CHAPTER ONE:

Basic Principles of
Engineering Metrology

DR. Serap Çelik

Content:
1.1 INTRODUCTION
1.2 METROLOGY
1.3 TYPES OF METROLOGY
1.4 NEED FOR INSPECTION
1.5 ACCURACY AND PRECISION
1.6 OBJECTIVES OF METROLOGY AND MEASUREMENTS
1.7 GENERAL MEASUREMENT CONCEPTS
1.8 METHODS OF MEASUREMENTS
1.9 METROLOGY ELEMENTS
1.10 ERRORS IN MEASUREMENTS

Reference book:ENGINEERING METROLOGY AND MEASUREMENTS

N.V. RAGHAVENDRA L. KRISHNAMURTHY

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 1.1 INTRODUCTION
 The importance of metrology as a scientific discipline gained momentum during
the industrial revolution. Continuing technological advancement further
necessitated refinement in this segment. Metrology is practised almost every day,
often unknowingly, in our day-to-day tasks.
 Measurement is closely associated with all the activities pertaining to scientific,
industrial, commercial, and human aspects. Its role is ever increasing and
encompasses different fields such as communications, energy, medical sciences,
food sciences, environment, trade, transportation, and military applications.
 Metrology concerns itself with the study of measurements.
 Metrology demands pure knowledge of certain basic mathematical and physical
principles.

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 1.2 METROLOGY
• Metrology word is derived from two Greek words metro which means
measurement and logy which means science.
• Metrology literally means science of measurements. In practical applications, it is
the enforcement, verification, and validation of predefined standards. Although
metrology, for engineering purposes, is constrained to measurements of length,
angles, and other quantities that are expressed in linear and angular terms, in a
broader sense, it is also concerned with industrial inspection and its various
techniques.
• Metrology also deals with establishing the units of measurements and their
reproduction in the form of standards, ascertaining the uniformity of
measurements, developing methods of measurement, analyzing the accuracy of
methods of measurement, establishing uncertainty of measurement, and
investigating the causes of measuring errors and subsequently eliminating them.

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Metrology is;

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1.3 TYPES OF METROLOGY
Legal Metrology
'Legal metrology' is that part of metrology which treats units of measurements, methods of
measurements and the measuring instruments, in relation to the technical and legal
requirements. The activities of the service of 'Legal Metrology' are:
• Control of measuring instruments;
• Testing of prototypes/models of measuring instruments;
• Examination of a measuring instrument to verify its conformity to the statutory
requirements etc.
Dynamic Metrology
'Dynamic metrology' is the technique of measuring sm ll v ri tions of a continuous nature. The
technique has proved very valuable, and record of continuous measurement, over a surface,
for instance, has obvious advantages over individual measurements of an isolated character.
Deterministic metrology
Deterministic metrology is a new philosophy in which part measurement is replaced by
process measurement. The new techniques such as 3D error compensation by CNC
(Computer Numerical Control) systems and expert systems are applied, leading to fully
adaptive control. This technology is used for very high precision manufacturing machinery
and control systems to a hieve micro technology and nanotechnology accuracies.
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1.4 NEED FOR INSPECTION
Inspection is defined as a procedure in which a part or product characteristic, such as a dimension, is examined to
determine whether it conforms to the design specification. Basically, inspection is carried out to isolate and evaluate a
specific design or quality attribute of a component or product.
Industrial inspection has become a very important aspect of quality control. Inspection essentially encompasses the
following:
1. Ascertain that the part, material, or component conforms to the established or desired standard.
2. Accomplish interchangeability of manufacture.
3. Sustain customer goodwill by ensuring that no defective product reaches the customers.
4. Provide the means of finding out inadequacies in manufacture. The results of inspection are recorded and reported to
the manufacturing department for further action to ensure production of acceptable parts and reduction in scrap.
5. Purchase good-quality raw materials, tools, and equipment that govern the quality of the finished products.
6. Coordinate the functions of quality control, production, purchasing, and other departments of the organizations.
7. Take the decision to perform rework on defective parts, that is, to assess the possibility of making some of these parts
acceptable after minor repairs.
8. Promote the spirit of competition, which leads to the manufacture of quality products in bulk by eliminating
bottlenecks and adopting better production techniques.

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1.5 ACCURACY AND PRECISION
ACCURACY
• Accuracy is the degree of agreement of the measured dimension with its true
magnitude.
• Accuracy can also be defined as the maximum amount by which the result differs
from the true value or as the nearness of the measured value to its true value,
often expressed as a percentage.
• True value may be defined as the mean of the infinite number of measured values
when the average deviation due to the various contributing factors tends to zero.
• In practice, realization of the true value is not possible due to uncertainties of the
measuring process and hence cannot be determined experimentally.
• Positive and negative deviations from the true value are not equal and will not
cancel each other.
• One would never know whether the quantity being measured is the true value of
the quantity or not.
• Accuracy of measurement is very important for manufacturing a quality product.

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1.5 ACCURACY AND PRECISION
PRECISION
• Precision is the degree of repetitiveness of the measuring process.
• Precision is the degree of agreement of the repeated measurements of a
quantity made by using the same method, under similar conditions.
• Precision is the repeatability of the measuring process.
• Repeatability is the ability of the measuring instrument to repeat the same
results during the act of measurements for the same quantity.
• Repeatability is random in nature and, by itself, does not assure accuracy,
though it is a desirable characteristic.
• Precision refers to the consistent reproducibility of a measurement.
• Reproducibility is normally specified in terms of a scale reading over a
given period of time.
• If an instrument is not precise, it would give different results for the same
dimension for repeated readings.

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1.5 ACCURACY AND PRECISION
Difference between Precision & Accuracy
• Accuracy gives information regarding how far the measured value is with respect
to the true value, whereas precision indicates quality of measurement, without
giving any assurance that the measurement is correct.
• These concepts are directly related to random and systematic measurement
errors.

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1.5 ACCURACY AND PRECISION

• The difference between the true value and the mean value of
the set of readings on the same component is termed as an
error.
• Error can also be defined as the difference between the
indicated value and the true value of the quantity measured.
E = Vm − Vt
where E is the error, Vm the measured value, and Vt the true
value.

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1.5 ACCURACY AND PRECISION

Accuracy of an instrument can also be expressed as % error. If an instrument

measures Vm instead of Vt, then,

𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸
% error= × 100
True value
Or
𝑉𝑉𝑚𝑚 − 𝑉𝑉𝑡𝑡
% error = × 100
𝑉𝑉𝑡𝑡

Accuracy of an instrument is always assessed in terms of error.Theinstrument

is moreaccurate if the magnitude of error is low.
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1.5 ACCURACY AND PRECISION
1.5.1 Accuracy and Cost:
It can be observed from Fig. 1.2 that as the requirement
of accuracy increases, the cost increases exponentially.
If the tolerance of a component is to be measured, then
the accuracy requirement will normally be 10% of the
tolerance values.
Demanding high accuracy unless it is absolutely
required is not viable, as it increases the cost of the
measuring equipment and hence the inspection cost.
Therefore, in practice, while designing the measuring
equipment, the desired/required accuracy to cost
considerations depends on the quality and reliability of
the component/product and inspection cost.

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1.6 OBJECTIVES OF METROLOGY AND MEASUREMENTS
In addition, metrology is an integral part of modern engineering industry consisting of various departments,
namely design, manufacturing, assembly, research and development, and engineering departments. The
objectives of metrology and measurements include the following:
1. To ascertain that the newly developed components are comprehensively evaluated and designed within
the process, and that facilities possessing measuring capabilities are available in the plant.
2. To ensure uniformity of measurements
3. To carry out process capability studies to achieve better component tolerances
4. To assess the adequacy of measuring instrument capabilities to carry out their respective measurements
5. To ensure cost-effective inspection and optimal use of available facilities
6. To adopt quality control techniques to minimize scrap rate and rework
7. To establish inspection procedures from the design stage itself, so that the measuring methods are
standardized
8. To calibrate measuring instruments regularly in order to maintain accuracy in measurement
9. To resolve the measurement problems that might arise in the shop floor
10. To design gauges and special fixtures required to carry out inspection
11. To investigate and eliminate different sources of measuring errors 14
1.7 GENERAL MEASUREMENT CONCEPTS
The three basic elements
of measurements:

1. Measurand, a physical quantity such as length, weight, and angle to be measured

2. Comparator, to compare the measurand (physical quantity) with a known
standard (reference) for evaluation
3. Reference, the physical quantity or property to which quantitative comparisons
are to be made, which is internationally accepted
All these three elements would be considered to explain the direct measurement
using a calibrated fixed reference.

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1.7 GENERAL MEASUREMENT CONCEPTS
1.7.1 CALIBRATION OF MEASURING INSTRUMENTS
The process of validation of the measurements to ascertain whether the
given physical quantity conforms to the original/national standard of
measurement is known as traceability of the standard.
• Calibration is the procedure used to establish a relationship between the
values of the quantities indicated by the measuring instrument and the
corresponding values realized by standards under specified conditions.
• If the values of the variable involved remain constant (not time dependent)
while calibrating a given instrument, this type of calibration is known as
Static calibration,
• whereas if the value is time dependent or time‐based information is
required, it is called Dynamic calibration
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1.8 METHODS OF MEASUREMENTS
These are the methods of comparison used in measurement process. In precision
measurement various methods of measurement are adopted depending upon the
accuracy required and the amount of permissible error. The methods of
measurement can be classified as:
l. Direct method
2. Indirect method
3. Absolute or Fundamental method
4. Comparative method
5. Transposition method
6. Coincidence method
7. Deflection method
8. Complementary method
9. Contact method
10. Contact less method

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 1.8 METHODS OF MEASUREMENTS
1.Direct method of measurement: This is a simple method of measurement, in which the
value of the quantity to be measured is obtained directly without any calculations. For
example, measurements by using scales, vernier callipers, micrometers, bevel protector
etc. This method is most widely used in production. This method is not very accurate
because it depends on human insensitiveness in making judgment.
2. Indirect method of measurement: In indirect method the value of quantity to be
measured is obtained by measuring other quantities which are functionally related to the
required value. E.g. Angle measurement by sine bar, measurement of screw pitch
diameter by three wire method etc.
3. Absolute or Fundamental method: It is based on the measurement of the base
quantities used to define the quantity. For example, measuring a quantity directly in
accordance with the definition of that quantity, or measuring a quantity indirectly by
direct measurement of the quantities linked with the definition of the quantity to be
measured.

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 1.8 METHODS OF MEASUREMENTS
4. Comparative method: In this method the value of the quantity to be measured is
compared with known value of the same quantity or other quantity practically related to
it. So, in this method only the deviations from a master gauge are determined, e.g., dial
indicators, or other comparators.
5. Transposition method: It is a method of measurement by direct comparison in which
the value of the quantity measured is first balanced by an initial known value A of the
same quantity, and then the value of the quantity measured is put in place of this known
value and is balanced again by another known value B. If the position of the element
indicating equilibrium is the same in both cases, the value of the quantity to be
measured is AB. For example, determination of a mass by means of a balance and
known weights, using the Gauss double weighing.
6. Coincidence method: It is a differential method of measurement in which a very small
difference between the value of the quantity to be measured and the reference is
determined by the observation of the coincidence of certain lines or signals. For
example, measurement by vernier calliper micrometer. 19
1.8 METHODS OF MEASUREMENTS
7. Deflection method: In this method the value of the quantity to be measured is
directly indicated by a deflection of a pointer on a calibrated scale.
8. Complementary method: In this method the value of the quantity to be
measured is combined with a known value of the same quantity. The combination is
so adjusted that the sum of these two values is equal to predetermined comparison
value. For example, determination of the volume of a solid by liquid displacement.
9. Method of measurement by substitution: It is a method of direct comparison in
which the value of a quantity to be measured is replaced by a known value of the
same quantity, so selected that the effects produced in the indicating device by
these two values are the same.
10. Method of null measurement: It is a method of differential measurement. In
this method the difference between the value of the quantity to be measured and
the known value of the same quantity with which it is compared is brought to zero.

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1.9 METROLOGY ELEMENTS
A measuring system is made of five basic elements. These five basic
metrology elements can be composed into the acronym SWIPE, for
convenient reference where:
1. STANDARD
2. WORK PIECE
3. INSTRUMENT
4. PERSON
5. ENVIRONMENT.
The most basic element of measurement is a standard without which no
measurement is possible. Once the standard is chosen a measuring
instrument incorporations this standard is should be obtained. This
instrument is then used to measure the job parameters, in terms of units of
standard contained in it. The measurement should be performed under
standard environment. And, lastly, there must be some person or mechanism
(if automatic) to carry out the measurement. 21
1.9 METROLOGY ELEMENTS
Factors affecting the accuracy of the Measuring System
• The basic components of an accuracy evaluation are the five elements of a
measuring system such as:
• Factors affecting the calibration Standards.
• Factors affecting the Workpiece.
• Factors affecting the inherent characteristics of the Instrument.
• Factors affecting the Person, who carries out the measurements,
• Factors affecting the Environment.

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1.9 METROLOGY ELEMENTS

1. Factors affecting the Standard: It may be affected by:

-Coefficient of thermal expansion
-Calibration interval
-Stability with time
-Elastic properties
-Geometric compatibility

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1.9 METROLOGY ELEMENTS

2. Factors affecting the Work piece: These are:

-Cleanliness
-Surface finish, waviness, scratch, surface defects etc.,
-Hidden geometry
-Elastic properties,
-adequate datum on the workpiece
-Arrangement of supporting work piece
-Thermal equalization etc.

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1.9 METROLOGY ELEMENTS
3.Factors affecting the inherent characteristics of Instrument:
-Adequate amplification for accuracy objective
-Scale error
-Effect of friction, backlash, hysteresis, zero drift error
-Deformation in handling or use, when heavy work pieces are measured
-Calibration errors
-Mechanical parts (slides, guide ways or moving elements)
-Repeatability and readability
-Contact geometry for both work piece and standard.

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1.9 METROLOGY ELEMENTS

4. Factors affecting person:

-Training, skill
-Sense of precision appreciation
-Ability to select measuring instruments and standards
-Sensible appreciation of measuring cost
-Attitude towards personal accuracy achievements
-Planning measurement techniques for minimum cost, consistent with
precision requirements etc.

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1.9 METROLOGY ELEMENTS
5. Factors affecting Environment:
-Temperature, humidity etc.
-Clean surrounding and minimum vibration enhance precision
-Adequate illumination
-Temperature equalization between standard, work piece, and
instrument
-Thermal expansion effects due to heat radiation from lights
-Heating elements, sunlight and people
-Manual handling may also introduce thermal expansion.

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1.10 ERRORS IN MEASUREMENTS
1.10.1 SYSTEMATIC OR CONTROLLABLE ERRORS
 A systematic error is a type of error that deviates by a fixed amount from the true
value of measurement.
 These types of errors are controllable in both their magnitude and their direction.
 These types of errors can be assessed and minimized if efforts are made to
analyze them.
Minimization of systematic errors increases the accuracy of measurement. The
following are the reasons for their occurrence:
1. Calibration errors
2. Ambient conditions
3. Deformation of workpiece
4. Avoidable errors
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1.10 ERRORS IN MEASUREMENTS
1.10.2 RANDOM ERRORS
• Random errors provide a measure of random deviations when measurements of
a physical quantity are carried out repeatedly.
• When a series of repeated measurements are made on a component under
similar conditions, the values or results of measurements vary.
• They are of variable magnitude and may be either positive or negative.
• Random errors can be minimized by calculating the average of a large number of
observations.
• Since precision is closely associated with the repeatability of the measuring
process, a precise instrument will have very few random errors and better
repeatability. Hence, random errors limit the precision of the instrument.

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1.10 ERRORS IN MEASUREMENTS
1.10.2 RANDOM ERRORS
The following are the likely sources of random errors:
1. Presence of transient fluctuations in friction in the measuring instrument
2. Play in the linkages of the measuring instruments
3. Error in operator’s judgement in reading the fractional part of engraved scale
divisions
4. Operator’s inability to note the readings because of fluctuations during
measurement
5. Positional errors associated with the measured object and standard, arising due
to small variations in setting
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1.10 ERRORS IN MEASUREMENTS
1.10.3 THE DIFFERENCES BETWEEN RANDOM AND SYSTEMATIC ERRORS
Figure 1.5 clearly depicts the relationship between systematic and random errors
with respect to the measured value.

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1.10 ERRORS IN MEASUREMENTS
1.10.3 THE DIFFERENCES BETWEEN RANDOM AND SYSTEMATIC ERRORS
The measure of a system’s accuracy is altered by both systematic and random
errors. Table 1.1 gives the differences between systematic and random errors.

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