Unit 1 CONCEPT OF MEASUREMENT

KIT – KALAIGNAR KARUNANIDHI INSTITUTE OF TECHNOLOGY,
COIMBATORE / ME6504 / V-SEM / 2015 METROLOGY & MEASUREMENTS
I
LESSON NOTES
ME6504
METROLOGY AND MEASUREMENTS

II
SYLLABUS

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LESSON NOTES
ME6504 METROLOGY AND MEASUREMENTS
UNIT – I

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UNIT I BASICS OF METROLOGY:
Introduction to Metrology – Need - Elements – Work piece, instruments – Persons –
Environment – their Effects on Precision and Accuracy – Errors – Errors in Measurements
– Types – Control – Types of standards
CONTENTS
1.0 INTRODUCTION TO METROLOGY
1. 1 NEED OF METROLOGY
1. 2 METROLOGICAL ELEMENTS AND CHARACTERISTICS OF MEASURING
INSTRUMENTS.
1. 3 VARIOUS EFFECTS ON PRECISION AND ACCURACY (WORK PIECE, INSTRUMENTS,
PERSONS, ENVIRONMENTS)
1. 4 ERRORS IN MEASUREMENTS AND CONTROL
1. 5 TYPES OF STANDARDS

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1.0 INTRODUCTION TO METROLOGY
Quantity:
Property of a phenomenon, body, or substance, where the property has a magnitude that can be
expressed as a number and a reference (A reference can be a measurement unit, a measurement
procedure, a reference material, or a combination of such.) Quantity can be a general quantity (e.g. length)
or particular quantity (e.g.wavelength of Sodium D line)
Measurand :
Quantity intended to be measured.
Estimate (Of The Measurand) Or Measured Quantity Value :
measured value of a quantity measured value quantity value representing a measurement result
Measurement Error: measured quantity value minus a reference quantity value
Metrology includes all theoretical and practical aspects of measurement, whatever the
measurement uncertainty and field of application.
Methods of measurements:
In precision measurement various methods are followed depends upon the accuracy required.
1. Direct method of measurement
2. Indirect method of measurement
3. Fundamental method of measurement
4. Comparison method of measurement
5. Substitution method of measurement
6. Transposition method of measurement
7. Coincidence method of measurement
8. Transposition method of measurement
9. Deflection method of measurement
10. Interpolation method of measurement
11. Extrapolation method of measurement
12. Complementary method of measurement
13. Composite method of measurement
14. Element method of measurement
15. Contact and contact less method of measurement
Measuring Instruments:
According to the functions:
1. Length measuring instrument
2. Angle measuring instrument
3. Instrument for checking deviation from geometrical forms

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4. Instrument for determining the quality of surface finish.
According to the accuracy:
1. Most accurate instruments Example - light interference instrument
2. Less accurate instrument Example - Pool room Microscope, Comparators, Optimeter
3. Still less accurate instrument Example - Dial indicator, vernier caliper.
1.1 NEED OF METROLOGY:
In order to determine the fitness of anything made, man has always used inspection. But
industrial inspection is of recent origin and has scientific approach behind it. It came into being
because of mass production which involved interchangeability of parts. In old craft, same
craftsman used to be producer as well as assembler. Separate inspections were not required. If any
component part did not fit properly at the time of assembly, the craftsman would make the
necessary adjustments in either of the mating parts so that each assembly functioned properly. So
actually speaking, no two parts will be alike/and there was practically no reason why they should
be.
Now new production techniques have been developed and parts are being manufactured in
large scale due to low-cost methods of mass production. So hand-fit methods cannot serve the
purpose any more. When large number of components of same part are being produced, then any
part would be required to fit properly into any other mating component part. This required
specialisation of men and machines for the performance of certain operations. It has, therefore,
been considered necessary to divorce the worker from all round crafts work and to supplant hand-
fit methods with interchangeable manufacture.
The modern production techniques require that production of complete article be broken up
into various component parts so that the production of each component part becomes an
independent process. The various parts to be assembled together in assembly shop come from
various shops.
Rather some parts are manufactured in other factories also and then assembled at one place. So it
is very essential that parts must be so fabricated that the satisfactory mating of any pair chosen
at random is possible. In order that this may be possible, the dimensions of the component part
must be confined within the prescribed limits which are such as to permit the assembly with a
predetermined fit. Thus industrial inspection assumed its importance due to necessity of suitable
mating of various components manufactured separately. It may be appreciated that when large
quantities of work-pieces are manufactured on the basis of interchangeability, it is not necessary
to actually measure the important features and much time could be saved by using gauges which
determine whether or not a particular feature is within the prescribed limits. The methods of
gauging, therefore, determine the dimensional accuracy of a feature, without reference to its actual

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size.
The purpose of dimensional control is however not to strive for the exact size as it is
impossible to produce all the parts of exactly same size due to so many inherent and random
sources of errors in machines and men. The principal aim is to control and restrict the variations
within the prescribed limits. Since we are interested in producing the parts such that assembly
meets the prescribed work standard, we must not aim at accuracy beyond the set limits which,
otherwise is likely to lead to wastage of time and uneconomical results.
Lastly, inspection led to development of precision inspection instruments which caused the
transition from crude machines to better designed and precision machines. It had also led to
improvements in metallurgy and raw material manufacturing due to demands of high accuracy
and precision. Inspection has also introduced a spirit of competition and led to production of
quality products in volume by eliminating tooling bottle-necks and better processing techniques.
The means of measurements could be classified as follows:
(i) Standards (Reference masters or setting standards) these are used to reproduce one
or several definite values of a given quantity.
(ii) Fixed gauges- these are used to check the dimensions, form, and position of product features.
(iii) Measuring instruments - these are used to determine the values of the measured
quantity.
1.2 METROLOGICAL ELEMENTS AND CHARACTERISTICS OF MEASURING
INSTRUMENTS:
Measuring instruments are usually specified by their metrological properties, such as range
of measurement, scale graduation value, scale spacing, sensitivity and reading accuracy.
Range of Measurement: It indicates the size values between which measurements may be
made on the given instrument.
Scale range: It is the difference between the values of the measured quantities corresponding
to the terminal scale marks.
Instrument range: It is the capacity or total range of values which an instrument is capable of
measuring. For example, a micrometer screw gauge with capacity of 25 to 50mm has instrument
range of 25 to 50mm but scale range is 25mm.
Scale Spacing: It is the distance between the axes of two adjacent graduations on the scale.
Most instruments have a constant value of scale spacing throughout the scale. Such scales are said
to be linear. In case of non linear scales, the scale spacing value is variable within the limits of
the scale.
Scale Division Value: It is the measured value of the measured quantity corresponding to one

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division of the instrument, e.g. for ordinary scale, the scale division value is 1mm. As a rule, the
scale division should not be smaller in value than the permissible indication error of an
instrument.
Sensitivity (Amplication or gearing ratio): It is the ratio of the scale spacing to the division
value. It could also be expressed as the ratio of the product of all the larger lever arms and the
product of all the smaller lever arms. It is the property of a measuring instrument to respond to
changes in the measurement quantity.
Sensitivity Threshold: It is d as the minimum measured value which may cause any
movement whatsoever of the indicating hand. It is also called the discrimination or resolving
power of an instrument and is the minimum change in the quantity being measured which
produces a perceptible movement of the index.
Reading Accuracy: It is the accuracy that may be attained in using a measuring instrument.
Reading Error: It is d as the difference between the reading of the instrument and the actual
value of the dimension being measured.
Accuracy of observation: It is accuracy attainable in reading the scale of an instrument. It
depends on the quality of the scale marks, the width or the pointer / index, the space between the
pointer and the scale, the illumination of the scale, and the skill of the inspector. The width of
scale mark is usually kept one tenth of the scale spacing for accurate reading of indications.
Parallax: It is apparent change in the position of the index relative to the scale marks, when
the scale is observed in a direction other than perpendicular to its plane.
Repeatability: It is the variation of indications in repeated measurements of the same
dimension. The variations may be due to clearances, friction and distortions in the instrument’s
mechanism. Repeatability represents the reproducibility of the readings of an instrument when a
series of measurements in carried out under fixed conditions of use.
Measuring force: It is the force produced by an instrument and acting upon the measured
surface in the direction of measurement. It is usually developed by springs whose deformation
and pressure change with the displacement of the instrument’s measuring spindle.
1.3 PRECISION AND ACCURACY:
Accuracy and precision and distinction between precision and accuracy.
The agreement of the measured value with the true value of the measured quantity is called
accuracy. If the measurement of a dimensions of a part approximates very closely to the true
value of that dimension, it is said to be accurate. Thus the term accuracy denotes the closeness of

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the measured value with the true value. The difference between the measured value and the true
value is the error of measurement. The lesser the error, more is the accuracy.
Precision and Accuracy
Precision, The terms precision and accuracy are used in connection with the performance
of the instrument. Precision is the repeatability of the measuring process. It refers to the group of
measurements for the same characteristics taken under identical conditions. It indicates to what
extent the identically performed measurements agree with each other. If the instrument is not
precise it will give different (widely varying) results for the same dimension when measured
again and again. The set of observations will scatter about the mean. The scatter of these
measurements is designated as , the standard deviation. It is used as an index of precision. The
less the scattering more precise is the instrument. Thus, lower, the value of , the more precise is
the instrument.
Accuracy: Accuracy is the degree to which the measured value of the quality characteristic
agrees with the true value. The difference between the true value and the measured value is
known as error of measurement.
Distinction between Precision and Accuracy
Accuracy is very often confused with precision though much different. The distinction
between the precision and accuracy will become clear by the following example. Several
measurements are made on a component by different types of instruments (A, B and C
respectively) and the results are plotted. In any set of measurements, the individual
measurements are scattered about the mean, and the precision signifies how well the various
measurements performed by same instrument on the same quality characteristics agree with each
other.

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The difference between the mean of set of readings of the same quality characteristic and
the true value is called as error. Less the error more accurate is the instrument.
Figure shows that the instrument A is precise since the results of number of measurements
are close to the average value. However, there is a large difference (error) between the true value
and the average value hence it is not accurate.
The readings taken by the instruments are scattered much from the average value and hence it is
not precise but accurate as there is a small difference between the average value and true value.
Figure shows that the instrument is accurate as well as precise.
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:
1. Factors affecting the calibration standards
2. Factors affecting the workpiece
3. Factors affecting the inherent characteristics of the instrument
4. Factors affecting the person, who carries out the measurements, and
5. Factors affecting the environment.
1. Factors affecting the standard. It may be affected by:
a. Coefficient of thermal expansion,
b. Calibration interval,
c. Stability with time,
d. Elastic properties,
e. Geometric compatibility
2. Factors affecting the Workpiece, these are:

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a. Cleanliness, surface finish, waviness, scratch, surface defects etc.,
b. Hidden geometry,
c. Elastic properties,
d. Adequate datum on the workpiece
e. Arrangement of supporting workpiece
f. Thermal equalization etc.
3. Factors affecting the inherent characteristics of Instrument
a. Adequate amplification for accuracy objective,
b. Scale error,
c. Effect of friction, backlash, hysteresis, zero drift error,
d. Deformation in handling or use, when heavy workpieces are measured
e. Calibration errors,
f. Mechanical parts (slides, guide ways or moving elements)
g. Repeatability and readability
h. Contact geometry for both workpiece and standard
4. Factors affecting person:
a. Training, skill
b. Sense of precision appreciation,
c. Ability to select measuring instruments and standards
d. Sensible appreciation of measuring cost,
e. Attitude towards personal accuracy achievements
f. Planning measurement techniques for minimum cost, consistent with precision
requirements etc
5. Factors affecting Environment:
a. Temperature, humidity etc.,
b. Clean surrounding and minimum vibration enhance precision,
c. Adequate illumination
d. Temperature equalization between standard, workpiece, and instrument,
e. Thermal expansion effects due to heat radiation from lights, heating elements,
sunlight and people,
f. Manual handling may also introduce thermal expansion.
Higher accuracy can be achieved only if, all the sources of error due to the above five elements in
the measuring system are analysed and steps taken to eliminate them. The above analysis of five
basic metrology elements can be composed into the acronym.
1.4 ERRORS:

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Sources of error
During measurement several types of error may arise as indicated and these error can be broadly
classified into two categories.
a) Controllable Errors:
These are controllable in both their magnitude and sense. These can be determined and
reduced, if attempts are made to analyse them. These are also known as systematic errors. These
can be due to:
1.Calibration Errors :
The actual length of standards such as slip gauges and engraved scales will vary from nominal
value by small amount. Sometimes the instrument inertia and hysteresis effects do not let the
instrument translate with complete fidelity. Often signal transmission errors such as a drop in
voltage along the wires between the transducer and the electric meter occur. For high order
accuracy these variations have positive significance and to minimize such variations calibration
curves much be used.
2. Ambient Conditions :
Variations in the ambient conditions from internationally agreed standard value of 20o
C,
barometric pressure 760mm of mercury and 10mm of mercury vapour pressure, can give rise to
errors in the measured size of the component. Temperature is by far the most significant of these
ambient conditions and due correction is needed to obtain error free results.
1.Stylus Pressure :
Error induced due to stylus pressure are also appreciable. Whenever any component in
measured under a definite stylus pressure both the deformation of the workpiece surface and
deflection of the workpiece shape will occur.
Avoidable Errors :
These error include the errors due to Parallel and the effect of misalignment of the workpiece
centers. Instrument location errors such as placing a thermometer is sunlight when attempting to
measure air temperature also being to this category.
b) Random Errors :
These occur randomly and the specific causes of such errors cannot be determined, but
likely sources of this type of error are small variations in the position of setting standards and
workpiece, slight displacement of lever joints in the measuring joints in the measuring instrument,
transient flaction in the friction in the measuring instrument and operator errors in reading scale
and pointer type displays or in reading engraved scale positions.

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From the above, it is clear that systematic errors are those which are repeated consistently
with repetition of the experiment, where as random errors are those which are accidental and
whose magnitude and sign cannot be predicted from a knowledge of the measuring system and
condition of measurement.
1.4 ERRORS IN MEASUREMENTS AND CONTROL:
Calibration: Calibration is the process of establishing the relationship between a measuring
device and the units of measure. This is done by comparing a devise or the output of an
instrument to a standard having known measurement characteristics. For example the length of a
stick can be calibrated by comparing it to a standard that has a known length. Once the
relationship of the stick to the standard is known the stick can be used to measure the length of
other things.
Sensitivity of a measuring instrument.
Instrument dy
Reading
dx
Measured quantity
Readability: In the sciences, readability is a measure of an instrument's ability to display
incremental changes in its output value. For example, a balance with a readability of 1 mg will not
display any difference between objects with masses from 0.6 mg to 1.4 mg, because possible
display values are 0 mg, 1 mg, 2 mg etc. Likewise, a balance with a readability of 0.1 mg will not
display any difference between objects with masses from 0.06 mg to 0.14 mg.
True size and Actual size:
True size  Theoretical size of a dimension which is free from errors.
Actual size  size obtained through measurement with permissible error.
Hysterisis: A system with hysteresis can be summarised as a system that may be in any number
of states, independent of the inputs to the system. To be exact, a system with hysteresis exhibits
path-dependence, or "rate-independent memory .
Range: Range is the difference between the highest and lowest value.
Change in the output signal
Sensitivity =
Change in the input signal

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Span: Span is the distance or interval between two points.
Example : In a measurement of temperature higher value is 200 C and lower value is 150 C means
span = 200 150 = 50 C.
Resolution: Resolution is the quantitative measure of the ability of an optical instrument to
produce separable images of different points on an object; usually, the smallest angular or linear
separation of two object points for which they may be resolved according to the Rayleigh criterion.
Verification: It is the process of testing the instrument for determining the errors.
Scale interval: It is the difference between two successive scale marks in units.
Dead Zone: Dead zone is the range through which a stimulus can be varied without producing a
change in the response of the measuring instrument.
Threshold: Threshold is the smallest detectable sensation of an instrument.
Discrimination: Discrimination is the ability of an instrument to differentiate between various
physical parameters or ability to measure even the minute changes in readings.
Back lash: Back lash is the play or loose motion in an instrument due to the clearance existing
between mechanically contacting parts. It is similar to hysterisis but more commonly applied to
mechanical systems. It often occurs between interacting mechanical parts as a result of looseness.
Response time : Response time (technology), the time a generic system or functional unit takes to
react to a given input
Repeatability: Repeatability is the variation in measurements taken by a single person or
instrument on the same item and under the same conditions. A measurement may be said to be
repeatable when this variation is smaller than some agreed limit.
Bias: Bias is a term used to describe a tendency or preference towards a particular perspective,
ideology or result. All information and points of view have some form of bias. A person is
generally said to be biased if a reasonable observer would conclude that the person is markedly
influenced by inner biases, rendering it unlikely for them to be able to be objective.
Magnification : It is the process of enlarging something only in appearance, not in physical size.
Magnification is also a number describing by which factor an object was magnified.
Drift: Drift is a slow change. In metrology and measurements it refers to delay in response of an
instrument for changes in input signals.

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Reproducibility : Reproducibility is one of the main principles of the scientific method, and
refers to the ability of a test or experiment to be accurately reproduced, or replicated, by someone
else working independently.
Uncertainty: The lack of certainty, A state of having limited knowledge where it is impossible to
exactly describe existing state or future outcome, more than one possible outcome. It applies to
predictions of future events, to physical measurements already made, or to the unknown.
Trace ability: Traceability refers to the completeness of the information about every step in a
process chain.
Fiducial value: The prescribed value of a quantity to which the reference is made.
Parallax, more accurately motion parallax, is the change of angular position of two observations
of a single object relative to each other as seen by an observer, caused by the motion of the
observer.
Accuracy and uncertainty with example:
Accuracy Closeness to the true value.
Example: Measuring accuracy is ± 0.02mm for diameter of part is 25mm.
Here the measurement true value lie between 24.98 to 25.02 mm.
Uncertainty about the true value ± 0.02mm.
Sources of errors in precision measurement:
Failure to consider the following factors may introduce errors in measurement :
Alignment Principle
Location of the measured part
Temperature
Parallax.
Alignment Principle (Abbe's Principle) :
Abbe's principle of alignment states that " the axis or line of measurement of the measured
part should consider with the measuring scale or axis or measurement of measuring instrument ".
The effect of simple scale alignment error is shown in fig.
L

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L
Q JCL
if Q = angle of scale misalignment
L = apparent length
Loose = true length
if e = induced error
then,
e = L-L cose
= L(1-CoseC)
An alignment error of 2o
over iN introduces an error of approximately 0.6mm.
Error in introduced to dial indicator readings if the plunger axis does not coincide with the
axis or line of measurement.
Q
If e = Induced error
L = change in indicator reading,
reading.
L case = Surface displacement
e = L (1-Cose) Line or axis of measure Dial gauge axis.
To ensure correct displacement readings on the dial indicator the plunger must, of course
be normal to the surface in both mutually perpendicular planes.
A second source of error will illustrated by the vernier Caliper and similar instruments or
circumstance is associated with measuring pressure or "feel". The measuring pressure in applied
by the adjusting screw which is adjacent and parallel to the scale. A bending moment in
introduced equal to the product of the force applied by the adjusting screw and the perpendicular
distance between the screw centre line and the line of measurement as in Fig.
Variation of force applied at the screw are augmented at the line of measurement and a hot
unusual form of damage to Vernier Caliper is permanent distortion to the measuring jaws
presumably from this source as in fig.

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Location :
when using a sensitive comparator, the measured part in located on a table which forms the
datum for comparison with the standard. The comparator reading in thus an indication of the
displacement of the upper surface of the measured part from the datum. Faults at the location
surface of the part damage, geometrical variations from part to part or the presence of foreign
matter are also transmitted to the indicator. This provides false information regarding the true
length of the part by introducing both sine and cosine error.
Where location conditions may not be ideal, ex:- inter stage measurement during
production, sensors, operating on each side of the component can be used which eliminate the
more serious sine type error. A two probe system measures length rather than surface
displacement and highly sensitive electronic comparators of this type are used for slip gauge
measurement.
Temperature :-
The standard reference temp. at which line and end standards are said to be at their true
length is 20o
and for highest accuracy in measurement this temp. Should be maintained. When
this is not possible and the length at reference temp. must be known, a correction is made to allow
for the difference between ambient and reference temp. The correction value required to
0.001375mm, when steel object exactly 25mm long at 20o
C and Co-efficient of linear expansion
11Mm c/m in measured at 25o
C, Which is rather larger than the increment step the M88/2 stip
gauge set.
However, for less stringent measurement requirements it is not essential that correction to
reference temperature is made provided that the following precautions and conditions are
observed.
a) The temp. at which measurement is made is not changing significantly.
b) The gauge and work being compared are at the same temp and the temp is the same as
ambient temp.
c) The gauge and work have the same Co-efficient of linear expansion.
Conditions a) and b) can be met if gauge and work allowed sufficient time to reach equal temp
with surrounding after being arranged in the measuring positions.
If the measurement can be carried out on the surface of a large mass, eg: Surface plate, then
temp. equalization will be family vapid as heat will be conducted away form the work and gauge
but will not contribute any significant temp. change to the plate.

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A component having a co-efficient of linear expansion significantly different from the gauge may
be said to correct to size only at a given temp.
Parallax Effect :
On most dials the indicating finger or pointer lies in a plane parallel to the scale but displaced a
small distance away to allow free movement of the pointer. It is then essential to observe the
pointer along a line normal to the scale otherwise a reading error will occur. This effect is shown
in fig. Where a dial is shown observed from three positions where the pointer is set at zero on the
scale, observed from position 1) ie, from the left, the pointer appears to indicate some value, to the
right off zero, and from position 2) Some value slightly to the left of zero, while only at position.
3) With the pointer Coincide with zero on the scale. Rules and micrometer thimbles are beveled to
reduce this effect and on dials the indicates may be arranged to lie in the same plane as the scale,
thus completely eliminating parallax, or a silvered reflector may be incorporated on the scale so
that the line between the of eye and pointer is normal to the scale
1.5 Types of Standards:
The Need for standards:
Standards define the units and scales in use, and allow comparison of measurements made in
different times and places. For example, buyers of fuel oil are charged by a unit of liquid volume.
In the U.S., this would be the gallon; but in most other parts of the world, it would be the liter. It is
important for the buyer that the quantity ordered is actually received and the refiner expects to be
paid for the quantity shipped. Both parties are interested in accurate measurements of the volume
and, therefore, need to agree on the units, conditions, and method(s) of measurement to be used.
Persons needing to measure a mass cannot borrow the primary standard maintained in France or
even the national standard from the National Institute of Standards and Technology (NIST) in the
U.S. They must use lower-level standards that can be checked against those national or
international standards.
Everyday measuring devices, such as scales and balances, can be checked (calibrated) against
working level mass standards from time to time to verify their accuracy. These working-level
standards are, in turn, calibrated against higher-level mass standards. This chain of calibrations or
checking is called traceability. A proper chain of traceability must include a statement of
uncertainty at every step.

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Basic or Fundamental Standards:
In the SI system, there are seven basic measurement units from which all other units are derived.
All of the units except one are defined in terms of their unitary value. The one exception is the unit
of mass.
It is defined as 1000 grams (g) or 1 kilogram (kg). It is also unique in that it is the only unit
currently based on an artifact. The U.S. kilogram and hence all other standards of mass are based
on one particular platinum/iridium cylinder kept at the BIPM in France. If that International
Prototype Kilogram were to change, all other mass standards throughout the world would be
wrong.
The seven basic units are listed in Appendix 1, Table 1. Their definitions are listed in Appendix 1,
Table 2.
Derived Standards:
All of the other units are derived from the seven basic units described in Appendix 1, Table 1.
Measurement standards are devices that represent the SI standard unit in a measurement. (For
example, one might use a zener diode together with a reference amplifier and a power source to
supply a known voltage to calibrate a digital voltmeter. This could serve as a measurement
standard for voltage and be used as a reference in a measurement.)
Appendix 1, Table 3 lists the most common derived SI units, together with the base units that are

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used to define the derived unit. For example, the unit of frequency is the hertz; it is defined as the
reciprocal of time. That is, 1 hertz (1 Hz) is one cycle per second.
The Measurement Assurance System:
The interrelationship of the various categories of standards throughout the world. While it gives
more detail to U.S. structure, similar structures exist in other nations. Indeed, a variety of regional
organizations exist that help relate measurements made in different parts of the world to each
other.

Unit 1 CONCEPT OF MEASUREMENT

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Unit 1 CONCEPT OF MEASUREMENT