UNIT 2 SYSTEM OF LIMITS, FITS, TOLERANCES AND...

Sridhara T., Asst. Professor, Dept. of Mechanical Engg. Unit 2

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UNIT 2

SYSTEM OF LIMITS, FITS, TOLERANCES AND GAUGING

Introduction

Definition of limits

Need for limit system

Tolerance

Tolerance dimensions ( system of writing tolerance)

Relationship between Tolerance Vs Cost

Compound tolerance.

Tolerance accumulation or tolerance “build –up”

Specifying tolerances in assembly

Interchangeability

Selective assembly

Limits of size

Indian standard (IS 919-1963)

Condition for the success of any system of limits and fits.

Concepts of Limits of size and Tolerance

Some Definitions

Definition of Fit

Types of Fit and their Designation (IS 919-1963)

Specific types of Fit

Allowance

Geometrical Tolerance

Positional Tolerance

Symbols and terms used in IS 919-1965

System of Fits

Hole Basis System

Staff Basis System

Significance of Hole Basis System

Tolerance Grade

Numerical Problems


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INTRODUCTION:

In nature two extremely similar (identical) things are difficult to obtain.

If at all we come across exactly similar things, it must be only by chance.

Its holds good for production of component parts in engineering.

Every process is combination of three elements namely, man, machine and material

A change in any of these constitutes a change in the process.

The above said three elements are subjected to inherent and characteristics variations.

Example: 1.Drilling operation is to be performed on castings.

2.Shaft rotating in bearing.

Thus we conclude that:

1. It is not possible to make any part precisely to a given dimension, due to variability of

elements of production process.

2. Even if by chance the part made exactly to a given dimension, it is impossible to measure

it accuracy enough to prove it.

3. If attempts are made to achieve perfect size the cost of production will increase

tremendously.

Therefore, the magnitude of permissible variation in dimension has to be allowed to account for

the variability.

******syllabus starts from here******

Limits: Definition: The maximum and minimum permissible sizes within which the actual size of a

component lies are called limits.

Limits are fixed with reference to the basic size of that dimension.

Upper limit (The high limit ) for that dimension is the largest size permitted and the low

limit is the smallest size permitted for that dimension.

Need for limit system: The correct and prolonged functioning of manufactured products depends upon its correct

size relationship between various components of the assembly.

This means that the parts must fit together in a certain way.

Example: Valve Assembly

Hence purpose of limit system is to establish the types of fits and recommend the dimensions of

the mating parts

Tolerance: Definition:

Tolerance can be defined as “the permissible variation in size or dimension “of a part. Or

Tolerance is the difference between the upper limit and lower limit of a part.

The word Tolerance indicated that a worker is not expected to produce the part to the exact size,

but a definite small size error is permitted.


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Tolerance Zone: The difference between upper limit and the lower limit of a dimension

represents the margin for variation in workmanship, and is called a “Tolerance zone”.

Example: a shaft of 25 mm basic size may be written as 25 + 0.02.

Upper limit = 25 + 0.02 = 25.02 mm

Lower limit = 25 – 0.02 = 24.98 mm

Tolerance = upper limit – lower limit

= 25.02 – 24.98 = 0.04 mm

NOTE: The tolerance is always a positive quantitative number.

*** very very imp.

System of writing Tolerance (Toleranced dimensions):

There are two systems of writing tolerance:

1. Unilateral system

2. Bilateral system

1. Unilateral system: When the two limit dimensions are only above or only below the nominal size (basic

size) then the tolerances are said to be Unilateral.

Example: +0.03 +0.01 -0.00 -0.01

25+0.02

, 25 +0.00 ,

25 -0.01

, 25 -0.02 etc…

Figure: unilateral system

2. Bilateral system: When the limit dimensions are given above and below the nominal size (basic size) then

the tolerances are said to be bilateral.

Example: 25+0.02

, 25 +0.00 etc…

Tole

ran

ce

Tole

ran

ce

Tole

rance

Tole

rance B

asi

c si

ze


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Unilateral tolerance is preferred over bilateral tolerances because the operator can machine to the

upper limit of the shaft (or lower limit of the hole) still having the whole tolerance left for

machining before the parts are rejected.

It is easy and simpler to determine deviations

GO gauge end can be standardized as the holes of different tolerance grades have the

same lower limit and all the shafts have same upper limit.

Relationship between Tolerance and Cost:

The relationship between tolerance and cost of production is shown in figure.

If the tolerance are made closer and closer, the cost of production goes on increasing,

because to manufacture the component with closer tolerance.

Basi

c si

ze

Tole

rance

Tole

ran

ce

Figure: Bilateral Tolerance


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Specifying tolerance in an assembly: The type of assembly or fit between the mating parts will be decided based on the functional

requirements (i.e., clearance type of fit like in bearing and shaft.)

Accordingly tolerances on the shaft and hole are decided using the following two methods:

1. complete interchangeability

2. Statistical approach.

In complete interchangeability, no risk is taken even for a single non-confirming assembly.

If the fit between shaft and hole is clearance type as shown in figure, then for the complete

interchangeability.

Tolerance on shaft = Tolerance on hole = Half of the maximum clearance – half of the minimum clearance

In Statistical approach:

Statistical approach bases the permissible tolerance on the normal distribution curve.

Considering that only 0.3% of the parts would lie outside ±3σ limits.

This approach, obviously, allow wider tolerances and permits cheaper production

methods especially in mass production.

It was estimated that about 33% more tolerance may be permitted by statistical approach

compared to complete interchangeability.

Compound Tolerance: A compound tolerance one which is derived by considering the effect of tolerance on

more than one dimension.

For example: in figure the tolerance on dimension L are dependent on tolerances on D, H,

and Ө.

This compound tolerance on L is the combined effect of all the three tolerances.

The dimension L will be maximum when the base dimension is D+a, θ+α and the vertical

dimension is H-d.

The dimension L will be minimum when the base dimension is D-b, θ-β and the vertical

dimension is H+c.

q

+a

-b

D

+a

-b

+c

-d

H

figure: Compound tolerance

L


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Tolerance accumulation or Tolerance “Build-up”: If a part consists of several steps, each step having some tolerance over its length, then overall

tolerance on complete length will be the sum of the tolerance on individual lengths as shown on

figure.

Interchangeability: Interchangeability occurs when one part in an assembly can be substituted for a similar part

which has been made to the same drawing.

Suppose there are 100 parts each with a hole, and 100 shafts which have to fit into any of

the holes.

If they is interchangeability then any one of the 100 shafts should fit into any of the holes

and the required kind of fit can be obtained.

Hence, for interchangeability of holes and shafts, we need a system of limits and fit

which gives standard values for the limits on the hole and shaft, so that particular type of

fit can be obtained.

Interchangeability is possible only when certain standard are strictly followed.

In Universal interchangeability the mating parts are drawn/manufactured from two

different manufacturing sources.

Universal interchangeability is desirable and which will be an international standard.

In Local interchangeability the mating parts are manufactured from same manufacturing

sources, in which local standard is followed.

The required type is obtained in an assembly either by universal or local/full

interchangeability or selective assembly.

.Selective Assembly: In selective assembly, the parts are graded according to their size by automatic gauging.

In which only matched grades are assembled.

This technique is most suitable for where close fit (Interference fit) of two component

assembles are required.

It results in complete protection against non-confirming assemblies and reduces

machining costs, since close tolerance can be maintained.

Example: practical example of this system is the assembly of piston with cylinder bores. Let the

bore size be mm & the clearance required for the assembly 0.12mm on the diameter. Let the

tolerance on bore and the piston each = 0.04mm. Then,

Dimension of bore diameter is 50+0.02

mm.

Dimension of piston shaft is 49.88+0.02

mm.

By grading and making the bores and the piston 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


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Selective assembly is often followed in aircraft, automobiles and other industries where

the tolerance are very narrow and are not possible to manufacturer by an sophisticated

machine at reasonable cost.

Here close tolerances to be achieved without actually being produced.

Limits of Size: In deciding the limits for a particular dimension it is necessary to consider following.

1. Functional requirements: the intended function that a component should perform

2. Interchangeability: replacements of the component in case of failure/ damage without

difficulty

3. Economy in production time and cost.

Thus degree of tolerance provided on the mating components calls for a compromise.

Number of standards on limit and fit systems has been published to help the designer in

selecting the uniform limits and fits.

Indian standard (IS 919 – 1963): The Indian standard system of limits and fits comprises suitable combination of 18 grades

of fundamental tolerances or grades of accuracy of manufacturer (IT0 to IT16), and 25

types of fundamental deviations represented by letter symbols for both holes and shafts

(capital letters A to ZC for holes and lower case letters a to zc for shafts).

In diameter steps up to 500mm.

The 25 fundamental deviations of hole are represented BY

A,B,C,D,E,F,G,H,JS,J,K,M,N,P,R,S,T,U,V,X,Y,Z,ZA,ZB,ZC

Maximum and minimum Metal Limits

(Or Maximum and Minimum Metal conditions):

If the tolerance for the shaft is given as 25+0.05

, the upper limit will be 25.05 mm and the

lower limit will be 24.94 mm.

The shaft is said to be have Maximum Metal Limit (MML) of 25.05mm, since at this

limit the shaft has maximum possible amount of metal.

The limit of 24.95 will then be the minimum or “Least metal Limit” (LML) because at

this the shaft will have the least possible amount of metal.

MM

L

LM

L

LM

L

MM

L

HOLE

SHAFT

Figure: MML & LML of Hole and Shaft


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Max

dia

Min

dia

Max

dia

Min

dia

HOLE

SHAFT

BASI

C SI

ZE

ZERO LINELower

dev

iation

Lower

dev

iation

Uppe

r de

viat

ion

Uppe

r de

viat

ion

Tole

ranc

e fo

r ho

le

Tole

ranc

e fo

r sh

aft

hole

shaft

Figure: Shaft and Hole System

Similarly, for hole is designated as 30+0.05

mm.

The upper limit will be 30.05 mm and the lower limit will be 29.95 mm.

Then, the maximum metal limit (MML) of hole will be equal to 29.95 mm, since at this

lower limit the hole has the maximum possible amount of metal.

While the minimum metal limit (LML) of hole will be equal to 30.05 mm. then, the upper

limit of the hole has the minimum possible amount of metal.

Some Definitions:

(Terminologies used in Limits and Fits)

Shaft: The term shaft refers not only to the diameter of a circular shaft but also to any external

dimension of a component.

Hole: The term shaft not only refers to the diameter of the circular hole but also any internal

dimension of a component.

When an assembly is made of two parts, one is known as male-surface and the other

mating part as female (enveloping) surface.

The male surface is called as shaft and the female surface is called as hole.

Basic Size or Nominal Size: It is the standard size of a part in relation to which all limits of

variation are determined. the basic size is same for hole and shaft.

Actual size: actual size is the dimension as measured on manufacturing part.

Zero line: it is straight line drawn horizontally to represent the basic size. In the graphical

representation of limits and fits, all the deviations are shown with respect to the zero line (datum

line).

The positive deviations are shown above zero line and negative deviation are shown

below zero line as shown in figure.


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zero line

uppe

r lim

it

lower

lim

it

lower

dev

iation

basic

size

tolerance zone

(fundamental

deviation)

tole

ranc

e

Deviation: deviation is the algebraic difference between the size (actual, maximum, etc) and

the corresponding basic size.

Upper deviation: it is the algebraic difference between the upper (maximum) limit of size

and the corresponding basic size.

It is positive quantity when the upper limit of size is greater than the basic size and

negative quantity when the upper limit of the size less than the basic size as shown in

figure.

It is denoted by „ES‟ for hole and „es‟ for shaft.

Lower deviation: it is it is the algebraic difference between the lower (minimum) limit of

size and the corresponding basic size.

It is positive quantity when the lower limit of size is greater than the basic size and

negative quantity when the lower limit of the size less than the basic size.

It is denoted by „EI‟ for hole and „ei‟ for shaft.

Fundamental deviation: either the upper or lower deviation, which is the nearest one to the

zero line for either a hole or a shaft.

It fixes the position of Tolerance zone in relation to the zero line.


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From the figure sit is very clear that when the tolerance zone is above the zero line, then lower

deviation is fundamental deviation. While, the tolerance zone is below zero line , then upper

deviation is fundamental deviation.

Basic shaft: basic shaft is the shaft whose upper deviation is zero. Thus upper limit of the basic

shaft is the same as the basic size. It is denoted by letter „h‟

Basic hole: basic hole is the hole whose lower deviation is zero. Thus lower limit of the basic

hole is the same as the basic size. It is denoted by letter „H‟

Size Tolerance: The relationship of deviation with tolerance is given by,

For shaft, IT = es – ei (upper deviation – lower deviation)

For hole, IT = ES – EI (upper deviation – lower deviation)

Definition of fits, types of fits and their Designation (Is 919 – 1963):

Fit: fit may be defined as a degree of tightness or looseness between two mating parts to perform

a definite function when they are assembled together.

Accordingly, a fit may result either in a moveable joint or a fixed joint.

For example: a shaft running in a bearing can move in relation to it and thus forms a moveable

joint, whereas, a pulley mounted on the shaft forms a fixed joint.

Types of fits (Classification of fits): On the basis of positive, zero and negative values of clearance, there are three types of fits:

1. Clearance fit

2. Interference fit

3. Transition fit.

zero line

lower

limi

t

uppe

r lim

it

toler

ance

funda

mnen

tal d

eviat

ion

(upper deviation)tolerance zone


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clea

renc

e

hole hole

shaftshaft

shafthole

1. Clearance fit: In this type of fit, the largest permitted shaft diameter is smaller than the diameter of the

smallest hole as shown in figure.

So that the shaft can rotate or slide through with different degree of freedom according to

the purpose of mating part.

In this type of fit shaft is always smaller than hole.

Figure: clearance fit

2. Interference fit: In this type of fit the minimum permissible diameter of the shaft is larger than the

maximum allowable diameter of the hole.

Here the shaft and hole members are intended to be attached permanently and used as a

solid component.

Example: bearing bushes, steel rings on a wooden bullock cart wheel etc.,

Zero line


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3. Transition fit. Transition fit lies mid way between clearance and interference fit.

In this type of fit, the diameter of the largest allowable hole is greater than that of the

smallest shaft, but the smallest hole is smaller than the largest shaft, so that a small

positive and negative clearance exists between the shaft and hole as shown in figure.

Example: Spigot in mating holes, coupling rings.

shafthole

shaft

hole

+ve

clea

renc

e

-ve clearance

hole

shaft

shaft

shafthole

hole

Inte

rfer

ence

Zero line

Zero line


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Maximum clearance: it is the difference between the minimum size of shaft and maximum size

of hole.

Minimum clearance: it is the difference between the maximum size of shaft and minimum size

of hole.

Special types of fit:

1. Slide fit: this type of fit has very small clearance, the minimum clearance being zero.

Sliding fits are employed when the mating parts required to moving slowly in relation to

each other.

It is clearance type of fit

Example: tailstock spindle of lathe, feed movement of spindle quill in drilling.

2. Driving fit: in this fit, the shaft is made slightly larger than the hole. Such that parts can be

assembled by driving force.

This is employed when the parts are to remain in a fixed position relative to each other.

It is an interference type of fit.

3. Push fit or Snug fit: this type of fit represent a close fit which permits assembling of parts by

hand.

It provides a small clearance

It is transition type of fit

Example: change gears.

4. Force fit or pressed fit: force fit are employed when the mating parts are not required to be

disassembled during their total service life.

In which assembly is obtained only when high pressure is applied.

It is interference type of fit.

Example: forging machine.

5. Selective fit or tight fit: it provides less interference than force fit.

Tight fits are employed for mating parts that may be replaced while overhauling of the

machine.


Example: cylindrical grinding machine.

6. Shrinkage fit: it refers to maximum negative allowance.

Considerable force is necessary for the assembly.

The fitting of frame on the rim can also be obtained first by heating the frame and then

rapidly cooling it in its position.


7. Freeze fit: in freeze fit the shaft (internal member) is contracted by cooling and assembled

with the hole (external member).


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When the assembled parts are exposed to the atmospheric temperature, the contracted shaft

(internal member) expands and thus fit into the hole (external member).

It is interference type fit.

Example: insertion of valve seat in engine cylinder heads.

Allowance: It is the intentional difference between the lower limit of the hole and upper limit of

the shaft.

The allowance may be positive or negative.

The positive allowance is called clearance and negative allowance is called

interference.

Figure: allowance

Difference between tolerance and Allowance;

Tolerance Allowance

1. It is the difference between the upper

limit and lower limit of a part

1.It is the intentional difference between

lower limit of hole to upper limit of shaft

2. It is the permissible difference in

dimension or size of a part.

2. It is the prescribed difference between the

dimensions of two mating parts.

3.it is absolute value without sign 3. allowance may be +ve or –ve

4. Tolerance provided because operator is

not possible to produce a part to exact size.

4. allowance provided on mating parts to

provide desired type of fit.

Geometrical Tolerance:

It is necessary to specify and control the geometric features of a component, such as

straightness, flatness, roughness etc., In addition to linear dimensions.

Geometric tolerances are concerned with the accuracy of the relationship of one

component to another, and it should be specified separately.

Geometric tolerance may be defined as the maximum permissible overall variation of

form, or position of form, or position of feature.

Geometric characteristics and symbols:

It is of two types


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1. Single feature

2. Related feature.

Positional Tolerance:

If A particular hole is to be drilled in a plate.

First axis of the hole will be defined and located. Some tolerance is allowed on this.

Thus center of hole itself can occupy any position within a square at the center depending on the

tolerance specified to locate center

Then some tolerance has to be specified for manufacturing hole. Thus hole obtained will be

having cumulative effect of two tolerances.

This problem is obviated by specifying positional tolerances.

In conventional method a positional tolerance is given by tolerance coordinates is as

shown in figure.

In case of hole illustrated, it will be seen that the tolerance zone for a hole center is

square.

If the tolerance coordinate are not equal then zone would be rectangle.

Thus permissible error in position of center varies within the direction of error.

But, in most of the cases, the designer wishes to restrict the amount by which the hole

may vary from its true position irrespective of direction of error.

The method of tolerancing as shown in figure a and figure b provides a circular tolerance

zone for the center and consequently permits the same error in any direction.

A careful study of figure shows how much tolerancing allows a large positional error for

a hole which is not on maximum metal condition.

UNIT 2 SYSTEM OF LIMITS, FITS, TOLERANCES AND...

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