METROLOGY & MEASUREMENT
METROLOGY & MEASUREMENTS
[COMMON TO III SEM MECHANICAL / I&P]
MME 3104 METROLOGY & MEASUREMENTS [3 0 0 3]
METROLOGY & MEASUREMENTS
No. of Lecture hours: 36
Measurements and measurement systems: Methods of
Measurement, Generalized Measurement System & its elements,
Static Characteristics of Instruments & measurement systems:
Accuracy, Precision, Sensitivity, Reproducibility, Repeatability,
Linearity, Hysteresis. Threshold, Dead zone, Resolution. Errors in
Measurement.
[03]
Measurement of pressure: Definition of Pressure. List of instruments
used to measure pressure. Methods of pressure measurement Elastic pressure elements (Bourdon Tube, Bellows, Diaphragm),
McLeod Gauge and Bridgman gauge, Related problems.
[04]
Measurement
of
temperature:
Methods
of
temperature
measurement
Pressure
thermometer,
Electrical
Resistance
thermometer, Thermocouples, Pyrometer (Disappearing filament type
optical pyrometer) & Problems, Bimetallic thermometer.
[03]
Measurement of strain: Types of electrical resistance strain gauges,
Theory of operation of wire wound strain gauge, Gauge Factor, Strain
gauge bridge circuit, Calibration Circuit, Temperature compensation,
Strain measurement on static and rotary shaft, Orientation of strain
gauges. Simple problems related to measurement of strain using
strain gauge.
[05]
Measurement of force, torque and shaft power: Measurement of
Force - Hydraulic & Pneumatic load cells, Proving ring, Strain gauge
load cell & related problems. Methods of Torque & Shaft power Cradled dynamometer, Torque Meter, Band Brake dynamometer,
Water Brake dynamometer.
[03]
Limits, Fits and Tolerances: Terminology (as per Indian Standards
IS 919), Grades of Tolerances, Letter symbols for tolerances, Fits –
definition, Types of fits – Clearance, Interference and Transition.
Numerical on limits and fit.
[03]
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METROLOGY & MEASUREMENTS
METROLOGY & MEASUREMENT
Gauges: Taylor’s principle for design of gauges – Statements and
explanation, Gauge Maker’s tolerance – as per 3rd system (present
British standards), Numerical on design of gauges (complete shaft and
hole pair) ,Types of gauges – Plug gauge, Ring gauge, Taper plug
gauge, Taper Ring gauge and slip gauges.
[03]
Measurement of form errors: Straightness measurement– using
straight edge, using Autocollimator. Squareness measurement –
Engineer’s Square tester, Optical Square. Simple numerical on
Straightness, Flatness and Squareness measurement.
[04]
Surface texture measurement: Definitions - I, II, III, IV order
(including their causes), Roughness and Waviness, Lays, Indian
standards symbols for Roughness, Analysis of traces – Ra, Rz, Rt, Rq,
Sampling length, hrms and Centerline Average (CLA), Simple numerical
on surface roughness.
[04]
Screw threads: Definitions of elements of external screw threads,
Pitch error in threads: Progressive and Periodic, Measurement of the
elements of the threads – Effective diameter using screw thread
micrometer, two wire and three wire methods, Best size wire, Simple
numerical on screw threads.
[04]
MME 3104 METROLOGY & MEASUREMENTS [3 0 0 3]
References:
1. Beckwith Thomas G., Mechanical Measurements, Pearson Education, Delhi,
2003.
2. Jain R.K., Engineering Metrology, Khanna Publishers, New Delhi, 1997.
3. Sawhney A.K., Mechanical Measurement & Instrumentation, Dhanpat Rai &
Co, New Delhi, 2002.
4. Nakra B.C. and Chaudry K.K., Instrumentation, Measurement & Analysis,
Tata McGraw Hill, New Delhi, 2002.
5. Gupta I. C., Engineering Metrology, Dhanpat Rai Publications, New Delhi,
1997
6. ASTME, Handbook of Engineering Metrology, Prentice Hall of India, New
Delhi, 1972
7. Raghavendra N.V. and Krishnamurthy L., Engineering Metrology and
Measurements, Oxford University Press, 2013.
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Temperature Measurements
Introduction
Temperature measurement is the most common and important measurement in
controlling any process. Temperature may be defined as an indication of intensity of
molecular kinetic energy within a system. It is a fundamental property similar to that
of mass, length and time, and hence it is difficult to define. Temperature cannot be
measured using basic standards through direct comparison. It can only be
determined through some standardized calibrated device.
Change in temperature of a substance causes a variety of effects such as:
i) Change in physical state,
ii) Change in chemical state,
iii) Change in physical dimensions,
iv) Change in electrical properties and
v) Change in radiating ability.
And any of these effects may be used to measure the temperature
The change in physical and chemical states cannot be used for direct temperature
measurement. However, temperature standards are based on changes in physical
state. A change in physical dimension due to temperature shift forms the basis of
operation for liquid-in-glass and bimetallic thermometers. Changes in electrical
properties such as change in electrical conductivity and thermoelectric effects which
produce electromotive force forms the basis for thermocouples. Another
temperature-measuring method using the energy radiated from a hot body forms the
basis of operation of optical radiation and infrared pyrometers.
Temperature Measurement by Electrical Effects
Electrical methods of temperature measurement are very convenient because they
provide a signal that can be easily detected, amplified, or used for control purposes.
In addition, they are quite accurate when properly calibrated and compensated.
Several temperature-sensitive electrical elements are available for measuring
temperature. Thermal emf and both positive and negative variations in resistance
with temperature are important among them.
Thermo resistive Elements
The electrical resistance of most materials varies with temperature. Resistance
elements which are sensitive to temperature are made of metals and are good
conductors of electricity. Examples are nickel, copper, platinum and silver. Any
temperature-measuring device which uses these elements are called resistance
thermometers or resistance temperature detectors (RTD). If semiconducting
materials like combination of metallic oxides of cobalt, manganese and nickel having
large negative resistance co- efficient are used then such devices are called
thermistors.
Electrical Resistance Thermometers
The desirable properties of resistance-thermometer materials are:
i) The material should permit fabrication in convenient sizes.
ii) Its thermal coefficient of resistivity should be high and constant
iii) They must be corrosion-resistant and should not undergo phase changes within
the temperature ranges
iv) Provide reproducible and consistent results.
Unfortunately, there is no universally acceptable material and the selection of a
particular material depends on the compromises.
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Although the actual resistance-temperature relation must be determined
experimentally, for most metals the following empirical equation may be used:
Rt = Ro (l + aT + bT2)
Where, Rt is the resistance at temperature T, Ro is the resistance at the reference
temperature, T is the temperature and a & b are constants depending on the
material.
Usually platinum, nickel and copper are the most commonly used materials, although
others like tungsten, silver and iron can also be used.
However, over a limited temperature range around 00 C (273 K), the following linear
relationship can be applied: Rt = Ro (l + α t)
Where, α = the temperature coefficient of resistance of material in (Ω/Ω)/0C, Ro is the
resistance at 00C, t is the temperature relative to 00C.
If a change in temperature from t1 to t2 is considered, the above equation becomes:
R2 = R1 + Ro α (t2 – t1), Rearranging gives: t2 = t1 + [(R2 – R1) / α R0]
Some typical values of α are: Copper = 0.00430C-1, Nickel = 0.00680C-1, Platinum =
0.00390C-1
The construction of the resistance thermometer is as shown in the figure, where the
wire of metal is wound on the grooved hollow insulating ceramic former covered with
protective cement. The ends of the coils welded to stiff copper leads that are taken
out to be connected in one of the arms of the Wheatstone bridge circuit. The
resistance thermometer is introduced in to the media whose temperature is to be
measured. Due to a change in temperature, the resistance wire of the thermometer
gets heated and due to this heats the resistance of the wire changes. Now this
change in resistance of the wire is measured using the Wheatstone bridge.
Example: The element of a resistance thermometer is constructed of a 50 cm length
and of 0.03 mm diameter nickel wire. The resistivity of nickel wire is wire is 7.8 μΩcm.
Nominal resistance R0 of the element is given by, R0 = ρ L / A
ρ = 7.8 x 10-8 Ω-m and L= 50 x 10-2m and A = (π / 4) x (0.03 x 10-3)2
R0 = [(7.8 x 10-8) x (50 x 10-2)] / 7.07 x 10-10 = 3.9 x 10-8 / 7.07 x 10-10 = 55.16Ω
Over a limited temperature range around 0ºC, the linear relationship is given by
Rt = R0 (1 + α t)
If a change in temperature from t1 to t2 is considered, the above equation becomes:
R2 = R1 + R0 α (t2 - t1)
i.e., (R2 - R1) / (t2 - t1) = R0 α
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By assuming temperature coefficient of resistance (0.0068ºC-1) is constant over the
common range of ambient temperatures, the change in resistance of the element per
degree centigrade is given by, ∆R / ∆t = R0 x α = 55.16 x 0.0068 = 0.3751Ω / ºC
Thermo-electric Sensors:
1. See beck Effect:
When two dissimilar metals are joined together as shown in the Fig. an electromotive
force (emf) will exists between the two points A and B, which is primarily a function of
the junction temperature. This phenomenon is called the see beck effect.
Junction of Two Dissimilar Metals
2. Peltier effect
If the two metals are connected to an external circuit in such a way that a current is
drawn, the emf may be altered slightly owing to a phenomenon called the peltier
effect.
3. Thomson effect
Further, if a temperature gradient exists along either or both of the metals, the
junction emf may undergo an additional slight alteration. This is called the Thomson
effect.
Hence there are, three emfs present in a thermoelectric circuit:
i) The See beck emf, caused by the junction of dissimilar metals
ii) The Peltier emf, caused by a current flow in the circuit and
iii) The Thomson emf, resulting from a temperature gradient in the metals.
The See beck emf is important since it depends on the junction temperature.
If the emf generated at the junction of two dissimilar metals is carefully measured as
a function of temperature, then such a junction may be used for the measurement of
temperature.
The above effects forms the basis for a thermocouple which is a temperature
measuring element.
Thermocouple
If two dissimilar metals are joined an emf exists which is a function of several factors
including the temperature. When junctions of this type are used to measure
temperature, they are called thermocouples
The principle of a thermocouple is that if two dissimilar metals A and B are joined to
form a circuit as shown in the Fig. It is found that when the two junctions J1 and J2
are at two different temperatures T1 and T2, small emf's e1 and e2 are generated at
the junctions. The resultant of the two emf's causes a current to flow in the circuit. If
the temperatures T1 and T2 are equal, the two emf's will be equal but opposed, and
no current will flow. The net emf is a function of the two materials used to form the
circuit and the temperatures of the two junctions. The actual relations, however, are
empirical and the temperature-emf data must be based on experiment. It is important
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that the results are reproducible and therefore provide a reliable method for
measuring temperature.
Basic Thermocouple Circuit
It should be noted that two junctions are always required, one which senses the
desired or unknown temperature is called the hot or measuring junction. The other
junction maintained at a known fixed temperature is called the cold or reference
junction.
Laws of Thermocouples
The two laws governing the functioning of thermocouples are:
Law of Intermediate Temperature: The emf generated in a thermocouple with
junctions at temperatures T1 and T3 is equal to the sum of the emf generated by
similar thermocouples, one acting between the temperatures T 1 and T2 and the other
between T2 and T3 when T2 lies between T1 and T3.
This law permits the thermocouple calibration for a given temperature to be used
with any other reference temperature through the use of a suitable correction. Also,
the extension wires having the same thermo-electric characteristics as those of the
thermocouple wires can be introduced in the circuit without affecting the net emf of
the thermocouple.
Law of Intermediate Metals: Insertion of an intermediate metal in to a thermocouple
circuit will not affect the net emf, provided the two junctions introduced by third metal
are at identical temperatures.
Application of this law is as shown in Fig. In Figure, if the third metal C is introduced
and the new junctions R and S are held at temperature T3, the net emf of the circuit
will remain unchanged. This permits the insertion of a measuring device or circuit
without affecting the temperature measurement of the thermocouple circuit
In the Figure the third metal is introduced at either a measuring or reference junction.
As long as junctions P1 and P2 are maintained at the same temperature TP the net
emf of the circuit will not be altered. This permits the use of joining metals, such as
solder used in fabricating the thermocouples. In addition, the thermocouple may be
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embedded directly into the surface or interior of a conductor without affecting the
thermocouple's functioning.
Thermocouple materials and Construction
Any two dissimilar metals can be used to form thermocouple, but certain metals and
combinations are better than others. The desirable properties of thermocouple
materials are:
i) Ability to withstand the temperature at which they are used,
ii) Immunity from contamination/oxidation, etc. which ensures maintenance of prcise
thermo-electric properties with continuous use,
iii) Linear temperature-emf relationship
The thermocouple materials can be divided into two types
1. Base-metal thermocouples, and
2. Rare-metal thermocouple.
Base-metal thermocouples are the combination of pure metals and alloys of iron,
copper and nickel and are used for temperature up to 1450 K. These are most
commonly used in practice as they are more sensitive, cheaper and have nearly
linear characteristics. Their chief limitation is the lower operating range because of
their low melting point and vulnerability to oxidation. On the other hand, rare-metal
thermocouples are the combination of pure metals and alloys of platinum for
temperature up to 16000C and tungsten, rhodium and molybdenum for temperature
up to 30000C.
Example: A copper-constantan thermocouple was found to have linear calibration
between 0C to 400C with emf at maximum temperature (reference junction
temperature 0C) equal to 20.68 mV. If the indicated emf is 8.92 mV in the
thermocouple circuit and the cold junction temperature is 25C, determine the
temperature of the hot junction by using the law of intermediate temperature.
Law of intermediate Temperatures states that the emf generated in a thermocouple
with junctions at temperatures T1 and T3 is equal to the sum of the emf’s generated
by similar thermocouples, one acting between the temperatures T 1 and T2 and the
other between T2 and T3 when T2 lies between T1 and T2.
E3 = E1 + E2
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A copper-constantan thermocouple was found to have linear calibration between 0C
to 400C with emf at maximum temperature (reference junction temperature 0C)
equal to 20.68 mV.
Sensitivity of the thermocouple = 20.68 / (400 – 0) = 0.0517 m V/ C.
If the indicated emf is 8.92 mV in the thermocouple circuit and the cold junction
temperature is 25C, then according to the law of intermediate temperature,
E3 = E1 + E2 = (0.0517 x 25C) + 8.92 = 1.293 + 8.92 = 10.213 mV.
Temperature of the hot junction = 10.213 / 0.0517 = 197.54C.
Temperature measurement by Radiation methods (Pyrometry):
Disappearing filament type optical pyrometer are a type of telescope having a
filament inside it. When the telescope is aimed and focused towards the red hot
object, the filament will be visible because of the difference in the two light intensities
(red hot object and the filament). Now the filament is fed current from a standard
battery through an adjustable resistance. The current is gradually increased until the
tip of the filament just disappears; i.e., the difference in two light intensities becomes
zero. At this instance, the current flowing through the lamp which is indicated by the
mille voltmeter connected to the lamp becomes a measure of the temperature of the
source when calibrated.
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Temperature measurement by non-electrical methods:
Bimetallic Thermometer:
The bimetallic thermometer uses the following two principles:
 All metals change in dimension, that is expand or contract when there is a
change in temperature.
 The rate at which this expansion or contraction takes place depend on the
temperature coefficient of expansion of the metal and this temperature
coefficient of expansion is different for different metals. Hence the difference
in thermal expansion rates is used to produce deflections which are
proportional to temperature changes.
A bimetallic strip is in the form of a cantilever beam. An increase in temperature will
result in the deflection of the free end of the strip as shown. This deflection is linear
and can be related to temperature change by
R = {t [3 (1 + m)2 + (1 + m n) x (m2 + 1/ m n)]} / [6 (αH – αL) (T2 - T1) (1 + m)2]
Where R = Radius of curvature at temperature T2
t = Total thickness of bimetallic strip = (t1 + t2)
m = Thickness of lower expansion metal / Thickness of higher expansion
metal
= t 1 / t2
n = Modulus of elasticity of lower expansion metal / Modulus of elasticity of
higher expansion metal
αH = Coefficient of expansion of higher expansion metal
αL = Coefficient of expansion of lower expansion metal
T1 = Initial température
T2 = Température of the source
Example: A bimetallic cantilever with invar & brass as two metal strips of equal
thickness has a total thickness of 0.125 cm & length 5 cm. Its one end is fixed;
estimate the end deflection for change of temperature of 40C. The thermal
coefficient of expansion of Invar & brass are respectively 1.7 x 10 -6/C and 20.2 x 106/C & their modulus of elasticity are respectively 147 GN/m 2 and 96.5 GN/m2.
The radius of curvature of a bimetallic strip due to change in temperature is given by
R = {t [3 (1 + m)2 + (1 + m n) x (m2 + 1/ m n)]} / [6 (αH – αL) (T2 - T1) (1 + m)2]
Where R = Radius of curvature at temperature T2
t = Total thickness of bimetallic strip = (t1 + t2)
m = Thickness of lower expansion metal / Thickness of higher expansion
metal
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= t 1 / t2 = 1
n = Modulus of elasticity of lower expansion metal / Modulus of elasticity of
higher expansion metal = 147 / 96.5 = 1.52
αH = Coefficient of expansion of higher expansion metal
αL = Coefficient of expansion of lower expansion metal
T1 = Initial température
T2 = Température of the source
T2 - T1 = 40ºC
R = {1.25 [3 (1 + 1)2 + (1 + 1.52) x (12 + 1/ 1.52)]} / [6 (20.2 x 10-6 – 1.7 x 10-6) (40) (1
+ 1)2]
= {1.25 [12 + (2.52 x 1.66)]} / [6 x 18.5 x 10-6 x 40 x 4] = 20.229 / 0.0178 = 1139 mm
Pressure Thermometer:
Pressure thermometer is based on the principle of fluid expansion due to an increase
in the pressure in a given volume of the temperature measuring systems. It is one of
the most economical, versatile and widely used devices in industrial temperature
measurements. It has relatively large metal bulb (often stainless steel) instead of
glass. This results in a robust, easy-to-read thermometer that may be read remotely
by connecting the bulb to a Bourdon gauge by means of a capillary tube as shown in
figure.
The entire assembly of the bulb, capillary and gauge is calibrated directly on the
basis of pressure change corresponding to the temperature change. The bulb of the
thermometer may be filled with either a liquid (usually mercury) or gas or a liquidvapour mixture and depending upon the type of fluid, the thermometer is termed as
mercury-in-steel thermometer or constant volume gas thermometer or vapour
pressure thermometer respectively.
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Review Questions
Q1) Explain with neat sketch the method of measurement of temperature with
resistance thermometer.
Q2) A platinum resistance thermometer is used at room temperature. Assuming a
linear resistance variation with temperature, calculate the sensitivity of the
thermometer.
Q3) The element of a resistance thermometer is constructed of a 50 cm length and
of 0.03 mm diameter nickel wire. The resistivity of nickel wire is 7.8 μΩ-cm. By
assuming temperature coefficient of resistance (0.0068ºC-1) is constant over the
common range of ambient temperatures, what will be the change in resistance of
the element per degree centigrade?
Solved in Notes
Q4) State the laws of thermo-electricity.
Q5) State and explain laws of thermocouples (with sketches). Write expression for
the relationship between thermoelectric emf and temperature gradient.
Q6) A copper constantan thermocouple was found to have linear calibration between
0C to 400C with emf at maximum temperature (reference junction temperature
0C) equal to 20.68 mV(i) determine the correction which must be made to the
indicated emf if the cold junction temperature is 25C. (ii) if the indicated emf is
8.92 mV in the thermocouple circuit, determine the temperature of the hot
junction. Solved in PPT
Q7)The hot junction of a chromel-alumel thermocouple is connected to a
potentiometer terminal at 24C. The potentiometer whose terminals are at 24C
reads 25.76 mV. What is the temperature of the thermocouple junction? The
Solved in PPT
calibration chart of the thermocouple is:
20 24
28
………….….
480
488
493
Temperature, C
Voltage, mV
0.8 0.95 1.12 ……………..
26.25 26.72 26.04
Q8) What are pyrometers? Explain the working of an optical pyrometer with neat
sketch.
Q9) Explain the working of disappearing filament optical pyrometer with neat sketch.
List its fields of application.
Q10) Explain the basic principle on which the bimetallic thermometer works. How
the deflection of the bimetallic strip is related to temperature change.
Q11) A bimetallic strip is constructed of strips of yellow brass & Invar bonded
together at 30C. Each has a thickness of 0.3mm. Calculate the radius of
curvature when a 60mm strip is subjected to a temperature of 100C. One end
of the bimetallic strip is fixed. The thermal coefficient of expansion of yellow
brass & Invar are respectively 20.2 x 10 -6/ C & 1.7 x 10-6/ C & their
modulus of elasticity are respectively 96.5 GN/m2 & 147 GN/m2. Solved in PPT
Q12) Explain with a neat sketch the working of a pressure thermometer.
Q13) A mercury in steel thermometer employs a Bourdon pressure gauge which has
a range of 0 to 6.0MPA for a pointer rotation from 0-270ºc. In the temperature
calibration process the pointer measurement set to 0º rotation at 0ºc and the
instrument indicated 250 º rotations corresponding to 200ºc. Determine the
sensitivity of the instrument in rad / ºc. Solved in PPT
Q14) A platinum resistance thermometer has a resistance of 140.5Ω and 100Ω at
1000C and 00C, respectively. If its resistance becomes 305.3Ω when it is in
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contact with a hot gas, determine the temperature of the gas. The temperature
Solved in PPT
coefficient of platinum is 0.00390C-1.
Q15) Explain the different thermocouple materials and their designation.
Q16) Explain See beck, Thomson and Peltier effects.
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