MMM MODULE 2-2022 BY. Dr. S B Mallur.pdf

Mechanical Measurement and Metrology (MMM) Note by – Dr. S B MALLUR, Professor, UBDTCE, Davanagere 1
Department of Studies in Mechanical Engineering
University BDT College of Engineering
Davanagere- 577004, Karnataka
(A Constituent College of VTU, Belgaum)
Off.: 08192-250716: Fax: 08192-233412 http://www.ubdtce.org
Module: 02:
System of Limits, Fits, Tolerance and Gauging:
STUDY MATERIAL
ON
MECHANICAL MEASUREMENTS AND METROLOGY
(18ME36B)
By
Dr. Shekharappa B Mallur
Professor
Module: 02 Systems of Limits, Fits, Tolerance and
Gauging

VISVESVARAYA TECHNOLOGICAL UNIVERSITY, BELGAUM
University BDT College of Engineering, Davangere
Mechanical Engineering Department
Sub Name: MECHANICALMEASUREMENTS AND METROLOGY
(18ME36B)
Dr. S B Mallur, Professor, MED, UBDTCE, Davanagere
System of Limits, Fits, Tolerance and Gauging:
Definitions, Tolerance, Tolerance analysis (addition & subtraction of tolerances) Inter changeability
& Selective assembly. Class & grade of tolerance Fits, Types of fits, Numerical on limits, fit and
tolerance. Hole base system & shaft base system. Taylor’s principle, Types of limit gauges,
Numerical on limit gauge design.
Comparators: Functional requirements, Classification, Mechanical- Johnson Mikrokator, Sigma
comparators, Dial indicator, Electrical comparators, LVDT, Pneumatic comparators- Principle of
back pressure, Solex comparators, Optical comparators- Zeiss ultraoptimeter.
Course Outcomes (CO2):
At the end of the module 2, Student will be able to explain the tolerance, limits of size, fits, geometric
and position tolerances, gauges and their design.
OBJECTIVES
Students will be able to
1. Understand the basic principles of fits and tolerances,
2. Explain various types of fits and their applications,
3. Analyses the various types of tolerances and applications, and
4. Know the fundamental of the systems of fits.
2.1 Definition:
Limits
The maximum and minimum permissible sizes within which the actual size of a component lies are called
Limits.
Tolerance:
It is impossible to make anything to an exact size, therefore it is essential to allow a definite tolerance or
permissible variation on every specified dimension. The difference between the upper and lower limit is
called tolerance.
What is Engineering Tolerance?
Engineering tolerance is the permissible variation in measurements deriving from the base measurement.
Tolerances can apply to many different units.
Limits & Fits:
1. 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
Why Tolerances are specified?
· 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 workpiece on the
machine, some errors are likely to creep in.

Figure 2.1. Tolerance
Consider the dimension shown in fig. When trying to achieve a diameter of 40 mm (Basic or Nominal
diameter), a variation of 0.05 mm on either side may result. If the shaft is satisfactory even if its diameter
lies between 40.05 mm & 39.95 mm, the dimension 40.05 mm is known as Upper limit and the dimension
39.95 mm is known as Lower limit of size. Tolerance in the above example is (40.05-39.95) =0.10 mm
Tolerance is always a positive quantitative number.
2.2. TOLERANCES
To satisfy the ever-increasing demand for accuracy, the parts have to be produced with less dimensional
variation. Hence, the labour and machinery required to manufacture a part has become more expensive.
It is essential for the manufacturer to have an in-depth knowledge of the tolerances to manufacture parts
economically but, at the same time, adhere to quality and reliability aspects. In fact, precision is
engineered selectively in a product depending on the functional requirements and its application. To
achieve an increased compatibility between mating parts to enable interchangeable assembly, the
manufacturer needs to practise good tolerance principles. Therefore, it is necessary to discuss some
important principles of tolerances that are usually employed for manufacturing products.
We know that it is not possible to precisely manufacture components to a given dimension because of the
inherent inaccuracies of the manufacturing processes. The components are manufactured in accordance
with the permissive tolerance limits, as suggested by the designer, to facilitate interchangeable
manufacture. The permissible limits of variations in dimensions have to be specified by the designer in a
logical manner, giving due consideration to the functional requirements. The choice of the tolerances is
also governed by other factors such as manufacturing process, cost, and standardization.
Tolerance can be defined as the magnitude of permissible variation of a dimension or other measured
value or control criterion from the specified value. It can also be defined as the total variation permitted
in the size of a dimension, and is 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 as established by the specification and design. If high
performance is the sole criterion, then functional requirements dictate the specification of tolerance
limits; otherwise, the choice of setting tolerance, to a limited extent, may be influenced and determined
by factors such as methods of tooling and available manufacturing equipment. The industry follows
certain approved accuracy standards, such as ANSI (American National Standards Institute) and ASME
(American Society of Mechanical Engineers), to manufacture different parts.

2.2.1. Computer-aided Modelling
Nowadays, computers are widely being employed in the design and manufacture of parts. Most leading
design tools such as AEROCADD, AUTOCAD, and Solid Works, which are currently being used in industries,
are equipped with tolerance features. The algorithms and programming codes that are in existence today
are aimed at enhancing the accuracy with minimum material wastage. These programs have the
capability of allotting tolerance ranges for different miniature parts of complex mechanical systems.
2.2.2. Manufacturing Cost and Work Tolerance
It is very pertinent to relate the production of components within the specified tolerance zone to its
associated manufacturing cost. As the permissive tolerance goes on decreasing, the manufacturing cost
incurred to achieve it goes on increasing exponentially. When the permissive tolerance limits are relaxed
without degrading the functional requirements, the
manufacturing cost decreases. This is clearly illustrated in Fig.
2.2.
Further, in order to maintain such close tolerance limits,
manufacturing capabilities have to be enhanced, which
certainly increases the manufacturing cost. The components
manufactured have to undergo a closer scrutiny, which
demands stringent inspection procedures and adequate
instrumentation. This increases the cost of inspection. Hence,
tolerance is a trade-off between the economical production
and the accuracy required for proper functioning of the
product. In fact, the tolerance limits specified for the
components to be manufactured should be just sufficient to
perform their intended functions.
Fig. 2.2 Relationship between work tolerance and manufacturing cost
2.3 Classification of Tolerance
Tolerance can be classified under the following categories:
1. Unilateral tolerance
2. Bilateral tolerance
3. Compound tolerance
4. Geometric tolerance
2.3.1. Unilateral Tolerance:
When the tolerance distribution is only on one side of the basic size, it is known as unilateral tolerance.
In other words, tolerance limits lie wholly on one side of the basic size, either above or below it. This is
illustrated in Fig. 3.3(a). Unilateral tolerance is employed when precision fits are required during
assembly. This type of tolerance is usually indicated when the mating parts are also machined by the
same operator. In this system, the total tolerance as related to the basic size is in one direction only.
Unilateral tolerance is employed in the drilling process wherein dimensions of the hole are most likely to
deviate in one direction only, that is, the hole is always oversized rather than undersized. This system is
preferred because the basic size is used for the GO limit gauge. This helps in standardization of the GO
gauge, as holes and shafts of different grades will have the same lower and upper limits, respectively.
Changes in the magnitude of the tolerance affect only the size of the other gauge dimension, the NOT GO
gauge size.
 When the two limit dimensions are only above the nominal size as shown in the figure or only
below the nominal size then the tolerance is said to be unilateral.

 Tolerances on a dimension may either be unilateral or bilateral.
 When the two limit dimensions are only on one side of the nominal size, (either above or below)
the tolerances are said to be unilateral.
 For unilateral tolerances, a case may occur when one of the limits coincide with the basic size.
2.3.2. Bilateral Tolerance:
When the tolerance distribution lies on either side of the basic size, it is known as bilateral tolerance. In
other words, the dimension of the part is allowed to vary on both sides of the basic size but may not be
necessarily equally disposed about it. The operator can take full advantage of the limit system, especially
in positioning a hole. This system is generally preferred in mass production where the machine is set for
the basic size. This is depicted in Fig. 3.3(b). In case unilateral tolerance is specified in mass production,
the basic size should be modified to suit bilateral tolerance.
Fig 2.3. Unidirectional/Bidirectional tolerance
When the two-limit dimension is above and below the nominal size, Then the tolerances are said to be
bilateral.
When the two limit dimensions are above and below nominal size,(i.e. on either side of the nominal size)
the tolerances are said to be bilateral. Unilateral tolerances, are preferred over bilateral because the
operator can machine to the upper limit of the shaft (or lower limit of a hole) still having the whole
tolerance left for machining to avoid rejection of parts.

2.3.3. Compound Tolerances:
When tolerance is determined by established tolerances on more than one dimension, it is known as
compound tolerance for example, tolerance for the dimension R is determined by the combined effects of
tolerance on 40 mm dimension, on 60o, and on 20 mm dimension. The tolerance obtained for dimension
R is known as compound tolerance (Fig. 2.5). In practice, compound tolerance should be avoided as far as
possible.
A compound tolerance is one which is derived by considering the effect of tolerances on more than one
dimension.
FIGURE 2.5 Compound Tolerance
For ex, the tolerance on the dimension L is dependent on the tolerances on D, H
The dimension L will be maximum when the base dimension is (D+a), the angle is ( +a), and the vertical
dimension is (H-d).
The dimension L will be minimum when the base dimension is (D-b), the angle is ( -b), and the vertical
dimension is (H+c).
2.3.4. Geometric Tolerance / Tolerance build up or Tolerance accumulation
If a part comprises of several steps, each step having some tolerance specified over its length, then the
overall tolerance on the complete length will be the sum of tolerances on individual lengths as shown in
fig (a). The effect of accumulation of tolerances can be minimized by adopting progressive dimensioning
from a common datum as shown in fig (b). Another example of tolerance build up is shown below.
Figure 2.6: Tolerance Build Up

2.4. LIMITS OF SIZE & TOLERANCE/ Terminology of limit systems:/Important Terms used in Limit System
The following terms used in limit system (or interchangeable system) is important from the subject point of view:
1. Nominal size. It is the size of a part specified in the drawing as a matter of convenience.
2. Basic size. It is the size of a part to which all limits of variation (i.e. tolerances) are applied to arrive at
final dimensioning of the mating parts. The nominal or basic size of a part is often the same.
3. Actual size. It is the actual measured dimension of the part. The difference between the basic size and
the actual size should not exceed a certain limit, otherwise it will interfere with the interchangeability of
the mating parts.
4. Limits of sizes. There are two extreme permissible sizes for a dimension of the part as shown in Fig. 2.7.
The largest permissible size for a dimension of the part is called upper or high or maximum limit, whereas
the smallest size of the part is known as lower or minimum limit.
Fig. 2.7. Limit of sizes
5. Allowance. It is the difference between the basic dimensions of the mating parts. The allowance may
be positive or negative. When the shaft size is less than the hole size, then the allowance is positive and
when the shaft size is greater than the hole size, then the allowance is negative.
6. Tolerance. It is the difference between the upper limit and lower limit of a dimension. In other words,
it is the maximum permissible variation in a dimension. The tolerance may be unilateral or bilateral.
When all the tolerance is allowed on one side of the nominal size, e.g. 20+0.000 –0.004 then it is said to
be unilateral system of tolerance. The unilateral system is mostly used in industries as it permits changing
the tolerance value while still retaining the same allowance or type of fit. When the tolerance is allowed
on both sides of the nominal size, e.g. 20+0.002 –0.002, then it is said to be bilateral system of tolerance.
In this case + 0.002 is the upper limit and – 0.002 is the lower limit. The method of assigning unilateral
and bilateral tolerance is shown in Fig. 2.8. (a) and (b) respectively.
Fig. 2.8. Method of assigning tolerances
7. Tolerance zone. It is the zone between the maximum and minimum limit size, as shown in Fig. 2.9.
Fig. 2.9. Tolerance Zone

8. 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.
9. Upper deviation. It is the algebraic difference between the maximum size and the basic size. The upper
deviation of a hole is represented by a symbol ES (Ecart Superior) and of a shaft, it is represented by es.
10. Lower deviation. It is the algebraic difference between the minimum size and the basic size. The
lower deviation of a hole is represented by a symbol EI (Ecart Inferior) and of a shaft, it is represented by
ei.
11. Actual deviation. It is the algebraic difference between an actual size and the corresponding basic
size.
12. Mean deviation. It is the arithmetical mean between the upper and lower deviations.
13. Fundamental deviation. It is one of the two deviations which is conventionally chosen to define the
position of the tolerance zone in relation to zero line, as shown in Fig. 2.10.
Fig. 2.10. Fundamental deviation
The terminology used in fits and tolerances is shown in Fig. 2.11. The important terms are
Fig.2.11. Terminology for fits and tolerances
2.5. 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. For example,
when a hole is drilled in a component, minimum amount of material is
removed at the lower limit size of the hole. This lower limit of the hole is
known 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. The
maximum and minimum metal conditions are shown in Fig. 2.12.
Fig.2.12. MML and LML

2.6. INTERCHANGEABILITY ASSEMBLY AND SELECTIVE ASSEMBLY:
Interchangeability Assembly: In Interchangeability Assembly when a large number of components are to
be produced then it is not economical to produce both the mating components by the same operators. In
Interchangeability Assembly to get required economy it is also the assumption to produce with in the
minimum component time.
This type is possible in the mass production system in the mass production system there is a division of
labor. the components are produced in one or more batch by using different operations on different
machines. by this method of operation, conditions, in order to assemble the mating components with a
desired, fit the strict control is needed.
In this system, the parts that are manufactured is done with specified tolerance limit. When a system of
this kind of operation is done with high output and when the components are assembled correctly. with
any other mating compounded that to selected at random then the system is called interchangeable
or Interchangeability assembly. The manufacturing of components in such conditions is called
interchangeable manufacture.
2.6.1.ADVANTAGES OF INTERCHANGEABILITY ASSEMBLY:
1. The production that done by Interchangeable basis results in increasing output. and reduces in the
manufacturing process.
2. Skills used by the process reduces he assemble time. When there is an error occurs.
3. This increases the quality due to the labour division is done in every operation, by this they get specialized
in a particular operation.
4. Defective parts and repair become easy in replacements.
5. There is reduced in the cost of maintenance and shut down period.
6. Precise dimension is not essential, produce component within small dimension error limit. Economic
oriented.
7. Mating parts can freely replace without custom fittings like fillets.
8. Readily available replacement component in the market.
9. Assembly process requires lesser skill.
2.7. SELECTIVE ASSEMBLY:
Selective Assembly: Selective Assembly refers to a concept where sub-components are assembled to form
a final assembly.
Assembly dissembles the old concept of inspection, when the component is used subjected into two
types like useful or not. if there is useful requirements present in it than it used to assembly. if not it will
be scrubbed. In this type of assembly, the components are divided into different groups according to the
size and dimensions, By this division there is an advantage in assembly, like every component is used to
match with the corresponding component to make the assembly.
In the Selective assembly the minimum value increases and maximum value decreases respectively, for
clearance and interference fit. But for transition fit maximum value for clearance and interference fit
decreases.
2.7.1. ADVANTAGES OF SELECTIVE ASSEMBLY IN MANUFACTURE:
1. Selective assembly is the fair, clear and low cost method in manufacturing.
2. It increases the efficiency
3. This gives high quality in assembly.
4. Cost of manufacturing is reduced.
5. Scrab rate in manufacturing reduces by this method.
6. It reduces the machining cost. and increases the efficiency of fit without reducing the tolerance
zone.

2.8. Types of Fits
A fit may be defined as the degree of tightness and
looseness between two mating parts.
There are different fit types in mechanical
engineering and each one is designed for different
circumstances. According to ISO, there are three
different types of fits used in manufacturing products.
2.8.1. Clearance Fits
 In clearance fit, an air space or clearance exists between the shaft and hole.
 Such fits give loose joint.
 A clearance fit has positive allowance, i.e. there is minimum
positive clearance between high limit of the shaft and low limit of
the hole.
 Allows rotation or sliding between the mating parts.
From its name, a clearance fit is used in situations that call for loose mating and components’ free
movement. Therefore, they are ideal in making products
whose components need to slide in and out with ease.
Clearance fits have a smaller shaft than the hole. This
results in two conditions. One is a maximum clearance in
which the shaft has the minimum diameter while the
hole has its maximum diameter. The other is the
minimum clearance in which the shaft is maxed, and the
hole is minimum.
Clearance fits are further divided into five categories
classified based on how loose they are. Below are the
different types of fits under this category:
Loose Running Fit
These are clearance fits with the largest
clearance used in places where accuracy is not
important
Free Running Fit
These fits are for situations that require the
movement of components with little
consideration to accuracy.
Close Running Fit
These fits are for situations that require small clearance with regard to accuracy.
Sliding Fit
These fits have high accuracy and are for situations that require high accuracy and small clearance.
Therefore, parts where they are used can turn and slide freely.
Locational Clearance Fit
Locational Clearance fits have high accuracy but can only provide minimal clearance.

2.8.2. Interference Fit
 A negative difference between diameter of the hole and the
shaft is called interference.
 In such cases, the diameter of the shaft is always larger than
the hole diameter.
 It used for components where motion, power has to be
transmitted.
What’s an interference fit? It is also called a press fit or friction fit is a fastening of two components by
pushing them together. The fastening
occurs via many mechanisms, and it
involves a substantial amount of force
to the couple and uncouples the
components. The mechanism also
determines the different categories of
interference fits to use.
In interference fit, the difference
between the shaft’s maximum size and
the hole’s minimum size is the
Maximum Interference. Also, the
difference between the shaft’s
minimum size and the hole’s maximum
size is the Minimum Interference.
Interference fits have three categories:
Press Fit
They have minimal interference as assembling is via cold pressing.
Driving Fit
These fits have a more prominent interference fit than press-fit, and it needs higher assembly force for
cold pressing.
Forced Fit
Assembling components requires heating the parts with a hole and freezing the shaft. Therefore,
disassembling can lead to broken parts.

2.8.3. 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.
These fits fall between clearance and interference fits and are ideal for situations in which accuracy is
very important. For example, they are ideal for aligning
where the mating component must be joined with extreme
precision.
Engineers and machinists also call transition fits slip or
push-fit. When you compared them in terms of the degree
of clearance, they have a larger clearance than an
interference fit. However, the clearance is not enough to
guarantee movement in the joint. You can say that
transition fits provide clearance or interference fit
depending on the situation.
Transition fit has two major forms:
Similar Fits
It leaves a small clearance or creates
a small interference, and assembly is
obtainable by using a rubber mallet.
Fixed Fits
It leaves a small clearance or creates
a small interference. Assembly is
possible using light force.
How to Choose Suitable Fit for Your
Projects
Choosing the right types of fits for your projects depends on understanding several factors. Below are the
important factors that you should watch out for:
Application
Based on what you need, there are different types of fits ideal for different kinds of purposes. By going
through properties such as accuracy and tolerance, exhibited by the different types of fits and the
product’s proposed function, you should decide on the right fits for a project.
Budget
Before deciding on the right types of fits for your products, you should know your budget. For example,
using fits with tighter tolerances will cost more than normal. Therefore, you must weigh your options
carefully. It would be best to get a fit that delivers the right tolerance needed to perform its functions
while reducing product development costs.
Tolerance
You must understand the concept of tolerance of a product to choose the right types of fits for such a
product. You have to be specific about what you want. Also, you must also answer questions such as
whether you want the components to rotate in a full circle or want them to be tight.
Another thing you also need to be careful about is the tolerance slack, which is the total maximum or
minimum tolerance of a particular measurement. For example, you have to be careful about the
aggregation of different parts’ tolerance to make up a single product. This is very important if the
resulting tolerance is very high.

Conclusion
Many things surround
using the different fit
types in mechanical
engineering and
employing each within
different mechanical
applications. By going
through this article,
you will have a perfect
understanding of a fit
and its different types.
The article also showed what you need to look out for to choose the right fits for your projects.
Understanding what a fit does is not as important as knowing how to apply it.
2.9. TOLERANCES
To satisfy the ever-increasing demand for accuracy, the parts have to be produced with less dimensional
variation. Hence, the labour and machinery required to manufacture a part has become more expensive.
It is essential for the manufacturer to have an in-depth knowledge of the tolerances to manufacture parts
economically but, at the same time, adhere to quality and reliability aspects. In fact, precision is
engineered selectively in a product depending on the functional requirements and its application. To
achieve an increased compatibility between mating parts to enable interchangeable assembly, the
manufacturer needs to practice good tolerance principles. Therefore, it is necessary to discuss some
important principles of tolerances that are usually employed for manufacturing products. We know that it
is not possible to precisely manufacture components to a given dimension because of the inherent
inaccuracies of the manufacturing processes. The components are manufactured in accordance with the
permissive tolerance limits, as suggested by the designer, to facilitate interchangeable manufacture. The
permissible limits of variations in dimensions have to be specified by the designer in a logical manner,
giving due consideration to the functional requirements. The choice of the tolerances is also governed by
other factors such as manufacturing process, cost, and standardization.
Tolerance can be defined as the magnitude of permissible variation of a dimension or other measured
value or control criterion from the specified value. It can also be defined as the total variation permitted
in the size of a dimension, and is 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 as established by the specification and design. If high
performance is the sole criterion, then functional requirements dictate the specification of tolerance
limits; otherwise, the choice of setting tolerance, to a limited extent, may be influenced and determined
by factors such as methods of tooling and available manufacturing equipment. The industry follows
certain approved accuracy standards, such as ANSI (American National Standards Institute) and ASME
(American Society of Mechanical Engineers), to manufacture different parts.

2.10. System of Fits /Hole Basis System and Shaft Basis System
For obtaining various types of fits, the amount of maximum and minimum clearance either positive or
negative must exist between the mating parts.
In practice, while providing the tolerance between two mating parts; from the production and economic
point of view, one of the mating parts limit dimensions is fixed and while that of another limit dimension
is varied, during so various types of fits are obtained based on this system of fits, are classified broadly
into,
 Hole basis system
 Shaft basis system
1. Hole Basis System
Difference between Hole Basis System and Shaft Basis System
In Hole Basis System In Hole basis system the hole is kept to constant and the shaft size is changed
according to the different types of fit where as in the Shaft Basis System shaft is kept constant and the
size of the hole is varied to view various types of fits, in this system the upper deviation of the shaft is
zero.The detailed explanation about Hole Basis System and Shaft Basis System explained as follows
Hole Basis System:
 Size of hole whose lower deviation is zero is assumed as the basis size.
 Limits on the hole kept constant and those of shaft desired type at fit.
 The Hole basis system is referred to in mass production because it is convenient and less costing
to make a hole of correct size due to availability by stand grills.
 It is more easily to vary a shaft size according to the fit required.
 It requires less amount of capital and storage space.
 Gauging of the shaft can be easily and conveniently done.
Shaft Basis System:
 Size of the shaft whose upper deviation is zero, is assumed as the basis size.
 Limits on the shaft kept constant and those on the hot varied to have necessary fit.
 This system is not suitable for mass production because it is inconvenient and time-consuming and
costly to have a shaft of the correct size.
 It is some difficult to find the hole size according to the fit required.
 It required large capital, storage space. for a large number of tools required to produce holes of
different size.
 Being internal measurement gauging of the hole cannot be easily conveniently done.

Difference between Hole Basis System and Shaft Basis System

1.11. LIMIT GAUGING
1.11.1. INTRODUCTION
Gauging, done in manufacturing processes, refers to the method by which it is determined quickly
whether or not the dimensions of the checking parts in production, are within their specified limits. It is
done with the help of some tools called gauges. A gauge does not reveal the actual size of dimension.
A clear distinction between measuring instruments and gauges is not always observed. Some tools that
are called gauges are used largely for measuring or layout work. Even some are used principally for
gauging give definite measurement.
High carbon and alloy steels have been the principal material used for many years. Objections to steel
gauges are that they are subjected to some distortion because of the heat-treating operations and that
their surface hardness is limited. These objections are largely overcome by the use of chrome plating or
cemented carbides as the surface material. Some gauges are made entirely of cemented carbides or they
have cemented carbides inserted at certain wear points.
Objectives
After studying this unit, you should be able to
1. understand the fundamental of the gauges and their classifications, and
2. explain the working principles of various types of gauges and their applications.
2.11.2. GAUGES AND THEIR CLASSIFICATIONS
Gauges are the tools which are used for checking the size, shape and relative positions of various parts
but not provided with graduated adjustable members. Gauges are, therefore, understood to be single-
size fixed-type measuring tools.
Classifications of Gauges
(a) Based on the standard and limit
(i) Standard gauges
(ii) Limit gauges or “go” and “not go” gauges
(b) Based on the consistency in manufacturing and inspection
(i) Working gauges
(ii) Inspection gauges
(iii) Reference or master gauges
(c) Depending on the elements to be checked
(i) Gauges for checking holes
(ii) Gauges for checking shafts
(iii) Gauges for checking tapers
(iv) Gauges for checking threads
(v) Gauges for checking forms
(d) According to the shape or purpose for which each is used
(i) Plug
(ii) Ring
(iii) Snap
(iv) Taper
(v) Thread
(vi) Form
(vii) Thickness
(viii) Indicating
(ix) Air-operated

2.11.3. Standard Gauges
Standard gauges are made to the nominal size of the part to be tested and have the measuring member
equal in size to the mean permissible dimension of the part to be checked. A standard gauge should mate
with some snugness.
2.11.4. Limit Gauges
These are also called „go‟ and „no go‟ gauges. These are made to the limit sizes of the work to be
measured. One of the sides or ends of the gauge is made to correspond to maximum and the other end to
the minimum permissible size. The function of limit gauges is to determine whether the actual
dimensions of the work are within or outside the specified limits. A limit gauge may be either double end
or progressive. A double end gauge has the „go‟ member at one end and „no go‟ member at the other
end. The „go‟ member must pass into or over an acceptable piece but the „no go‟ member should not.
The progressive gauge has „no go‟ members next to each other and is applied to a workpiece with one
movement. Some gauges are fixed for only one set of limits and are said to be solid gauges. Others are
adjustable for various ranges. 45 Limit Gauging
2.11.5. WORKING GAUGES, INSPECTION GAUGES AND REFERENCE GAUGES
To promote consistency in manufacturing and inspection, gauges may be classified as working, inspection,
and reference or master gauges:
Working Gauges
Working gauges are those used at the bench or machine in gauging the work as it being made.
Inspection Gauges
These gauges are used by the inspection personnel to inspect manufactured parts when finished.
Reference Gauges
These are also called master gauges. These are used only for checking the size or condition of other
gauges and represent as exactly as possible the physical dimensions of the product.
2.11.6. GAUGES FOR CHECKING ELEMENTS
Hole Gauge
It is used to check the dimensions of the hole present in the element.
Shaft Gauge
It is used to check the dimensions of the shaft.
Taper Gauge
It is used to check the dimensions of the tapers.
Thread Gauge
It is used to check the threading of the element.
Form Gauge
It is used to check the forms of the elements.
2.11.7. GAUGES COMMONLY USED IN PRODUCTION WORK
Some of the important gauges which are commonly used in production work have been discussed as
follows :
2.11.7.1. Plug Gauges
These gauges are used for checking holes of many different shapes and sizes. There are plug gauges for
straight cylindrical holes, tapered, threaded square and splined holes. Figure 2.11. shows a standard plug
gauge used to test the nominal size of a cylindrical hole. Figure 2.12. Shows a double-ended limit plug
gauge used to test the limits of size. At one end, it has a plug minimum limit size, the „go‟ end and; at the
other end a plug of maximum limit, the „no go‟ end. These ends are detachable from the handle so that
they may be renewed separately when worn in a progressive limit plug gauge. The „go‟ and „no go‟
section of the gauge are on the same end of the handle. Large holes are gauged with annular plug gauges,
which are shell-constructed for light weight, and flat plug gauges, made in the form of diametrical
sections of cylinders.

Figure 2.11: Standard Ring and Plug Gauges
Figure 2.12: Progressive and Double Ended Limit Plug Gauges
2.11.7.2. Ring Gauges
Ring gauges are used to test external diameters. They allow shafts to be checked more accurately since
they embrace the whole of their surface. Ring gauges,
however, are expressive manufacture and, therefore, find
limited use. Moreover, ring gauges are not suitable for
measuring journals in the middle sections of shafts. A
common type of standard ring gauge is shown in Figure
2.11. and 1.42. In a limit ring gauge, the „go‟ and „no go‟
ends are identified by an annular groove on the periphery.
About 35 mm all gauges are flanged to reduce weight and facilitate handling.
4.11.7.3. Taper Gauges
The most satisfactory method of testing a taper is to use taper gauges. They are also used to gauge the
diameter of the taper at some point. Taper gauges are made in both the plug and ring styles and, in
general, follow the same standard construction as plug and ring gauges. A taper plug and ring gauge is
shown in Figure 2.13.
Figure 1.13. : Taper Plug and Ring Gauge
When checking a taper hole, the taper plug gauge is inserted into the hole and a slight pressure is exerted
against it. If it does not rock in the hole, it indicates that the taper angle is correct.
The same procedure is followed in a ring gauge for testing tapered spindle.

The taper diameter is tested for the size by noting how far the gauge enters the tapered hole or the
tapered spindle enters the gauge. A mark on the gauge show the correct diameter for the large end of the
taper.
To test the correctness of the taper two or three chalk or pencil lines are drawn on the gauge about
equidistant along a generatrix of the cone. Then the gauge is inserted into the hole and slightly turned. If
the lines do not rub off evenly, the taper is incorrect and the setting in the machine must be adjusted
until the lines are rubbed equally all along its length. Instead of making lines on the gauge, a thin coat of
paint (red led, carbon black, Purssian blue, etc.) can be applied.
The accuracy of a taper hole is tested by a taper limit gauge as shown in Figure 2.13. This has two check
lines „go‟ and „no go‟ each at a certain distance from the end of the face. The go portion corresponds to
the minimum and „no go‟ to the maximum dimension.
Figure 2.13. : Limit Taper Plug Gauge
2.11.7.4. Snap Gauges
These gauges are used for checking external dimensions. Shafts are mainly checked by snap gauges. They
may be solid and progressive or adjustable or double-ended. The most usual types are shown in Figure
2.14.
Figure 2.14. : Snap Gauges
(a) Solid or non-adjustable caliper or snap gauge with „go‟ and „no go‟ each is used for large sizes.
(b) Adjustable caliper or snap gauge used for larger sizes.

This is made with two fixed anvils and two adjustable anvils, one for „go‟ and another for the „no go‟.
The housing of these gauges has two recesses to receive measuring anvils secured with two screws. The
anvils are set for a specific size, within an available range of adjustment of 3 to 8 mm. The adjustable
gauges can be used for measuring series of shafts of different sizes provided the diameters are within the
available range of the gauge.
(iii) Double-ended solid snap gauge with „go‟ and „no go‟ ends is used for smaller sizes.
2.11.7.5. Thread Gauges
Thread gauges are used to check the pitch diameter of the thread. For checking internal threads (nut,
bushes, etc.), plug thread gauges are used, while for checking external threads (screws, bolts, etc.), ring
thread gauges are used. Single-piece thread gauges serve for measuring small diameters. For large
diameters the gauges are made with removable plugs machined with a tang. Standard gauges are made
single-piece. Common types of thread gauges are shown in Figure 2.15.
Figure 2.15. : Thread Gauge
Standard plug gauges may be made of various kinds:
(a) Plug gauge with only threaded portion.
(b) Threaded portion on one end and plain cylindrical plug on opposite end to give correct “core”
diameter.
(c) Thread gauge with core and full diameters.
Limit plug gauges have a long-thread section on the „go‟ and a short-threaded section on the „no go‟ end
to correspond to the minimum and maximum limits respectively.
Roller rings gauges, similarly have „go‟ and „no go‟ ends. They may also be solid and adjustable.
Roller Snap gauges are often used in production practice for measuring external threads. They comprise a
body, two pairs „go‟ rollers and two pairs „no go‟ rollers.
Taper thread gauges are used for checking taper threads. The taper-ring thread gauge are made in two
varieties – rigid (non-adjustable) and adjustable. The “go”
non-adjustable ring gauges are full threaded while the „no
go‟ have truncated thread profile.
2.11.7.6 Form Gauges
Form gauges may be used to check the contour of a
profile of workpiece for conformance to certain shape or
form specifications.
Template Gauge
It is made from sheet steel. It is also called profile gauge.
A profile gauge may contain two outlines that represent
the limits within which a profile must lie as shown in
Figure 2.16.
Figure 2.16: A Template Gauge

2.11.7.7. Screw Pitch Gauges
Screw pitch gauges serve as an everyday tool used in picking out a
required screw and for checking the pitch of the screw threads. They
consist of a number of flat blades which are cut out to a given pitch
and pivoted in a holder as shown in Figure 4.8. Each blade is stamped
with the pitch or number of thread per inch and the holder bears an
identifying number designing the thread it is intended for. The sets
are made for metric threads with an angle 60o, for English threads
with an angle of 55o.
A set for measuring metric threads with 30 blades has pitches from
0.4 to 0.6 mm and for English threads with 16 blades has 4 to 28
threads per inch.
In checking a thread for its pitch the closest corresponding gauge
blade is selected and applied upon the thread to be tested. Several
blades may have to be tried until the correct is found.
Figure 2.17. : Screw Pitch Gauge
2.11.7.8 Radius and Fillet Gauges
The function of these gauges is to check the radius of curvature of convex and concave surfaces over a range from 1
to 25 mm. The gauges are
made in sets of thin plates
curved to different radius
at the ends as shown in
Figure 2.18. Each set
consists of 16 convex and
16 concave blades.
Figure 2.18 : Radius and Fillet Gauges
2.11.7.9 Feller Gauges
Feller gauges are used for checking clearances between mating surfaces. They are made in form of a set of steel,
precision machined blade 0.03 to 1.0 mm thick and 100 mm long. The blades are provided in a holder as shown in
Figure 4.10. Each blade has an indication of its thickness. The Indian standard establishes seven sets of feller gauges
: Nos 1, 2, 3, 4, 5, 6, 7, which differ by the number of blades in them and by the range of thickness. Thin blades
differ in thickness by 0.01 mm in the 0.03 to 1 mm set, and by 0.05 mm in the 0.1 to 1.0 mm set. To find the size of
the clearance, one or
two blades are
inserted and tried
for a fit between the
contacting surfaces
until blades of
suitable thickness
are found.
Figure 2.19. : Feller Gauge
2.11.7.10. Plate and Wire Gauges
The thickness of a sheet metal is checked by means of plate gauges and wire diameters by wire gauges. The plate
gauge is shown in Figure 2.20. It is used to check the thickness of plates from 0.25 to 5.0 mm, and the wire gauge,
in Figure 2.21., is used to check the diameters of wire from 0.1 to 10 mm.

Figure 2.21 : Wire Gauge
Figure 2.20: Plate Gauge
2.11.7.11 Indicating Gauges
Indicating gauges employ a means to magnify how much a dimension deviates, plus or minus, from a given
standard to which the gauge has been set. They are intended for measuring errors in geometrical form and size,
and for testing surfaces for their true position with respect to one another. Beside this, indicating gauges can be
adapted for checking the run out of toothed wheels, pulleys, spindles and various other revolving parts of
machines.
Indicating gauges can be of a dial or lever type, the former being the most widely used.
2.11.7.12 Air Gauges
Pneumatic or air gauges are used primarily to determine the inside characteristics of a hole by means of
compressed air. There are two types of air gauges according to operation: a flow type and a pressure type gauge.
The flow type operates on the principle of varying air velocities at constant pressure and the pressure type
operates on the principle of air escaping through an orifice.
2.11.8. SUMMARY
Gauging is the method by which it is determined quickly whether or not the dimensions of the checking parts, in
the production, are within their specified limits. The tools which are used for the same are called gauges.
Materials which are used for making gauges are high carbon and alloy steels, cemented carbides, etc. Gauges can
be classified mainly as follows :
(a) Based on the standard and limit
(i) Standard gauge
(ii) Limit gauge
(b) Based on the consistency in manufacturing process and inspection
(i) Working gauge
(ii) Inspection gauge
(iii) Reference gauge
(c) According to the shape or purpose for which each is used
(i) Plug (ii) Ring (iii) Snap (iv) Taper (v) Thread (vi) Form (vii) Indicating (viii) Feller (x) Air-gauges
2.11.9. KEY WORDS
Standard Gauges: These are made to the nominal size of the parts to be tested.
Limit Gauges: These are „go‟ and „no go‟ gauges.
Plug Gauges: These are used for checking holes of many different shapes and sizes.
Ring Gauges: External diameter measuring gauges.
Taper Gauges: Taper testing gauges.
Snap Gauges: These are used for checking shafts.
Thread Gauges: These are used for pitch diameter of the thread.
Form Gauges: These are used to check the contour of a profile.
Feller Gauges: For checking the clearance between the mating surfaces.
Indicating Gauges: To measure the position of the surfaces.
Air Gauge: To measure inside characteristics of a hole using air.

Tolerances
1. What are the functional dimensions?
a) Have to be machined and fit with other mating components b) Which have no effect on the
performance of quality c) Need not to be machined to an accuracy of the high degree d) Function is more
important than accuracy
2. Why tolerances are given to the parts?
a) Because it’s impossible to make perfect settings b) To reduce weight of the component c) To reduce
cost of the assembly d) To reduce amount of material used
3. What is bilateral tolerance?
a) Total tolerance is in 1 direction only b) Total tolerance is in both the directions c) May or may not be in
one direction d) Tolerance provided all over the component body
4. Which type of tolerance provided in drilling mostly?
a) Bilateral b) Unilateral c) Trilateral d) Compound
5. What is mean clearance?
a) Maximum size of hole minus maximum size of shaft b) Minimum size of hole minus minimum size of
shaft c) Mean size of hole minus mean size of shaft d) Average of both size of shaft and hole
6. Which of the following is incorrect about tolerances?
a) Too loose tolerance results in less cost b) Tolerance is a compromise between accuracy and ability c)
Too tight tolerance may result in excessive cost d) Fit between mating components is decided by
functional requirements
7. Quality control charts doesn’t depend on which factor?
a) Normal distribution b) Random sampling c) Independence between samples d) Binomial distribution
8. Which of the following option is true for given statements?
Statement 1: Bilateral tolerances are used in mass production techniques.
Statement 2: The basic size should be equal to upper and lower limits.
a) T, T b) F, F c) T, F d) F, T
9. If a clearance fit is present between shaft and hole, what is the tolerance on shaft or hole for a
complete interchangeable approach?
a) ½ of maximum clearance – ½ of minimum clearance b) ¼ of maximum clearance – ¼ of minimum
clearance c) Maximum clearance – minimum clearance d) ¾ of maximum clearance – ¾ of minimum
clearance
INTERCHANGEABILITY
1. Which of the following option is incorrect about interchangeability?
a) Increase output b) Increase cost of production c) Useful in mass production d) Assembly time increases
2. What are the main considerations for deciding the limits of a particular part?
a) Functional requirement b) Economics and interchangeability c) Interchangeability and functional
requirement d) Interchangeability, functional requirement and economics
3. For full interchangeability, what is the relation between the process capability of a machine and
manufacturing tolerance of the part?
a) Process capability = Manufacturing tolerance b) Process capability ≥ Manufacturing tolerance c)
Process capability > Manufacturing tolerance d) Process capability ≤ Manufacturing tolerance
4. Which of the following option is correct in given statements about interchangeability? Statement 1:
Standardisation is not so much of importance for interchangeability. Statement 2: Interchangeability
follows ‘normal distribution’.
a) F, T b) T, T c) F, F d) T, F
5. Which of the following option is not correct for ‘full interchangeability’?

a) This type of interchangeability is not feasible sometimes b) Requires machine which can maintain low
process capability c) Machines with very high accuracy are necessary d) For interchangeable production,
this type of interchangeability is not must
6. What is the main use of automatic gauge in selective assembly?
a) Check accuracy of parts b) Check parallelism of parts c) Divide group of parts with some tolerance in
smaller groups d) Use to check errors in parts
7. What is the correct formula to find no. of groups in selective assembly?
a) Process capability / Tolerance desired b) Tolerance desired / Process capability
c) Tolerance desired * Process capability d) Tolerance desired + Process capability
8. What is a limit system?
a) Series of tolerances b) Series of fits c) Series of clearances d) Series of limits
9. Which of the following is correct for selective assembly?
a) Not suitable for industrial purposes b) Cost increases due to automatic gauging c) Wastage is high due
to selective selection d) This method is followed in ball and roller bearing units
TERMINOLOGY
1. What does ‘50’ represents in 50H8/g7?
a) Basic size b) Actual size c) Maximum limit of size d) Minimum limit of size
2. Which of the following is incorrect regarding terminology?
a) Grades of tolerances decides manufacture’s accuracy b) For any basic size there are 20 different shafts
c) Line of zero deviation is known as zero line d) Tolerance has no sign
3. What is the actual deviation?
a) Algebraic sum between actual size and corresponding basic size b) Algebraic difference between actual
and corresponding basic size c) Average of actual and basic size d) Algebraic difference between upper
and lower deviation
4. What is the condition for a positive upper deviation?
a) Maximum limit of size > basic size b) Maximum limit of size is < basic size c) Minimum limit of size >
basic size d) Maximum limi t of size < basic size
5. How many holes are there for any basic size?
a) 22 b) 24 c) 26 d) 28
6. What does ES represent in terminology as per IS: 919?
a) Lower deviation of hole b) Upper deviation of shaft c) Lower deviation of shaft d) Upper deviation of
hole
7. What is ‘IT01’?
a) Basic size of hole b) Basic size of shaft c) Tolerance grade d) Standard tolerance factor
8. For tolerance grades 5 to 16, what is the formula for standard tolerance factor? (D=mean diameter in
mm) a) 0.45 (D)1/3 + 0.001D b) 10*D c) 0.45 (D)3 + 0.001 D d) 20*D 9. What is the hole size which is
covered by IT05? a) 500 mm b) 600 mm c) 700 mm d) 800 mm

GATE MCQ’s
1) Newall system is a type of
a. maximum hole size b. minimum hole size c. upper deviation which is zero d. none of the above
2) Which type of tolerance does a slip gauge have?
a. Unilateral tolerance b. Bilateral tolerance c. Both a. and b. d. None of the above
3) Which type of deviation is observed while calculating hole dimensions?
a. Positive b. Negative c. Zero d. All of the above
4) Which ISO standard is used in international automobile companies to set automotive quality system
standards ?
a. ISO 14000 b. TS 16949 c. ISO 9000 d. none of the above
5) ISO 14000 quality standard is related with
a. Environmental management systems b. Automotive quality standards c. Eliminating poor quality d.
Customer satisfaction
6) How is interference between shaft and hole calculated?
a. Interference = maximum shaft – minimum hole b. Interference = minimum shaft – maximum hole c.
Interference = minimum shaft + maximum hole d. None of the above
7) Which of the following is true for interference fit?
a. Shaft is always smaller than the hole b. Shaft is always bigger than the hole c. Interference fits have
shaft and hole of same dimension d. None of the above
8) Which among the following is a type of clearance fit?
a. Force fit b. Push fit c. Slide fit d. Tight fit
9) What is a loose running fit?
a. Loose running fit has minimum clearance b. They can be used in textile machinery c. Used in high
precision task d. All the above
10) Which of the following statements is/are false?
a. Interference is observed in tight fit b. Allowance represents minimum interference for interference fits
c. Clearance is observed in push fit d. All of the above
11) What does allowance represent in clearance fits?
a. It represents minimum clearance and is positive b. It represents maximum clearance and is positive c. It
represents minimum clearance and is negative d. It represents maximum clearance and is negative
12) The study of scientific metrology deals with
a. accuracy and methods of measurement b. standard specifications c. theories related to nature d. all of
the above
13. In a bilateral system of tolerance, the tolerance is allowed on
A. one side of the actual size B. one side of the nominal size C. both sides of the actual size D. both sides
of the nominal size
14. The algebraic difference between the minimum limit and the basic size is called
A. actual deviation B. upper deviation C. lower deviation D. fundamental deviation
15. Allowance in limits and fits refers to [GATE 2001]
(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
16. 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 ? [GATE 1992
(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

17. A shaft diameter ( 20−0.15+0.05 mm) and a hole ( diameter 20+0.1+0.20 mm) when assembled
would yield [GATE 1993]
(a) transition fit (b) interference fit (c) clearance fit (d) none of these
18. The fit on a hole-shaft system is specified as H7-s6. The type of fit is [GATE 1995]
a) clearance fit b) running fit (sliding fit) c) push fit (transition fit) d) force fit (interference fit)
19. In the specification of dimensions of fits, [GATE 1998]
a) allowance is equal to bilateral tolerance b) allowance is equal to unilateral tolerance c) allowance is
independent of tolerance d) allowance is equal to the difference between maximum and minimum
dimension specified by the tolerance.
20. A hole is specified as 40 +0.05. 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 [GATE 2007]
a) 0.04 b) 0.05 c) 0.10 d) 0.11
21. For the given assembly: 25 H7/g8, match Group A with Group B [GATE 2014]
Group A Group B
P. H (I) Shaft Type Q.
H IT8 (II) Hole Type R. IT7
P. (III) Hole Tolerance Grade
S. g (IV) Shaft Tolerance Grade
(A) P-I, Q-III, R-IV, S-II (B) P-I, Q-IV, R-III, S-II (C) P-II, Q-III, R-IV, S-I (D) P-II, Q-IV, R-III, S-I
22. Holes of diameter 25.0+0.020+0.040 mm are assembled interchangeably with the pins of diameter
25.0−0.008+0.005 mm. The minimum clearance in the assembly is *GATE 2015+
(A) 0.048 mm (B) 0.015 mm (C) 0.005 mm (D) 0.008 mm
Assignment Questions
1. Explain the concept of interchange ability with examples. Discuss the need of the use of selective
assembly by giving a practical example.
2. Define the terms:
Limits (b) Tolerance (c) Basic size (d) Fundamental Deviation (e) Fit (f ) Gaugemaker’s Tolerance (g)
Wear allowance (h) Go and NO-GO Gauge
3. Explain the need and types of giving the tolerances with examples. Discuss unilateral and bilateral
systems of writing tolerances with suitable examples and explain which system is preferred in
interchangeable manufacture and why.
4. State and explain Taylor’s principle of limit-gauge design.
5. Write a short note on limit gauges.
6. Define fits and explain in brief the types of fits. Explain with a neat diagram the essential conditions of
interference and clearance.
7. Write down the examples of use of the following types of fits:
i. Push fit (b) Press fit (c) Running clearance fit (d) Wringing fit (e) Sharing fit
8. Differentiate between
i. Tolerance and allowance
ii. Interchangeable manufacturing and selective assembly concepts
iii. Hole-base system and shaft-base system
iv. Measuring instrument and gauge
v. Workshop gauge and inspection gauge
9. Explain with a sketch the allocation of gauge tolerance and wear allowance for workshop, inspection
and general grade conditions.
10. Enumerate the types of plug gauges and draw neat sketches of them by stating their applications.
************************************************************************************

MMM MODULE 2-2022 BY. Dr. S B Mallur.pdf

Recommended

Recommended

More Related Content

Similar to MMM MODULE 2-2022 BY. Dr. S B Mallur.pdf

Similar to MMM MODULE 2-2022 BY. Dr. S B Mallur.pdf (20)

Recently uploaded

Recently uploaded (20)

MMM MODULE 2-2022 BY. Dr. S B Mallur.pdf