MACHINE ELEMENTS IN

MECHANICAL DESIGN

Chapter 13:
Tolerances and Fits

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 INTRODUCTION

• No two parts can be produced with identical measurements by any

manufacturing process.

• In any production process, regardless of how well it is designed or how carefully

it is maintained, a certain amount of variation (natural) will always exist.

 INTRODUCTION

Variations arises from;

• Improperly adjusted machines

• Operator error

• Tool wear

• Defective raw materials etc.

Such variations are referred as ‘assignable causes’ and can be identified

and controlled.
 INTRODUCTION

• It is impossible to produce a part to an exact size or basic size, some

variations, known as tolerances, need to be allowed.

• The permissible level of tolerance depends on the functional requirements,

which cannot be compromised.

 INTRODUCTION

• No component can be manufactured precisely to a given dimension; it can only

be made to lie between two limits, upper (maximum) and lower (minimum).

• Designer has to suggest these tolerance limits to ensure satisfactory operation.

• The difference between the upper and lower limits is termed permissive

tolerance.
 INTRODUCTION

Example

Shaft has to be manufactured to a diameter of 40 ± 0.02 mm.

The shaft has a basic size of 40 mm.

It will be acceptable if its diameter lies between the limits of sizes.

Upper limit of 40+0.02 = 40.02 mm

Lower limit of 40-0.02 = 39.98 mm.

Then, permissive tolerance is equal to 40.02 − 39.98 = 0.04 mm.

General Terminology
 General Terminology

• Basic size: Exact theoretical size arrived at by design. Also called as nominalsize.

• Actual size: Size of a part as found by measurement

• Zero Line: Straight line corresponding to the basic size. Deviations are measured

from this line.

• Limits of size: Maximum and minimum permissible sizes for a specific dimension.

• Tolerance: Difference between the maximum and minimum limits of size.

Allowance: refers to an intentional difference between the maximum material limits of

mating parts.
 General Terminology

• Deviation: Algebraic difference between a size and its corresponding basic size.

It may be positive, negative, or zero.

• Upper deviation: Algebraic difference between the maximum limit of size and its

corresponding basic size.

Designated as ‘ES’ for a hole and as ‘es’ for a shaft.

• Lower deviation: Algebraic difference between the minimum limit of size and its

corresponding basic size.

Designated as ‘EI’ for a hole and as ‘ei’ for a shaft.

 General Terminology

• Actual deviation: Algebraic difference between the actual size and its

corresponding basic size.

• Tolerance Zone: Zone between the maximum and minimum limit size.
 Tolerances

• To satisfy the ever-increasing demand for accuracy.

• Parts have to be produced with less dimensional variation.

• It is essential for the manufacturer to have an in-depth knowledge of the

tolerances to manufacture parts economically, adhere to quality and reliability

• To achieve an increased compatibility between mating parts.

 Tolerances

• The algebraic difference between the upper and lower acceptable dimensions.

• It is an absolute value.

• The basic purpose of providing tolerances is to permit dimensional variations in

the manufacture of components, adhering to the performance criterion.

 Tolerances
Classification of Tolerance

1. Unilateral tolerance

2. Bilateral tolerance

3. Compound tolerance

4. Geometric tolerance
 Tolerances
Classification of Tolerance
1. Unilateral tolerance

• When the tolerance distribution is only on one side of the basic size.
Either positive or negative, but not both.

Tolerances (a) Unilateral (b) Bilateral

1. Unilateral tolerance: Below zero line: Negative
1. Unilateral tolerance: Above zero line: Positive
2. Bilateral tolerance
When the tolerance distribution lies on either side of the basic size.

• It is not necessary that Zero line will divide the tolerance zone equally on both sides.
• It may be equal or unequal
 Classification of Tolerance

3. Compound tolerance

Tolerance for the dimension R is

determined by the combined effects of

tolerance on 40 mm dimension, on 60o, and

on 20 mm dimension
 Classification of Tolerance

4. Geometric tolerance

Geometric dimensioning and tolerancing (GD&T) is a method of defining parts

based on how they function, using standard symbols.

 Classification of Tolerance
4. Geometric tolerance

• Diameters of the cylinders need be concentric with each other.

• For proper fit between the two cylinders, both the centres to be in line.
• This information is represented in the feature control frame.
• Feature control frame comprises three boxes.
 Classification of Tolerance

4. Geometric tolerance

• First box: On the left indicates the feature to be controlled, represented

symbolically (example: concentricity).
• Centre box: indicates distance between the two cylinders, centres cannot be
apart by more than 0.01 mm (Tolerance).

• Third box: Indicates that the datum is with X.

 MAXIMUM AND MINIMUM METAL CONDITIONS

Consider a shaft having a dimension of 40 ± 0.05 mm and Hole having a dimension of 45 ± 0.05 mm.

For Shaft
Maximum metal limit (MML) = 40.05 mm
Least metal limit (LML) = 39.95 mm

For Hole
Maximum metal limit (MML) = 44.95 mm
Least metal limit (LML) = 45.05 mm
 FITS
The Assembly of Two Mating Parts is called Fit.
 RUNNING FIT: One part assembled into other so as to allow motion eg.
Shaft in bearing
 PUSH FIT : One part is assembled into other with light hand pressure & no
clearance to allow shaft to rotate as in locating plugs.
 DRIVING FIT : One part is assembled into other with hand hammer or
medium pressure. Eg pulley fitted on shaft with a key
 FORCE FIT: One part is assembled into other with great pressure eg. Cart
wheels, railway wheels
 FITS

• The degree of tightness and or looseness between the two mating parts.

Three basic types of fits can be identified, depending on the actual limits of the
hole or shaft.

1. Clearance fit

2. Interference fit

3. Transition fit
 FITS

1. Clearance fit Upper limit of shaft is less than the lower limit of the hole.

The largest permissible dia. of the shaft is smaller than the dia. of the smallest hole.
E.g.: Shaft rotating in a bush
 FITS
2. Interference fit Upper limit of the hole is less than the lower limit of shaft.

• No gap between the faces and intersecting of material will occur.

• Shaft need additional force to fit into the hole.
 3. Transition fit
Dia. of the largest permissible hole is greater than the dia. of the smallest shaft.

• Neither loose nor tight like clearance fit and interference fit.
• Tolerance zones of the shaft and the hole will be overlapped between the interference and
clearance fits.
 Hole Basis and Shaft Basis Systems

• To obtain the desired class of fits, either the size of the hole or the size of the
shaft must vary.

Two types of systems are used to represent three basic types of fits, clearance,

interference, and transition fits.

(a) Hole basis system

(b) Shaft basis system.

 Hole Basis systems

• The size of the hole is kept constant and the shaft size is varied to give

various types of fits.

• Lower deviation of the hole is zero, i.e. the lower limit of the hole is same as

the basic size.

• Two limits of the shaft and the higher dimension of the hole are varied to

obtain the desired type of fit.

 Hole Basis systems

(a) Clearance fit (b) Transition fit (c) Interference fit

 Hole Basis systems

This system is widely adopted in industries, easier to manufacture shafts of

varying sizes to the required tolerances.

Standard-size plug gauges are used to check hole sizes accurately.

 Shaft Basis systems

• The size of the shaft is kept constant and the hole size is varied to obtain

various types of fits.

• Fundamental deviation or the upper deviation of the shaft is zero.

• System is not preferred in industries, as it requires more number of standard-

size tools, like reamers, broaches, and gauges, increases manufacturing and

inspection costs.
 Shaft Basis systems

(a) Clearance fit (b) Transition fit (c) Interference fit

 Tolerance symbols

Used to specify the tolerance and fits for mating components.

Example: Consider the designation 40 H7/d9

• Basic size of the shaft and hole = 40 mm.

• Nature of fit for the hole basis system is designated by H

• Fundamental deviation of the hole is zero.

• Tolerance grade: IT7.

• The shaft has a d-type fit, the fundamental deviation has a negative value.

• IT9 tolerance grade.

 Tolerance symbols

• First eight designations from A (a) to H (h) for holes (shafts) are used for

clearance fit

• Designations, JS (js) to ZC (zc) for holes (shafts), are used for interference or

transition fits
 Tolerance symbols

• Fundamental Deviation: Deviation either the upper or lower deviation, nearest to the

zero line. (provides the position of the tolerance zone).

It may be positive, negative, or zero.

• Upper deviation: Designated as ‘ES’ for a Hole and as ‘es’ for ashaft.

• Lower deviation: Designated as ‘EI’ for a Hole and as ‘ei’ for ashaft.
 • Upper deviation: Designated as ‘ES’ for a Hole and as ‘es’ for a shaft.
• Lower deviation: Designated as ‘EI’ for a Hole and as ‘ei’ for a shaft.

Typical representation of different types of fundamental deviations

(a) Holes (internal features) (b) Shafts (external features)
Above: Tolerance grades

Above: Tolerances for some tolerance grades

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 Fit

Refers to clearances that are permissible between mating parts in a mechanical

device that must assemble easily and that must often move relative to each during
normal operation of the device.
Clearance fit.
For clearance between mating parts.
Nine classes (RC1 – RC9), ranging from precision fit (RC1) to loose fit (RC9)
Next slide shows a table extracted from ANSI Standard B4.1-1967 for Clearance fits.

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Interference fit are those in which the inside member is
larger than the outside member.
Require to apply force during assembly resulting in some deformation and
pressure on the mating surfaces.
Force fit: designed to provide a controlled pressure
between mating parts throughout the range of sizes for
a given class.
Five classes (FN1 – FN5), ranging from light drive fit (FN1) to force fit (FN5).
Next slide shows a table extracted from ANSI Standard B4.1-1967 for force
fits.

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Transition fit: used where accuracy of location is
important, but where a small amount of clearance or a
small amount of interference is acceptable.
Six classes available (LT1 – LT6).

Stress analysis for force fits.

As mentioned stresses exist on the surfaces of the mating parts.
Such stresses can cause failure in brittle materials.
Stress analysis related to the analysis of thick-walled cylinders.

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Procedure for computing stresses for force fits.
1. Determine the amount of interference from the design of the parts.

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2. Compute the pressure at the mating surface using the following
equations for members of the same material and for members of
different materials respectively:

E  (c 2  b 2 )(b 2  a 2 ) 
p  
b  2b 2 (c 2  a 2 ) 

p
 1  c2  b2  1  b2  a 2 
b  2  vo    2  vi 
 c b  Ei  b  a
2 2
 Eo 

where p = pressure at the mating surface total diametral interference.

E = modulus of elasticity of each member if they are the same.
Eo = modulus of elasticity of outer member.
Ei = modulus of elasticity of inner member.
vo = Poisson’s ratio for outer member.
vi = Poisson’s ratio for inner member.

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3. Compute the tensile stress in the outer member and inner member
using the following equations respectively.

 c2  b2 
o  p
 c2  b2 

 

 b2  a 2 
 i   p
 b2  a 2 

 

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The use of a spreadsheet may be useful in the above computations. An
example of a spreadsheet may look like on in the diagram below:

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 3. General Tolerancing Methods

For decimals dimensions:

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Geometric Dimensioning and Tolerancing (GD&T)

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