# Tolerance

Tolerance

Tolerance

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LIMITS, TOLERANCES AND FITS

• Introduction

• Need of limits and fits

• Nomenclature of limit system

• Fits

• Fundamentals of tolerances

• Considerations for tolerances

• Grades of tolerances

• **Tolerance** grade for different processes

• **Tolerance** values

• Empirical calculation of tolerance

• Linear tolerance indication

• **Tolerance** dimensioning

2

INTRODUCTION

• It is very difficult to manufacture machine

component to an exact size because of the

inherent limitations of men, machines and

materials.

• The workman has to be given some allowable

margin so that he can produce a part, dimension

of which will lie between two acceptable limits, a

maximum and a minimum.

• The system in which a variation is accepted is

called the limit system.

• The allowable deviations are called tolerances.

• The relationship between the mating parts are

called fits.

3

INTRODUCTION

• Two extreme permissible sizes of a part between

which the actual size is contained are called

limits

• In mass production, variations in dimensions in

the basic size is allowed depending upon the

functional requirements of the components to be

assembled, material used and the cost of

production

4

NEED OF LIMITS AND FITS

The need of limits and fits is due to;

(1)Mass production and specialization:

• Due to mass production, it is not possible for

single industry to manufacture all components

of a machinery

• To overcome this problem, the designer gives a

range of limits to the basic size within which he

expects the finished size of the job

5

NEED OF LIMITS AND FITS

(2) Standardization:

• Standardization means specifying the size of

component nationally and if possible

internationally in order to enjoy the benefit of

large scale production and specialization

• This calls for the maximum and minimum size of

the components so that it can be used in any part

of the country/ of the world

• Standardization reduces the manufacturing costs,

helps in improving the quality of products,

simplifies repair and maintenance of machines

and reduces the time and effort needed to make

the new machines

6

NEED OF LIMITS AND FITS

(3) Interchangeability:

• Interchangeability ensures the possibility of

assembling a unit or machine or replacing a worn

out component without resorting to the extra

machining or fitting operation

• Thus, if machines are provided with

interchangeable parts, they can be easily

replaced in service conditions

• This necessitates that the components must be

manufactured within the permitted variation in

size so that they can be accepted without any

change

7

NOMENCLATURE OF LIMIT SYSTEM

Following basis terms are defined as per BIS

system of limits and fits which are frequently used

in dimensioning of drawing

(1)Size of dimensions: It is a number expressed in

any particular unit which gives the numerical

value of a dimension

(2) Basic size: It is the theoretical size of a part

obtained by design. It is the size based on which

the dimensional deviations are given

(3) Actual size: It is the size of the component

obtained by actual measurement after it is

manufactured

8

Basic size

Lower Limit

Upper Limit

Lower Limit

Upper Limit

Lower Limit

Upper Limit

NOMENCLATURE OF LIMIT SYSTEM

(4) Limits of size: The two extreme permissible

sizes between which the actual size is contained

are called limits

• The maximum size is called the upper limit and

it is the greater of the two limit sizes

• The minimum size is called the lower limit and it

is the smaller of the two limit sizes

9

NOMENCLATURE OF LIMIT SYSTEM

Basic size

Lower Limit

Upper Limit

(5) **Tolerance**: The permissible variation of a size is

called tolerance

• It is the difference between Upper limit and

Lower limit of the size

• It is always positive and is expressed only as a

number without a sign

**Tolerance**

10

Basic Size

NOMENCLATURE OF LIMIT SYSTEM

• If the variation is provided on one side of the basic

size, it is termed as Unilateral tolerance

e.g. 50 +0.03 or 50 -0.03

• If the variation is provided on both sides of the

basic size, it is termed as Bilateral tolerance

e.g. 50 ±0.02

(6) **Tolerance** Zone: The graphical representation of

tolerance is called tolerance zone

(7) Zero line: It is a straight line to which the

deviations are referred and represents the basic

size

Zero line

**Tolerance** zone

11

NOMENCLATURE OF LIMIT SYSTEM

(8) Deviation: It is the algebraic difference

between a size (actual or maximum or

minimum) and the corresponding basic size

Basic size, deviations and tolerances 12

NOMENCLATURE OF LIMIT SYSTEM

Upper Deviation: It is the algebraic difference

between the upper limit and the corresponding

basic size (by symbol ES (Hole) or es (shaft)

Lower Deviation: It is the algebraic difference

between the lower limit and the corresponding

basic size (Represented by EI (Hole) or ei (shaft)

ES,es=E’ Cart Superior

EI,ei=E’ Cart Inferior

13

NOMENCLATURE OF LIMIT SYSTEM

Fundamental Deviation: It is either the upper or

the lower deviation which is nearer to the zero

line. It is chosen to locate the tolerance zone with

respect to the zero line

Actual Deviation: It is the algebraic difference

between the actual size and the corresponding

basic size

(9) Shaft: It is a term conventionally used to

designate all external features of a part including

those which are not cylindrical

(10) Hole: It is a term conventionally used to

designate all internal features of a part including

those which are not cylindrical

14

NOMENCLATURE OF LIMIT SYSTEM

(11) Basic shaft: It designates a shaft whose upper

deviation is zero

(12) Basic hole: It designates a hole whose lower

deviation is zero

(13) Allowance: The difference between the

dimensions of two mating parts is called the

allowance

(14)Maximum Metal Condition: Maximum metal

condition (MMC) is related to retention of

maximum amount of metal in any machine

part. All external features (shaft) need

maximum limit of size while all internal

features (hole) need minimum limit of size.

15

NOMENCLATURE OF LIMIT SYSTEM

(15) Least Metal Condition: Least metal condition

(LMC) is related to retention of minimum

amount of metal in any machine part. All

external features (shaft) need minimum limit

of size while all internal features (hole) need

maximum limit of size.

16

FITS

• The relationship resulting from the difference

between the actual size of the two mating parts

which are to be assembled is known as a fit.

• In assembly, the joints may be either movable or

permanent depending upon the functions

• e.g. shaft rotating in bush (movable) or flywheel

mounted on a shaft (fixed)

• Depending upon the actual limits of the hole or

shaft sizes, fits may be classified as;

(1) Clearance fit

(2) Transition fit and

(3) Interference fit

17

FITS

(1) Clearance fit: It is a fit that gives a clearance

between the two mating parts.

• Here, hole size is always greater than shaft size.

• The actual amount by which the hole exceeds

the saft is termed as the clearance.

Clearance fit

18

FITS

Minimum Clearance fit:

It is the difference

between the minimum

size of the hole and the

maximum size of the

shaft in a clearance fit.

Maximum Clearance fit:

It is the difference

between the maximum

size of the hole and the

minimum size of the shaft

in a clearance or transition

fit. 19

(2) Transition fit:

• This fit may result in

either an interference or

a clearance, depending

upon the actual values of

the tolerance of

individual parts.

• It results in a clearance

fit, when shaft diameter

is smaller than hole

diameter

• It results in interference

fit, when shaft diameter

is greater than hole

diameter

FITS

Transition fit

20

(3) Interference fit:

FITS

• If the difference between the hole and shaft sizes is

negative before assembly; an interference fit is

obtained.

Interference fit

21

FITS

Minimum Interference fit:

• It is the magnitude of the

difference (negative) between

the maximum size of the hole

and the minimum size of the

shaft in an interference fit

before assembly.

Maximum Interference fit:

•It is the magnitude of the

difference between the

minimum size of the hole and

the maximum size of the shaft

in an interference or a

transition fit before assembly.

22

FITS

Schematic representation of fits

23

HOLE & SHAFT BASIS SYSTEM

• Hole basis system: In this system, the size of the shaft

is obtained by subtracting the allowance from the basic

size of the hole.

• The lower deviation of the hole is zero. The letter

symbol for this situation is ‘H’.

• This system is preferred in most cases, since standard

tools like drills, reamers, broaches, etc., are used for

making a hole.

24

HOLE & SHAFT BASIS SYSTEM

• Shaft basis system: In this system, the size of the hole

is obtained by adding the allowance to the basic size of

the shaft.

• The upper deviation of the shaft is zero. The letter

symbol for this situation is ‘h’.

• Used by industries using semi-finished shafting as raw

materials, e.g., textile industries, or when several parts

having different fits but one nominal size is required on

a single shaft

25

FUNDAMENTALS OF TOLERANCES

• The tolerance is a factor or percentage of the

nominal value, a maximum deviation from a nominal

value, an explicit range of allowed values, be

specified by a note or published standard with this

information or be implied by the numerical accuracy

of the nominal value.

• To maintain proper functionality, the largest

possible tolerance needs to be specified.

•Closer or tighter tolerances are more difficult and

costly to achieve.

•Conversely, large or looser tolerances may

significantly affect the operation of the device.

26

CONSIDERATIONS FOR SETTING TOLERANCE

Following aspects should be adhered to while

assigning the amount of tolerance;

(a)Adopting proper scientific principles, adequate

engineering knowledge, professional experience

and experimental investigation will help

determine the amount of tolerance such that it

should not affect other factors or the outcome of

the process.

(b) The choice of tolerance is also affected by the

intended statistical plan for statistical analysis.

27

CONSIDERATIONS FOR SETTING TOLERANCE

(c) The amount of engineering tolerances as provided

in any specification may not always be achieved

due to inherent variation in input and output of

operation system, system and operational errors

and statistical uncertainty in measurement.

(d) The process capabilities of systems, materials and

products must be compatible with the specified

engineering tolerances. In order to achieve these,

total quality management (TQM) should be

observed which will be reflected through process

capability index (PCI).

28

GRADES OF TOLERANCES

• Large variety of tolerance is classified by the

International **Tolerance** (IT) Grade.

• Lower IT number refers to low tolerance and is

used for making precision instruments.

• ISO: 286 (Part I & II) - 1988 specifies these

tolerance grades.

• For each nominal step, there are 18 grades of

tolerances, designated as IT01, IT0, IT1 to IT16,

known as fundamental tolerances.

29

TOLERANCE GRADE FOR VARIOUS PROCESSES

IT01 IT0 IT1 IT2 IT3 IT4 IT5 IT6 IT7 IT8 IT9 IT10 IT11 IT12 IT13 IT14 IT15 IT16

Most Precise tools

●

Slip Gauges ● ● ●

Lapping ● ● ● ●

Honing ● ● ●

Super finishing ● ● ●

Cylindrical Grinding ● ● ● ●

Diamond turning ● ● ● ●

grinding, broaching,

reaming

● ● ● ● ●

Boring, Turning ● ● ● ● ● ● ●

Sawing ● ● ●

Milling ● ● ● ● ●

Shaping, Planning ● ●

Extruding ● ● ● ●

Cold rolling, drawing ● ● ● ● ●

Drilling ● ● ● ●

Die Casting ● ● ● ●

Forging ● ● ● ●

Sand casting, hot rolling ● ● 30 ●

TOLERANCE VALUE FOR DIFFERENT IT GRADES

31

EMPIRICAL CALCULATION OF STD. TOLERANCE

• The fundamental tolerance is a function of the

nominal size and its unit is given by the empirical

relation,

standard tolerance unit, i 0.45

D 0.001D

Where…

i = In microns and

D = Geometrical mean of basic diameter steps in

mm

• The relation is valid for grades 5 to 16 and

nominal sizes from 3 to 500mm

• Relative magnitude is given in table below

3

32

EMPIRICAL CALCULATION OF STD. TOLERANCE

• For grades below IT5, there are other empirical

relations which are given as per IS: 1919–1963.

The expressions are;

• For IT01, i = 0.3 + 0.008D

• For IT0, i = 0.5 +0.012D and

• For IT1 to IT4, i = 0.8 + 0.02D

33

LINEAR TOLERANCE INDICATION

• **Tolerance** is denoted by two symbols, a letter

symbol and a number symbol, called the grade.

• The letter symbols range from A to ZC for holes

and from a to zc for shafts.

• The letters I, L, O, Q, W and i, l, o, q, w have not

been used.

• These letter symbols represent the degree of

closeness of the tolerance zone (positive or

negative) to the basic size.

34

LINEAR TOLERANCE INDICATION

(a) Basic characteristics of letter symbol for

internal (hole) features:

• The shaded length of each rectangle represents

total IT grade value

• For Positive side, the upper deviation = lower

deviation + IT grade value

• For Negative side, the lower deviation = upper

deviation + IT grade value

• For A, the magnitude of positive lower deviation

is maximum and is zero for H.

• The upper deviation becomes negative from K

onwards up to ZC

35

LINEAR TOLERANCE INDICATION

(b) Basic characteristics of letter symbol for

external (shaft) features:

• The shaded length of each rectangle represents

total IT grade value

• For Positive side, the upper deviation = lower

deviation + IT grade value

• For Negative side, the lower deviation = upper

deviation + IT grade value

• For a, the magnitude of negative upper

deviation is maximum and is zero for h.

• The upper deviation becomes positive from k

onwards up to zc

36

GRAPHICAL ILLUSTRATION OF TOLERANCE ZONES

37

TOLERANCE DIMENSIONING

There are three methods used for tolerance

individual dimensions

(1) Method 1: In this method, tolerance

dimension is given by its basic value followed

by a symbol comprising of both a letter and a

number.

e.g. Φ25H7

Φ25=Basic size is 25mm

H= Signifies the basic hole with lower deviation

zero

7 = Signifies the tolerance grade IT7

38

TOLERANCE DIMENSIONING

Method 2:

• In this method, the basic size and the tolerance

values are indicated above the dimension line;

• The tolerance values being in a size smaller than

that of the basic size and the lower deviation

value being indicated in line with the basic size.

39

TOLERANCE DIMENSIONING

Method 3:

•In this method, the maximum and minimum sizes

are directly indicated above the dimension line

•When assembled parts are dimensioned, the fit is

indicated by the basic size common to both the

components, followed by the hole tolerance symbol

first and then by the shaft tolerance symbol (e.g.,

Φ 25 H7/h6, etc…)

40

TOLERANCE DIMENSIONING

**Tolerance** dimensioning of assembled parts:

41

LIMITS

TOLERANCES

&

FITS

42