FITS AND TOLERANCES

• Tolerance types and representation on the

drawing
• Fits types and selection for different applications
• Basic hole systems
• Basic shaft systems
• Allowances
• Geometric tolerances - Form and positional.
• Datum and datum features symbols used to
represent geometric tolerances.
Fits & Tolerances
 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 Too tight tolerance  High manufacturing cost
d Too large tolerance Part may not function as expected

Dr. Serkan Dağ

Fits

Dr. Serkan Dağ

 Tolerances
Application, Process Tolerance (m)
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
Dr. Serkan Dağ
 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. D max 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. d min is prescribed according to the specified
tolerance.

Dr. Serkan Dağ

 Basic Systems for Fit Specification
tolerance zone

Fund. Dev.
BHS BSS

Fund. Dev.
tolerance zone
basic size
hole
hole basic size

shaft
shaft
tolerance zone
Dr. Serkan Dağ
 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 (m) 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 Dr. Serkan Dağ
 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.

Dr. Serkan Dağ

 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 m)
i  0.453 D  0.001D (unit tolerance, in m)

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 

Dr. Serkan Dağ

 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 m
K  101.6 7 6   16
Ts  K  i  21.45 m  0.021 mm

Same result is obtained using Table A-11

Dr. Serkan Dağ
 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 Ts  0.02 mm
d min  25.93 mm

Dmax  26.03 mm
Th  0.03 mm
Dmin  26.00 mm
shaft

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 t
largest hole diameter.
d max  25.04 mm
shaft Ts  0.02 mm
hole d min  25.02 mm
I max Dmax  25.01 mm
Th  0.01 mm
Dmin  25.00 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 Ts  0.02 mm
hole d min  25 . 02 mm
I max Dmax  25.03 mm
Th  0.03 mm
Dmin  25.00 mm

Allowance of the fit corresponds to maximum material condition (Imax).

Dr. Serkan Dağ
 Fundamental Deviation

tolerance zone
Tolerance zones for the hole and the
Fund. Dev.
shaft are prescribed by IT numbers.
BHS
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
• Letters are combined with tolerance grades to establish a preferred fit.
shafts.
• Specification for the holes: H7, D8, J6
• Specification for the shafts: h6, b8, k7

Dr. Serkan Dağ

 Specification for the Fits

tolerance zone

Fund. Dev. 25 H7/g6

BHS basic size IT grade
fund. dev. for the shaft
for the hole fund. dev.
IT grade for the shaft
for the hole

• 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.
Dr. Serkan Dağ
 Specification for the Fits, Example.

34 H11/c11
+ Basic Size (Datum)
H11
Th
fund. dev. (BHS)
Ts
-
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. d max  34  0.12  33.88 mm.
Dmax  34.16 mm. d min  34  0.12  0.16  33.72 mm.
Dr. Serkan Dağ
 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…, Ex: B8/h8
- h shaft

+ H Datum Line
H…/h…, snug fit.

- h shaft

Note: Fund. dev. table for BSS is not given in the textbook.
Dr. Serkan Dağ
 Fundamental Deviations (Letter Specification)
+ BHS: H…/(a-g)… (negative) BSS: (A-G)…/h… (positive)
A H…/(j-k)… (depends on size) (J-K)…/h… (depends on size)
H…/(m-z)… (positive) (M-Z)…/h… (negative) y z
x
BC u v
DE t
F p r s
G
H mn
F basic size F
k
JK F F h j
MN g
PR e f
ST cd
UV b
HOLE
XY
Z SHAFT
a

- Dr. Serkan Dağ

 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 interference

Cmin Imin Imax

Cmax

T f  Cmax  Cmin T f  I max  I min

Cmax
transition Imax
T f  I max  Cmax
Dr. Serkan Dağ
 Example

For a nominal diameter of 25 mm and for a fit specification of H7/j5

determine the following:

a) Type of the tolerancing system

b) Tolerance on the hole
c) Tolerance on the shaft
d) Upper and lower limits of the hole ( Dmax, Dmin)
e) Upper and lower limits of the shaft ( dmax, dmin)
f) Type of the fit
g) Tolerance on the fit
h) Allowance

Dr. Serkan Dağ

 Example

a) H7/j5  Basic Hole System

b) D = 25 mm, from the given table:

 21 m  5 m
H7  j5 
0 m - 4 m

+ H7 nominal size

j5
-
Th  21 m

c) Ts  9 m

Dr. Serkan Dağ

 Example

d) Dmin  0, (Basic Hole System)

Dmax  25  0.021  25.021 mm
e) d min  25  0.004  24.996 mm
d max  25  0.005  25.005 mm
f) Interference fit.
g) Tolerance on the fit:
T f  Th  Ts  21  9  30 m
or, I max  5 m, Cmax  21  4  25 m.
T f  I max  Cmax  30 m.

h) Allowance = Imax= 5 m.

Dr. Serkan Dağ

 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 m
clearence fit.
Cmin  7 m
 28 m 0 m
G7  h6 
 7 m  13 m

Cmin G7
Cmax
h6
Dr. Serkan Dağ
 Fits, Interference and Clearence Values

Consider H7/m6, D = 20 mm.

From the table we read:
Cmax  13 m
interference fit.
I max  21 m

 21 m  21m
H7  m6 
0  8 m

H7 m6 nominal size

Dr. Serkan Dağ

 Tolerance Dimensioning
• Tolerance is the total amount that a specific
dimension is permitted to vary;
• It is the difference between the maximum and the
minimum limits for the dimension.
• For Example a dimension given as 1.625 ± .002
means that the manufactured part may be 1.627”
or 1.623”, or anywhere between these limit
dimensions.
 Tolerances

The Tolerance is 0.001” for the Hole as well as for the Shaft
Allowance & Clearance

Interchangeable Fit
 Size Designations
• Nominal Size: It is the designation used for general
identification and is usually expressed in common fractions.
For Ex. In the previous figure, the nominal size of both hole
and shaft, which is 11/4” would be 1.25” in a decimal system
of dimensioning.
• Basic Size or Basic dimension: It is the theoretical size from
which limits of size are derived by the application of
allowances and tolerances.
• Actual Size: is the measured size of the finished part.
• Allowance: is the minimum clearance space (or maximum
interference)intended between the maximum material
condition of mating parts.
 Fits Between Mating Parts
• Fit is the general term used to signify the range of
tightness or looseness that may result from the
application of a specific combination of allowances and
tolerances in mating parts.
There are four types of fits between parts
1. Clearance Fit: an internal member fits in an external
member (as a shaft in a hole) and always leaves a space
or clearance between the parts.

Minimum air space is 0.002”. This is the allowance and is always

positive in a clearance fit
2. Interference Fit: The internal member is larger than the
external member such that there is always an actual
interference of material. The smallest shaft is 1.2513”
and the largest hole is 1.2506”, so that there is an actual
interference of metal amounting to at least 0.0007”.
Under maximum material conditions the interference
would be 0.0019”. This interference is the allowance,
and in an interference fit it is always negative.
3. Transition Fit: may result in either a clearance or
interference condition. In the figure below, the smallest
shaft 1.2503” will fit in the largest hole 1.2506”, with
0.003” to spare. But the largest shaft, 1.2509” will have
to be forced into the smallest hole, 1.2500” with an
interference of metal of 0.009”.
4. Line Fit: the limits of size are so specified
that a clearance or surface contact may
result when mating parts are assembled.
 Basic Hole System
• Minimum hole is taken as the basic size, an allowance is
assigned, and tolerances are applied on both sides of and
away from this allowance.
1. The minimum size of the hole
0.500” is taken as the basic size.
2. An allowance of 0.002” is decided
on and subtracted from the basic
hole size, making the maximum
shaft as 0.498”.
3. Tolerances of 0.002” and 0.003” Minimum clearance: 0.500”-
respectively are applied to the 0.498” = 0.002”
hole and shaft to obtain the
maximum hole of 0.502” and the Maximum clearance: 0.502” –
minimum shaft of 0.495”. 0.495” = 0.007”
 Basic Shaft System
• Maximum shaft is taken as the basic size, an allowance is
assigned, and tolerances are applied on both sides of and
away from this allowance.
1. The maximum size of the shaft
0.500” is taken as the basic size.
2. An allowance of 0.002” is decided
on and added to the basic shaft
size, making the minimum hole as
0.502”.
3. Tolerances of 0.003” and 0.001” Minimum clearance: 0.502”-
respectively are applied to the 0.500” = 0.002”
hole and shaft to obtain the
maximum hole of 0.505” and the Maximum clearance: 0.505” –
minimum shaft of 0.499”. 0.499” = 0.006”
 Specifications of Tolerances
1. Limit Dimensioning

The high limit is placed above

the low limit.

In single-line note form, the low limit

precedes the high limit separated by a
dash
 Specifications of Tolerances
2. Plus-or-minus Dimensioning
• Unilateral Tolerance

• Bilateral Tolerance
Cumulative Tolerances
Tolerances Related to Machining Processes
Terms related to Metric Limits & Fits
 Some Definitions
• Basic Size: is the size from which limits or
deviations are assigned. Basic sizes, usually
diameters, should be selected from a table of
preferred sizes.
• Deviation: is the difference between the basic size
and the hole or shaft size.
• Upper Deviation: is the difference between the
basic size and the permitted maximum size of the
part.
• Lower Deviation: is the difference between the
basic size and the minimum permitted size of the
part.
 Some Definitions

• Fundamental Deviation: is the deviation closest to

the basic size.
• Tolerance: is the difference between the
permitted minimum and maximum sizes of a part.
 • International Tolerance Grade (IT):

They are a set of tolerances that varies according to the basic size
and provides a uniform level of accuracy within the grade.
 Definitions
• Tolerance Zone: refers to the relationship of the
tolerance to basic size. It is established by a
combination of the fundamental deviation indicated
by a letter and the IT grade number. In the dimension
50H8, for the close running fit, the H8 specifies the
tolerance zone.

• The hole-basis system of preferred fits is a system in

which the basic diameter is the minimum size. For
the generally preferred hole-basis system, the
fundamental deviation is specified by the upper-case
letter H.
• The shaft-basis system of preferred fits is a system in
which the basic diameter is the maximum size of the
shaft. The fundamental deviation is given by the
lowercase letter h.

• An interference fit results in an interference between

two mating parts under all tolerance conditions.
• A transition fit results in either a clearance or
an interference condition between two
assembled parts.
• Tolerance symbols are used to specify the tolerance
and fits for mating parts. For the hole-basis
system ,the 50 indicates the diameter in millimeters;
the fundamental deviation for the hole is indicated by
the capital letter H, and for the shaft it is indicated by
the lowercase letter f. The numbers following the
letters indicate this IT grade. Note that the symbols
for the hole and shaft are separated by the slash.
Tolerance symbols for a 50-mm-diameter hole may
be given in several acceptable forms. The values in
parentheses for reference only and may be omitted.
 SYSTEM OF FITS AND TOLERANCES
The standard reference temperature is 20 C for industrial
measurements
and, consequently, for dimensions defined by the system.

Due to the inevitable inaccuracy of manufacturing methods, a part

cannot be made precisely to a given dimension, the difference between
maximum and minimum limits of size is the tolerance.

When two parts are to be assembled, the relation resulting from the
difference between their sizes before assembly is called a fit.
 Tolerance
• How to decide tolerance?
– Functional requirements of mating parts
– Cost of production
– Available manufacturing process

• Choose as coarse tolerance as possible without

compromising functional requirements
• Proper balance between cost and quality of parts
 HOLE SHAFT
Max Hole size – Basic Size = Upper Max shaft size – Basic Size = Upper
Deviation Deviation
Min Hole size – Basic Size = Lower Min shaft size – Basic Size = Lower
Deviation Deviation
 CLEARANCE FIT

Maximum shaft dimension < Minimum hole

dimension
FIT - condition of looseness or tightness between two mating parts being
 INTERFERANCE FIT

Maximum Hole size < Minimum Shaft

 TRANSITION FIT

Obtained by overlapping of tolerance zones of shaft and hole

……Does not guarantee neither clearance nor interference fit
To obtain different types of fits, it is general practice to vary tolerance
zone of one of the mating parts

HOLE BASED SYSTEM-

Size of hole is kept constant,
shaft size is varied
to get different fits.

SHAFT BASED SYSTEM-

Size of shaft is kept constant,
hole size is varied
to get different fits.
A fit is indicated by the basic size common to both components,
followed by symbol corresponding to each component, the hole being
quoted first.

E.g. 45 H8/g7
The selection of letter Representation of
freezes one limit of hole / Tolerance
shaft
1) Letter Symbol
(how much away from Basic Basic Size
size) 45 E8/e7

One can have different

possible combinations; eg.
45H6g7, 45H8r6, 45E5p7
E.S. – upper deviation
E.I. – lower deviation
H : lower deviation of
hole is zero
h : upper deviation of
shaft is zero
Representation of Tolerance Tolerance Grade defines range
2) Number or Grade of dimensions (dimensional
IT01, IT0, IT1,….IT16 variation)
There are manufacturing
constraints on tolerance grade
chosen
RANGE IN A GIVEN TOLERANCE GRADE
The selection of Representation of
Tolerance grade Tolerance
number freezes the
other limit of hole /
shaft

H : lower deviation of
hole is zero
Representation of Fit Together (Letter &
Grade) on both mating
components decide
quality of fit
0.021

INTERFERENCE FIT Φ30.035

Φ30.022
Φ30.021
0.013
0.022
Φ30.000

H7 : Tol Grade 7 mean 21μ

variation (H means upper deviation
zero)
p6 : Tol Grade 6 means 13μ
 Important Terms – Single Part

• Nominal Size – general size, usually expressed in

mms
• Actual Size – measured size of the finished part
• Limits – maximum and minimum sizes shown by
tolerances (larger value is the upper limit and the
smaller value is the lower limit)
• Tolerance – total allowable variance in dimensions
(upper limit – lower limit) – object dimension could
be as big as the upper limit or as small as the lower
limit or anywhere in between.
Characteristics of Tolerances
Characteristics of Tolerances

Connection btw the characteristics:

US = N + UD
LS = N – LD
T = US – LS =
IT: International Tolerance
• 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.
Fits Between Mating Parts
ILLUSTRATION OF DEFINITIONS
 Fits Between Mating Parts
Fit: degree of tightness between two parts.
Fit types:
– Clearance Fit – tolerance of mating parts always
leaves a space
– Interference Fit – tolerance of mating parts
always results in interference
– Transition Fit – sometimes interferes, sometimes
clears
 Clearance Fit

The mating parts have such upper and lower limits that a
clearance always results when the mating parts are
assembled.
Clearance Fit (e.g.: H7/f6)
Clearance Fit (pl. H7/f6)
Clearance Fit (pl. H7/f6)
 Transition Fit

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.
Transition Fit (e.g.: H7/j6)
Transition Fit (e.g.: H7/j6)
Transition Fit (e.g.: H7/j6)
Transition Fit (e.g.: H7/j6)
 Interference Fit

The mating parts have such limits that the lowest shaft
diameter is larger than the largest hole diameter..
Interference Fit (e.g. H7/p6)
Interference Fit (e.g. H7/p6)
Interference Fit (e.g. H7/p6)
 Basic Systems for Fit Specification
In order to standardize dimensioning of fits, two basic
systems are used:
1)Basic Hole System: 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: 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.
 Basic Hole System
• Toleranced dimensions are commonly
determined using the basic hole system in
which the minimum hole size is taken as the
basic size.
Fits in Basic Hole System
 Basic Shaft System
• In this system, the maximum shaft is taken as
the basic size and is used only in specific
circumstances.
Fits in Basic Shaft System
 Two ways of indicating tolerances on technical
drawings
Limits of a dimension or the tolerance values are specified
directly with the dimension.

Questions ?
 Indicating tolerances

The dimension is given by:

•a shape symbol,
•nominal size,
•a letter indicating the position
of the tolerance zone in relation
to zero line,
•a number indicating the width
of the tolerance zone.
(quality of production?)
Specifying Fits in Technical Drawings
 DIMENSIONING OF TOLERANCES -RULES

• The upper deviation should be

written above the lower
deviation value irrespective of
whether it is a shaft or a hole.
• Both deviations are expressed
to the same number of decimal
places, except in the cases
where the deviation in one
direction is nil.
 Example
For a nominal diameter of 25 mm and for a fit
specification of H7/j5 determine the following:
•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
 Key

a) H7/j5  Basic Hole System

b) D = 25 mm, from the given table:

 21 m  5 m
H7  j5 
0 m - 4 m

+ H7 nominal size

j5
-
Th  21 m

c) Ts  9 m
Tolerance on
Components
 Φ30H7s6

Φ30H8e6

Φ30G7r6 Φ30F8r6
Estimate kind of fit
FITS APPLICATIONS
 FITS AND TOLERANCES

The components of the toleranced dimension shall be

indicated in the following order:
a) the basic size, and
b) the tolerance symbol.
If, in addition to the symbols it is necessary to express the values of
the
deviations or the limits of size, the additional information shall be
shown
in brackets.
Permissible deviation

•If a dimension needs to be limited in one

direction only, this should be indicated by
adding “min” or “max” to the dimension.
•The upper deviation or the upper limit of size
shall be written in the upper position and the
lower
deviation or the lower limit of size in the lower
position, irrespective of whether a hole or a
•The istolerance symbol for
shaft
the hole shall be placed
toleranced.
before that for the shaft or
above it, the symbols being
preceded by the basic size
indicated once only.
Indication of Tolerances on Angular Dimensions
STUFFING BOX