This document provides an overview of limits, fits, and tolerances in manufacturing. It defines key terms like basic size, tolerance, allowance, and describes different types of fits (clearance, interference, transition) and how they are specified using hole basis and shaft basis systems. It also discusses interchangeability and selective assembly, explaining how classifying components by size within their tolerance ranges enables proper assembly of mating parts from different sources.

1. Limits, Fits and Tolerances
(Sub: Measurement and Metrology)
Code: BMEC0003
Instructor
Mr. Gaurav Bharadwaj
Assistant Prof.
Department of ME
GLA University

2. INTRODUCTION
• No two parts can be produced with identical measurements by any
manufacturing process.
• Every production process involves a combination of three elements
viz, materials, machines and men.
• Variations in properties of the material being machined introduce
errors.
• The production machines themselves may have some inherent
inaccuracies.
• It is impossible for an operator to make perfect settings. While
setting up the tools and work piece on the machine, some errors are
likely to creep in.

3. Why study Limits & Fits?
· Exact size is impossible to achieve.
· Establish boundaries within which deviation from perfect form
is allowed but still the design intent is fulfilled.
· Enable interchangeability of components during assembly
The designer has to suggest these tolerance limits, which are
acceptable for each of the dimensions used to define shape and
form, and ensure satisfactory operation in service.

4. TERMINOLOGY
Basic Size: The size with reference to which the limits of size are fixed.
Actual Size: Actual measured dimension of the part.
Zero Line: It is a straight line corresponding to the basic size. The deviations are measured from this line.
The positive and negative deviations are shown above and below the zero line respectively.
Limits of Size: The two extreme permissible sizes of a part between which the actual size should lie.
Maximum Limit of Size: The greater of the two limits of size.
Minimum Limit of Size: The smaller of the two limits of size.
Shaft: A term used by convention to designate all external features of a part, including those which are not
cylindrical.
Hole: A term used by convention to designate all internal features of a part, including those which are not
cylindrical.

5. Allowance: It is the intentional difference between the hole dimensions and shaft
dimension for any type of fit.
Deviation: It is the algebraic difference between a limit of size and the
corresponding basic size.
Upper Deviation: It is the algebraic difference between the maximum limit of
size and the corresponding basic size. It is denoted by letters ‘ES’ for a hole and
‘es’ for a shaft.
Lower Deviation: It is the algebraic difference between the minimum limit of
size and the corresponding basic size. It is denoted by letters ‘EI’ for a hole and
‘ei’ for a shaft.
Fundamental Deviation: It is the deviation, either upper or lower deviation,
which is nearest to the zero line for either a hole or a shaft. It fixes the position of
the tolerance zone in relation to the zero line.

6. CONVENTIONAL DIAGRAM OF LIMITS

7. SPECIFICATION OF TOLERANCES
Unilateral Tolerance
In this system, the dimension of a
part is allowed to vary only on
one side of the basic size, i.e.
tolerance lies wholly on one side
of the basic size either above or
below it.
• e.g. Ø25 +0.18
• +0.10
• Basic Size = 25.00 mm
• Upper Limit = 25.18 mm
• Lower Limit = 25.10 mm
• Tolerance = 0.08 mm
e.g. Ø25 -0.10
-0.20
Basic Size = 25.00 mm
Upper Limit = 24.90 mm
Lower Limit = 24.80 mm
Tolerance = 0.10 mm

8. SPECIFICATION OF TOLERANCES
Bilateral Tolerance
In this system, the dimension of the
part is allowed to vary on both
the sides of the basic size, i.e. the
limits of tolerance lie on either
side of the basic size.
• e.g. Ø25 ±0.04
• Basic Size = 25.00 mm
• Upper Limit = 25.04 mm
• Lower Limit = 24.96 mm
• Tolerance = 0.08 mm

9. Maximum and Minimum Metal Conditions:
Let us consider a shaft having a dimension of 40 ± 0.05 mm.
•The maximum metal limit (MML) of the shaft will have a dimension of 40.05 mm
because at this higher limit, the shaft will have the maximum possible amount of metal.
•The shaft will have the least possible amount of metal at a lower limit of 39.95 mm, and
this limit of the shaft is known as minimum or least metal limit (LML).
Similarly, consider a hole having a dimension of 45 ± 0.05 mm.
•The hole will have a maximum possible amount of metal at a lower limit of 44.95 mm
and the lower limit of the hole is designated as MML.
•The higher limit of the hole will be the LML. At a high limit of 45.05 mm, the hole will
have the least possible amount of metal.

10. Why unilateral system is preferred in interchangeable
manufacturing?
• It is easy and simple to determine deviations.
• Another advantage of the system is that GO gauge ends can be
standardized as the holes of different tolerance grades have the same
lower limit and all the shafts have same upper limit.
• This form of tolerance greatly assists the operator, when
machining of mating parts. The operator machine to the upper limit
of shaft (lower limit for hole) knowing fully well that still has some
margin left for machining before the parts are rejected.
Tolerances are specified
(a) To obtain desired fits
(b) because it is not possible to manufacture a size exactly
(c) to obtain higher accuracy
(d) to have proper allowances

11. Relationship between Manufacturing Cost and Work Tolerance:
If the tolerances are made closer and closer, the cost of production goes on
increasing, because to manufacture the component with closer tolerances, we
need:
• precision machines, tools, materials.
• tight inspection and more precise testing and inspection devices.
• it needs more concentration of the operators, frequent checking and more
time which slows down the rate of production.

12. S.NO. TOLERANCES ALLOWANCE
1. It is the permissible variation in dimension of
a part (either a hole or shaft)
It is the prescribed difference between the dimensions
of two mating parts (hole and shaft)
2. It is the difference between higher and lower
limits of a dimension of a part.
It is the intentional difference between the lower
limits of hole and higher limit of shaft.
3. The tolerance is provided on the basic size of a
part.
Allowance is to be provided on the dimension of
mating parts to determine desired type of fit.
4. It has absolute value without sign. Allowance may be positive or negative.
Difference between Tolerance and Allowance

13. FIT
•A fit may be defined as the degree of tightness and looseness between two
mating parts.
•An ideal fit is required for proper functioning of the mating parts. Three
basic types of fits can be identified, depending on the actual limits of the hole
or shaft.

14. Clearance Fit
•The largest permissible diameter of the shaft is smaller than the diameter of the smallest hole.
•A clearance fit has positive allowance.
• Allows rotation or sliding between the mating parts.
• Used in tailstock spindle of lathe machine, feed movement of the spindle quill in a dill machine, cylinder and
piston, shaft pulley, etc.
The clearance fits may be slide fit, easy sliding fit, running fit, slack running fit and loose running fit.

15. Interference fit
• The minimum permissible diameter of the shaft exceeds the maximum allowable diameter of the hole.
• Interference fit has negative allowance.
• When two mating parts are assembled with an interference fit, it will be an almost permanent assembly, that is, the
parts will not come apart or move during use. To assemble the parts with interference, heating or cooling may be
required.
• Used in keyed pulley and shaft, car wheels, etc.
The interference fits may be shrink fit, heavy drive fit and light drive fit.

17. Transition Fit
• It may result in either clearance fit or interference fit depending on the actual value of the individual tolerances of
the mating components.
• Transition fits are a compromise between clearance and interference fits.
• They are used for applications where accurate location is important but either a small amount of clearance or
interference is permissible.
• Used in railway wheels, fixing keys, changing gears, etc.
The transition fits may be force fit, tight fit and push fit.

18. Systems of obtaining different types of fits:
Hole Basis: In this system, the basic diameter of the hole is constant while the
shaft size is varied according to the type of fit.
Shaft Basis system: In this system, the basic diameter of the shaft is constant
while the hole size is varied according to the type of fit.

19. Significance of Hole basis system:
• The bureau of Indian Standards (BIS) recommends both hole basis and
shaft basis systems, but their selection depends on the production methods.
Generally, holes are produced by drilling, boring, reaming, broaching, etc.
whereas shafts are either turned or ground. If the shaft basis system is used to
specify the limit dimensions to obtain various types of fits, number of holes of
different sizes are required, which in turn requires tools of different sizes.
• If the hole basis system is used, there will be reduction in production costs
as only one tool is required to produce the ole and the shaft can be easily
machined to any desired size. Hence hole basis system is preferred over shaft
basis system.

20. S.NO. Hole basis system Shaft basis system
1. Size of the hole whose lower
deviation is zero is assumed as the
basic size.
Size of the shaft whose upper
deviation is zero is assumed as
the basic size.
2. Limits on the hole are kept
constant and those of shaft are
varied to obtain desired type of fit.
Limits on the shaft are kept
constant and those of hole are
varied to obtain desired type of
fit.
3. Hole basis system is preferred in
mass production.
Not suitable for mass
production.
4. It requires less amount of capital
and storage space for tools needed
to produce shafts of different sizes
Needs large amount of capital
and storage space for large
number of tools required to
produce holes of different sizes.
Difference between hole basis and shaft basis system

21. Holes and Shaft Designations According to BIS
Hole Designation:
By upper case letters from A, B, … Z, Za, Zb, Zc (excluding I, L, O, Q, W and
adding Js, Za, Zb, Zc) - 25 nos. Indian Stds
Shaft Designation:
By lower case letters from a, b, … z, za, zb, zc (excluding i, l, o, q, w and
adding js, za, zb, zc) - 25 nos.
Tolerance grades
Grade of Tolerance: It is an indication of the level of accuracy. There are 18
grades of tolerances –IT01, IT0, IT1 to IT16
IT01 to IT4 - For production of gauges, plug gauges, measuring instruments
IT5 to IT 7 - For fits in precision engineering applications
IT8 to IT11 – For General Engineering
IT12 to IT14 – For Sheet metal working or press working
IT15 to IT16 – For processes like casting, general cutting work
Standard Tolerance: Various grades of tolerances are defined using the
‘standard tolerance unit’, (i) in µ m.
where, D (mm) is the geometric mean of the lower and upper diameters of a
particular diameter step within which the chosen the diameter D lies.

22. Diameter steps in I.S-919 are:
1-3, 3-6, 6-10, 10-18, 18-30, 30-50, 50-80, 80-120, 120-180, 180-250, 250- 315,
315-400 and 400-500 mm
It is understood that the tolerances have parabolic relationship with the size of
the products. As the size increases, the tolerance within which a part can be
manufactured also increases.
IT01 – 0.3 + 0.008D
IT0 – 0.5 + 0.012 D
IT1 – 0.8 + 0.020D
Grades of Tolerance IT2 to IT4 – the values of tolerance grades are placed
geometrically between the tolerance grades of IT1 and IT5.
IT6 – 10 i; IT7 – 16i; IT8 – 25i; IT9 – 40i; IT10 – 64i; IT11 – 100i; IT12 –
160i; IT13 – 250i; IT14 – 400i; IT15 – 640i; IT16 – 1000i.

24. For Shaft
ei = es – IT
es = ei + IT
For Hole
EI = ES – IT
ES = EI + IT
es = upper deviation of shaft
ei = lower deviation of shaft
ES = upper deviation of hole
EI= lower deviation of hole
Calculation for Upper and Lower Deviation

25. Interchangeability:
Interchangeability occurs when one part in an assembly can be substituted for a
similar part which has been made to the same drawing. Interchangeability is
possible only when certain standards are strictly followed.
Universal interchangeability means the parts to be assembled are from two
different manufacturing sources.
Local interchangeability means all the parts to be assembled are made in the same
manufacturing unit.
Advantages:
• the operator is not required to waste his skill in fitting the mating components by
trial and error and thus the assembly time is reduced.
• there is increased output with reduced production cost.
• it facilitates production of mating components at different places by different
operators.
• the replacement of worn out or defective parts and repair becomes very easy.
• the cost of maintenance and shutdown period is also reduced to minimum.

26. Selective assembly:
In the selective assembly the components produced are classified into groups
according to their sizes by automatic gauging.
This is done for both mating parts, holes and shaft, and only matched groups of
mating parts are assembled.
It results in complete protection against defective assemblies and reduces
matching costs since the parts since the parts may be produced with wider
tolerances.
Examples:
A practical example is the assembly of pistons with cylinder bores. Let the bore
size be 50 mm and the clearance required for the assembly is 0.12mm on the
diameter. Let the tolerance on bore and the piston each = 0.04 mm. Then,
Dimension of bore diameter is 50+0.02 mm and 50-0.02 mm
Dimension of piston shaft is 49.88+0.02 mm and 49.88-0.02 mm
By grading and marking the bores and pistons they may be selectively
assembled to give the clearance of 0.12 mm as given below:
Cylinder bore 49.98 50.00 50.02
Piston 49.86 49.88 49.90

27. Expressing a dimension as 25.3±0.05 mm is the case of
(a) Unilateral tolerance
(b) Bilateral tolerance
(c) Limiting dimensions
(d) All of the above
A shaft has a dimension, The respective values of
fundamental deviation and tolerance are
0.009
0.025
35



(a) 0.025, 0.008 (b) 0.025,0.016
(c) 0.009, 0.008 (d) 0.009,0.016
  
  

28. Two shafts A and B have their diameters specified as 100 ±
0.1 mm and 0.1 ± 0.0001 mm respectively.
Which of the following statements is/are true?
(a) Tolerance in the dimension is greater in shaft A
(b) The relative error in the dimension is greater in shaft A
(c) Tolerance in the dimension is greater in shaft B
(d) The relative error in the dimension is same for shaft A
and shaft B

29. In an interchangeable assembly, shafts of size
mm mate with holes of size mm. The
maximum possible clearance in the assembly will be
(a) 10 microns
(b) 20 microns
(c) 30 microns
(d) 60 microns
0.040
0.0100
25.000


0.020
0.000
25.000


0.02 0.02
0.00 0.00
Dimension of the hole is 50 mm and shaft is 50 mm.
The minimum clearance is
(a) 0.02 mm (b) 0.00 mm
(c) -0.02 mm (d) 0.01 mm
 
 

30. A hole is specified as mm. The mating shaft has
a clearance fit with minimum clearance of 0.01 mm. The
tolerance on the shaft is 0.04 mm. The maximum
clearance in mm between the hole and the shaft is
(a) 0.04
(b) 0.05
(c) 0.10
(d) 0.11
0.050
0.000
40

31. Interference fit joints are provided for:
(a) Assembling bush bearing in housing
(b) Mounting heavy duty gears on shafts
(c) Mounting pulley on shafts
(d) Assembly of flywheels on shafts
In order to have interference fit, it is essential that the lower limit
of the shaft should be
(a) Greater than the upper limit of the hole
(b) Lesser than the upper limit of the hole
(c) Greater than the lower limit of the hole
(d) Lesser than the lower limit of the hole

33. A shaft and hole pair is designated as 50H7d8. This assembly constitutes
(a) Interference fit
(b) Transition fit
(c) Clearance fit
(d) None of the above
Which of the following is an interference fit?
(a) Push fit
(b) Running fit
(c) Sliding fit
(d) Shrink fit

34. Consider the following fits:
1. I.C. engine cylinder and piston
2. Ball bearing outer race and housing
3. Ball bearing inner race and shaft
Which of the above fits are based on the interference
system?
(a) 1 and 2
(b) 2 and 3
(c) 1 and 3
(d) 1, 2 and 3
Allowance in limits and fits refers to
(a) Maximum clearance between shaft and hole
(b) Minimum clearance between shaft and hole
(c) Difference between maximum and minimum size of
hole
(d) Difference between maximum and minimum size of
shaft

35. Clearance in a fit is the difference between
(a) Maximum hole size and minimum shaft size
(b) Minimum hole size and maximum shaft size
(c) Maximum hole size and maximum shaft size
(d) Minimum hole size and minimum shaft size
Basic shaft and basic hole are those whose upper deviations and
lower deviations respectively are
(a) +ve, -ve (b) -ve, +ve
(c) Zero, Zero (d) None of the above

38. A fit is specified as 25H8/e8. The tolerance value for a nominal
diameter of 25 mm in IT8 is 33 microns and fundamental deviation
for the shaft is - 40 microns. The maximum clearance of the fit in
microns is
(a) -7
(b) 7
(c) 73
(d) 106
The dimensional limits on a shaft of 25h7 are
(a) 25.000, 25.021 mm
(b) 25.000, 24.979 mm
(c) 25.000, 25.007 mm
(d) 25.000, 24.993 mm