Chapter 1
Tolerances and Fits
Department of Mechanical Engineering
Middle East Technical University
ME307 Machine Elements I
Fall 2006-2007
Dr. Serkan Dağ
Tolerances and Fits
Deviations from the exact dimensions are inavoidable due to the nature
of manufacturing processes. These deviations must not be so large that
the part is useless. Designer specifies upper and lower limits to the
dimensions
Tolerance is the difference between the maximum and
minimum size limits of a part:
d  d max  d min
dmin
dmax
d
Too tight tolerance  High manufacturing cost
Too large tolerance Part may not function as expected
Dr. Serkan Dağ
Fits
Dr. Serkan Dağ
Tolerances
Application, Process
Tolerance (mm)
Slip blocks, reference gages
1-2
High quality gages, plus gages
2-3
Good quality gages, gap gages
3-5
Fits produced by lapping
4-10
Ball bearings, Diamond or fine boring, fine grinding
5-12
Grinding, fine honing
6-20
High quality turning, broaching
12-35
Center lathe turning and boring, reaming
14-50
Horizontal or vertical boring machine
30-80
Milling, slotting, planing, metal rolling or extrusion
50-100
Drilling, rough turning and boring, precision tubing
70-140
Light press work, tube drawing
120-240
Press work, tube rolling
150-500
Die casting or molding, rubber moulding
250-1000
Stamping
400-1400
Sand casting, flame cutting
500-2000
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Basic Systems for Fit Specification
In order to standardize dimensioning of fits, two basic systems are used
1) Basic Hole System (BHS)
Minimum hole diameter is taken as the basis. Lower deviation for the
hole is equal to zero. Dmax is prescribed according to the specified
tolerance.
2) Basic Shaft System (BSS)
Maximum shaft diameter is taken as the basis. Upper deviation for the
Shaft is equal to zero. dmin is prescribed according to the specified
tolerance.
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Basic Systems for Fit Specification
tolerance zone
Fund. Dev.
BHS
tolerance zone
hole
basic size
BSS
Fund. Dev.
hole
basic size
shaft
shaft
tolerance zone
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International Tolerance Grade Numbers
• In order to establish a preferred fit we need
1) The magnitude of the tolerance zone for the shaft and the hole
2) Fundamental deviation for the shaft (in BHS)
Fundamental deviation for the hole (in BSS)
• International tolerance grade numbers (IT numbers) designate groups of
tolerances such that tolerances for a particular IT number have the same
relative level of accuracy but vary depending on the basic size.
• The magnitude of the tolerance zone is the variation in part size. The
tolerance zones are specified in international tolerance grade numbers
called IT numbers.
• These numbers range from IT0 to IT16. The smaller grade numbers specify
a smaller tolerance zone.
• IT numbers are given in Tables A-11 and A-13 in the textbook.
Dr. Serkan Dağ
International Tolerance Grade Numbers
Application,Process
Tolerance (mm)
IT Grade
Slip blocks, reference gages
1-2
1
High quality gages, plus gages
2-3
2
Good quality gages, gap gages
3-5
3
Fits produced by lapping
4-10
4
Ball bearings, Diomand or fine boring, fine grinding
5-12
5
Grinding, fine honing
6-20
6
High quality turning, broaching
12-35
7
Center lathe turning and boring, reaming
14-50
8
Horizontal or vertical boring machine
30-80
9
Milling, slotting, planing, metal rolling or extrusion
50-100
10
Drilling, rough turning and boring, precision tubing
70-140
11
Light press work, tube drawing
120-240
12
Press work, tube rolling
150-500
13
Die casting or molding, rubber moulding
250-1000
14
Stamping
400-1400
15
Sand casting, flame cutting
500-2000
16
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International Tolerance Grade Numbers
Example: A shaft of nominal diameter 25 mm is going to be manufactured.
IT grade is required to be IT7. Determine the tolerance on the shaft.
Use Table A-11 (tolerance grades, metric series)
Basic size  18-30 (Consider the 1st appearance)
Ts  d  d max  d min  0.021 mm
• Tables can be used for both shafts and the holes.
• Tolerance on a shaft or a hole can be calculated by using
the formulas provided by ISO.
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Tolerance Designation (ISO R286)
Tolerance on a shaft or a hole can also be calculated by using the formulas
provided by ISO.
T  K i
where,
T is the tolerance (in mm)
i  0.453 D  0.001D
(unit tolerance, in mm)
D  D1 D2 (D1 and D2 are the nominal sizes marking the beginning and
the end of a range of sizes, in mm)
K  101.6  ITn  IT 6 
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International Tolerance Grade Numbers
Example: Consider the previous example (D = 25 mm and IT grade of
IT7) and calculate the tolerance on the shaft using the formulas given in
ISO standards.
i  0.453 D  0.001D
Note: When the nominal sized marking the beginning and end of a range of
sizes are not available, nominal size can be directly used to calculate i.
i = 1.341 mm
K  101.6 7 6   16
Ts  K  i  21.45 mm  0.021mm
Same result is obtained using Table A-11
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Fit Types
There are three types of fits
a) Clearence Fits b) Interference Fits c) Transition Fits
Clearence Fits
The mating parts have such upper and lower limits that a clearence always
results when the mating parts are assembled.
hole
d max  25.95 mm
Cmin
d min  25.93 mm
Dmax  26.03 mm
shaft
Dmin  26.00 mm
Ts  0.02 mm
Th  0.03 mm
Allowance of the fit corresponds to maximum material condition (Cmin).
Allowance can be calculated by considering tightest fit.
Dr. Serkan Dağ
Fit Types
There are three types of fits
a) Clearence Fits b) Interference Fits c) Transition Fits
Interference Fits
The mating parts have such limits that the lowest shaft diameter is larger than the
largest hole diameter.
hole
shaft
d max  25.04 mm
I max
Dmax  25.01 mm
d min  25.02 mm
Dmin  25.00 mm
Ts  0.02 mm
Th  0.01 mm
Allowance of the fit corresponds to maximum material condition (Imax).
Dr. Serkan Dağ
Fit Types
There are three types of fits
a) Clearence Fits b) Interference Fits c) Transition Fits
Transition Fits
Either a clearance or an interference may result depending on the exact value
of the dimensions of the machined shaft and hole within the specified tolerance
zones
d max  25.04 mm
shaft
hole
I max
d min  25.02 mm
Dmax  25.03 mm
Dmin  25.00 mm
Ts  0.02 mm
Th  0.03 mm
Allowance of the fit corresponds to maximum material condition (Imax).
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Fundamental Deviation
tolerance zone
Fund. Dev.
BHS
Tolerance zones for the hole and the
shaft are prescribed by IT numbers. Note
that we also need the fundamental
deviation for the shaft to completely
specify the fit. ISO standard uses tolerance
position letters with capital letters for the
holes and lowercase letters for the shafts.
• Letters are combined with tolerance grades to establish a preferred fit.
• Specification for the holes: H7, D8, J6
• Specification for the shafts: h6, b8, k7
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Specification for the Fits
tolerance zone
25 H7/g6
Fund. Dev.
BHS
basic size
fund. dev.
for the hole
IT grade
for the hole
IT grade
for the shaft
fund. dev.
for the shaft
• H…/(a-z)…  BHS (fund. dev. for the hole is zero)
• (A-Z)…/h…  BSS (fund. dev. for the shaft is zero)
• Letters I, L, O, Q, W, i, l, o, q, w are not used.
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Specification for the Fits, Example.
+
34 H11/c11
Basic Size (Datum)
H11
Th
fund. dev.
-
Ts
(BHS)
c11
What are the max. and min. limits for the hole and the shaft for the given fit spec.?
Table A-12 (Fund. devs. for shafts (BHS)).
D  34 mm, for c,  F  0.12 mm.
D  34 mm, IT11, T  0.16 mm. (Table A-11)
Dmin  34 mm.
Dmax  34.16 mm.
d max  34  0.12  33.88 mm.
d min  34  0.12  0.16  33.72 mm.
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Specification for the Fits
In Basic Shaft System (BSS), fund. dev. of the shaft is given by h and
it is equal to zero. (Upper limit of the shaft is on datum line).
+
B
Datum Line
(A-Z)…/h…,
h
+
-
H
shaft
Datum Line
h
Ex: B8/h8
H…/h…,
snug fit.
shaft
Note: Fund. dev. table for BSS is not given in the textbook.
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Fundamental Deviations (Letter Specification)
+
A
BSS: (A-G)…/h… (positive)
BHS: H…/(a-g)… (negative)
(J-K)…/h… (depends on size)
H…/(j-k)… (depends on size)
(M-Z)…/h… (negative)
H…/(m-z)… (positive)
z
BC
DE
F
F
G
p
mn
H
JK
MN
P
HOLE
rs
v
u
t
RS
TU
VX
F
b
YZ
cd
e f
j
gh
y
F
basic size
F
x
k
SHAFT
a
-
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Tolerance on the Fit
Tolerance on the fit is defined as the sum of the tolerance on the hole and
tolerance on the shaft.
T f  Th  Ts  Dmax  Dmin   d max  d min 
clearence
Cmin
interference
Imin
Cmax
Imax
T f  I max  I min
T f  Cmax  Cmin
Cmax
Imax
transition
T f  I max  Cmax
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Example
For a nominal diameter of 25 mm and for a fit specification of H7/j5
determine the following:
a)
b)
c)
d)
e)
f)
g)
h)
Type of the tolerancing system
Tolerance on the hole
Tolerance on the shaft
Upper and lower limits of the hole (Dmax, Dmin)
Upper and lower limits of the shaft (dmax, dmin)
Type of the fit
Tolerance on the fit
Allowance
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Example
a) H7/j5  Basic Hole System
b) D = 25 mm, from the given table:
H7 
 21 mm
0 mm
+
-
j5 
 5 mm
- 4 mm
nominal size
H7
j5
Th  21 mm
c) Ts  9 mm
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Example
d) Dmin  0, (Basic Hole System)
Dmax  25  0.021  25.021 mm
e) dmin  25  0.004  24.996 mm
dmax  25  0.005  25.005 mm
f) Interference fit.
g) Tolerance on the fit:
T f  Th  Ts  21  9  30 mm
or, I max  5 mm, Cmax  21  4  25 mm.
T f  I max  Cmax  30 mm.
h) Allowance = Imax= 5 mm.
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Fits, Interference and Clearence Values
In the second table, interference and clearence values for commonly used
fits are given.
For example, consider G7/h6, D = 20 mm.
From the table we read:
Cmax  41 mm
clearence fit.
Cmin  7 mm
G7 
Cmin
 28 mm
 7 mm
h6 
0 mm
 13 mm
G7
Cmax
h6
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Fits, Interference and Clearence Values
Consider H7/m6, D = 20 mm.
From the table we read:
Cmax  13 mm
interference fit.
I max  21 mm
H7 
H7
 21 mm
0
m6 
m6
 21mm
 8 mm
nominal size
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