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LIMITS, FITS AND

TOLERANCES Dr. Dayananda Pai

Aero & Auto Engg. Dept.,

M.I.T. Manipal

Objectives

• After studying the material in this module, student should

be able to :

• Read and create limit dimensions.

• Describe the nominal size, tolerance, limits and allowance

of two mating parts.

• Identify a clearance fit, interference fit and transition fit.

• Describe the basic hole and basic shaft system.

• Dimension two mating parts using limit dimensions,

unilateral tolerances, and bilateral tolerances.

• Describe the classes of fit and give example of each.

Why study Limits & Fits?

• In manufacturing it is impossible to produce components

to an exact size, even though they may be classified as

identical.

• However, industry does demand that parts should be

produced between a given basic size.

• The difference between these sizes is called the

“tolerance” which can be defined as “the amount of

variation in size which is tolerated”. A broad, generous

tolerance is cheaper to produce and maintain than a

narrow precise one.

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• The maximum and minimum permissible sizes within

which the actual size of a component lies are called Limits

• Upper limit

• Lower Limit

• Nominal Size

UNILATERAL SYSTEM OF

TOLERANCE • This tolerance allows

variation in only one direction form the basic size. This method is advantageous when a critical size is approached as material is removed during manufacturing, as in case of close-fitting holes and shafts. A unilateral tolerance is always all plus or all minus; that is either the plus or the minus value be zero.

BILATERAL SYSTEM OF TOLERANCE

• This tolerance allows

variation in both

directions from the

basic size. Bilateral

tolerances are usually

given with location

dimensions or with any

dimensions that can be

allowed to vary in

either direction

• If it is desired to specify an equal variation in both

directions, the combined plus or minus symbol (±) is used

with a single value.

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Definitions

• BASIC SIZE This is the size about which the limits of

particular fit are fixed. It is the same for both “shaft” and

“hole”. It is also called the “nominal size”.

• TOLERANCE: Tolerance is defined as the difference

between maximum and minimum limits of size for a hole

or shaft. It is also the difference between the upper and

lower deviations

• FIT

• A fit may be defined as the relative motion which can exist

between a shaft and hole (as defined above) resulting

form the final sizes which achieved in their manufacture.

There are three classes of fit in common use : clearance,

transition and interference.

Clearance fit

• This fit results when the shaft size is always less than the hole size for all possible combinations within their tolerance ranges. Relative motion between shaft and hole is always possible.

• The minimum clearance occurs at the maximum shaft size and the minimum hole size.

• The maximum clearance occurs at the minimum shaft size and the maximum hole size.

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TRANSITION FIT

• A pure transition fit occurs when the shaft and hole are exactly the same size. This fit is theoretically the boundary between clearance and interference and is practically impossible to achieve, but by selective assembly or careful machining methods, it can be approached within very fine limits.

• Practical transition fits result when the tolerance are such

that the largest hole is greater than the smallest shaft and

the largest shaft is greater than the smallest hole. Two

transition fits are given on the data sheet.

INTERFERENCE FIT

• This is a fit which always results in the minimum shaft size being larger than the maximum hole size for all possible combinations within their tolerance ranges. Relative motion between the shaft and hole is impossible. The minimum interference occurs at the minimum shaft size and maximum hole size.

• This is a fit which always results in the minimum shaft size being larger than the maximum hole size for all possible combinations within their tolerance ranges. Relative motion between the shaft and hole is impossible. The minimum interference occurs at the minimum shaft size and maximum hole size.

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• 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.

ALLOWANCE

• Allowance is the term given to the minimum clearance (

called positive allowance) or maximum interference

(called negative allowance) which exists between mating

parts. It may also be describe as the clearance or

interference which gives the tightest possible fit between

mating parts.

Hole Basis System

• In the hole basis system, the size of the hole is kept constant and shaft sizes are varied to obtain various types of fits.

• In this system, lower deviation of hole is zero, i.e. the low limit of hole is same as basic size. The high limit of the hole and the two limits of size for the shaft are then varied to give desired type of fit.

• The hole basis system is commonly used because it is more convenient to make correct holes of fixed sizes, since the standard drills, taps, reamers and branches etc. are available for producing holes and their sizes are not adjustable. On the other hand, size of the shaft produced by turning, grinding, etc. can be very easily varied.

Shaft Basis System

• In the shaft basis system, the size of the shaft is kept

constant and different fits are obtained by varying the size

of the hole. Shaft basis system is used when the ground

bars or drawn bars are readily available. These bars do

not require further machining and fits are obtained by

varying the sizes of the hole.

• In this system, the upper deviation (fundamental

deviation) of shaft is zero, i.e. the high limit of the shaft is

same as basic size and the various fits are obtained by

varying the low limit of shaft and both the limits of the

hole.

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• 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.

• Selective Assembly:

• In selective assembly, the parts are graded according to the size and only matched grades of mating parts are assembled. This technique is most suitable where close fit of two components assembled is required.

• Suppose some parts (shafts & holes) are manufactured to a tolerance of 0.01 mm, then an automatic gauge can separate them into ten different groups of 0.001 mm limit for selective assembly of the individual parts. Thus high quality and low cost can be achieved.

• Selective assembly is used in aircraft, automobile industries where tolerances are very narrow and not possible to manufacture at reasonable costs.

• A 50 mm diameter shaft is made to rotate in the bush. The

tolerances for both shaft and bush are 0.050 mm.

Determine the dimension of the shaft and bush to give a

maximum clearance of 0.075 mm with the hole basis

system.

• Solution:

• In the hole basis system, lower deviation of hole is zero,

therefore low limit of hole = 50 mm

High limit of hole = Low limit + Tolerance

= 50.00 + 0.050

= 50.050 mm = 50.050 X10– 3 m

High limit of shaft = Low limit of hole – Allowance

= 50.00 – 0.075

= 49.925 mm = 49.925 X10– 3 m

Low limit of the shaft = High limit – Tolerance

= 49.925 – 0.050

= 49.875 mm = 49.875X10– 3 m

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• For each of the following hole and shaft assembly, find

shaft-tolerance, hole tolerance and state whether the type

of fit is (a) clearance, (b) transition, and (c) interference.

• Hole Shaft

• Hole Shaft

• Hole Shaft

mm025.000.050 mm05.0

005.050

mm05.000.050

mm02.0

05.050

mm04.000.050

mm06.0

04.050

Hole : High limit of hole = 50.025 mm

Low limit of hole = 50.00 mm

Hole tolerance = 50.025 – 50.00 = 0.025 mm

Shaft : High limit of shaft = 50.05 mm

Low limit of shaft = 50.005 mm

Shaft tolerance = 50.05 – 50.005 = 0.045 mm

If we choose high limit of hole with high limit of shaft then

Allowance = 50.025 – 50.05

= – 0.025 (Interference)

But high limit of hole is smaller than low limit of shaft (clearance)

Thus, we conclude that the type of fit is Transition fit.

• Hole : High limit = 50.05 mm

• Low limit = 50.00 mm

• Tolerance = 0.05 mm

• Shaft : High limit = 50 – 0.02 = 49.98 mm

• Low limit = 50 – 0.05 = 49.95 mm

• Tolerance = 49.98 – 49.95 = 0.0 3 mm

• If we select high limit of hole and high limit of shaft then

• Allowance = 50.05 – 49.98 = 0.07 mm

• If we choose low limit of hole and high limit of shaft then

• Allowance = 50.00 – 49.98 = 0.02 mm

• Thus, we conclude that the type of fit is Clearance fit.

• High limit = 50.04 mm

• Low limit = 50.00 mm

• Tolerance = 50.04 – 50.00

• = 0.04 mm

• Shaft : High limit = 50.06 mm

• Low limit = 50.04 mm

• Tolerance = 50.06 – 50.04

• = 0.02 mm

• If we select high limit of shaft and low limit of hole, then

• Allowance = 50.00 – 50.06

• = – 0.06 mm

• It is clear that for any combination of hole and shaft the allowance will be negative.

• Thus, we conclude that the type of fit is Interference fit.

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• In a limit system the following limits are specified for a

hole and shaft assembly.

Hole= Shaft=

Determine the tolerance and allowance.

Ans:

mm02.000.030 mm02.0

05.030

• For the following hole and shaft assembly determine a)

hole and shaft tolerance and b) type of fit.

• Hole= Shaft=

Sol: Find min clearance and max. Clearance

mm025.000.020

mm080.0

005.020

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SYSTEM OF LIMITS AND FITS

• Rapid growth of national & International Business

• Economic success of Manufacturing industries.

• International Organisation for Standardisation (ISO) specifies the internationally accepted system of limits and fits.

• IS system of limits and fits comprises 18 grades of fundamental tolerances to indicate the level of accuracy.

• They are designated by ‘IT’ followed by a Number.

• 18 grades are IT01, IT0, and IT1 to IT16. (ISO system comprise 20 grades)

• Fine grades are referred to by the first few numbers. As the numbers get larger, so the tolerance zone becomes progressively wider

Tolerance grade on different applications

Fundament

al Tolerance

Applications

IT01-IT4 For production of gauges and measuring

Instruments

IT5-IT7 Super finishing operations and grinding

IT8-IT11 Turning, Boring, Rolling, Extrusion etc.

IT12-IT14 Sheet metal working

IT15-IT16 Casting, stamping, flame cutting etc.

Derivation of standard tolerance

• The tolerance grades may be numerically determined in terms of the standard tolerance unit ‘i’ where i in microns is given by

• (for basic size upto and including 500 mm)

• and

• (for basic size above 500 mm upto and including 3150 mm),

• where D is in mm and it is the geometric mean of the lower and upper diameters of a particular step in which the component lies.

DDmicronsi 001.045.0)( 3

1.2004.0)( DmicronsI

Dimension steps for sizes up to 500mm

Millimeters Millimeters

Above Upto Above Upto

- 3 80 120

3 6 120 180

6 10 180 250

10 18 250 315

18 30 315 400

30 50 400 500

50 80

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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. It determines the type of fit. The quality of fit is

determined by tolerance grades.

• IS:919 recommend 25 different deviations for both hole

and the shaft.

Designation of holes, shafts & Fit

• Fundamental deviation for shafts for sizes upto 500mm

34.0

41.0

41.0

44.0

2.0

5.2

5.5

11

16

40)8.095(

4052

Dg

Df

De

Dd

DforD

DforDc

……And upto zc

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Dowel Pins

Values of tolerance grades

Tolerance

grade

value Tolerance

grade

value

IT6 10i IT12 160i

IT7 16i IT13 250i

IT8 25i IT14 400i

IT9 40i IT15 640i

IT10 64i IT16 1000i

IT11 100i

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Tolerance grades IT01 to IT05

• IT01=0.3+0.008D

• IT0=0.5+0.012D

• IT1=0.8+0.020D

• IT5=0.7*IT6=0.7*10i=7i and so on.

Calculation of tolerance and limit of size

• 60H8f7

• Step 1: (Calculation of basic size)

Given size falls in the diameter steps 50-80mm Hence

D=

• Step 2: (fundamental deviation for hole)

For H hole FD=0

• Step 3:(Fundamental deviation for shaft)

For f shaft es= -5.5D0.41

= -30.113 microns~ -30 microns= -0.030mm

mm25.638050

• Step 4: (Tolerance unit)

• Step 5: Tolerance grade IT8 for hole =25i=46.4

microns=0.046mm

• Similarly Tolerance grade for IT7=0.030mm

• Step 5: Calculation of limits

• (i) Hole: Low limit

Basic size +FD for hole=60+0.000=60.000 mm

High Limit

Low limit + Tolerance=60.046mm

micronsDDmicronsi 856.1001.045.0)( 3

• (ii) Shaft: High limit =Basic size - FD for Shaft=

60.00-0.030=59.970mm

Low Limit=High limit – tolerance =

59.970 – 0.030 = 59.940mm

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Limit Gauges

• To check the dimensions within the limits or not.

• GO Gauge and NOT GO Gauge

• The difference between two sizes is the tolerance.

• GO gauge checks the max. metal limit (MML) and NOT

GO gauge checks the least or minimum metal limit (LML).

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Types of gauges

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Position gauges

Taylor Principle of Gauge Design

• Taylor Principle states that the GO gauge is designed to

check maximum metal conditions. It also simultaneously

check many related dimensions. The NOT GO gauge is

designed to check minimum metal conditions. It should

check only one dimension at a time.

Important points for gauge design

• The form of GO gauge should be the replica of of the form

of the opposed parts.

• GO gauges enable several related dimensions to be

checked simultaneously.

• During inspection, GO gauges must always be put in to

conditions of maximum impassability.

• NOT GO gauge checks a single feature at time.

• During inspection, NOT GO gauges must always be put in

to conditions of maximum passability.

• MATERIALS FOR GAUGING:

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Gauge Tolerance

• There is no universally accepted policy for

deciding the amount of tolerance to be

provided on the gauges. (10% of the work

tolerance)

• Wear tolerance: GO gauge wears. But NOT

GO gauge does not.

• A wear allowance of 10% of gauge

tolerance is widely used.

Method of Tolerance specification on

Gauges (BS or IS system) This system works according to the following guidelines

• The specified tolerance should be wide and at the same

time consistent with satisfactory functioning economical

production and inspection.

• During inspection the work that lies outside the specified

limits should not be accepted.

Thus in this system the same tolerance limits are specified

on w/s and insp. gauges.

Example

• Design a general type of GO and NOT GO gauges as per

the BS system for a 40 mm shaft and hole pair designated

as 40H8/d9 given that

• Diameter range 30-50 mm.

• IT8=25i IT9=40i

• Upper deviation of shaft =-16D0.44

• Wear allowance= 10% of gauge tolerance.

DDmicronsi 001.045.0)( 3