9 O 8-B 89
5
>
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Ob87575 0003037 q 2 T
A G H A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
where
F
Sixth distance along line of action, c6
c6 = C, sin 9,
(Eq 3.11)
= effective face width at mn = 1.0
For spur gears, m F = 0.0
First distance along line of action, C1
3.2 Minimum Length of the Lines of Contact.
C1 = 2 [C6-(Ro2- Rbz)0*5]
where
Ro2
(Eq 3.12)
For spur gears with m < 2.0 the minimum
P
length of contact lines, Lmin, is:
= addendum radius of gear, for
=F
L,in
internal or external gears
(Eq 3.21)
For helical gears, two cases must be considered:
Third distance along line of action, C3
Case I, for nu 5 1
- n,
(Eq 3.13)
(Eq 3.22)
Fourth distance along line of action, Cq
Case II, for na > 1 - nr
(Eq 3.14)
- m p F - (1 - n a )(i - n r )
Lmin -
Fifth distance along line of action, C5
where
nr
(Eq 3.15)
where
Example :
for a contact ratio, m of 1.4, then n, = 0.4
P’
Second distance along line of action, C2
(Eq 3.16)
3.3 Load Sharing Ratio, mN
Active length of line of contact, Z
For helical gears:
(Eq 3.17)
Distance C2 locates the lowest point of single
tooth contact (LPSTC) and distance C4 locates
the highest point of single tooth contact (HPSTC) ,
where C,, Rol and RO2 are values for mn = 1.0.
mN =
For spur gears with m < 2.0,
P
L,
= F, therefore:
m N = 1.0
Axial pitch, p x
= L
PX
sin JI
F
-
(Eq 3.19)
3.5 Operating Normal Pressure Angle, +nr
(Eq 3.20)
+nr = si<’ (COSQb sin +r 1
6
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(Eq 3.26)
(Eq 3.27)
PX
AGMA
(Eq 3.25)
3.4 Operating Helix Angle, Qr
Axial contact ratio, mF
mF=
(Eq 3.21) gives
For LACR helicals, ( m F I. l.O), load sharing is
accomodated by CQ, therefore:
(Eq 3.18)
pb
(Eq 3.24)
m N = 1.0
Transverse contact ratio, mp
“P =
F
min
3.1 Contact Ratios.
L
(Eq 3.23)
= fractional part of m
P
= fractional part of mF
nu
Ro 1 = addendum radius of pinion
z = cg - c l
cos @b
PX
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(Eq 3.28)
908-B89
m
A G M A 908-B
Ob87575 0003038 3bb
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
4. Pitting Resistance Geometry Factor, I
= addendum radius, gear, internal or
Ro2
external
The pitting resistance geometry factor, I , is a
dimensionless number. It takes into account the
effects of:
(1) radii of curvature
(2) load sharing
(3) normal component of the transmitted load
4.1
Pitting Resistance
Calculation.
Radius of curvature of the pinion profile at
the point of contact stress calculation, pl
.L
(Eq 4.4)
where
Rbl
Geometry Factor
= base radius, pinion
Radius of curvature of the gear profile at the
point of contact stress calculation, p 2
where
= sixth distance along line of action
C6
(see Eq 3.11)
where
+,.
= operating transverse pressure angle
C,,,
= helical overlap factor (See 4.4 and
Appendix E)
d
= pinion operating pitch diameter
rnN
= load sharing ratio
p
= radius of curvature of pinion profile
at point of contact stress calculation
4.3.2 Spur and Low Axial Contact Ratio
Helical Gears.
For spurs and LACR helicals
(mF 5 1.0) the radii of curvature are calculated
at the LPSTC
0%
P 1 = c2
4.6)
where
= second distance along line of action
C2
(see Eq 3.16)
= radius of curvature of gear profile at
p2
point of contact stress calculation
4.4 Helical Overlap Factor, CQ*
4.2 Operating Pitch Diameter of Pinion, d.
For LACR helical gears (rnF 5 1.0)
' ) r
br
d =
"G!:
where
mG
1
C
Jr
= gear ratio
=
[-
rn
l
F(l-
prn1prn2z )]Oa5
P ~ P ~ P N
(Eq 4.8)
where
Radii of Curvature of Profiles a t Stress
Calculation Point
4.3
Z
= active length of line of action
pN
= normal base pitch
4.3.1 Conventional Helical Gears. For
conventional helical gears (mF > 1.0) the radii of
curvature are calculated at the mean radius or
middle of the working profile of the pinion where:
Radius of curvature of the pinion profile at
the mean radius of the pinion, prnl
Mean radius of pinion, Rrnl
Radius of curvature of the gear profile at the
mean radius of the gear, prn2
. r
1
(Eq 4.10)
where
Rol
*
For spurs and conventional helicals
c+ =
= addendum radius, pinion
1.0
(Eq 4.11)
See Appendix E for derviation of C
zlr
'
9 08-B 89
7
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A G f l A 908-6
0687575 0003039 2 T 2
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
5. Bending Strength Geometry Factor, J
(Eq 5.4)
The bending strength geometry factor, J , is a
dimensionless number. It takes into account the
effects of:
(1) shape of the tooth
(2) worst load position
(3) stress concentration
(4) load sharing between oblique lines of
contact in helical gears
Both tangential (bending) and radial (compressive) components of the tooth load are included. This analysis applies to external gears
only.
The J factor calculation procedure must be
repeated for both the pinion and the gear using
the appropriate dimensions for each.
J =
Virtual outside radius, rna
rna = rn
Kf
mN
(Eq 5 . 5 )
n
= nl
(Eq 5-61
rn
= R i
(Eq 5.7)
'nb = R b l
(Eq 5-81
'na =
(Eq 5.9)
5.2 Pressure Angle a t the Load Application
Point. Spur gears develop the most critical stress
when load is applied at the highest point of the
tooth where a single pair of teeth is carrying all of
the load. Spur gears having variations that prevent two pairs of teeth from sharing the load may
be stressed most heavily when the load is applied
at the tip. Table 5-1 has been used in previous
standards to establish the variation in base pitch
between the gear and pinion, which determines
whether or not load sharing exists in steel spur
gears. Values in excess of those shown in Table
5-1 require the use of tip loading.
Kf M N
C,,,
- R1
For spur gears, the actual geometry is used
y cJr
-
where
Y
+ Ro
= tooth form factor (See 5.13)
= helical overlap factor (See 4.4)
= stress correction factor (See 5.11)
= load sharing ratio (See 3.3)
Table 5-1
Limiting Variation in Action for Steel Spur
Gears for Load Sharing
(Variation in Normal Base Pitch)
It is recognized that an anomaly exists when
calculating the J factor for LACR gears where the
value obtained may be greater than a conventional
helical gear. For this reason, it is recommended
that the J factor be calculated for both the LACR
condition and as a conventional helical gear, using
a value for F which is slightly greater than p x .
The resulting conservative value should be used
unless otherwise justified.
Number
Of
Pinion
Teeth
15
Maximum Allowable Variation in
inches (mm),When Teeth Share Load
Load per Inch of Face (per mm of face)
500 lb 1000 lb 2000 lb 4000 lb 8000 lb
(90 N) (175 N) (350 N) (700 N) (1400 N)
0.0004 0.0007 0.0014 0.0024
(0.01) (0.02) (0.04) (0.06)
0.0042
(0.11)
5 . 1 Virtual Spur Gear. The following analysis
is based on the work of Errichello [4] [5] [6].
20
Helical gears are considered to be virtual spur
gears with the following virtual geometry:
0.0003 0.0006 0.0011 0.0020 0.0036
(0.01) (0.02) (0.03) (0.05) (0.09)
25
0.0002 0.0005 0.0009 0.0017 0.0030
(0.01) (0.01) (0.02) (0.04) (0.08)
Virtual tooth number, n
For helical gears and spur gears that are analyzed where the load is applied at the tip of the
tooth, the pressure angle at load application point,
+nw,is given by:
Standard (reference) pitch radius of virtual spur
gear, rn
r - -n
n - 2
(Eq 5.10)
Virtual base radius, rnb
AGMA
8
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908-B89
A G M A 908-B
W Ob87575 0003040 T L 4 W
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
For spur gears, where the highest bending
stress occurs when the load is at the highest point
of single tooth contact (HPSTC) , the pressure angle is given by:
As,
x
c4
-- rnb
tan+
nW
(Eq 5.11)
Equation 5.11 may also be used for LACR
helical gears, but distance C4 must be based on
the virtual spur gear. The following equations are
developed from analogy with Eqs 3.3, 3.6, 3.11,
3.12, 3.14, 5.5 and 5.11.
Standard (reference) pitch radius of virtual spur
gear, rn2
-
‘n2
(Eq 5.12)
‘n m G
Virtual base radius, 5 b 2
--
‘nb2
(Eq 5.13)
--
‘na2
‘n2
+
+ A S, - rr I2
2 tan +n
sn = normal circular tooth thickness
measured on the Standard (reference)
pitch cylinder
sn =
IT
+2
2
x tan +n
g
defines the load angle, +nL, and the load radius,
rnL‘ The load is shown applied at an arbitrary
point “W” , such that:
- inv +nP
= pressure angle at radius where gear
tooth is pointed. see Fig 5-2
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
First distance along line of action, Cn 1, of virtual
spur gear
2
=
[Cná- (‘na2-‘$2
)O’”]
(Eq 5 . l 6 )
Fourth distance along line of action,Cn4, of virtual spur gear
‘n4
=
‘ni
PN
(Eq 5.17)
+
The pressure angle at load application point, +nw
=
Cn 4
-
(Eq 5.18)
‘nb
5.3 Generating Rack Shift Coefficient. The
generating rack shift coefficient, xg , applies to
the completely finished teeth. It includes the rack
shift for addendum modification plus the rack
shift for thinning the gear teeth to obtain backlash:
=
xg
x -
Asn
2 tan +n
(Eq 5.19)
where
x
= addendum modification coefficient
at zero backlash
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(Eq 5.22)
where
Sixth distance along line of action, C n 6 , of virtual spur gear
cn 6 = ( ‘nb 2 + ‘nb Itan +nr
(Eq 5.15)
cn1
(Eq 5.21)
5.4 Load Angle and Load Radius. Figure 5-1
(Eq 5.14)
R02 - R2
(Eq 5.20)
where
9,
ga2
Virtual outside radius,
S,
+nL = tan r$nW
mG
‘nb
=
= amount gear tooth is thinned for
backlash
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A G H A 908-B
W Oh87575 000304L 950 W
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
equal a large number such as nc = 10 000. When
exact cutter dimensions are not known, refer to
Appendix D. Helical gears are considered to be
generated by a virtual shaper cutter with the following virtual geometry:
V i a l tooth number of tool, no
nc
no = CO9
where
nc
Jr
(Eq 5.29)
= tool tooth number
Standard (reference) pitch radius of virtual tool,
‘no
rn0 =
2
(Eq 5.30)
Virtual base radii of tool, rnbo
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
‘nbo
-- ‘no
cos 4n
(Eq 5.31)
For spur gears, the actual cutter geometry is
used
Fig 5-2 Pressure Angle Where Tooth
Come&to Point
inv+ = inv+,
nP
but
‘ “ ~ 9= ~ tan+n
2rn
=
sn
+ zn
-
(Eq 5.23)
9,
n
+ +n-
n
‘no = Rc
(Eq 5.33)
where
Rc
= standard pitch radius of tool
‘nbo = Rbc
(Eq 5.25)
where
+sny
= tanQnw- tan4,
(Eq 5.32)
(Eq 5.24)
inv+ = tan+n - 4n
(Eq 5.26)
nP
Substituting this value in Eq 5.22 gives:
+nL
no = n c
(Eq 5.27)
Equation 5.27 gives the load angle for any
load position specified by tan 4nnw.
From Fig 5-1, the virtual load radius, rnL, is:
(Eq 5.28)
5.5 Tool Geometry. The following analysis is
based on pinion type generating tools commonly
referred to as shaper cutters. However, the
method applies equally well to rack-type generating tools by letting the tooth number of the tool
Rbc
= base radius of tool
Figure 5-3 shows a shaper cutter with protuberance,öO. A tool without protuberance is a
particular case for which 8, = O. The center of
the tip radius, point “S”, is located by radius
r
and angle &/2.
The nominal tool addendum is h,, . The reference addendum related to
the virtual radius, rno , is hu0 + x0, where Xo is
the addendum modification coefficient corresponding to the present sharpening condition of
the cutter. The addendum modification coefficient of the tool, x0, relates the actual normal circular tooth thickness of the tool, sno, to the
nominal value of m / 2 . If sno is known from
measurements of the tool, x0 may be calculated
from:
io
9O 8-B8 9
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(Eq 5.34)
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Ob87575 0003042 897
A G M A 908-B
a
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
where
Roc
(Eq 5.35)
= outside radius of tool
where sno, u s , Roc, and Rcare values for
where
S
no
= reference normal circular tooth
mn = 1.0.
thickness of tool
Finishing hobs usually have sno=rr12 in
which case xo = O. A pre-grind hob which has
teeth thinner than 1712 to provide stock allowance
for grinding usually has a tooth thickness of:
NOTE: xo is positive when sno> IT/^ (corresponding to a new shaper cutter), or
negative when sno < rr12 (corresponding to
a used shaper cutter). Near the mid-life of
the cutter, its tooth thickness equals ~ r / 2
and xo = 0.0.
r
sno -- r -
2
- 2u,
(Eq 5.37)
where
= stock allowance per side of the gear
us
tooth
Since us is removed during grinding, the basic
rack corresponding to the finished gear teeth is
used for the analysis; Le., let sno = 7 ~ 1 2and reduce the amount of protuberance:
xo
=
o
suo
=
so
- us
cos 4Jn
(Eq 5.38)
where
Tr
“O
suo
= amount of effective protuberance,
8,
tool
= amount of protuberance, tool
from Fig 5-3
.
‘no
where
r S
radius
gs,
&TOOL SPACE
Fig 5-3 Shaper Cutter with
Protuberance
+ns
The nominal tool addendum is defined as the
addendum where the normal circular tooth thickness of the tool equals the nominal value of ~ 1 2 .
If the outside radius of the tool is known from
measurements, the nominal tool addendum, hu0 ,
may be calculated from:
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(Eq 5.39)
Figure 5-4 shows an involute drawn through
point “S”. The pressure angle at point “S” on
tool,
is:
@TOOL TOOTH
AGMA
pa0
= tool tip radius
Pau
Rc- x 0
-
= radius to center “S” of tool tip
no
bao= Roc-
t huo t xo
= cos -1
(--)nbo
no
inv+ns = tan 4~~~
-
(Eq 5.40)
,+
(Eq 5.41)
The reference circular tooth thickness of the
cutter is:
‘no
-
7T
2 + 2 x 0 tan+,
(Eq 5.42)
In Fig 5-5, 4Jnpo is the pressure angle where
the cutter tooth comes to a point. It is given by:
(Eq 5.36)
90 8-B 8 9
11
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--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
r,So =
= O687575
A G M A 908-B
00030Ll3 7 2 3
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
-
= inv +n+ ,no
inv+
nP0
2rno
but:
inv+n
‘no
= tan +n - +n
(Eq 5.44)
-
(Eq 5.45)
- no
inv+
= tan +n
nP0
from Fig 5-6
-=
(Eq 5.43)
-
+n
+-‘no
inv+npo - inv+ns
+ (800- pa0 )
rnbo
2
where
A,
(Eq 5.46)
n0
(Eq 5.47)
= angle to center “S” of tool tip radius
inv
Fig 5-5 Pressure Angle Where Cutter
Tooth Comes to a Point
5.6 Generating Pressure Angle. The generating
pressure angle, 4; , depends on the virtual center
distance between the cutter and the gear which is
determined by xg and Xo. The generating pressure angle, 4; , is obtained from:
inv+i
=
+
2(x
+ xo )tan+n
8
n
+ no
(Eq 5.48)
Fig 5-6 Angle to Center, S, of Tool Tip
Radius (Effective Cutter)
9O 8-B89
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--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Fig 5-4 Involute Drawn Through Point
“S”
Ob87575 0003044 bbT
A L M A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Arc involute may be solved by iteration.[5]
Let the first trial value for
be:
From Fig 5-8 the auxiliary angle locating point
“ S ” , p n o , is:
;+
+;i= (3 inv ;+
0.33
(Eq 5.49)
)
This trial value is successively improved upon
using:
where
a,
= angle of surface normal
a
5.6.1 Generating Pitch Radii. The generating pitch radius of virtual spur gear, r l , is:
(Eq 5.51)
The generating pitch radius of virtual tool,
il
5; , is:
(Eq 5.52)
5.7 Algorithm for Determining the Critical
Point. Figure 5-7 shows the critical point of
maximum bending stress located at the intersection of the Lewis parabola and the gear tooth fillet. To locate this point, we consider the relative
motion between the shaper cutter and the generated gear tooth. Figure 5-8 shows the shaper cutter generating an arbitrary point “F” on the gear
tooth fillet. From the law of conjugate gear tooth
action, point “F” lies on a line which extends
from the generating pitch point “ P ” through the
center of the tool tip radius, point “ S ” . The fillet
coordinates are best expressed by selecting the angle a, as the independent parameter. Then for
a n = n / 2 , generating starts at the lowest point on
the fillet and proceeds up the fillet as a n is diminished corresponding to clockwise rotation of the
tool and counter-clockwise rotation of the gear.
I
.
VERTEX
GEAR TOOTH
CENTERLINE
Fig 5-7 Critical Point of Maximum
Bending Stress
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Fig 5-8 Shaper Cutter Generation
13
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--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
.CRITICAL
POINT
0687575 00030V5 5Tb W
A G M A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Distance from pitch point to point “S”, K S , is:
= height of Lewis parabola
hF
Differentiating Eq 5.63 gives:
The distance from pitch point to point “F”, K F ,
is:
K F = K S - Pa,
(Eq 5.55)
K F and K S are vectors and may be positive or
negative.
The angular displacement of tool,
II
eno, is:
r
sin a,,
(Eq 5.56)
n
en =
(Eq 5.57)
en,
where
= angular displacement of gear
e,
(Eq 5.58)
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
The slope of the line tangent to the fillet at
point ”F” is:
ß,= an -8,
(Eq 5.59)
where
= angle between tangent to fillet and
ß,
tooth center line
The coordinates of critical point “F” are:
sin
en +
KF cos ß n
(Eq 5.60)
The ordinate of critical point “ F ” , qnF
q n F = r i cos9,
+
KF
sinß,
= derivative of iteration function
Assuming an initial approximation for a!, = 7~14,
it is successively improved upon by using Newton’s
Method of iteration.
L
(Eq 5.65)
an1 = a n - y’
On each iteration, a n is set equal to ani and
Eq 5.53 through Eq 5.65 are iterated until [y[in
Eq 5.63 is a negligible tolerance.
5.8 Iteration Convergence. Equation 5.63, expressing the function y = f ( a! n ) , is plotted in Fig
5-9 for a typical case. By selecting an=n/4as
the initial approximation, rapid convergence to
the proper root is obtained, usually within 3 to 5
iterations. This choice for the initial value prevents convergence to the incorrect root which exists closer to a = O. This incorrect root corresponds to the case where the Lewis parabola is
inverted, opening upward rather than downward.
15
,
The abscissa of critical point “ F ” , gnF
En, = r;
(Eq 5.64)
where
y’
The gear rotation angle is:
1
(Eq 5.61)
10
Let
Y = f(a!n)
(Eq 5.62)
5
For point “F” to be on the Lewis parabola,
the following equation must be satisfied:
O
hF
y
= rnL-
nF
= 2hF tanß,
where
y
- knF
= O
(Eq 5.63)
-5
= iteration function
I
I
O
ml4
Fig 5-9 Iteration Function
9O 8-B 89
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an
I
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A G M A 908-B
Ob87575 000304b 432
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
5.9 Radius of Curvature of Root Fillet. The
radius of curvature of the fillet curve,
at any
point defined by a n is given by:
Pk,
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
KS
addendum beyond the loaded portion (see Fig
5-10)
(Eq 5.66)
=
r"
no
-T'
no
(Eq 5.67)
The J factor uses the minimum radius of curvature which occurs at the point where the fillet
curve is tangent to the root circle, where a = n / 2
and pno = O.
NOTE: Full Buttressing Exists When
5 2 One Addendum
Fig 5-10 Oblique Contact Line
For Spur and LACR Helical Gears(mF 5 1.0), a
unity value is used,
Subsituting, the minimum radius of curvature of
fillet curve, pF, is:
Ch = 1.0
(Eq 5.69)
For conventional Helical Gears, when mF > 1.0
c -
1
h-
5.10 Helical Factor, Ch. The helical factor,
C h , is the ratio of the root bending moment produced by tip loading to the root bending moment
produced by the same intensity of loading applied
along the oblique helical contact line. It is based
on the work of Wellauer and Seireg [7].
(Eq 5.70)
o .5
where
w
= angle of inclination of helical
contact line in degrees
w
If the worst condition of load occurs where
full buttressing exists, the value of Ch may be increased by 10 percent. Full buttressing exists
when the face of the tooth extends at least one
= tan-1 (tan+ sin+n)
Equation 5.70 is valid for
(Eq 5.71)
+ < 50'.
Ch values can be taken from Fig 5-11
2.0
= 30'
1.8
= 22O
P
O
.CI
1.6
= 15'
o
9
L
1.2
1 .o
Helix Angle, $
Fig 5-11 Helical Factor,
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ch
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90 8-B 8 9
A G M A 908-B
Ob87575 0003047 379
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
The helical factor, C h , is based on the work
of Wellauer and Seireg [7].
6. Determining Addendum Modification
Coefficients
5.11 Stress Correction Factor, Kf. The stress
correction factor, KI, includes the effects of stress
concentration and load location, based on the
work of Dolan and Broghamer [i]. It is given by:
In order to use Section 5, x1 and x2 must be
determined. If these values are not known, this
Section provides a method for determining them.
(Eq 5.72)
6.1 Generating Rack Shift Coefficients. If the
normal circular tooth thicknesses are known, the
generating rack shift coefficients are found from
Eqs 6.1 and 6.2.
where
sF
= tooth thickness at critical section
=
2EnF
x
- 51-?
gl - 2 tan+n
hF
= minimum radius of curvature of
fillet curve
= height of Lewis parabola
H
= 0.331 - 0.436+n
(Eq 5.74)
L
= 0.324 - 0.492&
= 0.261 t 0.545+n
(Eq 5.75)
M
exg
P 22tan
- T
c$~
= x 82 +
- x 81
(Eq 6.3)
where
X
gl
(Eq 5.76)
X
82
where
+n
)
(Eq 5.73)
xg2 =
pF
0% 6.1)
= standard normal pressure angle
= generating rack shift coefficient,
pinion
= generating rack shift coefficient,
gear
Exg = sum of generating rack shift
coefficients
Note: In order to calculate an accurate
value for Kf , the significant decimal
places in Eq 5.74 through 5.76 are necessary. The resulting values of H, L and M
may be rounded to two decimal places.
5.12 Helix Angle Factor, KJ,. The helix angle
factor, KJ,, depends on the type of gear.
For Spur and LACR Helical Gears(mF <_ l.O), a
unity value is used, KJ,= 1.0
For Conventional Helical Gears, when mF > 1.0
KJ, =
Snl
= reference normal circular tooth
thickness, pinion (see Eq 5.21)
Sn2
= reference normal circular tooth
thickness, gear (see Eq 5.21)
6.2 Sum of Addendum Modification Coefficients for Zero Backlash. Although the amount
of tooth thinning applied to each gear may be unknown, the sum of the addendum modification
coefficients for the gear pair, ex, can be established.
c (inv 4,. - inv +)
ex =
tan
+
(Eq 5.77)
ex
= x2 f
5.13 Tooth Form Factor, Y. The tooth form
factor, Y, is calculated by:
C
= R 2 f Ri
COS$,.
COS$
x1
(Eq 6.5)
0% 6-61
where
x = addendum modification coefficient,
pinion
x2 = addendum modification coefficient,
gear
AGMA
908-B89
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
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AGMA 908-El
0687575 0003048 205
=
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
C = standard center distance
criteria listed in 7.1 through 7.10 were used in calculating the table values.
R 1 = standard pitch radius, pinion
The following paragraphs and equations use
dimensionless numbers to describe the gear geometry. To make actual measurements dimensionless, they are converted to ratios by multiplying them by diametral pitch, dividing them by
module, or comparing them to a IT (3.1416) circular pitch at the standard pitch diameter. Any consistent system of units can be used for this conversion, see Section 3.
R2 = standard pitch radius, gear
6.3 Tooth Thinning for Backlash. It is usually
impossible to determine the ratio As, / A sn2
that was used for existing gears. The following
analysis is based on common practice where
Asnl = Asn2, in which case:
7.1 Using the Tables.
Each table of I and J
values was generated for a specific tool form (basic rack) defined by whole depth factor, normal
pressure (profile) angle and tool edge (tip) radius.
Each tool form was used to generate 66 tables of
values:
Asnl= Asn2=
where
B,
=
normal operating circular backlash
C,
=
operating center distance
For spur gears:
Loaded at Tip
x1 = x p = o
x1 = 0.25, xz = -0.25
X I = 0.50, xp = -0.50
A ~n1= tooth thinning for backlash, pinion
tooth thinning for backlash, gear
A
s2=
Loaded at HPSTC
x1 = x2 = o
x1 = 0.25, xp = -0.25
x1 = 0.50, xp = -0.50
6.4 Addendum Modification Coefficients. The
addendum modification coefficients, xi and x2,
can be established from Eq 6.9 and 6.10.
x 2 = xg2 2
"n2
2 tan Qn
For helical gears:
10 degree standard helix angle
x1 = xp = o
X I = 0.25, xp = -0.25
x1 = 0.50, xp = -0.50
(Eq 6.10)
15 degree standard helix angle
x1 = x p = o
x1 = 0.25, x p = -0.25
x1 = 0.50, xp = -0.50
7. Geometry Factor Tables
The following tables provide the Geometry
Factor for Pitting Resistance, I , and the Geometry
Factor for Bending Strength, J , for a range of
typical pairs of gears. The tables were prepared
by computer, programmed in accordance with
Section 5. The values were rounded to two significant figures. The tables cover various combinations of helix angle, pressure angle, whole
depth, tool edge radius, tooth load point and addendum modification. The Tables do not cover all
tooth forms, pressure angles, and pinion or gear
modifications, and are not applicable to all gear
designs. In addition to the basic geometry, the
AGMA
20 degree standard helix angle
x1 = xp = o
x1 = 0.25, x2 = -0.25
x1 = 0.50, x2 = -0.50
25 degree standard helix angle
x1 = xp = o
x1 = 0.25, x p = -0.25
x1 = 0.50, x2 = -0.50
30 degree standard helix angle
x1 = x p = o
x1 = 0.25, xp = -0.25
XI = 0.50, xp = -0.50
17
908-B89
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
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A G H A 908-B
œ
Ob87575 0003049 1 4 1
œ
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
To obtain values for I and J , enter the table
for the appropriate whole depth factor tool, helix
angle, loading condition and addendum modification factor and select values for the numbers of
pinion and gear teeth. If the exact values for your
gearset are not listed, the calculation method of
Section 5 is recommended. Interpolation is not
recommended.
c = -n l +n2
2cos
where
C
x1+x2 =
7.3 Outside Diameter. The tabulated values are
calculated for gears having an outside diameter
(addendum diameter) equal to (in terms of mn
= 1.0):
3
+2
cos
(1
+ x2)
cos*
*
x
= addendum modification coefficient,
pinion
x2
= addendum modification coefficient,
gear
A sn =
0.024
-
= 0.024
pnd
If the gears being evaluated have different
minimum tooth thicknesses, the Bending Strength
Geometry Factor, J, can be approximated using
Eq 7.6. The Pitting Resistance Geometry Factor,
I , is unaffected by variations in tooth thickness.
where
Ji
=(%J
nl
n2
Jr
= pinion tooth number
Dai
= pinion addendum diameter
J1
= adjusted geometry -jctor
Da2
= gear addendum diameter
Js
= geometry factor from table
= gear tooth number
JS
= standard helix angle, degrees
where
snl = adjusted circular tooth thickness
7.4 Type of Gearing. The tables apply to
external gears only. An analytical method for
determining the Bending Strength Geometry Factor, J , for internal gears is beyond the scope of
this Standard.
Sns
= standard tooth thickness, thinned
per Eq 7.5
Example:
From the table at the top of page 32 for 20'
pressure angle spur gears, loaded at the highest
point of single tooth contact, the J factor for a 21
tooth pinion operating with a 35 tooth gear is
found to be 0.34. The table is based on a circular
tooth thickness of:
7.5
Center Distance. The tables apply to
gearsets that operate on a standard center distance. This center distance is the tight mesh
center distance for gears not yet thinned for
backlash. See 7.6.
18
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.'.
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9 O 8-B 89
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
+ Xi)
(Eq 7-41
7.6 Tooth Thickness Backlash Allowance.
The values in the tables are calculated based on a
backlash allowance. The circular tooth thicknesses for the pinion and the gear are each
thinned by an amount, A S n , shown in Eq 7.5.
or 1 normal module. The actual generated depths
are slightly greater due to tooth thinning for backlash.
(1
o
where
7.2 Whole Depth. Whole depth is expressed in
the Tables as a "whole depth factor", the whole
depth of a basic rack for 1 normal diametral pitch
+2
= standard center distance.
For this center distance the sum of the addendum modification coefficients is zero (See 5.3 for
definitions),
A "U" in the tables indicates a gear tooth
combination which should be avoided due to undercutting.
A "T" in the tables indicates a gear tooth
combination which should be avoided due to
pointed pinion teeth.
=
*
A G M A 908-B
= Ob87575
0003050 963
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
-IT_
7.9 Cutter Geometry. The hob geometry used
in the calculation of I and J is as follows:
= 3’1416
- - 0.024 = 1.547
2
(from Sections 7 and 7.3)
0.024
2
For a 10 normal diametral pitch gear or pinion, the equivalent circular tooth thickness would
be:
-1.547
10
-
0.155
(Eq 7.7)
A 6.5% reduction in tooth thickness reduces J
by 12%.
7.7 Undercutting. The tables do not include
geometry factors when an undercutting condition
exists in either of the two gears. This condition
can be evaluated using Eq 7.8 and Fig 7-1 where
the generating rack shift coefficient, x g , must be
equal to or greater than the expression in Eq 7.8.
gmin
=
where
hao
h -p
ao
ao
= 10 O00
‘no
= 1.5708
xo
= 0.0
¿io
= 0.0
where
nc
If a value for J for a 0.010 inch thinner pinion, having a circular thickness of
0.155 - 0.010 = 0.145 inch
is required, the approximate value is:
X
nC
= tool tooth number
‘no
= reference normal circular tooth
xo
= addendum modification coefficient
Bo
of tool
= amount of protuberance
thickness of tool
Hl
-DATUM
- - - _PITCH
_ LINE
n sin2+
(1-sin+)-n
2
n
(Eq 7.8)
= nominal tool addendum
r = A
= tool tip radius
= pinion or gear tooth number
n
7.8 Top Land. The tables do not include geometry factors when either the pinion or gear
tooth top land is less than the value expressed in
Eq 7.9.
%a min
2
/
Fig 7-1 Undercutting Criteria
0.3
%d
7.10 Axial Contact Ratio. The I and J factors
for helical gears are calculated using an axial contact ratio, m F ,equal to 2.0. When the axial contact ratio is other than 2.0, the resulting values for
I and J may be reduced by as much as 10%.
(Eq 7.9M)
where
= tooth thickness at outside diameter,
in (mm)
AGMA
19
908-B89
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
I
*
-
Sna min ? 0 . 3 m n
sna
n
Copyright American Gear Manufacturers Association
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A G H A 908-B
Obi37575 000305L 8 T T
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
14.5
DEG. PRESSURE ANGLE
DEG. HELIXANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM ( x 1= x = O)
2.157 WHOLE DEPTH FACTOR
0.024 TOOTH THINNING FOR BACKLASH
LOADED AT TIP
0.0
0.157
GEAR
TEETH
14
12
17
P
G
u
u
u
u
u
u
u
u
u
PINION TEETH
21
26
P
G
P
G
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
G
u
u
u
35
P
55
G
P
G
P
135
G
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
0.061
0.18
0.074
0.18 0.19
0.096
0.18 0.20
0.18
0.061
0.19 0.19
0.088
0.19 0.20
0.061
0.20 0.20
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
O. 157 TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION (x I
14.5
0.0
2.157
WHOLE DEPTH FACTOR
0.024 TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.25)
25 PERCENT SHORT ADDENDUM GEAR ( x 2 = - 0.25)
GEAR
TEETH
14
12
17
PINION TEETH
21
26
P
G
P
G
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
G
P
G
u
u
u
u
u
u
u
u
u
u
u
u
35
P
55
G
P
G
12 I
J
14 I
J
P
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
i AND J FACTORS FOR:’
135
G
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
0.060
0.20 0.16
0.071
0.20 0.17
0.087
0.20 0.18
0.111
0.20 0.19
0.059
0.20 0.17
O. 077
0.20 0.18
0.106
0.20 0.19
0.060
0.20 0.18
O. 092
0.20 0.19
0.060
0.20 0.19
1 The letter “U” indicates a gear tooth combination which produces a n undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
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9 08-B 89
m
A G H A 908-B
Ob87575 0003052 73b D
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
)
I AND J FACTORS FOR:’
2.157
WHOLE DEPTH FACTOR
DEG. PRESSURE ANGLE
0.024
TOOTH THINNING FOR BACKLASH
DEG. HELIX ANGLE
LOADED AT TIP
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x = O. 50)
14.5
0.0
0.157
50 PERCENT SHORT ADDENDUM GEAR ( x 2 =
- 0.50)
PINION TEETH
GEAR
TEETH
14
12
21
17
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
G
P
G
u
u
u
u
u
u
u
u
u
u
u
u
P
26
G
P
55
35
G
P
G
P
135
G
P
G
12 I
J
14 I
c
I
I
~
I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
0.056
0.21 0.12
0.067
0.21
0.13
0.081
0.21 0.15
o. 100
0.21 0.17
O. 127
0.21
0.19
0.056
0.21 0.13
0.071
0.21 0.15
0.091
0.21
0.17
0.123
0.21
0.19
0.056
0.21 0.15
0.078
0.21 0.17
0.114
0.21 0.19
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
I
0.057
0.21
0.17
0.096
0.21
0.19
0.060
0.21 0.19
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
I AND J FACTORS FOR:’
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM ( x 1 = x = O)
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT HIGHEST POINT OF SINGLE TOOTH CONTACT
14.5
0.0
O. 157
2.157
0.024
PINION TEETH
GEAR
TEETH
I
12 I
J
14 I
J
14
12
17
P
G
u
u
u
u
u
u
u
u
u
21
G
G
u
u
u
u
u
u
u
u
J
u
u
u
u
u
u
u
u
u
u
u
u
u
u
- u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
U
u
u
u
u
u
u
t r u
u
u
u
35
P
G
G
26
P
P
P
P
55
G
P
135
G
P
G
17 I
J
21 I
J
26 I
J
1
,,
I
35 I
J
55 I
J
135 I
J
f
0.061
0.29
0.29
0.074
0.30 0.31
0.096
0.31
0.34
0.061
0.33
0.33
0.088
0.35
0.35
0.061
0.38
0.38
I
t
I
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
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Provided by IHS under license with AGMA
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21
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
908-B89
A G U A 908-B
Ob87575 0003053 6 7 2
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
14.5
DEG. PRESSURE ANGLE
0.0
DEG. HELIX ANGLE
0.157 TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION (x
25 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT HIGHEST POINT OF SINGLE TOOTH CONTACT
= 0.25)
2.157
0.024
( ~ 2=
- 0.25)
~
PINION TEETH
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
GEAR
TEETH
12 I
J
14 I
12
14
P
G
u
u
17
P
G
21
P
G
26
P
G
J
u
u
u
u
17 I
J
u
u
u
u
u
u
21 I
J
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
26 I
J
35 I
J
55 I
J
135 I
J
P
35
G
0.060
0.32
0.22
0.071
0.32
0.24
0.087
0.33
0.27
0.111
0.35 0.29
P
55
G
0.059
0.34
0.24
0.077
0.35 0.27
O. 106
0.36
0.30
P
135
G
0.060
0.37 0.29
0.092
0.39
0.32
P
G
0.060
0.41 0.35
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
I AND J FACTORS FOR:l
14.5
DEG. PRESSURE ANGLE
2.157
WHOLE DEPTH FACTOR
0.0
DEG. HELIX ANGLE
0.024
TOOTH THINNING FOR BACKLASH
O. 157 TOOL EDGE RADIUS
LOADED AT HIGHEST POINT OF SINGLE TOOTH CONTACT
50 PERCENT LONG ADDENDUM PINION (x = 0.50)
50 PERCENT SHORT ADDENDUM GEAR
~~
(x,
=
- 0.50)
~
~
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
17
14
P
G
P
G
u
u
u
u
u
u
u
u
u
u
u
u
21
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
26
G
0.056
0.35
0.15
0.067
0.36
0.17
0.081
0.36
0.19
0.100
0.37 0.22
O. 127
0.38
0.26
P
35
G
0.056
0.37
0.17
0.071
0.37
0.20
0.091
0.38 0.23
O. 123
0.39
0.26
P
55
G
0.056
0.38
0.20
0.078
0.39
0.24
0.114
0.40
0.27
P
135
G
O . 057
0.41
0.25
0.096
0.42
0.29
P
G
0.060
0.43
0.32
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
9 O 8-B 89
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
m
A G H A 908-B
m
Ob87575 0003054 509
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM ( x 1 = x = O )
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
14.5
10.0
0.157
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
)
2.157
0.024
PINION TEETH
14
12
17
21
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
G
u
u
u
u
u
u
u
u
u
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
35
P
P
G
26
P
P
P
35 I
J
55 I
J
135 I
J
P
55
G
0.122
0.43
0.43
0.1ss
0.45 0.46
0.212
0.47 0.50
P
135
G
0.132
0.48
0.48
0.197
0.50
0.52
P
G
O. 145
0.55
0.55
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
) I AND J FACTORS FOR:’
14.5
DEG. PRESSURE ANGLE
10.0
DEG. HELIX ANGLE
0.157
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION ( x
25 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.25)
2.157
0.024
(x2 =
- 0.25)
PINION TEETH
GEAR
TEETH
12
14
P
G
17
P
G
21
P
G
26
P
G
P
3s
G
P
135
55
G
P
G
P
G
12 I
J
u
u
14 I
J
17 I
u
u
u
u
J
u
u
u
u
u
u
21 I
J
26 I
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
O. 107
0.43
0.34
0.137
0.44
0.38
0.181
0.45
0.41
u
u
u
u
u
u
u
u
0.47
J
35 I
J
55 I
J
135 I
J
)
0.250
0.46
0.117
0.46
0.39
0.159
0.47
0.43
0.233
0.49 0.47
0.129
0.50
0.45
0.206
0.52 0.49
O. 144
0.56
0.53
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
9 08-B 89
23
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
m
A G H A 908-B
m
Ob87575 0003055 445
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
I AND J FACTORS FOR:?
DEG. PRESSURE ANGLE
10.0
DEG. HELIX ANGLE
O. 157 TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION (xl
14.5
50 PERCENT SHORT ADDENDUM GEAR
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.50)
2.157
0.024
(x2 =
- 0.50)
PINION TEETH
12
P
G
u
w
u
w
u
u
u
u
u
u
u
w
u
u
u
u
u
u
u
u
u
u
u
w
u
u
u
P
G
u
u
u
21
17
14
P
G
P
0.054
0.42 0.20
0.085
0.42
0.24
0.117
0.43 0.27
0.160
0.43
0.30
0.218
0.44
0.34
O. 300
0.45
0.39
26
P
G
0.071
0.44 0.25
0.101
0.44
0.28
O . 141
0.45 0.31
O. 198
0.46 0.35
0.282
0.46
0.40
55
35
G
0.086
0.46
0.29
0.124
0.46
0.32
0.179
0.47
0.37
0.264
0.48
0.42
P
G
0.102
0.48
0.34
0.154
0.49
0.38
O. 242
0.50
0.44
P
135
G
o. 120
0.51 0.41
O. 208
0.52
0.46
P
G
O. 141
0.56
0.51
1 The letter ?U?indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
I AND J FACTORS FOR:?
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM ( x 1= x = O)
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
14.5
15.0
0.157
2.157
0.024
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
17
14
12
P
G
26
21
P
G
P
G
55
35
P
G
P
G
u
u
u
u
w
u
w
u
w
u
u
u
u
u
w
u
u
u
u
u
u
u
u
u
w
u
w
u
u
u
w
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
G
O. 124
0.43
0.43
0.156
0.45
0.46
0.214
0.47
0.50
P
135
G
0.133
0.48
0.48
O. 198
0.50
0.52
P
G
O. 146
0.54 0.54
1 The letter ?U? indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
24
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
908-B89
A G M A 908-B
W Ob87575 000305b 381
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
i AND J FACTORS FOR:’
)
14.5
DEG. PRESSURE ANGLE
15.0
DEG. HELIXANGLE
0.157
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION (x
25 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.25)
2.157
0.024
(x2 =
- 0.25)
PINION TEETH
GEAR
TEETH
17
14
12
P
G
u
u
u
u
u
u
u
u
u
J
55 I
J
G
u
u
u
u
u
u
U
u
u
u
u
u
u
u
u
u
u
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
L
u
u
u
u
u
u
u
u
G
u
u
J
u
17 I
J
21 I
26
21
P
P
P
P
35
G
P
55
G
P
135
G
P
G
12 I
J
14 I
J
26 I
J
35 I
135 I
J
T
0.109
0.43 0.35
0.138
0.44
0.38
0.182
0.45
0.41
0.250
0.47
0.46
0.118
0.46
0.39
0.161
0.47
0.43
0.233
0.49
0.47
0.130
0.50
0.45
O. 206
0.52 0.49
0.145
0.55
0.53
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
D
I AND J FACTORS FOR:’
DEG. PRESSURE ANGLE
15.0
DEG. HELIX ANGLE
O. 157 TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x
14.5
50 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.50)
2.157
O. 024
(x2 = - 0.50)
PINION TEETH
G
u
u
u
u
u
u
u
J
26 I
J
35 I
u
u
u
u
u
u
u
u
J
55 I
J
u
u
u
u
u
u
u
u
J
14 I
J
17 I
J
21 I
135 I
J
P
G
u
u
u
u
u
u
21
17
P
12 I
)
14
12
u
P
G
0.059
0.42
0.21
0.090
0.43
0.25
o. 121
0.43 0.27
0.162
0.44
0.31
0.219
0.44
0.35
0.299
0.45
0.39
P
26
G
P
0.075
0.44 0.26
0.104
0.45 0.28
0.144
0.45 0.32
0.199
0.46
0.36
0.281
0.47
0.40
55
35
G
0.089
0.46
0.29
0.126
0.46
0.33
0.180
0.47
0.37
0.264
0.48
0.42
P
G
0.105
0.48
0.35
0.156
0.49
0.39
O. 242
0.50
0.44
P
G
P
135
G
o. 122
0.51
0.41
O. 209
0.52
0.46
O. 142
0.56
0.51
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
GEAR
TEETH
1 The letter “U” indicates a gear tooth combination which produces a n undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
25
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
90 8-B 89
m
AGMA 908-B
Ob87575 0003057 218
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
14.5
DEG. PRESSURE ANGLE
20.0
DËG. HELIXANGLE
O. 157 TOOL EDGE RADIUS
EQUAL ADDENDUM (x 1= x = O)
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
2.157
0.024
PINION TEETH
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
GEAR
TEETH
14
12
21
17
P
G
u
u
u
u
u
u
u
u
u
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
G
u
u
u
26
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
35
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
55
G
P
135
G
P
G
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
o. 125
0.43
0.43
0.158
0.44
0.45
0.215
0.46
0.49
0.134
0.47
0.47
0.199
0.49
0.50
O. 146
0.53
0.53
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
I AND J FACTORS FOR:’
14.5
DEG. PRESSURE ANGLE
20.0
DEG. HELIX ANGLE
0.157
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
(Y
25 PERCENT SHORT ADDENDUM GEAR
(x2 =
2.157
0.024
= 0.25)
- 0.25)
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
14
12
P
G
u
u
u
P
G
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
135 I
J
21
17
P
26
G
O. 104
0.40
0.32
0.126
0.41 0.34
0.156
0.42 0.37
0.198
0.43
0.40
0.262
0.44
0.43
P
35
G
0.111
0.43 0.35
O. 140
0.43
0.38
0.183
0.44 0.41
0.250
0.46
0.44
P
55
G
0.120
0.45
0.39
O. 162
0.46
0.42
0.234
0.48
0.46
P
135
G
0.131
0.49
0.44
0.207
0.50
0.48
P
G
0.145
0.53
0.51
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
26
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
9 O 8-B 8 9
= Ob87575
A G H A 908-B
0003058 154
=
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
14.5
DEG. PRESSURE ANGLE
20.0
DEG. HELIX ANGLE
0.157 TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x
1
50 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.50)
2.157
0.024
(x2 =
- 0.50)
PINION TEETH
GEAR
TEETH
14
12
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
J
u
u
u
u
135 I
J
u
u
u
u
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
P
G
u
u
u
P
26
21
17
G
P
0.065
0.41 0.22
0.095
0.42 0.25
0.125
0.42 0.28
0.166
0.43
0.31
0.220
0.43
0.34
0.297
0.44
0.38
P
G
0.081
0.43 0.26
0.109
0.43 0.29
0.147
0.44
0.32
0.201
0.45
0.35
0.280
0.45
0.40
35
G
0.094
0.45 0.30
0.130
0.45 0.33
0.182
0.46
0.37
0.264
0.47
0.41
P
55
G
0.108
0.47
0.34
0.158
0.47
0.38
0.242
0.48
0.43
P
135
G
O. 124
0.50
0.41
0.209
0.50
0.45
P
G
0.143
0.54 0.49
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
I AND J FACTORS FOR:’
14.5
25.0
O. 157
EQUAL
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
ADDENDUM ( X 1= x = O )
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
2.157
0.024
~~~
PINION TEETH
GEAR
TEETH
12
14
P
G
u
u
u
u
u
u
u
u
u
21
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
G
u
u
u
J
21 I
J
12 I
J
14 I
J
17 I
17
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
26 I
J
35 I
J
55 I
J
135 I
J
1
35
26
P
G
0.121
0.38
0.38
O. 142
0.39
0.40
O. 174
0.40
0.42
0.225
0.42
0.45
P
55
G
O. 127
0.41
0.41
O. 160
0.42
0.43
0.218
0.44
0.46
P
135
G
0.135
0.45 0.45
0.201
0.47
0.48
P
G
O. 147
0.50
0.50
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
27
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
908-B89
Ob87575 0003059 090
A G M A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
14.5
DEG. PRESSURE ANGLE
25.0
DEG. HELIX ANGLE
0.157
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION ( x
25 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.25)
2.157
0.024
(x2 = - 0.25)
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
14
P
G
u
u
u
17
P
G
u
u
u
u
u
u
u
u
u
21
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
26
G
0.108
0.39
0.31
0.129
0.40
0.33
0.158
0.40
0.36
0.200
0.41 0.38
0.262
0.42
0.41
P
35
G
0.115
0.41 0.34
0.143
0.42
0.36
0.185
0.43
0.39
0.250
0.44
0.42
P
55
G
O. 123
0.43
0.38
O. 164
0.44 0.40
0.234
0.45
0.44
P
135
G
O. 133
0.46
0.42
0.208
0.47
0.46
P
G
0.146
0.50 0.48
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
Z AND J FACTORS FOR:‘
14.5
DEG. PRESSURE ANGLE
25.0
DEG. HELIX ANGLE
0.157
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x
50 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= O. SO)
2.1.57
0.024
(x2 =
- 0.50)
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
17
14
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
G
0.057
0.38
0.19
O. 086
0.39
0.22
O. 117
0.39
0.24
O. 148
0.39
0.27
0.188
0.40
0.29
0.240
0.40
0.32
0.311
0.41
0.36
P
26
21
G
0.073
0.40
0.23
o. 102
0.40
0.25
O. 131
0.40
0.28
O. 170
0.41
0.30
0.222
0.41 0.33
0.295
0.42
0.37
P
G
0.087
0.41 0.26
0.114
0.42
0.29
0.151
0.42
0.31
0.203
0.42
0.34
0.279
0.43 0.38
P
35
G
0,099
0.43
0.29
0.134
0.43
0.32
0.185
0.44
0.35
0.263
0.44
0.39
P
55
G
0.112
0.45
0.34
0.161
0.45
0.37
0.242
0.46
0.41
P
135
G
0.127
0.47
0.39
0.210
0.48
0.43
P
G
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
I
0.144
0.51
0.47
1 The letter “U” indicates a gear tooth combination which produces a n undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
28
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
9 08-B 89
A G H A 908-B
Ob87575 O003060 802
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
1
I AND J FACTORS FOR:’
2.157
WHOLE DEPTH FACTOR
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
14.5
DEG. PRESSURE ANGLE
30.0
DEG. HELIX ANGLE
0.157 TOOL EDGBRADIUS
EQUAL ADDENDUM ( x 1= x = O )
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
14
P
G
u
u
u
17
P
G
u
u
u
u
u
u
u
u
u
PINION TEETH
21
26
P
G
P
G
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
O. 123
0.36 0.36
O. 145
0.37 0.37
O. 177
0.38 0.39
O. 227
0.39 0.42
35
P
55
G
O. 129
0.38 0.38
0.163
0.39 0.40
0.220
0.41 0.43
P
G
0.137
0.41 0.41
o. 202
0.43 0.44
P
135
G
O. 148
0.46 0.46
1 The letter “U” indicates a gear tooth combination which produces a n undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
1
I AND J FACTORS FOR:’
14.5
DEG. PRESSURE ANGLE
2.157
WHOLE DEPTH FACTOR
30.0
DEG. HELIX ANGLE
0.024
TOOTH THINNING FOR BACKLASH
0.157 TOOL EDGE RADIUS
LOADED AT TIP
25 PERCENT LONG ADDENDUM PINION ( x = 0.25)
25 PERCENT SHORT ADDENDUM GEAR
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
)
14
12
P
G
u
u
u
( x =~- 0.25)
17
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
G
0.105
0.35 0.27
0.126
0.35 0.29
O. 147
0.36 0.31
0.176
0.36 0.33
0.216
0.37 0.35
0.272
0.38 0.38
PINION TEETH
21
26
P
G
P
G
0.112
0.37 0.30
0.133
0.37 0.32
0.161
0.38 0.34
0.201
0.38 0.36
0.261
0.39 0.39
0.118
0.38 0.33
O. 146
0.39 0.34
0.187
0.40 0.37
0.250
0.41 0.39
55
35
P
G
0.126
0.36
0.166
0.41 0.38
0.235
0.42 0.41
P
G
P
135
G
0.40
0.13.5
0.43 0.39
0.209
0.44 0.42
0.147
0.46 0.45
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
29
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
908-B89
Ob87575 00030bL 7q9
A G M A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Slrenglh of Spur and Helical Gear Teeth
I AND J FACTORS FOR:
2.157
WHOLE DEPTH FACTOR
14.5
DEG. PRESSURE ANGLE
.O24
TOOTH THINNING FOR BACKLASH
30.0
DEG. HELIX ANGLE
LOADED AT TIP
0.157
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x = 0.50)
50 PERCENT SHORT ADDENDUM GEAR
(x2 =
- 0.50)
PINION TEETH
GEAR
TEETH
12 I
14
17
21
26
35
J
I
J
I
J
I
J
I
J
I
J
55 I
J
135 I
J
14
12
P
G
0.055
0.35 0.17
0.078
0.35
0.19
0.107
0.35
0.21
O. 138
0.36
0.24
O. 168
0.36
0.25
0.206
0.36
0.28
0.256
0.37 0.30
0.320
0.37
0.33
P
21
17
G
0.068
0.36
0.20
0.095
0.36
0.22
o. 125
0.37
0.24
O. 154
0.37
0.26
0.191
0.37
0.28
0.241
0.38
0.31
0.307
0.38
0.33
P
P
G
0.082
0.37
0.23
0.110
0.37
0.25
O. 137
0.38
0.27
O. 174
0.38
0.29
0.223
0.39
0.32
0.292
0.39
0.35
35
26
G
P
0.095
0.38
0.26
0.120
0.39
0.28
O. 156
0.39
0.30
o. 205
0.40
0.33
0.277
0.40
0.36
G
P
55
G
P
135
G
P
G
o. 105
0.40
0.29
O. 139
0.40
0.31
O. 187
0.40
0.34
0.262
0.41 0.37
0.117
0.41 0.32
O. 164
0.42
0.35
0.242
0.42
0.38
0.130
0.43
0.37
0.211
0.44
0.40
O. 145
0.46
0.43
I AND J FACTORS FOR:'
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
2.250
0.024
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM ( x 1= x = O)
20.0
0.0
0.250
PINION TEETH
GEAR
TEETH
17
14
12
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
G
u
u
u
u
u
u
u
u
u
G
u
u
u
P
35
26
21
P
P
P
G
P
G
P
55
G
P
135
G
P
G
12 I
J
14 I
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
0.078
0.24
0.24
0.084
0.24
0.25
0.091
0.24
0.26
o. 102
0.24
0.28
O. 118
0.24
0.29
0.079
0.25 0.25
0.088
0.25 0.26
0.101
0.25 0.28
0.121
0.25 0.29
0.080
0.26
0.26
0.095
0.26
0.28
0.120
0.26
0.29
O. 080
0.28
0.28
0.112
0.28
0.29
O. 080
0.29 0.29
1 The letter "U" indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
30
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
9 O 8-B 8 9
m
A G H A 908-B
Ob87575 00030b2 b85
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
r AND J FACTORS FOR:’
20.0
DEG. PRESSURE ANGLE
0.0
DEG. HELIXANGLE
0.250
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION
(X
25 PERCENT SHORT ADDENDUM GEAR
(x2 =
GEAR
TEETH
12
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
0.080
0.27
0.19
0.087
0.27
0.21
0.094
0.27
0.22
u
u
u
u
0.27
u
u
u
u
0.27
u
u
u
u
0.27
J
u
u
14 I
J
17 I
u
21
26
35
55
135
P
- 0.25)
PINION TEETH
21
26
G
P
G
P
P
G
J
I
J
I
J
I
J
I
J
I
J
= 0.25)
17
14
P
12 I
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
2.250
0.024
G
0.080
0.27
0.21
0.088
0.27
0.22
0.098
0.27
0.24
0.113
0.27
0.26
O. 103
0.24
0.115
0.26
0.131
0.080
0.28
0.22
0.092
0.28
0.24
O. 108
0.28
0.26
0.134
0.28
0.27
0.133
0.28
0.28
0.28
55
35
P
G
0.080
0.28
0.24
0.099
0.28
0.26
0.129
0.28
0.28
P
G
0.080
0.29
0.26
0.116
0.29
0.28
P
135
G
0.080
0.28
0.30
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
I AND J FACTORS FOR:’
20.0
DEG. PRESSURE ANGLE
0.0
DEG. HELIX ANGLE
0.250
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x
2.250
0.024
50 PERCENT SHORT ADDENDUM GEAR
= - O . 50)
(X
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= O. 50)
PINION TEETH
GEAR
TEETH
12
14
P
G
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
P
17
G
P
21
G
P
26
G
P
35
G
P
55
G
P
135
G
P
G
12 I
J
35 I
J
55 I
J
135 I
J
0.080
0.30
0.12
0.088
0.30
0.15
0.097
0.30
0.17
o. 105
0.30 0.19
0.116
0.30
0.21
0.130
0.30
0.24
O. 148
0.30 0.27
0.080
0.30
0.15
0.090
0.30 0.17
0.099
0.30 0.19
0.111
0.30 0.21
O . 127
0.30 0.24
O. 149
0.30
0.27
0.080
0.31 0.17
0.090
0.31 0.19
O. 103
0.31 0.21
o. 122
0.31 0.24
O . 148
0.31 0.27
0.080
0.19
0.094
0.31
0.21
0.114
0.31
0.24
O. 145
0.31 0.27
0.31
0.080
0.30
0.21
0.101
0.30 0.24
O . 136
0.30 0.27
0.080
0.24
o. 120
0.30
0.27
0.30
0.080
0.30
0.27
1 The letter “T” indicates a gear tooth combination which produces pointed teeth with a top land less than O. 3/ Pnd in one or both
components and should be avoided. See Section 7.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
31
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
J
14 I
J
17 I
J
21 I
J
26 I
908-B89
AGHA 908-B
Ob87575 00030b3 511
=
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM ( x 1= x = O )
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT HIGHEST POINT OF SINGLE TOOTH CONTACT
20.0
0.0
0.250
2.250
0.024
PINION TEETH
14
GEAR
TEETH
P
G
12 I
J
u
u
u
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
17
P
G
u
u
u
u
u
u
u
u
u
21
26
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
0.078
0.33 0.33
0.084
0.33 0.35
0.091
0.34 0.37
0.102
0.34
0.40
u
u
u
u
u
u
0.35
P
G
P
35
G
P
135
55
G
P
G
P
G
14 I
J
17 I
0.118
0.43
0.079
0.35
0.35
0.080
0.088
0.36
0.38
o. 101
0.37
0.41
o. 121
0.38
0.44
0.39
0.39
0.095
0.40
0.42
o. 120
0.41
0.45
0.080
0.43
0.43
0.112
0.45
0.47
0.080
0.49
0.49
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
I AND J FACTORS FOR:1
20.0
DEG. PRESSURE ANGLE
0.0
DEG. HELIX ANGLE
0.250
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION (x I
25 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT HIGHEST POINT OF SINGLE TOOTH CONTACT
2.250
0.024
= 0.25)
( ~ =2
- 0.25)
PINION TEETH
12
14
P
G
u
u
J
u
17 I
J
21 I
17
P
G
u
u
u
u
u
u
u
J
26 I
J
35 I
J
55 I
u
u
u
u
u
u
u
u
u
u
u
u
J
u
u
u
u
u
u
u
u
12 I
J
14 I
135 I
J
P
21
G
0.080
0.36
0.24
o. 087
0.37
0.26
0.094
0.37
0.29
O. 103
0.37
0.32
o. 115
0.38
0.35
0.131
0.39
0.39
P
26
G
P
0,080
0.39
0.27
0.088
0.39 0.29
0.098
0.40
0.32
0.113
0.40
0.36
0.134
0.41
0.40
35
G
0.080
0.41 0.30
0.092
0.41
0.33
0.108
0.42
0.36
0.133
0.43
0.41
P
55
G
0.080
0.43
0.34
0.099
0.44
0.37
O . 129
0.45
0.42
P
135
G
P
G
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
GEAR
TEETH
0.080
0.47
0.39
O . 116
0.48
0.44
0.080
0.51 0.46
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
32
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
9O 8-B 89
m
A G M A 908-8
Ob87575 00030b4 458
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
20.0
DEG. PRESSURE ANGLE
0.0
DEG. HELIX ANGLE
0.250 TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION
(X
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT HIGHEST POINT OF SINGLE TOOTH CONTACT
= 0.50)
50 PERCENT SHORT ADDENDUM GEAR
(X2
=
2.250
0.024
- 0.50)
PINION TEETH
GEAR
TEETH
14
12
P
G
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
P
17
G
P
21
G
P
26
G
P
35
G
P
55
G
P
135
G
P
G
12 I
J
14 I
J
I
J
I
J
I
J
I
J
I
J
I
J
17
21
26
35
55
135
0.080
0.40
0.14
0.088
0.41 0.17
0.097
0.41
0.20
o. 105
0.41
0.23
0.116
0.42
0.26
0.130
0.42
0.30
O. 148
0.43
0.34
0.080
0.42
0.18
0.090
0.43
0.21
0.099
0.43
0.23
0.111
0.43
0.27
0.127
0.44
0.31
O. 149
0.44
0.35
0.080
0.44
0.21
0.090
0.45
0.24
O. 103
0.45 0.27
0.122
0.45 0.31
O. 148
0.46
0.36
0.080
0.46
0.24
0.094
0.46
0.28
0.114
0.47
0.32
0.145
0.47
0.37
0.080
0.48
0.29
0.101
0.48
0.33
0.136
0.49
0.38
0.080
0.50 0.34
0.120
0.50
0.40
0.080
0.52
0.43
1 The letter “T” indicates a gear tooth combination which produces pointed teeth with a top land less than 0.3/Pnd in one or both
components and should be avoided. See Section 7.
I AND J FACTORS FOR:’
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM (X 1= x = O)
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
20.0
10.0
0.250
2.250
0.024
PINION TEETH
GEAR
TEETH
12
14
P
G
u
u
J
u
17 I
J
21 I
12 I
J
17
P
G
u
u
u
u
u
u
u
u
u
21
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
26
G
P
35
G
P
55
G
P
135
G
P
G
14 I
26
35
55
135
J
I
J
I
J
I
J
I
J
0.127
0.46
0.46
0.143
0.47
0.49
O. 164
0.48 0.52
o. 195
0.49 0.55
0.241
0.50
0.60
0.131
0.49
0.49
0.153
0.50 0.53
0.186
0.52
0.56
0.237
0.53
0.61
O. 136
0.54
0.54
O. 170
0.55
0.57
0.228
0.57
0.62
O. 143
0.59
0.59
0.209
0.60
0.63
0.151
0.65 0.65
1 The letter “U” indicates a gear tooth combination which produces a n undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-3.
AGMA
33
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
908-B89
m
A G M A 908-B
Ob87575 0003065 394
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
DEG. PRESSURE ANGLE
2.250
WHOLE DEPTH FACTOR
DEG. HELIX ANGLE
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
0.250 TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION ( x = 0.25)
20.0
10.0
25 PERCENT SHORT ADDENDUM GEAR
(x, =
- 0.25)
PINION TEETH
GEAR
TEETH
12
14
P
G
u
u
u
u
P
17
G
P
21
G
P
26
G
P
35
G
P
55
G
P
135
G
P
G
12 I
J
14 I
17
21
26
35
55
135
J
I
J
I
J
I
J
I
J
I
J
I
J
O. 109
0.30
0.46
O. 129
u
u
u
u
u
u
u
u
u
u
u
u
0.47
0.34
O. 151
0.47
0.38
O. 172
0.48
0.41
0.200
0.48
0.44
0.236
0.49 0.49
0.286
0.50
0.54
0.116
0.49 0.35
0.137
0.50
0.38
0.157
0.50
0.42
0.185
0.51 0.45
0.223
0.52
0.50
0.276
0.53
0.55
0.122
0.52
0.39
0.142
0.53
0.42
O. 170
0.53
0.46
0.209
0.54
0.51
0.266
0.55
0.56
0.127
0.55 0.43
0.155
0.55 0.47
0.194
0.56
0.52
0.255
0.57
0.57
O. 134
0.58
0.49
O. 173
0.59
0.53
0.240
0.60
0.58
0.141
0.62
0.55
0.214
0.63
0.60
0.151
0.66
0.63
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
0.250
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x
20.0
50 PERCENT SHORT ADDENDUM GEAR
(X
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= O. 50)
2.250
0.024
10.0
,= -
O. 50)
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
P
14
G
0.077
0.18
0.099
0.51 0.22
0.126
0.51 0.26
0.154
0.52
0.30
0.182
0.52
0.33
0.217
0.53
0.37
0.263
0.53
0.42
0.321
0.54
0.48
P
17
G
P
21
G
P
26
G
P
35
G
P
55
G
P
135
G
P
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
I AND J FACTORS FOR:
G
0.51
0.088
0.53
0.22
0.113
0.53
0.26
0.141
0.53
0.30
O. 168
0.54
0.34
0.203
0.54
0.38
0.248
0.55
0.43
O. 309
0.55
0.49
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
0.099
0.55
0.27
0.125
0.55
0.31
0.151
0.55 0.35
O. 185
0.56
0.39
0.231
0.56
0.44
0.295
0.57
0.50
0.109
0.57
0.32
0.134
0.57 0.36
0.167
0.57
0.40
0.213
0.58
0.45
0.280
0.58
0.52
0.118
0.58
0.37
o. 150
0.59
0.41
O. 196
0.59
0.47
0.266
0.60
0.53
0.127
0.61 0.43
0.172
0.61 0.48
0.247
0.62 0.55
34
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
0.137
0.63 0.50
0.216
0.64
0.57
O. 149
0.67
0.61
9 O 8-B 89
m
A G M A 908-B
Ob87575 00030bb 220
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
2.250
0.024
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM ( X 1= x = O)
20.0
15.0
0.250
I
PINION TEETH
GEAR
TEETH
12
14
P
G
J
u
u
14 I
J
17 I
u
17
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
21
G
P
26
G
P
35
G
P
55
G
P
135
G
P
G
12 I
21
26
35
55
135
J
I
J
I
J
I
J
I
J
I
J
u
u
u
u
O. 124
0.43
0.43
0.139
0.44 0.46
0.154
0.45 0.49
O. 175
0.46
0.52
0.204
0.47
0.55
0.244
0.48
0.59
O. 128
0.47
0.47
0.143
0.48 0.50
0.165
0.49
0.53
0.196
0.50
0.56
0.132
0.50
0.50
0.154
0.51 0.53
0.187
0.53 0.57
0.137
0.54
0.54
0.171
0.56
0.58
0.59
0.241
0.51 0.60
0.237
0.54
0.61
0.229
0.57
0.62
0.209
0.61
0.64
O. 143
0.59
0.151
0.65 0.65
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
I AND J FACTORS FOR:’
20.0
DEG. PRESSURE ANGLE
2.250
WHOLE DEPTH FACTOR
15.0
DEG. HELIX ANGLE
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
0.250
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION ( x = 0.25)
25 PERCENT SHORT ADDENDUM GEAR
(X2
= - 0.25)
PINION TEETH
12 I
J
14 I
J
17 I
21
26
35
55
135
J
I
J
I
J
I
J
I
J
I
J
14
12
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
17
G
0.111
0.47
0.32
O. 131
0.48
0.35
O. 152
0.48
0.39
O. 173
0.49
0.42
o. 200
0.50
0.45
0.236
0.50
0.49
0.285
0.51
0.54
P
21
G
0.117
0.50
0.36
O. 138
0.51 0.40
0.158
0.51 0.43
O. 186
0.52
0.46
0.223
0.53
0.50
0.275
0.54
0.55
P
26
G
P
35
G
P
55
G
P
135
G
P
G
O. 123
0.53
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
GEAR
TEETH
0.40
O. 143
0.53
0.44
O. 171
0.54
0.47
0.209
0.55 0.51
0.265
0.56
0.56
O. 128
0.55 0.44
0.155
0.56
0.48
0.195
0.57
0.53
0.255
0.58
0.58
0.134
0.58
0.49
O. 174
0.59
0.54
0.240
0.60
0.59
O. 142
0.62 0.56
0.214
0.63
0.61
0.151
0.67
0.63
1 The letter “U” indicates a gear tooth combination which produces a n undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
35
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
908-B89
Ob87575 0 0 0 3 0 b ï L b ï
AGHA 908-El
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:
20.0
DEG. PRESSURE ANGLE
15.0
DEG. HELIX ANGLE
0.250
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION (x
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
50 PERCENT SHORT ADDENDUM GEAR
GEAR
TEETH
12 I
14
17
21
26
35
55
135
J
I
J
I
J
I
J
I
J
I
J
I
J
I
J
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.50)
2.250
0.024
(X2 =
- 0.50)
PINION TEETH
P
17
14
12
G
0.081
0.52
0.20
o. 102
0.52
0.23
0.128
0.52
0.27
O. 156
0.53 0.31
0.183
0.53
0.34
0.218
0.54 0.38
0.262
0.54
0.43
0.319
0.55
0.49
P
G
0.091
0.53
0.24
0.116
0.54 0.28
0.143
0.54
0.31
0.169
0.55
0.35
O. 203
0.55
0.39
0.248
0.55
0.44
O. 307
0.56
0.50
P
26
21
G
P
0.102
0.55 0.28
0.127
0.56
0.32
0.152
0.56
0.36
O. 186
0.57
0.40
0.231
0.57
0.45
0.294
0.58
0.51
P
G
0.111
0.57
0.33
0.135
0.58 0.37
O. 168
0.58
0.41
0.213
0.59
0.46
0.279
0.59
0.52
35
G
P
55
G
P
135
G
P
G
0.119
0.59
0.38
0.151
0.60
0.42
0.196
0.60
0.48
0.265
0.61 0.54
0.128
0.61 0.44
0.173
0.62
0.49
0.246
0.62
0.55
0.138
0.64
0.51
0.216
0.65
0.58
O. 149
0.67
0.61
I AND J FACTORS FOR:’
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM ( x 1= x = O)
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
20.0
20.0
0.250
2.250
0.024
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
21
26
35
55
135
J
I
J
I
J
I
J
I
J
I
J
14
12
17
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
G
u
u
u
P
26
21
G
0.125
0.44
0.44
O. 140
0.45
0.46
0.156
0.45 0.49
O. 177
0.46
0.51
0.205
0.47
0.54
0.245
0.48
0.58
P
P
G
0.129
0.47
0.47
O. 145
0.48
0.49
0.167
0.49
0.52
0.197
0.50 0.55
0.242
0.51 0.59
35
G
0.133
0.50
0.50
o. 155
0.51
0.53
0.188
0.52
0.56
0.238
0.54 0.60
P
55
G
0.138
0.54
0.54
O. 172
0.55 0.57
0.229
0.57
0.61
P
135
G
0.144
0.58
0.58
0.209
0.60
0.62
P
G
0.151
0.64
0.64
1 The letter “U”indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
36
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
908-B89
W Ob87575 00030b8 O T 3 W
A G M A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:
2.250
WHOLE DEPTH FACTOR
20.0
DEG. PRESSURE ANGLE
0.024
TOOTH THINNING FOR BACKLASH
20.0
DEG. HELIX ANGLE
LOADED AT TIP
0.250 TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION (xl = 0.25)
25 PERCENT SHORT ADDENDUM GEAR
(x2 =
- 0.25)
PINION TEETH
12 I
12
P
14
G
P
17
G
P
21
G
P
26
G
P
35
G
0.108
0.45
0.29
O. 124
0.45 0.32
0.144
0.46
0.35
0.114
0.47
0.33
O. 133
0.48
0.36
0.119
0.50
0.37
O. 165
0.47
0.39
O. 154
0.48
0.39
0.140
0.51 0.40
26 I
J
0.186
0.47
0.41
0.49
0.42
0.51
35 I
J
0.212
0.48
0.44
0.201
0.50
0.45
0.52
55 I
J
0.246
0.48
0.48
0.236
0.50 0.49
0.223
0.52 0.50
0.209
0.54 0.51
0.56
135 I
J
0.291
0.49
0.53
0.284
0.51 0.53
0.274
0.53
0.54
0.265
0.55 0.56
0.255
0.57
0.57
J
14 I
J
17 I
J
21 I
J
O. 174
0.160
0.43
55
G
P
135
G
P
G
0.125
0.53
0.41
O. 145
0.53
O. 187
0.44
0.130
0.55
0.45
O. 172
0.46
P
0.54
O. 156
0.47
0.55
0.48
O. 135
0.58
o. 195
0.52
0.49
O. 175
0.53
O. 142
0.61 0.55
0.240
0.59
0.58
0.214
0.62 0.60
0.58
0.151
0.65 0.62
I AND J FACTORS FOR:
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
2.250
0.024
20.0
20.0
0.250
= O. SO)
(x2 =
50 PERCENT SHORT ADDENDUM GEAR
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
GEAR
TEETH
- 0.50)
PINION TEETH
GEAR
TEETH
12 I
14
17
21
26
J
I
J
I
J
I
J
I
J
35 I
J
55 I
J
135 I
J
14
12
P
G
0.086
0.52
0.21
O. 106
0.52
0.24
O. 132
0.52
0.28
0.159
0.53
0.32
0.185
0.53
0.35
0.219
0.53
0.39
0.261
0.54
0.43
O. 317
0.54
0.48
P
G
0.095
0.53
0.25
o. 120
0.53
0.29
0.146
0.54
0.32
0.171
0.54
0.36
O. 204
0.54
0.39
0.248
0.55 0.44
0.305
0.55
0.49
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
21
17
P
G
O. 105
0.55 0.29
O. 130
0.55 0.33
O. 155
0.56
0.37
0.187
0.56
0.40
0.231
0.56
0.45
0.292
0.57
0.50
P
P
0.114
0.57
0.34
0.138
0.57
0.38
O. 170
0.57
0.41
0.214
0.58
0.46
0.278
0.58
0.52
55
35
26
G
G
P
G
P
135
G
P
G
o. 121
0.58
0.38
O. 152
0.59
0.43
0.197
0.59
0.47
0.265
0.60
0.53
0.130
0.60
0.44
O. 173
0.61
0.49
O. 246
0.61 0.55
37
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
O. 139
O. 3
o. 1
0.216
0.63
0.57
0.150
0.66 0.60
908-B89
m
AGMA 908-B
Ob87575 00030b9 T 3 T
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM (x 1= x = O)
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
20.0
25.0
0.250
2.250
0.024
PINION TEETH
GEAR
TEETH
12 I
J
12
14
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
14 I
J
17 I
J
21 I
26
35
55
135
J
I
J
I
J
I
J
I
J
P
17
G
O. 123
0.40
0.40
O. 137
0.41
0.43
O. 152
0.41
0.45
O. 167
0.42
0.47
0.187
0.43
0.49
0.213
0.44
0.52
0.248
0.45 0.55
P
21
G
P
O. 126
0.43
0.43
O. 142
0.44
0.45
0.157
0.44
0.47
0.178
0.45 0.50
0.207
0.46 0.52
O. 247
0.47
0.56
26
G
P
0.130
0.46
0.46
O. 146
0.47 0.48
O. 168
0.48
0.50
0.199
0.49 0.53
0.244
0.50
0.56
35
G
0.134
0.49
0.49
0.156
0.50 0.51
0.189
0.51 0.54
0.239
0.52
0.57
P
55
G
0.138
0.52
0.52
0.173
0.53
0.55
0.230
0.54
0.58
P
135
G
O. 144
0.56 0.56
0.210
0.57 0.59
P
G
0.151
0.61 0.61
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
Z AND J FACTORS FOR:
20.0
DEG. PRESSURE ANGLE
25.0
DEG. HELIX ANGLE
TOOL EDGE RADIUS
0.250
25 PERCENT LONG ADDENDUM PINION ( x I
25 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.25)
2.250
0.024
(x2 =
- 0.25)
PINION TEETH
12 I
J
14 I
J
17 I
21
26
35
55
135
J
I
J
I
J
I
J
I
J
I
J
14
12
P
G
P
17
G
P
21
G
P
26
G
P
35
G
P
55
G
P
135
G
0.112
0.44
0.30
0.127
0.45
0.33
O. 146
0.45
0.36
0.167
0.46
0.38
0.187
0.46
0.41
0.213
0.116
0.46
0.33
O. 135
0.47
0.36
0.156
0.47
0.39
0.176
0.48
0.41
0.202
o. 122
0.49
0.37
0.142
0.49
0.40
0.161
0.50
0.42
O. 188
O. 127
0.51 0.41
O. 146
0.51 0.43
0.173
0.131
0.53
0.44
0.158
0.47
0.44
0.246
0.48
0.44
0.236
0.50
0.45
0.224
0.52
0.46
0.210
0.53
0.47
0.196
0.55
0.48
0.175
0.47
0.47
0.289
0.49
0.48
0.282
0.51 0.48
0.273
0.53
0.49
0.264
0.54 0.50
0.254
0.56
0.51
O. 240
0.58
0.53
0.214
0.48
0.50
0.52
0.53
0.55
0.57
0.59
0.51
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
0.51
0.52
0.53
0.54
P
G
O. 137
38
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
0.56
O. 143
0.57
0.151
0.62
0.59
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
GEAR
TEETH
908-B89
W Ob87575 0003070 751 W
A G M A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:
20.0
DEG. PRESSURE ANGLE
2.250 WHOLE DEPTH FACTOR
25.0
DEG. HELIX ANGLE
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
0.250 TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x = 0.50)
50 PERCENT SHORT ADDENDUM GEAR
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
P
0.092
0.50 0.23
o. 112
0.50 0.25
0.136
0.51 0.29
0.162
0.51 0.32
0.187
0.51 0.35
0.219
0.52 0.38
0.260
0.52 0.42
0.313
0.52 0.47
P
= - O. 50)
17
14
G
(X
G
P
G
PINION TEETH
21
26
P
G
P
G
P
0,117
0.55 0.34
0.140
0.55 0.37
0.171
0.55 0.41
0.214
0.55 0.45
0.276
0.56 0.50
0.132
0.58 0.43
O. 174
0.58 0.48
0.245
0.58 0.53
35
55
G
P
G
P
135
G
o. 100
0.51
0.26
O. 124
0.52 0.29
O. 149
0.52 0.33
0.174
0.52 0.36
0.206
0.53 0.39
0.247
0.53 0.43
0.302
0.53 0.48
0.109
0.53 0.30
0.133
0.53 0.34
0.157
0.54 0.36
0.189
0.54 0.40
0.231
0.54 0.44
0.290
0.55 0.49
O. 124
0.56 0.38
0.154
0.56 0.42
O. 197
0.57 0.46
0.263
0.57 0.51
O. 140
0.60 0.49
0.216
0.60 0.55
0.150
0.62 0.57
I AND J FACTORS FOR:?
20.0
30.0
0.250
EQUAL
GEAR
TEETH
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
ADDENDUM ( x 1= x = O)
2.250 WHOLE DEPTH FACTOR
0.024 TOOTH THINNING FOR BACKLASH
LOADED AT TIP
14
12
P
G
u
u
J
u
u
17 I
J
21 I
u
u
J
u
u
u
u
u
u
u
u
u
u
P
17
G
P
G
PINION TEETH
21
26
P
G
P
G
P
0.132
0.44 0.44
0.148
0.45 0.46
O. 170
0.45 0.48
0.200
0.46 0.50
0.245
0.47 0.53
0.139
0.49 0.49
0.174
0.50 0.51
0.231
0.51 0.54
35
55
G
P
G
P
135
G
12 I
J
14 I
26 I
J
35 I
J
55 I
J
135 I
J
0.125
0.39 0.39
0.139
0.39 0.41
0.154
0.40 0.43
0.169
0.41 0.44
0.189
0.41 0.46
0.215
0.42 0.49
0.250
0.43 0.51
O. 128
0.41 0.41
O. 144
0.42 0.43
0.159
0.43 0.45
0.180
0.43 0.47
0.208
0.44 0.49
0.248
0.45 0.52
0.135
0.46 0.46
0.158
0.47 0.48
0.190
0.48 0.50
0.240
0.49 0.53
0.145
0.52 0.52
0.210
0.53 0.55
0.151
0.56 0.56
1 The letter ?U? indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
39
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
908-B89
m
A G M A 908-B
Ob87575 000307L 698
=
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:
20.0
DEG. PRESSURE ANGLE
30.0
DEG. HELIX ANGLE
0.250
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION ( x
25 PERCENT SHORT ADDENDUM GEAR
2.250
WHOLE DEPTH FACTOR
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.25)
(x2 =
- 0.25)
PINION TEETH
GEAR
TEETH
P
12 I
J
14 I
17
21
26
35
55
135
14
12
G
0.115
0.42
0.30
0.130
0.43
0.32
0.149
0.43
0.35
0.169
0.44
0.37
o. 188
0.44
0.39
0.213
0.45
0.42
0.245
0.45 0.44
0.286
0.46
0.48
J
I
J
I
J
I
J
I
J
I
J
I
J
P
17
G
P
21
P
G
26
G
P
35
G
P
55
G
P
135
G
P
G
o. 119
0.44
0.33
O. 138
0.45
0.35
0.158
0.45
0.38
0.177
0.45
0.40
0.202
0.46
0.42
0.236
0.46
0.45
0.280
0.47
0.48
0.124
0.46 0.36
0.144
0.47
0.39
0.163
0.47
0.41
0.189
0.47
0.43
0.224
0.48
0.46
O. 272
0.49
0.49
O. 129
0.48
0.39
0.148
0.48
0.42
0.174
0.49
0.44
0.210
0.49
0.47
0.263
0.50
0.50
0.133
0.50
0.42
o. 159
0.50 0.45
0.196
0.51 0.48
0.253
0.51 0.51
0.138
0.52
0.46
O. 176
0.52 0.49
0.239
0.53
0.52
O. 144
0.54
0.50
0.213
0.55 0.53
0.151
0.57
0.55
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
I AND J FACTORS FOR:
20.0
DEG. PRESSURE ANGLE
30.0
DEG. HELIX ANGLE
0.250
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION
(X
= 0.50)
50 PERCENT SHORT ADDENDUM GEAR
(X
=
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
2.250
O. 024
- O. 50)
PINION TEETH
12
P
14
G
0.098
0.47
0.24
0.117
0.48
0.26
O. 141
0.48
0.29
0.166
0.48
0.32
0.190
0.48
0.34
o. 220
0.49
0.37
0.259
0.49
0.40
0.309
0.49
0.44
P
17
G
0.106
0.48
0.27
0.128
0.49
0.30
0.153
0.49
0.32
0.176
0.49
0.35
0.207
0.49
0.38
0.246
0.50
0.41
0.299
0.50
0.45
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
P
21
G
0.114
0.50 0.30
0.137
0.50
0.33
0.160
0.50 0.36
0.190
0.51 0.39
0.231
0.51 0.42
0.287
0.51
0.46
P
26
G
P
o. 121
0.51
0.34
0.143
0.51 0.37
O. 173
0.52 0.40
0.214
0.52
0.43
0.274
0.52
0.47
35
G
0.127
0.52
0.37
O. 156
0.52
0.40
0.198
0.53
0.44
0.262
0.53
0.48
P
55
G
0.134
0.54
0.42
0.175
0.54
0.45
0.244
0.54
0.49
40
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
P
135
G
0.141
0.55
0.47
0.215
0.56
0.51
P
G
0.150
0.57
0.53
908-B89
W 0687575 0003072 524 W
A G H A 708-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
1 AND J FACTORS FOR:’
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM (X 1= x = O )
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
25.0
0.0
0.270
2.350
0.024
PINION TEETH
GEAR
TEETH
12
14
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
21
17
G
P
G
P
26
G
P
35
G
P
55
G
P
135
G
P
G
12 I
J
14 I
17
21
26
35
55
135
J
I
J
I
J
I
J
I
J
I
J
I
J
0.086
0.28
0.28
0.091
0.28
0.30
0.095
0.28
0.31
o. 100
0.28
0.33
O. 106
0.28
0.34
0.113
0.28
0.36
0.123
0.28
0.38
0.090
0.30
0.30
0.096
0.30 0.31
o. 101
0.30
0.33
0.109
0.30
0.34
0.119
0.30 0.36
0.132
0.30 0.38
0.092
0.31
0.31
0.099
0.31 0.33
O. 108
0.31 0.34
0.121
0.31 0.36
0.139
0.31 0.38
0.094
0.33
0.33
O. 104
0.33
0.34
0.119
0.33 0.36
O . 142
0.33 0.38
0.095
0.34
0.34
0.112
0.34
0.36
0.141
0.34 0.38
0.095
0.36
0.36
0.131
0.36 0.38
0.096
0.38
0.38
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
I AND J FACTORS FOR:
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
0.270
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION (x
25.0
0.0
25 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.25)
2.350
0.024
(x2 =
- 0.25)
PINION TEETH
GEAR
TEETH
12 I
14
17
21
26
35
55
135
J
I
J
I
J
I
J
I
J
I
J
I
J
I
J
12
P
14
G
0.091
0.32 0.20
0.095
0.32
0.22
0.100
0.32
0.25
O. 106
0.32
0.27
0.111
0.32 0.29
0.118
0.32
0.31
O. 127
0.32
0.34
0.138
0.32
0.37
P
17
G
0.093
0.33
0.22
0.099
0.33 0.25
O. 106
0.33
0.27
0.112
0.33
0.29
o. 120
0.33
0.31
0.131
0.33
0.34
O. 145
0.33
0.37
AGMA
P
26
21
G
0.094
0.34 0.25
o. 102
0.34
0.27
o. 109
0.34
0.29
0.119
0.34
0.31
O . 133
0.34
0.34
0.151
0.34
0.37
P
G
P
0.095
0.36
0.27
O. 103
0.36
0.29
0.115
0.36
0.31
0.131
0.36
0.34
0.153
0.36
0.37
35
G
0.095
0.36
0.29
0.108
0.36
0.31
O . 126
0.36
0.34
O . 153
0.36
0.37
P
55
G
0.096
0.37
0.31
0.116
0.37
0.34
0.148
0.37
0.37
135
G
0.096
0.38
0.34
0.135
0.38
0.37
P
G
0.096
0.39 0.37
908-B89
41
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
P
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
m
A G H A 908-B
Ob87575 0003073 4b0
m
Geometry Factors for Determiniig the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
25.0
DEG. PRESSURE ANGLE
0.0
DEG. HELIX ANGLE
0.270 TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x
50 PERCENT SHORT ADDENDUM GEAR
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
14
12
P
G
T
T
T
2.350
WHOLE DEPTH FACTOR
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= O. 50)
(x2 = - 0.50)
17
P
G
T
T
T
T
T
T
T
T
T
P
G
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
PINION TEETH
21
26
P
G
P
G
P
0.096
0.40 0.23
O. 106
0.40 0.25
o. 120
0.40 0.28
O. 139
0.40 0.32
O. 167
0.40 0.36
0.096
0.40 0.28
0.118
0.40 0.32
o. 155
0.40 0.36
0.096
0.40 0.25
0.110
0.40 0.28
0.131
0.40 0.32
O. 163
0.40 0.36
35
55
G
P
G
0.096
0.40 0.32
O. 138
0.40 0.36
P
135
G
0.096
0.40 0.36
1 The letter “T” indicates a gear tooth combination which produces pointed teeth with a top land less than 0.3/Pnd in one or both
components and should be avoided. See Section 7.
I AND J FACTORS FOR:’
25.0
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
0.270 TOOL EDGE RADIUS
EQUAL ADDENDUM ( x 1= x = O)
2.350
WHOLE DEPTH FACTOR
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT HIGHEST POINT OF SINGLE TOOTH CONTACT
0.0
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
14
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
P
17
G
0.086
0.33 0.33
0.091
0.33 0.36
0.095
0.33 0.39
o. 100
0.33 0.41
O. 106
0.34 0.44
0.113
0.34 0.47
0.123
0.35 0.51
P
G
0.090
0.36 0.36
0.096
0.36 0.39
o. 101
0.37 0.42
0.109
0.37 0.45
0.119
0.38 0.48
0.132
0.38 0.52
PINION TEETH
21
26
P
G
P
G
P
O. 092
0.39 0.39
0.099
0.40 0.42
o. 108
0.40 0.45
o. 121
0.41 0.49
0.139
0.42 0.53
0.095
0.46 0.46
0.112
0.47 0.50
0.141
0.48 0.54
0.094
0.43 0.43
0.104
0.43 0.46
0.119
0.44 0.49
0.142
0.45 0.53
35
55
G
P
G
0.095
0.51 0.51
0.131
0.53 0.56
P
135
G
0.096
0.57 0.57
1 The letter “U”indicates a gear tooth combination which produces a n undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
42
...
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
..
908-B89
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
?
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
m
A G M A 908-B
Ob87575 000307Y 3T7
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
’
I AND J FACTORS FOR:
25.0
DEG. PRESSURE ANGLE
0.0
DEG. HELIX ANGLE
0.270 TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION (x
25 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT HIGHEST POINT OF SINGLE TOOTH CONTACT
= 0.25)
2.350
0.024
(x2 =
- 0.25)
PINION TEETH
GEAR
TEETH
12 I
14
17
21
26
35
55
135
I
J
I
J
I
J
I
J
I
J
I
J
I
J
I
J
12
P
14
G
P
17
G
P
21
G
P
26
G
P
35
G
P
55
G
P
135
G
0.091
0.38
0.22
0.095
0.38
0.25
o. 100
0.38
0.29
O. 106
0.38
0.32
0.111
0.39
0.35
0.118
0.39
0.38
O. 127
0.39
0.42
0.093
0.40
0.25
0.099
0.40
0.29
0.106
0.41
0.32
o. 112
0.41 0.35
0.120
0.41 0.39
O. 131
0.42
0.43
0.094
0.43
0.29
o. 102
0.43
0.33
o. 109
0.44
0.36
0.119
0.44 0.39
0.133
0.44
0.44
0.095
0.46
0.33
0.103
0.46
0.36
0.115
0.47
0.40
0.131
0.47 0.44
0.095
0.48
0.37
0.108
0.49
0.41
0.126
0.49
0.45
0.096
0.51 0.41
0.116
0.52
0.46
0.096
0.55 0.47
0.138
0.40 0.47
0.145
0.42 0.48
0.151
0.45 0.49
0.153
0.48
0.49
0.153
0.50
0.50
O . 148
0.53
0.51
0.135
0.56
0.53
P
G
0.096
0.59
0.55
I AND J FACTORS FOR:’
25.0
DEG. PRESSURE ANGLE
0.0
DEG. HELIX ANGLE
0.270
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT HIGHEST POINT OF SINGLE TOOTH CONTACT
= 0.50)
(X
50 PERCENT SHORT ADDENDUM GEAR
(x2 =
2.350
0.024
- 0.50)
PINION TEETH
GEAR
TEETH
12
14
P
G
12 I
J
14 I
T
T
J
T
J
21 I
J
17
P
G
T
T
T
T
T
T
T
T
T
21
P
G
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
P
26
G
P
35
G
P
55
G
P
135
G
P
G
17 I
T
0.096
0.52 0.27
O. 106
0.52 0.30
0.120
0.52 0.35
0.096
0.53
0.31
0.110
0.53
0.35
0.096
0.55 0.36
T
T
0.139
0.52 0.40
0.131
0.54
0.41
0.118
0.56
0.42
T
T
O. 167
0.53
0.46
0.163
0.54
0.47
0.56
26 I
I
J
35 I
J
55 I
J
135 I
J
o. 155
0.48
0.096
0.58
0.43
O. 138
0.58
0.50
0.096
0.60
0.53
1 The letter “T” indicates a gear tooth combination which produces pointed teeth with a top land less than O. 31Pnd in one or both
components and should be avoided. See Section 7.
‘
AGMA
43
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
908-B89
m 0687575
AGHA 908-8
0003075 233
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:'
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
2.350
0.024
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM (x 1= x = O)
25.0
10.0
0.270
PINION TEETH
GEAR
TEETH
12 I
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
J
P
G
u
u
u
u
u
u
u
u
14 I
17
21
26
35
55
135
J
I
J
I
J
I
J
I
J
I
J
I
J
u
u
u
u
u
u
u
u
P
G
O. 129
0.47
0.47
O. 144
0.48
0.51
0.159
0.48 0.55
0.175
0.49
0.58
0.195
0.50
0.61
0.221
0.51 0.65
0.257
0.52
0.70
P
G
P
0.133
0.52
0.52
O. 149
0.52 0.55
0.165
0.53 0.58
0.186
0.54
0.62
0.215
0.55
0.66
0.255
0.56
0.71
P
G
55
35
26
21
17
14
12
G
P
G
P
135
G
0.136
0.56
0.56
0.152
0.57
0.59
0.175
0.57 0.63
0.206
0.58
0.67
0.251
0.139
0.60 0.60
0.162
0.61 0.64
0.195
0.62
0.68
0.246
0.143
0.64 0.64
O. 178
0.65
0.69
0.236
0.148
0.70
0.70
0.215
0.60
0.63
0.67
0.71
0.72
0.73
0.74
0.75
P
G
0.154
0.76
0.76
1 The letter "U" indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
I AND J FACTORS FOR:
2.350
WHOLE DEPTH FACTOR
DEG. PRESSURE ANGLE
0.024
TOOTH THINNING FOR BACKLASH
DEG. HELIX ANGLE
LOADED AT TIP
0.270
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION (x = 0.25)
25.0
10.0
25 PERCENT SHORT ADDENDUM GEAR
(X2
= - 0.25)
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
P
G
o. 120
0.53
0.33
O. 136
0.54
0.37
0.155
0.54
0.41
0.175
0.55
0.46
0.194
0.55
0.49
0.219
0.56
0.54
0.251
0.56
0.59
0.293
0.57
0.65
P
G
0.125
0.56
0.38
0.143
0.57
0.42
0.163
0.57
0.46
O. 183
0.58
0.50
0.208
0.58 0.55
0.242
0.59
0.60
0.286
0.60
0.66
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
P
G
0.129
0.60 0.43
0.149
0.60
0.47
O. 168
0.61 0.51
0.194
0.61 0.56
0.229
0.62 0.61
0.278
0.63
0.67
P
35
26
21
17
14
12
G
O. 134
0.63 0.48
0.153
0.64 0.52
0.179
0.64
0.57
0.216
0.65
0.62
0.269
0.66
0.68
P
G
O. 137
0.66 0.53
0.164
0.67 0.57
0.201
0.67
0.63
0.259
0.68
0.69
P
55
G
O. 142
0.69
0.59
0.180
0.70 0.64
0.244
0.71 0.71
44
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
P
135
G
0.147
0.73 O.
0.218
0.74
0.72
P
G
0.154
0.78
0.74
9 0 8-B 8 9
Ob87575 0 0 0 3 0 7 b L 7 T
A G I A 908-B
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Z AND J FACTORS FOR:’
1
25.0
DEG. PRESSURE ANGLE
10.0
DEG. HELIX ANGLE
0.270 TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION
(X
50 PERCENT SHORT ADDENDUM GEAR
(X
GEAR
TEETH
12
14
2 =
17
P
G
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
P
G
T
T
T
T
T
T
T
T
T
P
G
12 I
J
14 I
T
T
J
T
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
2.350 WHOLE DEPTH FACTOR
0.024 TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= O. 50)
- O. 50)
PINION TEETH
21
26
P
G
P
G
P
0.126
0.69 0.40
0.148
0.69 0.44
0.178
0.70 0.50
0.220
0.70 0.56
0.280
0.70 0.64
O. 138
0.73 0.52
O. 180
0.74 0.S9
0.249
0.74 0.67
0.132
0.71 0.45
0.161
0.71 0.51
0.203
0.72 0.57
0.267
0.72 0.65
35
55
G
P
135
G
O. 145
0.76 0.61
0.220
0.76 0.69
P
G
O. 153
0.79
0.72
1 The letter “T” indicates a gear tooth combination which produces pointed teeth with a top land less than 0.3/Pnd in one or both
components and should be avoided. See Section 7.
I AND J FACTORS FOR:’
25.0
15.0
0.270
EQUAL
I
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
ADDENDUM ( x 1= x = O)
14
12
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
35 I
J
55 I
J
135 I
J
1
2.350 WHOLE DEPTH FACTOR
0.024 TOOTH THINNING FOR BACKLASH
LOADED AT TIP
P
17
G
0.130
0.49 0.49
O. 144
0.50 0.53
0.160
0.50 0.56
0.175
0.51 0.59
0.195
0.52 0.63
o. 222
0.52 0.67
0.257
0.53 0.72
P
G
0.133
0.53 0.53
O. 149
0.54 0.57
0.165
0.55 0.60
0.186
0.55 0.64
0.215
0.56 0.68
0.255
0.57 0.72
PINION TEETH
21
26
P
G
P
G
P
0.137
0.58 0.58
O. 153
0.58 0.61
0.175
0.59 0.64
0.206
0.60 0.68
0.251
0.61 0.73
0.143
0.66 0.66
0.178
0.67 0.70
0.236
0.68 0.75
O. 140
0.61 0.61
0.163
0.62 0.65
0.195
0.63 0.69
0.246
0.64 0.74
35
55
G
P
G
O. 148
0.71 0.71
0.214
0.72 0.76
P
135
G
0.154
0.78 0.78
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
1
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
45
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
90 8-B 89
M Ob87575 0003077 OOb M
A G M A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:
25.0
DEG. PRESSURE ANGLE
15.0
DEG. HELIX ANGLE
0.270 TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION ( x
25 PERCENT SHORT ADDENDUM GEAR
12
P
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 J
J
135 I
J
0.122
0.55 0.35
O. 137
0.56 0.39
O. 155
0.56 0.43
0.175
0.57 0.48
0.195
0.57 0.51
0.219
0.57 0.55
0.251
0.58 0.61
0.292
0.59 0.66
G
P
( ~ =2 - 0.25)
17
14
GEAR
TEETH
2.350
WHOLE DEPTH FACTOR
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.25)
G
0.126
0.58 0.39
0.144
0.59 0.44
0.164
0.59 0.48
O. 183
0.60 0.52
0.208
0.60 0.56
0.241
0.61 0.61
0.285
0.62 0.67
P
G
0.130
0.62 0.45
O. 149
0.62 0.49
0.169
0.63 0.53
0.195
0.63 0.57
0.229
0.64 0.62
O. 277
0.64 0.68
PINION TEETH
26
21
P
G
P
G
P
0.134
0.65 0.50
0.153
0.65 0.54
O. 179
0.66 0.58
0.215
0.66 0.63
0.268
0.67 0.70
0.142
0.71 0.60
0.180
0.71 0.66
0.244
0.72 0.72
0.138
0.68 0.55
0.164
0.68 0.59
0.201
0.69 0.64
0.258
0.70 0.71
35
55
G
P
G
0.147
0.75 0.67
0.218
0.75 0.74
P
135
G
0.153
0.79 0.76
I AND J FACTORS FOR:'
25.0 DEG. PRESSURE ANGLE
15.0 DEG. HELIX ANGLE
0.270 TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x
50 PERCENT SHORT ADDENDUM GEAR
GEAR
TEETH
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
14
P
G
T
T
T
T
2.350
WHOLE DEPTH FACTOR
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= O. 50)
( ~ =2 - 0.50)
17
P
G
T
T
T
T
T
T
P
G
PINION TEETH
21
26
P
G
P
G
P
0.127
0.71 0.42
O. 149
0.71 0.46
O. 179
0.71 0.52
0.220
0.72 0.58
0.279
0.72 0.65
0.138
0.75 0.54
0.180
0.75 0.60
0.249
0.75 0.68
35
55
G
P
G
P
135
G
o. 121
0.69
0.36
O. 144
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
0.69 0.41
0.166
0.69 0.45
0.196
0.69 0.50
0.236
0.70 0.57
0.292
0.70 0.64
0.133
0.73 0.47
0.162
0.73 0.53
0.203
0.73 0.59
0.266
0.74 0.67
O. 145
0.77 0.62
0.219
0.78 0.70
0.152
0.80 0.73
i The letter "T" indicates a gear tooth combination which produces pointed teeth with a top land less than 0.3/Pnd in one or both
components and should be avoided. See Section 7.
AGMA
.
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
908-B89
46
p-w
:
-
','i
-
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
D Ob87575 0003078 T 4 2 D
A G M A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM ( x 1= x = O )
25.0
20.0
0.270
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
2.350
0.024
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
P
14
G
0.128
0.47
0.47
0.140
0.47
0.50
0.154
0.48
0.53
0.169
0.48
0.56
0.184
0.49
0.59
0.202
0.49
0.62
0.227
0.50
0.66
0.258
0.51 0.70
P
17
G
0.131
0.50
0.50
O. 145
0.51 0.54
0.161
0.51
0.57
O. 176
0.52 0.60
0.196
0.53
0.63
0.222
0.53
0.67
0.257
0.54
0.71
P
21
G
P
0.134
0.54
0.54
o. 150
0.55 0.58
O. 166
0.55 0.60
0.187
0.56
0.64
0.215
0.57
0.67
0.255
0.58
0.72
26
G
0.137
0.58
0.58
0.153
0.59 0.61
O. 176
0.60 0.64
0.206
0.60 0.68
0.251
0.62
0.72
P
35
G
P
55
G
P
135
G
P
G
O. 140
0.62
0.62
O. 163
0.62 0.65
0.196
0.63 0.69
0.246
0.65 0.73
0.144
0.66
0.66
O. 178
0.67
0.70
0.236
0.68
0.74
0.148
0.71 0.71
0.214
0.72 0.75
O. 53
0.76
0.76
I AND J FACTORS FOR:
25.0
DEG. PRESSURE ANGLE
20.0
DEG. HELIX ANGLE
0.270
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION ( x
25 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.25)
2.350
0.024
(x2 =
- 0.25)
PINION TEETH
GEAR
TEETH
12 I
.
I
14 I
17
21
26
35
55
135
J
I
J
I
J
I
J
I
J
I
J
I
J
12
P
14
G
O. 123
0.56
0.37
0.138
0.56
0.40
0.156
0.57
0.45
O. 176
0.57
0.49
0.195
0.58
0.52
0.219
0.58
0.56
0.250
0.59
0.61
0.290
0.59
0.66
P
17
G
O. 127
0.59
0.41
O. 145
0.59
0.45
O. 164
0.60
0.49
0.184
0.60
0.53
0.208
0.61
0.57
0.241
0.61
0.61
0.284
0.62
0.67
AGMA
P
21
G
0.131
0.62 0.46
o. 150
0.62
0.50
0.169
0.63
0.54
0.195
0.63
0.58
0.229
0.64
0.62
0.276
0.65 0.68
P
26
G
0.135
0.65 0.51
0.154
0.65 0.54
0.180
0.66 0.59
0.215
0.66 0.63
0.267
0.67 0.69
P
35
G
O. 138
0.67
0.55
0.164
0.68
0.59
0.201
0.69
0.64
0.257
0.69
0.70
P
55
G
0.143
0.70
0.60
o. 180
0.71 0.65
0.243
0.72 0.71
P
135
G
O. 147
0.74
0.67
0.217
0.75 0.73
G
0.153
0.78
0.75
9 O 8-B89
47
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
P
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
W Ob87575 0003079 989
A L M A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:’
25.0
DEG. PRESSURE ANGLE
20.0
DEG. HELIX ANGLE
0.270 TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x
2.350
WHOLE DEPTH FACTOR
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.50)
50 PERCENT SHORT ADDENDUM GEAR
=
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
14
12
17
P
G
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
P
G
T
T
T
(X
P
G
0.123
0.68 0.37
O. 145
0.69 0.42
O. 167
0.69 0.46
0.197
0.69 0.51
0.236
0.70 0.57
0.290
0.70 0.64
- O. 50)
PINION TEETH
21
26
P
G
P
G
P
0.129
0.70 0.43
0.150
0.71 0.47
0.179
0.71 0.52
0.219
0.71 0.58
0.277
0.72 0.65
0.139
0.74 0.54
O. 180
0.74 0.61
0.248
0.75 0.68
0.134
0.72 0.48
O. 162
0.72 0.53
0.203
0.73 0.59
0.265
0.73 0.66
35
55
G
P
G
0.145
0.76 0.62
0.219
0.77 0.70
P
135
G
0.152
0.79 0.72
1 The letter “T” indicates a gear tooth combination which produces pointed teeth with a top land less than 0.3/Pnd in one or both
components and should be avoided. See Section 7.
I AND J FACTORS FOR:
25.0
25.0
0.270
EQUAL
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
ADDENDUM ( x 1= x = O)
2.350
WHOLE DEPTH FACTOR
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
14
GEAR
TEETH
12
P
12 I
J
14 I
J
17 I
J
23 I
J
26 I
J
35 I
J
55 I
J
135 I
J
O. 129
0.47 0.47
0.141
0.47 0.50
0.155
0.48 0.53
0.170
0.48 0.55
0.185
0.49 0.58
0.203
0.49 0.61
0.227
0.50 0.64
0.259
0.51 0.68
G
P
17
G
0.132
0.50 0.50
0.146
0.51 0.53
0.162
0.51 0.56
0.177
0.52 0.58
O. 197
0.52 0.61
0.223
0.53 0.65
0.258
0.54 0.68
AGMA
P
G
0.135
0.54 0.54
0.151
0.54 0.57
0.166
0.55 0.59
0.188
0.56 0.62
0.216
0.56 0.65
0.255
0.57 0.69
PINION TEETH
26
21
P
G
P
G
P
O. 138
0.57 0.57
0.154
0.58 0.60
0.176
0.58 0.63
0.207
0.59 0.66
0.251
0.60 0.70
O. 144
0.64 0.64
0.178
0.65 0.67
0.235
0.66 0.71
0.141
0.60 0.60
0.163
0.61 0.63
O. 196
0.62 0.67
0.246
0.63 0.70
48
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
55
35
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
G
P
G
0.148
0.68 0.68
0.213
0.69 0.72
P
135
G
O. 152
0.73
0.73
908-B89
A G M A 908-B
Ob87575 0003080 bTO
=
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
)
I AND J FACTORS FOR:
25.0
DEG. PRESSURE ANGLE
25.0
DEG. HELIX ANGLE
0.270
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
(X
25 PERCENT SHORT ADDENDUM GEAR
(x2 =
2.350
0.024
= 0.25)
- 0.25)
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
12
P
14
G
O. 125
0.55
0.38
0.139
0.56
0.41
0.157
0.56
0.45
O.177
0.57
0.48
0.195
0.57
0.52
0.219
0.57
0.55
O. 249
0.58
0.59
0.288
0.59
0.64
P
17
G
o. 128
0.58
0.42
0.146
0.58 0.45
0.165
0.59
0.49
O. 184
0.59
0.52
0.208
0.60
0.56
0.240
0.60
0.60
0.281
0.61 0.65
P
21
G
P
0.132
0.61
0.46
o. 151
0.61
0.50
O. 170
0.61 0.53
0.195
0.62
0.57
0.228
0.62
0.61
O. 274
0.63
0.66
26
G
P
0.136
0.63
0.51
0.154
0.64 0.54
0.180
0.64
0.57
0.215
0.65 0.62
0.265
0.65
0.67
35
G
0.139
0.65
0.54
0.164
0.66
0.58
0.201
0.66
0.63
0.256
0.67
0.68
P
55
G
O. 143
0.68
0.59
0.180
0.69
0.64
O.242
0.69
0.69
P
135
G
0.147
0.71 0.65
0.216
0.72
0.70
P
G
o. 152
0.74
0.72
I AND J FACTORS FOR:’
25.0
DEG. PRESSURE ANGLE
25.0
DEG. HELIX ANGLE
0.270
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION (x
50 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= O. 50)
2.350
0.024
(x2 =
- 0.50)
PINION TEETH
GEAR
TEETH
12
14
P
G
J
T
T
14 I
J
17 I
T
T
T
T
T
T
T
T
T
T
P
17
G
P
21
G
P
26
G
P
35
G
55
G
P
P
135
G
P
G
12 I
J
21 I
J
26 I
J
0.140
35 I
J
55 I
J
135 I
J
)
0.119
0.65 0.33
T
T
T
T
0.65
0.38
0.163
0.65 0.42
0.184
0.65
0.46
0.213
0.66
0.50
0.249
0.66
0.55
0.298
0.66
0.61
0.125
0.66
0.38
O. 147
0.67
0.43
O. 168
0.67
0.46
0.197
0.67
0.51
0.235
0.67
0.56
0.287
0.68
0.62
0.130
0.68
0.43
0.151
0.68 0.47
0.180
0.69
0.52
0.219
0.69
0.57
0.275
0.69
0.63
0.135
0.70
0.48
O. 163
0.70
0.53
0.203
0.70 0.58
0.263
0.70
0.64
O. 140
0.71
0.54
o. 180
0.72 0.59
0.246
0.72
0.66
0.145
0.73 0.61
0.218
0.73 0.67
0.151
0.75
0.70
1 The letter “T” indicates a gear tooth combination which produces pointed teeth with a top land less than 0.3/Pnd in one or both
components and should be avoided. See Section 7.
AGMA
49
908-B89
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
I
m
A G M A 908-B
Ob87575 0003081 537
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
TOOL EDGE RADIUS
EQUAL ADDENDUM (x 1= x 2= O)
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
25.0
30.0
0.270
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
21
26
35
55
135
2.350
0.024
J
I
J
I
J
I
J
I
J
I
J
14
12
P
G
0.130
0.46
0.46
0.142
0.47
0.49
0.156
0.47
0.51
O. 171
0.48
0.54
O. 186
0.48
0.56
0.204
0.49
0.58
0.228
0.49
0.61
0.259
0.50
0.64
P
17
G
0.133
0.49
0.49
O. 147
0.50
0.52
O. 163
0.50
0.54
0.178
0.51 0.56
0.198
0.51 0.59
0.223
0.52
0.61
0.257
0.53
0.64
P
21
G
P
0.136
0.52
0.52
o. 151
0.53 0.55
0.167
0.53
0.57
0.188
0.54
0.59
0.216
0.54
0.62
0.255
0.55
0.65
26
G
0.138
0.55 0.55
0.154
0.56
0.57
0.176
0.56
0.60
0.207
0.57
0.62
0.251
0.58
0.66
P
35
G
0.141
0.58
0.58
0.163
0.58
0.60
0.196
0.59
0.63
0.245
0.60
0.66
P
55
G
O. 144
0.61 0.61
O. 178
0.62
0.64
0.234
0.62
0.67
P
135
G
O. 147
0.64
0.64
0.212
0.65 0.68
P
G
0.151
0.68
0.68
I AND J FACTORS FOR:
DEG. PRESSURE ANGLE
DEG. HELIX ANGLE
0.270
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION ( x
25.0
30.0
25 PERCENT SHORT ADDENDUM GEAR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
= 0.25)
2.350
0.024
(x2 =
- 0.25)
PINION TEETH
GEAR
TEETH
12 I
14
17
21
26
35
J
I
J
I
J
I
J
I
J
I
J
55 I
J
135 I
J
12
P
14
G
O. 127
0.54
0.38
0.141
0.54
0.41
0.159
0.54 0.44
O. 177
0.55
0.47
0.195
0.55
0.50
0.218
0.56
0.53
0.247
0.56
0.57
0.285
0.56
0.61
P
17
G
0.130
0.56
0.42
0.147
0.56
0.45
0.166
0.57
0.48
0.184
0.57
0.51
0.208
0.57
0.54
0.238
0.58 0.57
0.279
0.58
0.61
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
P
21
G
0.133
0.58
0.46
0.152
0.58
0.49
0.170
0.59
0.51
O. 194
0.59
0.54
0.227
0.60
0.58
0.272
0.60
0.62
P
26
G
0.137
0.60
0.49
0.155
0.61 0.52
0.180
0.61 0.55
0.214
0.61 0.59
0.263
0.62 0.63
P
35
G
O. 140
0.62
0.53
O. 164
0.63
0.56
0.200
0.63
0.59
0.254
0.64
0.64
P
55
G
O. 143
0.64
0.57
O. 180
0.65
0.60
0.240
0.65
0.65
50
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
P
135
G
O. 147
0.67
0.61
0.215
0.67
0.66
P
G
0.151
0.70 0.67
9 O 8-B 8 9
A G H A 908-B
m
Ob87575 0003082 473
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
1
I AND J FACTORS FOR:
2.350
WHOLE DEPTH FACTOR
DEG. PRESSURE ANGLE
0.024
TOOTH THINNING FOR BACKLASH
DEG. HELIX ANGLE
LOADED AT TIP
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( x = O. 50)
25.0
30.0
0.270
( ~ =2 - 0.50)
50 PERCENT SHORT ADDENDUM GEAR
PINION TEETH
GEAR
TEETH
P
12 I
14
17
21
26
35
55
135 I
J
P
G
P
21
G
P
26
G
P
P
55
G
P
135
G
P
G
o. 122
0.62
0.34
O. 142
0.38
O. 164
0.62
0.42
0.185
0.62
0.45
O. 127
0.63
0.39
O. 148
0.63 0.42
0.169
0.63
0.46
0.132
0.64 0.43
0.152
0.64 0.46
0.136
0.65
0.47
0.225
0.61 0.48
0.212
0.62
0.48
O. 196
0.64
0.49
0.180
0.65 0.50
O. 163
0.66
0.51
0.67
0.259
0.62
0.52
0.247
0.63
0.53
0.233
0.64
0.54
0.218
0.65
0.55
0.202
0.66
0.56
O. 179
0.67
0.57
0.145
0.68
0.58
O. 303
0.62 0.57
0.294
0.63
0.58
0.283
0.64
0.59
0.272
0.65 0.60
0.261
0.66
0.61
0.244
0.67
0.62
0.216
0.69
0.64
0.62
STUB TOOTH (SYKES FORM
DEG. PRESSURE ANGLE TRANSVERSE
30.
DEG. HELIX ANGLE
0.157
TOOL EDGE RADIUS
EQUAL ADDENDUM (x 1= x = O>
O. 140
0.52
o. 151
0.65
0.70
ADDENDUM FACTOR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
0.8
1.900
0.024
20.0
GEAR
TEETH
PINION TEETH
12
14
P
G
12 I
J
14 I
u
u
J
u
17
P
G
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
u
17 I
21
26
35
55
135
b
35
G
I AND J FACTORS FOR:’
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
)
G
0.117
0.60
0.30
0.134
0.61 0.34
O. 155
0.61
0.37
O. 177
0.61 0.41
o. 198
0.61 0.44
J
I
J
I
J
I
J
I
J
I
J
I
J
17
14
12
J
I
J
I
J
I
J
I
J
I
J
P
21
G
P
35
26
P
G
G
P
55
G
P
135
G
u
0.115
0.37
0.37
O. 129
0.38
0.39
O. 143
0.38
0.40
0.163
0.39
0.41
0.189
0.40 0.43
0.119
0.39 0.39
0.133
0.40
0.41
0.153
0.40 0.42
0.181
0.41 0.44
0.122
0.41 0.41
O. 143
0.42
0.43
0.173
0.43 0.44
0.127
0.43 0.43
0.158
0.44
0.45
0.132
0.46
0.46
u
0.226
0.41 0.45
0.223
0.43 0.46
0.219
0.44
0.47
0.211
0.46
0.47
0.193
0.47
0.48
P
G
O. 139
0.50
0.50
1 The letter “U” indicates a gear tooth combination which produces an undercut tooth form in one or both components and should be avoided.
See Section 7 and Fig 7-1.
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
51
Licensee=Electric Boat/9993263100
Not for Resale, 06/07/2005 09:58:05 MDT
9 08-B89
m
AGNA 908-B
Ob87575 0003083 30T
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
I AND J FACTORS FOR:
ADDENDUM FACTOR
WHOLE DEPTH FACTOR
0.024
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
0.8
STUB TOOTH (SYKES FORM
1.900
20.0
DEG. PRESSURE ANGLE TRANSVERSE
30.0
DEG. HELIX ANGLE
0.157
TOOL EDGE RADIUS
25 PERCENT LONG ADDENDUM PINION ( x = 0.25)
25 PERCENT SHORT ADDENDUM GEAR
(x2 =
- 0.25)
PINION TEETH
GEAR
TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
P
17
14
12
G
O. 097
0.38
0.27
0.112
0.38
0.29
0.131
0.38
0.31
0.151
0.39
0.33
O. 171
0.39 0.34
0.197
P
G
P
21
P
G
35
26
P
G
G
P
55
G
P
135
G
G
o. 102
0.39
0.30
o. 120
0.39
0.32
O. 140
0.40
0.33
0.160
0.40
0.35
0.186
0.108
0.41 0.32
O. 127
0.41 0.34
0.147
0.41 0.36
0.172
0.113
0.42 0.35
0.132
0.43
0.37
0.158
0.118
0.44 0.37
0.143
0.40 0.36
0.229
0.41 0.37
0.219
0.42
0.38
0.207
0.43 0.39
0.194
0.44
0.39
O. 180
0.46
0.40 0.38
0.272
0.41 0.39
0.264
0.42 0.40
0.255
0.44 0.41
0.246
0.45
0.42
0.236
0.46
0.43
0.221
0.48
0.44
0.197
0.41
0.42
0.43
0.44
0.45
0.47
0.48
0.41
P
0.41
0.42
0.43
0.124
0.44
0.40
0.130
0.160
0.45
0.47
0.138
0.50
0.49
I AND J FACTORS FOR:
L L
ADDENDUM FACTOR
WHOLE DEPTH FACTOR
TOOTH THINNING FOR BACKLASH
LOADED AT TIP
0.8
1.900
0.024
STUB TOOTH SYKES FORM
DEG. PRESSUR ANG E TRANSVERSE
20.0
DEG. HELIX ANGLE
30.0
0.157
TOOL EDGE RADIUS
50 PERCENT LONG ADDENDUM PINION ( X = 0.50)
50 PERCENT SHORT ADDENDUM GEAR
(W
2 =
- O. SO)
PINION TEETH
12 I
J
14 I
J
17 I
J
21 I
J
26 I
J
35 I
J
55 I
J
135 I
J
P
G
0.069
0.41 0.21
0.089
0.41 0.23
O. 114
0.41 0.25
0.141
0.41 0.28
0.167
0.41 0.29
0.199
0.42
0.32
0.240
0.42
0.34
0.293
0.42
0.37
P
G
0.079
0.42
0.24
0.103
0.42
0.26
O. 129
0.42
0.28
0.154
0.42 0.30
0.186
0.43
0.32
0.227
0.43 0.35
0.283
0.43 0.38
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
P
26
21
17
14
12
G
0.090
0.43
0.27
0.114
0.43 0.29
0.138
0.43 0.31
0.170
0.43
0.33
0.212
0.44
0.36
0.270
0.44 0.39
P
G
P
35
G
P
55
G
P
135
G
o. 100
0.44
0.30
o. 122
0.44
0.32
0.153
0.44
0.34
0.195
0.45
0.37
0.257
0.45 0.40
0.108
0.45 0.33
0.137
0.45
0.35
0.179
0.46
0.38
0.244
0.46
0.41
52
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0.116
0.47
0.37
O. 158
0.47 0.39
0.226
0.47
0.43
P
G
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
GEAR
TEETH
O. 126
0.48
0.41
0.198
0.48 0.44
0.137
0.50
0.47
908-B 89
A G M A 708-B
= Ob87575
0003084 246
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Bibliography
1 Dolan, T. J. and Broghamer, E. L., A Photoelastic Study of the Stresses in Gear Tooth Fillets,
University of Illinois, Engineering Experiment Station, Bulletin No. 335, 1942
2
Lewis, W., Investigation of the Strength of Gear Teeth, Proc. of the Engineers Club, Philadelphia,
PA, 1893, pp.16-23.
3
Chong, T.H., and Kubo A., Simple Stress Formulae for a Thin-Rimmed Spur Gear, parts 1, 2 and 3,
ASME papers 84-DET-62, 63 and 64.
4
Errichello, R.,An Efficient Algorithm for Obtaining the Gear Strength Geometry Factor on a
Programmable Calculator, AGMA Paper No. P139.03, October 198 1
5
Errichello, R., An Efficient Algorithm for Obtaining the Gear Strength Geometry Factor for Shaper
Cut Gears, AGMA Paper N o . P139.05, October 1983
6
Errichello, R., Calc Program Finds Inverse of an Involute, Machine Design, Vol 51, No. 5 ,
March 8, 1979, p. 80
7
Wellauer, E. J., and Seireg, A., Bending Strength of Gear Teeth b y Cantilever Plate Theory, Journal
of Engineering for Industry, Trans. ASME, Series B, Vol. 82, 1960, pp. 213-222
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
AGMA
Copyright American Gear Manufacturers Association
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No reproduction or networking permitted without license from IHS
53
908-B 89
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A G M A 908-B
Ob87575 0003085 I182
=
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
(this page has been left blank)
AGMA
54
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
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No reproduction or networking permitted without license from IHS
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9 O 8-B 8 9
A G M A 908-B
W Ob87575 000308b 019
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Appendix A
Original Derivation of AGMA Geometry Factor for Pitting Resistance, I
This Appendix is not part of AGMA 908-B89, INFORMATION SHEET - Geometry Factors for
Determining the Pitting Resistance and Bending Strength for Spur, Helical and Herringbone Gear Teeth,
but is included for informational purposes only.
For helical gear teeth, at the operating pitch
diameter:
Al.
Purpose. This Appendix provides an
historical record for the original derivation of the
pitting resistance geometry factor, I , based on the
Hertzian theory for contact compressive stress
between two contacting cylinders as first
introduced in AGMA 229.06, June 1962.
where
A2. Derivation. The surface contact compressive
stress between two contacting cylinders is:
sc
=
where
Sc
4P
mb
= load per linear unit of contact length
b
= total width of contact band
where
R1
= radius of curvature of body 1
R2
= radius of curvature of body 2
= normal load in transverse plane
Wt
= tangential load in transverse plane
+t
= operating transverse pressure angle
@b
= base helix angle
L~~~ = minimum total length of lines of
contact
= surface contact compressive stress
P
WN
2
d
= operating pitch diameter of pinion
D
= operating pitch diameter of gear
E
Making proper substitutions and multiplying by -
1- P1
K1 - -
E1
= Cp
SC
,/y
F d+D2
cos+t sin+t Lmin d D F
(Eq A.lO)
Regrouping terms
where
El, E2 = modulus of elasticity for material
of cylinders 1 and 2
p1, ~2 = Poisson’s ratio for material of
cylinders 1 and 2
Combining Eqs A. 1 and A.2.
1
cos +t sin +t
(Eq A. 1 i)
but
cos+t sin+t - D 2
d+ D
-
55
AGMA
-
908-B89
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No reproduction or networking permitted without license from IHS
cos +t sin +t m G
2
mG+1
(Eq A.12)
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m
A G M A 908-B
Ob87575 0003087 T55
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
solving for P at operating diameters:
letting
c,
cos +t sin+t mG
=
2
F
mN =
(Eq A.21)
(Eq A.13)
m +1
G
solving for P at mean tooth diameters:
(Eq A.14)
Lmin
I
=
then
=
P
&
MN
($J
(Eq A.15)
R2m
R i m + R2m
where
(Eq A.16)
(Eq A.23)
To adapt Eq A.16 to actual gears, AGMA
added additional factors to the equation. These
factors are:
Ca
= application factor for pitting
resistance
C,
= dynamic factor for pitting resistance
C,
= size factor for pitting resistance
Cm
= load distribution factor for pitting
resistance
(Eq A.24)
cx =
A.25)
+ 5 mis always equal to
Cf
noting that Rlm
=
The Cq2 factor modifies Cx for the three face
contact ratio conditions, see Fig A-1:
mF = 0.0 for spur gears
= surface condition factor for pitting
resistance
Putting these factors in Eq A.16 gives:
s,
(Eq A.22)
c*
C,
dF
(Eq A.17)
I
Equation A. 17 is the fundamental formula for
pitting resistance and is identical to Eq 5.1 in
AGMA 2001-B88 and Eq 5.1 in AGMA 218.01.
O < mF 5 1.0 for LACR gears
mF > 1.0 for conventional helical gears
In rating standard 218.01, Dec., 1982, the I
factor was expanded to include two new terms:
C
I = __c- expanded to I =
mN
-
For spur gears and conventional helical gears:
c$ = 1.0.
-
For low axial contact ratio gears, LACR, the
C Q ~factor provides a linear interpolation of I
between spur and conventional helical gears, see
Fig A-2.
The Cx multiplier was added to consider the
criterion rating stress at the mean diameters, d,
and Dm,of the meshing elements rather than at
the operating diameters d and D . Its derivation
follows:
-iy
Premise:
IMCR = I s + m F ( I H - I , )
From Eq A.5
sc = cP
=
‘ ( RRi 1 + R
R ,2)
AGMA
ILAcR= geometry factor for the low axial
contact ratio helical gear
(Eq A.20)
I,
= geometry factor for the spur gear
IH
= geometry factor for the conventional
helical gear
9 08-B8 9
56
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
”~
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No reproduction or networking permitted without license from IHS
(Eq A.26)
where
(Eq A.19)
dividing b y 5 and squaring:
($J
Ri+ R2
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= Ob87575
A G H A 908-B
0003088 991
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
for spur gears
for conventional helicals
where
“N
C,,
CJ:
I’=
(Eq A.27)
I, =
‘4
‘c‘xh
-
‘c
“N
‘xh
(Eq A.28)
MN
where
= FIL min
Cxh = Cx as determined at d,
diameter
“N
= 1.0
= Cx as determined for LPSTC
= 1.0
m
F
=O
c$
m
= 1.0
< 1.0
F -
LACR GEAR
SPUR GEAR
>1.0
CONVENTIONAL HELICAL GEAR
m
F
FOR CASE (2) : FACE, F‘,O F AN
IMAGINARY GEAR WITH m F = 1 .O
F‘ =
‘.-F
0 STRESS CALCULATION LOCATION
Fig A-1
F
m-
Cx Determination in Plane of Action
/
Conventional helical gear I factor ( )’I
is based on stress computed at d,
Low axial contact ratio (LACR) gear I factor ( ILACR)is
based on linear interpolation between Is & IH
Spur gear I factor ( I , ) is based on stress computed at LPSTC
I
O
0.5
1.0
m
F
Fig A-2 Variation of I for LACR Gear
AGMA
57
908-B89
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Ob87575 0003089 8 2 8 D
A G H A 908-B
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Substituting in Eq A.31
for LACR gears
c c c 2u
= cCcx,C$
ILACR -
(Eq A.29)
mN
Substituting in Eq A.26 using Eq A.27, Eq A.28
and Eq A.29:
where
MN
C
,
Rearranging
= 1.0
C 2 = 1-m
JI
= C
, as determined for LPSTC
= a transition factor for spurs to
conventional helicals, for LACR
gears
C$
Dividing by Cc and CXS
(
C$ = l + m
cxh
'xsmN
-3
I =
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
F'
mN=-
z
R
-
"F
=
Z
sin q b
AGMA
Copyright American Gear Manufacturers Association
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No reproduction or networking permitted without license from IHS
c$
(Eq. A.39)
(Eq A.33)
From AGMA 908-B89, Eq 4.1 is:
(Eq A.34)
= + t , p1= R 1 & p2 = R2 in Eq A.40,
Letting
it can now be shown that:
b
Lmin
c c cx
= 1.0
z
=
(EqA.37)
MN
and the associated load sharing ratio
F'
)
From AGMA 2001-B88, Eq 6.1 is:
mF
%un=
Fsin $b
A3. Proof for Equivalency of I . The remainder
of this appendix is a proof that the formulation for
I factor given in AGMA 2001-B88 is identical to
the I factor in AGMA 908-B89.
(Eq A.32)
For the case of M
m;
helical having m F = 1.0 and face = F', CXS
is Cx for equivalent spur gear with contact
stress computed at LPSTC.
(EqA.31)
F
-
mN= L
xh
NOTE: Cxh is Cx for the imaginary
The equivalent face, F', of such a gear is:
=
(cc,,
Taking the square root results in the expressiom
found in 218.01.
where
The mN represents an imaginary conventional helical gear having a face contact ratio of
1 .o
F'
F
+
F sin q
mF
=
I = -
(EqA.35)
cc
58
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- 2
" 2
9 O 8-B 89
m
A G H A 908-B
Ob87575 0003090 5 4 T
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
so
m
cancelling
2c = c =
N
2
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
cos +t
=
c,c,
,(;+i)
RI+ R2
sin +t
(Eq A.49)
see Fig A-3
(Eq A.42)
cancelling and letting D = mG d
= cos +t- mG
R1R2
mG+l d mG sin
cos +t
+*
(Eq A.43)
solve for d
(
=
d
Fig A-3
)(L+L)
2 R1R2
sin+t(mG+l)
Ri
(Eq A.44)
Therefore, Eq A.41 holds and it is shown that
the I factor given in ANSVAGMA 2001-B88 is
numerically identical to that in AGMA 908-B89.
R2
note that
R1 R2
R1 R2
then
d
=
2 R1R2
R1+R2
sin+t(mG+l) R1 R 2
(Eq A.45)
=
2 ( R i + "2)
(mG+1) sin +t
(Eq A.46)
SO
d
rearranging
(mG+l)
2
= - R1+R 2
sin Qt
(Eq A.47)
but
2C
=
d ( m +1)
G
AGMA
Copyright American Gear Manufacturers Association
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No reproduction or networking permitted without license from IHS
(Eq A.48)
59
908-B89
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A G H A 908-B
W Ob87575 0003091 48b W
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
908-B89
AGMA
Copyright American Gear Manufacturers Association
Provided by IHS under license with AGMA
No reproduction or networking permitted without license from IHS
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--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
(this page has been left blank)
A G H A 708-B
Ob87575 O003072 312
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Appendix B
ANWAGMA 2001-B88 Pitting Resistance Formula Derivation
This Appendix is not part of AGMA 908-B89, INFORMATION SHEET - Geometry Factors for
Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth,
but is included for informational purposes only
B1. Purpose. This Appendix presents the derivation of the pitting resistance formula and the I
factor as used in this Information Sheet. The I
factor given here is a simplified version of that derived in Appendix A. This simplificationresults in
the same numerical value of I .
pending on the face contact ratio of the gearset,
this point can be the mean diameter of the pinion
or the lowest point of single tooth contact on the
pinion. Additional rating factors are also added to
the basic equation to adjust the stress due to factors peculiar to gearing. Starting with the general
Hertz equation:
B2. Derivation. The AGMA pitting resistance
formula is based on the Hertz contact stress equation for cylinders with parallel axes. See Fig B- l .
The load applied to the cylinder is the load normal to the tooth flank, and the length of contact is
the minimum total length of lines of contact in the
contact zone of the gear set. The radii of the cylinders are the radii of curvature of the teeth at the
point of contact for the mating pair of gears. De-
sc =
2w
w b L
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
b
.J
Rr2
\
/
Rr1
Fig B-1 Tooth Contact Stress Area
AGMA
Copyright American Gear Manufacturers Association
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No reproduction or networking permitted without license from IHS
61
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A G H A 90ô-B
Ob87575 0003093 259
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
where
SC
W
d l , d2
= maximum contact stress of parallel
axis cylinders, lb/in2
Figure B-2 shows the oblique contact line between helical gear tooth profiles. It can be represented as the line of two contacting cones. The
radii of curvature, pnl, pn2, of the pinion and
gear teeth at any point along the contact line are
perpendicular to the line of contact and the involute profiles at the point of contact. They are
contained in the plane of action and are inclined
at the base helix angle, qb, relative to the transverse plane.
= contact load normal to the
cylinders, lb
b
= semi-width of contact between
cylinders, in
L
= length of contact between cylinders,
in
pl,p2
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
El, E2
= contact diameter of cylinders 1 and 2
= Poisson’s ratio of material in
cylinders 1 and 2
= modulus of elasticity of material in
cylinders 1 and 2
Fig B-2 Contacting Cones of Helical Gears
(Extracted from AGMA 229.06)
62
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908-B89
A G H A 908-B
9 Ob87575 0003094 1 9 5 9
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
by defining Cp as:
Converting the general nomenclature in Eqs
B . l and B.2 to those used in AGMA 908-B89:
L
Also transferring the load and radii of curvature from the normal to the transverse plane
where the geometry is more readily defined:
transmitted load in the plane of
action (normal to the tooth flank)
minimum total length of lines of
contact in contact zone
where
= transmitted tangential load at the
radius of curvature normal to the
profile at point of stress calculation
for pinion and gear, respectively
operating pitch diameter of the
pinion
Poisson’s ratio for pinion and gear
material, respectively
+t
= operating transverse pressure angle
qb
= base helix angle
p1, p2
modulus of elasticity for pinion and
gear material, respectively
= radii of curvature of profile in
transverse plane at the point of
stress calculation
Eq B.3 can now be shown as:
Rearranging Eqs B-1 and B-2, then using
AGMA 908-B89 terms:
Eq B. 12 was originally developed before calculators and computers, and it has some terms
that made calculation simpler. These terms are
not necessarily needed today, but data and values
have been developed over the years, and changing
terms could cause a great deal of confusion. The
load sharing ratio, m N , and the pitting resistance
geometry factor, I , are these terms.
NOTE: Double signs are used in Eq B.3;
Le., 2 , to generalize the equation for both
external and internal gears. The upper sign
applies to external gear sets and the lower
sign applies to internal gear sets.
AGMA
Copyright American Gear Manufacturers Association
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No reproduction or networking permitted without license from IHS
They are developed by multiplying Eq B.8 by
fi 6
and
63
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--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
W
AGMA 908-B
m
0 6 8 3 5 3 5 0003095 021
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
To adapt Eq B.11 to actual gears, AGMA
has added additional factors to the equation.
These factors are:
and then recombining terms so that mN and I can
be defined as follows:
F
=-
na
Lmin
(Eq B.lO)
Ca
= application factor for pitting
resistance
Cv
= dynamic factor for pitting resistance
C,
= size factor for pitting resistance
Cm
= load distribution factor for pitting
resistance
Cf
= surface condition factor for pitting
resistance
where
F
= effective face width of gear set
d
= operating pitch diameter of pinion
C,,, = helical overlap factor
Putting these factors in Eq B . l l gives:
The helical overlap factor, C is added to
iIr '
the equation for I to give a smooth transition between the I factors of spurs and low axial contact
ratio (LACR) helicals. See Appendix E for its
definition and derivation.
Now Eq B.8 can be rewritten as:
sc=
c p p ! L
Equation B. 12 is the fundamental formula for
pitting resistance and is identical to Eq 5 . 1 in
ANWAGMA 2001-B88 and Eq 5.1 in AGMA
218.01.
(Eq B . l l )
d FI
AGMA
(Eq B.12)
C
9 O 8-B 89
64
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No reproduction or networking permitted without license from IHS
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A G M A 908-B
Ob87575 0 0 0 3 0 ï b Tbô
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Appendix C
Explanation of the AGMA Gear Tooth Strength Rating Derivation For External Gears
This Appendix is not part of AGMA 908-B89, INFORMATION SHEET - Geometry Factors for
Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth,
but is included for informational purposes only.
C1. Purpose. This Appendix explains the
derivation of the AGMA strength rating formula
for external gears. The formula is derived from a
simplified cantilever beam theory for stress. It is
based on the method of Lewis [i] where the
beam is assumed to be parabolic in shape and
inscribed within the gear tooth. References are
sometimes made to the stress parabola which
refers to the beam assumption.
The formulas given are for helical gears;
however, spur gears may be calculated by setting
the helix angle at zero degrees so that the
transverse plane equals the normal plane. Many
of the variables used in this appendix are not fully
derived as they are more fully explained in other
sections of this information sheet.
Fig C-1 Tooth Load Acting at
Inscribed Parabola
C2. Tooth load. To simplify the geometry of
helical gear teeth in the normal plane, the concept
of the virtual spur gear is used. The concept
incorporated is a spur gear whose shape in the
transverse plane is similar to that of a helical gear
in the normal plane. The calculation of this
virtual spur gear is explained in other sections.
The load normal to the tooth is calculated at the
working pitch diameter of the tooth. This load is
then applied along the line of action (tangent to
the base circle) and passing through the tip of the
tooth. Figure C-1 shows a tooth with the load
applied and the inscribed parabola. Certain spur
gears may have this load applied at the highest
point of single tooth contact.
The basic bending stress equation (see Fig
C-2) for a cantilever parabolic shaped beam is:
7
b -
The basic compressive stress equation for this
beam is:
where
C3. Derivation of the stress equation. The
following procedure is used to derive the
equations necessary for calculating the tooth form
factor, Y,geometry factor, J , and corrected tensile
stress, St
.
AGMA
6 h P1
s -
Sb
= bending stress, lb/in2
sc
= compressive stress, Ib/in2
pl
= bending load on beam, Ib
pc
= compressive load on beam, Ib
h
= height of beam, in
L
= length of beam, in
65
908-B89
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A G H A 908-B
Ob87575 0003097 9 T 4
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
t = tooth thickness at the critical section
(tangent point of the stress parabola
and the tooth root), in
The compressive stress is
sc
=
WN sin+L
'min
t
where
+'
= load angle
= minimum length of lines of
contact
The tangential component of this load causing
bending stress is
4
where
ch
Fig C-2 Gear Tooth as a Simple Beam
The actual load applied normal to the tooth at
the pitch circle is:
= helical factor: A helical factor
must be added to account for the
oblique lines of contact in helical
gears, see 5.10 and Eq 5.70, based
on work of Weilauer and Seireg [2]
This gives a bending stress of:
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
wt
=
T
=
2T
d
Bending and compressive stresses are
combined to find the maximum tensile stress.
63 O00 P
n
P
where
wN
= load normal to the tooth, lb
= load tangential to the tooth, lb
T
= torque on the pinion, lb in
d
= operating pitch diameter of the
St'
'min
"P
+*
Jr
where
si
= transmitted horsepower, hp
= pinion speed, rpm
= operating helix angle
The load, Ww is applied at the load angle,
+L. Calculation of angle +L appears in other
sections (see Fig C-i). The radial component of
this load causing compressive stress is:
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= maximum uncorrected tensile stress
When the orginal derivations were made, calculations were done using tooth layouts and not
computer calculations. The equation was therefore modified to make t h i s task easier. Layouts
were done to a scale of 1 Normal Diametral Pitch
(NDP) so they would be large enough to measure.
Therefore, the stress equation had to be multiplied by the Normal Diametral Pitch, pd , to con-
= operating normal pressure angle
AGMA
t
(Eq C.11)
pinion, in
P
=
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908-B89
A G M A 908-B
W Ob87575 0 0 0 3 0 9 8 830
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
vert these 1 NDP dimensions to actual dimensions. A load sharing ratio, mN, was defined to
relate face width of the tooth to Lmin. A stress
correction factor, Kf , based on photoelastic experiments of Dolan and Broghamer [ 31, was introduced to account for the radius of the tooth root.
where
Note the following right triangle relationships
in Fig C-3.
=
h
-t 2
therefore
-6 -h
t2
-
1.5
-
(Eq C.13)
U
=
wt
cos l+, cos qf
mN
=
F
Lmin
(Eq C.15)
Kf
= stress correction factor (see 5.11)
pd
= nominal pitch in the plane of
rotation (introduced to convert J to
a dimensionless value).
(Eq C.12)
4u
WN
qs
= standard helix angle
F
= face width
Eq C.14 can be subdivided into two variables;
tooth form factor, Y, and geometry factor, J ,
where
E Tooth
Ps
= normal diametral pitch of layout
(scale pitch), usually 1 .O in-'
The Form Factor includes a term Ps which is
the diametral pitch to which the layout is drawn.
This term converts the values of u and t to actual
values and was added to account for layouts or
calculations that are done to a scale other than
one NDP.
Substituting Eq C.13 and letting:
I
SF= t , hF= h (see AGMA 908-B89 Fig 5-7)
r
occurs at point
where trochoid
meets root radius
Scale pitch Ps = 1.0in-'
Kq =
NOTE: Shown in the Normal Plane
Through the Pitch Point
q
COS
Qs
(Eq C.17)
where
Kq
Fig C-3 Tooth Form Factor Layout
With Load Sharing
1
COS
= a factor which converts the pitch
and load from the normal plane to
the transverse plane. (see Eq C.17)
Rearranging equation C.11, adding these
factors and substituting, gives the following:
which is identical to AGMA 908-B89, Eq 5.78
J
(Eq C.14)
AGMA
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=
y CJI
K m
f N
(Eq C.19)
9 08-B 89
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--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
where
A G H A 908-B
9 Ob87575 0003099 777 9
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
where
J
Y
= tooth form factor
C$
= helical overlap factor
mN
= load sharing ratio
strength
Km
= load distribution factor for bending
strength
= dynamic factor for bending
strength
Ky
e
resulting in the final stress equation:
st
-
wt
Ka
Kv
pd
F
Ks Km
J
(Eq C. 21)
where
st
The stress equation now can be written as:
wt ‘d
-
= application factor for bending
Ka
The Geometry Factor, J , includes a helical
overlap factor, C
C is a factor used to
interpolate the values for ACR gears for J, from
that for spurs to conventional helicals. This factor
accounts for low axial contact ratio gearing which
has a face contact ratio, rn F , less than or equal to
1.0. For normal helical gears and spur gears, t h i s
factor is 1.0. see 4.4.
s; =
= size factor for bending strength
Ks
= geometry factor for bending strength
= corrected tensile stress
Eq C.21 is the fundamental formula for
bending strength and is identical to Eq 5.10 in
AGMA 218.01.
Eq 5.10 in ANSIIAGMA
2001-B88 is similar, but a rim thickness factor,
K B , has been added.
(Eq C.20)
F J
Rating factors are added to the equation to
account for increased loads that occur in gearing:
Bibliography
1
Lewis, W., Investigation of the Strength of Gear Teeth, Proc. of the Engineers Club, Philadelphia,
PA, 1893, pp.16-23.
2
Wellauer, E. J., and Seireg, A., Bending Strength of Gear Teeth by Cantilever Plate Theory, Journal
of Engineering for Industry, Trans. ASME, Series B, Vol. 82, 1960, pp. 213-222.
3
Dolan, T. J. and Broghamer, E. L.,A Photoelastic Study of the Stresses in Gear Tooth Fillets,
University of Illinois, Engineering Experiment Station, Bulletin No. 335, 1942.
AGMA
68
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
Copyright American Gear Manufacturers Association
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908-B 89
A G U A 908-B
= Ob87575
0003100 219
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Appendix D
Selection Of Shaper Cutter Geometry
-
This Appendix is not part of AGMA 908-B89, INFORMATION SHEET
Geometry Factors for
Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth,
but is included for informational purposes only.
disk cutters have a small chamfer at the
tooth tip, rather than a radius. If this is
the case, the cutter should be considered
sharp cornered at the inner edge of the
chamfer.
D2. General. This method allows a wide choice
of cutter geometries to be used in generating the
root trochoid form of the virtual spur gear and the
J factor. For very accurate work, the exact cutter
form should be used, but for most cases, the
cutter form can be approximated. The method
assumes that generation takes place in the normal
plane. Cutters which act in the transverse plane,
such as helical disc shaper cutters and some rack
shaper cutters will generate root trochoid forms
which are slightly different from those assumed by
this method. This has a minor effect on the
accuracy of the J factor.
The knowledge required to convert the
actual dimensions of a disk type cutter to
the values necessary to determine the J
factor of a specific gear is beyond the
scope of this Information Sheet. Cutter
manufacturers have different designs and
production techniques, which affect the
final tooth form and the resulting J factor.
The simplified information given here is
intended to provide typical values which
may be used as a guide to usual practice.
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
D1. Purpose. This Appendix provides default
shaper cutter data for use in calculating the
bending strength geometry factor, J , when the
original cutter data at the time of gear
manufacture is unavailable.
If the exact geometry at its worst condition is
known, that geometry should be used to calculate
the J factor. If the dimensions are not known, the
geometry of a minimum cutter may be estimated
from the following information:
D3. Rack Shaped Cutters and Hobs. Rack
cutters and hobs are represented as disk cutters
with large numbers of teeth, such as 9999. The
actual form of the cutter, in the normal plane,
should be used, with all dimensions made
dimensionless. To make actual measurements
dimensionless, they are scaled by multiplying them
by diametral pitch, dividing them by module or
comparing them to a T (3.1416) circular pitch at
the standard pitch diameter. Any consistent
system of units can be used for this conversion.
See Section 3 of AGMA 908-B89 for examples.
D4.1 Number of Teeth. The maximum
pitch diameter of the cutter is limited by the size
of the gear shaper to 3, 4, 5 , 6 or 8 inch. This
limits the number of cutter teeth as a function of
the pitch. The following table is typical.
Table D-1
Number of Cutter Teeth Default Values
Diametral Pitch
D4. Disk Shaped Cutters. Disk shaped cutters
are not as standardized as hobs or other rack
shaped cutters. The geometry of disk shaped
cutters changes with each sharpening. Generally,
the radius of the root fillet generated by these
cutters decreases as they are sharpened.
to 20
16
12
10
8
6
CAUTION: The tip radii and cutting
depths which are commonly assumed for
hobs must not be used for disk (pinion)
shaped cutters without verification of the
actual tool design. For example, many
AGMA
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4
3
Number of Teeth
40
32
32
30
24
18
16
15
Coarser pitches require consultation with the
manufacturer.
69
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A G H A 908-B
m Ob87575 0003LOL 155 m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Table D-2
Typical 20" NPA Spur Disk Cutter Proportions* - Inches
Diametral
Pitch,
'nd
Life
Number of
Teeth
3
3
3
90
50
25
15
15
15
0.523
0.505
0.495
0.00
-0.08
-0.11
5.918
5.804
5.756
0.410
0.427
0.416
0.030 chamfer
0.020 chamfer
0.030 chamfer
6
6
6
90
50
10
24
24
24
0.266
0.245
0.221
0.04
-0.14
-0.34
4.430
4.365
4.297
O. 209
0.202
0.204
0.020 radius
0.010 chamfer
0.000 sharp
10
10
10
90
40
10
30
30
30
O. 140
0.158
0.01
-0.23
-0.45
3.256
3.201
3.167
O. 128
O. 123
O. 128
0.010 chamfer
0.010 chamfer
0.010 radius
*
95
Tooth
Addendum
Tool
Thickness Modification Outside Addendum
'no
xO
Diameter
huo
0.124
Tip
Radius
(chamfer)
The table values are actual measurements of cutters in the field and are included to illustrate the difference between
different cutter manufacturers' standards and different sharpening conditions.
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
D4.2
Tooth Proportions.
Table D-2,
comprised of actual cutter measurements, is
typical.
the cutter design data. To furnish a starting point
when the cutter design data is not available,
approximate cutter geometry values are provided.
D4.3 Tip Radius. For cutters with less than
24 teeth, assume a sharp comer. Over 24 teeth,
assume a 0.1 I Gd radius.
The dimensions used are those of the spur
gear equivalent to the actual cutter, in the
transverse plane. These dimensions are made
dimensionless and are converted to virtual spur
gear dimensions in the normal plane.
D4.4 Tooth Thickness. See D5.
D4.5 Cutter Addendum and Clearance.
Assume that cutter addendum is 1.25 1 G d for
full depth cutters, and 1.0 /Gd for stub depth
cutters. Clearances are 0.251Gd and 0.20/ì&
respectively.
The approximate geometry is based on the
assumption that the cutter has 18 teeth, a sharp
tip radius and will reach the end of its useful life
when it is sharpened to the condition where the
outside diameter is equal to the standard pitch
diameter plus 1.8 cutter addendums. Cutters with
outside diameters larger than these will generate
gears with J factors larger than or equal to the
approximate cutter.
D4.6
Protuberance
Disk
Cutters.
Protuberance (pregrind and preshave) disk cutters
are usually specially designed for a specific part.
No default values are given here for these special
cutters.
Approximate minimum cutter
geometry - dimensionless
D5. Spur Gear Disc Shaper Cutters. If the
actual cutter is at hand, the tooth thickness can be
measured by the span method (see ANSIIAGMA
2002-B88 Tooth Thickness Specifications and
Measurement) and the outside diameter can be
measured. The tooth thickness at the standard
pitch diameter, the addendum modification
coefficient and the tool addendum can be
calculated from involute geometry and the
information in Section 5 of AGMA 908-B89.
Number of teeth
18
Std. tooth thickness, transverse 1.5708
Tool Addendum
1.25
Addendum modification
-0.35
Tip radius
0.0 (sharp)
Depending on pressure angle, actual cutters
with this geometry may not be feasible due to
involute interference with the work gear. If it is
possible, or if cutters with less than 18 teeth must
be used, consult a cutter manufacturer for more
information.
D6. Helical Gear Disc Shaper Cutters. Helical
disk shaper cutters cannot be measured as
described above, so they must be described from
AGMA
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908-B8 9
A G M A 908-B
m
Ob87575 0003102 O91
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
Appendix E
Derivation of Helical Overlap Factor, C$
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
This Appendix is not part of AGMA 908-B89, INFORMATION SHEET - Geometry Factors for
Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth,
but is included for informational purposes only.
I
I
E l . Purpose. This Appendix provides the
derivation for a simplified method for calculating
C as used in AGMA 908-B89. The results are
4f
identical to AGMA 218.01, but the procedure
eliminates the need for Cx and C,h for LACR
gears.
where
2
0.5
( R m l - Rbl>
(Eq E.3)
Pm2'
' 6 7 Pml
(Eq E.4)
P1
E2. Derivation. In AGMA 218.01, the helical
overlap factor for LACR helical gears is:
2
Pm1'
= c2
(Eq E.5)
P2 = ' 6 7 P 1
(Eq E 4
Substituting Eq E.2 into Eq E . l together with
Eq E.7 and Eq E.8 gives the new expression for
c4f
m
The term, C,h / C, , is the ratio of the radii
of curvature at the mean diameter of the pinion to
the radii of curvature at the LPSTC. i.e.;
X
= -F
px
-
'N - ' x
sin
b
(Eq E.8)
P1 P2
AGMA
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71
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A G M A 908-B
m Ob87575 0003103
T28
m
Geometry Factors for Determining the Pitting Resistance and Bending Strength of Spur and Helical Gear Teeth
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
(this page has been left blank)
1
AGMA
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908-B89
AGHA 908-B
Geometry Factors for De-
Ob87575 0003L04 964
the pittinl Resistance and Bending Strength of Spur and Helical Gear Teeth
Appendir F
High Transverse Contact Ratio Gears
This Appendix is not part of AGNA 908-B89, INFORMATION SHEET - Geometry Factors for
Determining the Pitting Resistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth,
but is included for informational purposes only.
This Appendix provides a
reference for accommodating load distribution in
a pair of high contact ratio gears.
two pairs of teeth in contact at the highest point of
F2. High transverse contact ratio gears.
When the transverse contact ratio is greater than
or equal to 2.0, the load disuibution between the
Studies have been done on the subject of high
transverse contact ratio, HTCR gears. See, for
instance, the reference paper of Ekholy [i].
Purpose.
double tooth contact becomes indeterminate,
depending on tooth accuracy and stiffness.
--`,```,,`,``,,,,`,`,`,,,,,`,``-`-`,,`,,`,`,,`---
F1.
Bibliography
1. Ekholy, A. H . , Tooth Load Sharing in High-Contact Ratio Spur Gears, ASME paper 84-DET-65.
908-BS9
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