This document provides an overview of mechanical measurements and metrology. It discusses various methods for measuring force, torque, strain, and temperature. For force measurement, it describes direct methods using analytical balances and platform balances, as well as indirect methods using load cells and proving rings with strain gauges. Torque measurement uses dynamometers like the Prony brake. Strain is measured using electrical resistance strain gauges. Temperature is sensed using contact sensors like thermocouples and resistance temperature detectors or non-contact sensors like pyrometers.

1. Department of Mechanical Engineering
JSS Academy of Technical Education, Bangalore-560060
MECHANICAL MEASUREMENTS AND METROLOGY
(Course Code:18ME36B)

2. TEXT BOOKS
• Mechanical Measurements, Beckwith Marangoni and Lienhard, Pearson Education, 6th Ed., 2006.
• Instrumentation, Measurement and Analysis, B C Nakra, K K Chaudhry, 4th Edition, McGraw Hill.
• Engineering Metrology, R.K. Jain, Khanna Publishers, Delhi, 2009
REFERENCE BOOKS:
• Engineering Metrology and Measurements, N.V.Raghavendra and L.Krishnamurthy, Oxford
University Press..
Further Reference:
 National Programme on Technology Enhanced Learning (NPTEL)
http://nptel.ac.in/courses/112104121/1

3. MECHANICAL MEASUREMENTS AND METROLOGY
CHAPTER 9: Applied Mechanical Measurement
MODULE 5

4. Learning Objectives
Understand the basics and describe methods of force, torque, and strain
measurements

5. Module 5
Applied mechanical measurement:
Applied mechanical measurement: Measurement of force, Torque, Pressure,
Types of Dynamometers, Absorption dynamometer, Prony brake and Rope brake
dynamometer, and Power Measuring Instruments. Use of elastic members,
Bridgeman gauge, McLeod gauge, Pirani gauge.

6. Measurement of force
Force measurement can be classified into two basic categories:
1. Direct
2. Indirect

7. Direct Method
• Direct methods involves comparison of an unknown force with a known
gravitational force on the standard mass.
• A force is exerted on a body of mass m due to the earth’s gravitational field,
represented by the following equation:
W = mg
m = standard mass
g = acceleration due to gravity
W = weight of the body

8. Analytical Balance / Equal arm balance
• An unknown force is directly compared with a known gravitational force.
• Comparison of masses is done by beam balance.
• It is sufficient to find only the magnitude, as the unknown force and the
gravitational force act in direction parallel to each other.
• The working principle is illustrated schematically.

9. Analytical Balance / Equal arm balance
• The fig. shows the balance in an
unbalanced condition.
• dG = Distance between the fulcrum and the
centre of gravity point CG.
• WB = Weight of the balance arms and
pointer.
• W1 & W2 = Two weights acting on either
side of the balance.
• When the two weights W1 and W2 are
equal, angle θ = 0.

10. Analytical Balance / Equal arm balance
• Deflection per unit unbalance gives a
measure of the sensitivity of the balance.
• The difference between the two weights, i.e.
W1 − W2, gives the unbalance.
Disadvantage
• Set of weights should be equal to the
maximum weight to be measured.

11. Platform Balance
• For measurement of large weights, a platform balance or multiple-lever system is
preferred.
• In a platform balance, two smaller weights are used;
Wx = poise weight & Wy, = pan weight for measurement of W (Large weight)
• The initial zero balance is set by an adjustable counterpoise.

12. Platform Balance

13. Platform Balance
• The poise weight Wx is set to zero.
• The counterpoise is adjusted to obtain the initial balance
before applying the unknown weight W on the platform.
• For analysis, it is assumed that the two weights W1 and
W2 are substituted by W.
• As Wx is adjusted to zero, the unknown weight W is
balanced by pan weight Wy.

14. Platform Balance
T × b = Wy × a -------(1)
T × c = W1 (f/d) e + W2 × h ------(2) (The linkage proportion is h/e = f/d)
we have, T × c = (W1 + W2)h = Wh ------(3)
From (1) & (3)
=
S is known as the scale multiplication ratio

15. The multiplication ratio gives an indication of the weight that should be applied to
the pan in order to balance the weight on the platform.
Example
• If the multiplication factor is 100, then a weight of 1 kg applied on the pan can
balance a weight of 100 kg placed on the platform.

17. Elastic members
Use of a strain gauge for force determination
• When force is applied on an elastic member the dimensions undergo a change.
• If the strain gauge is bonded to the elastic member, the gauge is stretched or compressed,
resulting in a change in its length and diameter.
• The dimension of the strain gauge changes due to a change in resistance.
• The change in resistance of the strain gauge gives a measure of the applied force.
Principle

18. Elastic members
The two most common instruments used for force measurement.
1. Load cells
2. Proving rings
Both employ strain gauges

19. Load Cells
• In load cells, elastic members act as primary transducers and strain gauges as
secondary transducers.
• A load cell is an indirect method of force measurement, i.e. Force or weight is
converted into an electrical signal.

20. Load Cells
• A load cell comprises four strain gauges; mounted at
90° to each other.
• Two are used for measuring the longitudinal strain &
the other two for measuring the transverse strain.
• Two gauges experience tensile stresses, the other two
are subjected to compressive stresses.
• At the no-load condition, resistance in all the four
gauges will be same & potential across the terminals B
and D are same.
• The Wheatstone bridge is balanced and output voltage
is zero.

21. Load Cells
When the specimen is stressed due to the
applied force, the strain induced is
measured by the gauges.
• Gauges R1 and R4 measure the
longitudinal (compressive) strain and
gauges R2 and R3 measure the
transverse (tensile) strain.

22. Proving Rings
• A proving ring is a metal ring (usually a steel alloy)
• To measure the displacement, a displacement
transducer is connected between the top and bottom of
the ring.
• Measurement of the relative displacement gives a
measure of the applied force.

23. Proving Rings
• Used for measuring static loads & Calibration of tensile
testing machines.
• Employed over a wide range of loads (1.5 kN to 2 MN).
• A proving ring comprises a circular ring having a
rectangular cross-section.
• R = radius R, t = thickness, and b = axial width.
• Four strain gauges are mounted on the walls of the
proving ring.
• The applied force induces strain (compressive) in gauges
2 and 4, while gauges 1 and 3 undergo tension.

24. Proving Rings
The four strain gauges are connected to the bridge circuit,
and the unbalanced voltage caused by the applied force
can be measured.

25. Measurement of Torque
Measurement of torque is important for the following reasons;
• To obtain load information for the analysis of stress.
• To evaluate the performance characteristics of machines.
• To determine the mechanical power.
• T = Fr (in N m)
• P = 2πNT
• Dynamometers are used to measure torque.

26. Measurement of Torque
Dynamometers Classification
Absorption Dynamometers
 Prony Brake dynamometer
 Rope Brake dynamometer
Transmission Dynamometers
• Belt transmission dynamometer
• Epicyclic dynamometer
• Torsion dynamometer

27. Measurement of Torque
Absorption Dynamometers
 Prony Brake dynamometer

28. Measurement of Torque
Absorption Dynamometers
 Prony Brake dynamometer

29. Measurement of Torque
Invented by Gaspard de Prony, a French engineer, in 1821, to measure engine
power.
• It comprises two wooden blocks mounted on either side of the fly wheel.
• The fly wheel is attached to the shaft whose power needs to be determined.
• A lever arm is fixed to one block and the other arm is connected to an
arrangement, to tighten the rope.
• Tightening of the rope is to enhance the frictional resistance between the blocks
and the flywheel.

30. Measurement of Torque
• The torque is given by the following equation: T = FL
• The power dissipated in the brake is calculated by the equation;
or

31. Measurement of Torque
• The No. of turn of rope is wound on the rotating drum
that is attached to the output shaft.
• One end of the rope is connected to the spring balance
and the other end is connected to the loading device.
• The power is absorbed between the rope and the drum
and hence the drum requires cooling.
• Not very accurate since the friction coefficient of the
rope changes with the temperature.

32. MEASUREMENT OF STRAIN
Principle of electrical resistance strain gauges
• When stress is applied to a metal wire, apart from undergoing changes in both
length and diameter, there will be some changes in the electrical resistance of
the wire.
• When a force or load is applied to a body, it undergoes some deformation.
• The deformation per unit length is known as strain.

33. MEASUREMENT OF STRAIN
Principle of electrical resistance strain gauges
Strain gauges are for two purposes:
1. To determine the state of strain existing at a point on a loaded member.
2. To act as a transducer element in the measurement of quantities such as force,
pressure, displacement etc.

34. MEASUREMENT OF STRAIN
Two types of strain gauges are employed:
1. Mechanical strain gauges
2. Electrical strain gauges

35. MEASUREMENT OF STRAIN
Electrical strain gauges:
A change in strain produces a change in electrical characteristics such as
capacitance, inductance, or resistance.
Types of resistance strain gauges:
1. Unbonded
2. Bonded.

36. Unbonded Resistance Strain Gauges
• The electrical resistance element or the grid is not supported.
• A fine wire is stretched between two or three points, which become part of a rigid base
that itself is strained.
• Used to measure compressive strain as it is preloaded.
• The four resistance wires are connected, such that, they act as a full bridge.

37. Bonded Resistance Strain Gauges
• If a strain gauge is bonded to the surface of the
material to be tested, it is known as a bonded
strain gauge.
• A thin wire in the form of a grid pattern is
cemented in between thin sheets of insulating
materials such as paper or plastic.

38. Bonded Resistance Strain Gauges
• The resistance type of electric strain gauges exist
in the following forms;
1. Wire-type strain gauge (ϕ =0.025 mm)
2. Foil-type strain gauge (ϕ =0.005 mm)
3. Semiconductor or piezo-resistive strain gauge
Wire-type Foil-type
Semiconductor type
Rectangular filament of 10 × 0.25 × 0.05 mm

39. BONDING OF GAUGES
The steps to be followed while bonding the gauge to the specimen:
• The working desk area should be kept clean.
• Bare hands should not be used to grasp the gauge.
• Tweezers can be used to hold the gauge.
• Place the gauge on a clean working area with the bonding side down.
• Use a length about 15 cm, of cellophane tape to pick up the strain gauge and transfer it to the
gauging area of the specimen.
• Align the gauge with the layout lines.
• Press one end of the tape to the specimen, and gently apply the whole tape and gauge into
position.

40. BONDING OF GAUGES
• Lift one end of the tape such that the gauge does not contact the gauging area and the bonding
site is exposed.
• Apply the catalyst evenly and gently on the gauge.
• Apply enough adhesive to provide sufficient coverage under the gauge for proper adhesion.
• Some iteration may be required in determining ‘sufficient’ coverage.

41. GAUGE FACTOR
• It is a measure of the amount of resistance change for a given strain.
• It is an index for the strain sensitivity of the gauge.
• Gauge factor is supplied by the manufacturer and range from 1.7 to 4, depends on
the length of the gauge.
Mathematically expressed as;
F = Gauge factor
ΔR = Change in resistance
ΔL = Change in length
R and L are the initial resistance and length of the strain gauge

42. METHODS OF MEASURING TEMPERATURE
Temperature can be sensed using many devices, classified into two categories:
1. Contact
2. Non-contact-type sensors
Contact-type sensors
1. Thermocouples
2. Liquid-in-glass thermometers
3. Resistance temperature detectors (RTDs)
4. Pressure thermometers
5. Thermistors
6. Bimetallic strip thermometers
Non-contact type sensors
1. Radiation pyrometers
2. Optical pyrometers
3. Fibre-optic thermometers

43. THERMOCOUPLES
When two dissimilar metals are joined together to form two junctions such that
one junction is at a higher temperature than the other junction, a net emf is
generated.
Seebeck effect

44. Laws of Thermocouples
1. Law of Homogeneous Circuit: Two dissimilar materials are required for the formation
of any thermocouple circuit
2. Law of Intermediate Metals: If an intermediate metal is inserted into a thermocouple
circuit at any point, the net emf will not be affected provided the two junctions
introduced by the third metal are at identical temperatures.
3. Law of Intermediate Temperatures: If a thermocouple circuit generates an emf e1
when the junctions are at temperatures T1 and T2 & emf e2 when the junctions are at
temperatures T2 and T3, then an emf of e1 + e2 when the junction temperatures are
maintained at T1 and T3.

45. Temperature range of various thermocouple materials

46. PYROMETRY
The term pyrometer is of Greek origin, wherein pyro means ‘fire’ and metron means
‘to measure’.
Pyrometers are classified into two categories:
1. Total radiation pyrometers
2. Optical pyrometers

47. TOTAL RADIATION PYROMETER

48. TOTAL RADIATION PYROMETER
• A total radiation pyrometer comprises an optical system.
• The heat emitted from the hot body is focused by an optical system onto the
detector.
• The heat is sensed by the detector (thermocouple) is converted to analogous
electrical signal, read on a temperature display device.
• The pyrometer has to be aligned in line with the furnace or hot body and is placed
as close as possible to minimize the absorption of radiation by the atmosphere.

49. Optical Pyrometer

50. Optical Pyrometer
• Optical pyrometers work on the disappearing filament principle.
• To measure temperature, the brightness generated by the radiation of the unknown
source, is compared with the intensity of the reference lamp.
• The brightness of the reference lamp is adjusted such that the intensity is equal to
the brightness of the hot body.
• The light intensity of the object depends on its temperature.
• A battery supplies the current required for heating the filament.
• The current passing through the circuit is proportional to the temperature of the
unknown source.

51. Optical Pyrometer
Disappearing filament principle
(a) Current passing though the filament is low.
(b) Current passing though the filament is exact.
(c) Current passing though the filament is high.

52. End of Module