force,torque & strain

1. Presented by
Department of Mechanical Engineering
Chapter - 03
Measurement of Force, Torque and Strain
Mechanical Measurement & Metrology
2141901

2. Force Measurement
Load Cells
Cantilever Beams
Proving Rings
Differential
Transformers
Chapter – 03 Part – 01 (Measurement of Force)
6 hours 14% Weightage (Approx. 10 Marks)

3.  Force is defined as an influence that causes an object to change
its rate or direction of movement or rotation.
 A force can accelerate objects by pulling or pushing them.
 The relationship between force, mass, and acceleration was
defined by Isaac Newton in his second law of motion, which
states that an object's force is the product of its mass and
acceleration.
Force = Mass x Acceleration
N = kg x m/s2
Force

4. Force Measurement Method
1) Balancing the unknown force against known gravitational
force due to standard mass. Scales and balances works
based on this principle.
2) Applying unknown force to an elastic member (spring,
Beam, Cantilever, etc.) and measuring the resulting
deflection on calibrated force scale or the deflection may be
measured by using a secondary transducers. i.e. Elastic
force meter, providing ring.
3) Translating the force to a fluid pressure and then measuring
the resultant pressure. Hydraulic and Pneumatic load cells
works on this principle.
4) Applying force to known mass and then measuring the
resulting acceleration.
5) Balancing force against a magnetic force which is developed
by interaction of a magnet and current in coil.

5. Weight Measurement Method
Scales and Balances
1. Equal arm beam balance scale
2. Unequal arms beam balance scale
3. Multi-lever platform scale
4. Pendulum scale
Elastic force meter
1. Spring scale
Load Cell
1. Strain gauge load cell
2. Hydraulic load cell
3. Pneumatic load cell
4. LVDT

6. For null balance W1l1 = W2l2
(1)

7. For null balance W1b = W2a
W2 =W1 x
𝑏
𝑎
(2)

8. W = (
𝑎
𝑏
x
𝑐
ℎ
)Ws or = M . Ws
Where M = (
𝑎
𝑏
x
𝑐
ℎ
)
(3)

9. (4)

10. F = K . x
F = Load, K stiffness of spring, x = Deflection
(1)

11. Balancing of Wheatstone Bridge Circuit
V0 = Vs x (
𝑅2
𝑅2
+𝑅1
-
𝑅4
𝑅4
+𝑅3
)
Resistance in ohms
Load Cell (1)

12. Measured forces in the range 0 to 2.5 MN,
Accuracy 0.1% of full scale.
Load Cell (2)

13. Measured forces in the range 0 to 250 kN,
Accuracy 0.5% of full scale.
Load Cell (3)

14. K = spring constant (N/mm),
E = Young’s Modulus (N/mm2)
I = Moment of Inertia (mm4) ,
L = Length of cantilever beam (mm)
b = Width (mm), h = Thickness (mm)
Cantilever Beams

15. Deflection of proving ring can be measured by LVDT
Proving Ring

16. LVDT load cell – Linear variable differential transformer
 Convert linear displacement into an electrical signal (Voltage)
 Used for measure Force, (Weight, pressure, acceleration)
 Consist of 3 coils wound on a single non-magnetic tube
 A.C supply to Primary winding
 Armature core is ferromagnetic, attached to free moving
 Movable core couple with primary transducer like spring, bellows, diaphragm

17. Working of LVDT
 AC current supply to PW, the magnetic flux generated by coil is
distributed by the armature.
 So that voltage are induced in the SW.
 When core placed centrally
E2 = E1
∴ E2 – E1 = 0
 This called null position of armature or balance point.
 Armature moves towards left
 E2 voltage is increases and E1 voltage is decreases
Net voltage available V0 = E2 – E1
 Armature moves towards right
 E1 voltage is increases and E2 voltage is decreases
Net voltage available V0 = E1 – E2

18. Advantages of LVDT
 Linearity 0.05% is available in commercial LVDT
 High sensitivity : 40 volt/mm
 High voltage output
 Less friction
 Low hysteresis, repeatability is excellent
 Low power consumption (1W)
 Simple, light in weight, easy to align and maintain
Disadvantages of LVDT
 Relatively large displacement required for appreciable differential o/p
 Temperature effects the performance
 Not suitable for dynamic measurement

19. Power is defined as the rate of doing work and is equal
to the product of force and linear velocity or the product of
torque and angular velocity.
The measurement of power involves the measurement
of force (or torque) as well as speed. The force or torque is
measured with the help of a dynamometer and the speed by a
tachometer.
Where,
P = Power (Break Power) in kW
T = Torque in N-m
N = Rotational speed in RPM
The torque may be measured in terms of reaction force
and arm length or angular twist.
Torque and Power

20. Measurement of Torque and Power
1] Absorption dynamometer
1] Prony brake dynamometer
1] Block type dynamometer
2] Band type dynamometer
2] Rope brake dynamometer
3] Hydraulic dynamometer
4] Eddy current dynamometer
2] Transmission dynamometer
1] Torsion dynamometer
3] Servo Controlled dynamometer

21. Block type prony brake dynamometer
Where, N = Revolution of shaft in RPM
ω = Angular velocity of shaft
F = Frictional force
l = Length of arm
W = Applied load at end of arm

22. Advantages:
Simple in construction
Less cost
Suitable for measurement of small power
Disadvantages:
Not suitable for large power
Cooling system required
Shaft is not uniform, dynamometer is subjected to severe oscillations.
Block type prony brake dynamometer

23. Rope brake dynamometer
Advantages:
1. Simple construction
2. More suitable then PBD.
3. Use for wide range power
4. Used for long test with little overheating
Disadvantages:
1. Less accuracy because of change
co-efficient of rope with temp.
1. Cooling system is required

24. Hydraulic Dynamometer (Fluid friction)
 Operates on the water brake principle, used fluid friction rather than dry friction
 Rotating disc is fixed on engine or motor shaft and it rotates with shaft inside stationary
casing.
 Casing rotate freely except restraint imposed by the brake arm
 Casing is in two halves, Semi elliptical grooves.
 Grooves match inside rotating disc to form helix chamber which maintain water flow

25. Working of Hydraulic Dynamometer
 Rotor rotating with speed of engine shaft
 Due to rotation of rotor with respect to stator, the vortex (turbulence of water) are set up in
water
 These tend to turn casing (stator) in direction of rotation of rotor.
 Stator to rotor is opposed by an arm with balancing weights that measure torque.
 Control of braking by changing quantity of water of pressure or changing space between stator
and rotor.

26. Power = WN / K
W = weight placed at end of lever arm in N
N = RPM of shaft
K = Dynamometer constant
Range and Speed
Used for measure power upto 20,000 kW and Speed upto 10,000 rpm.
Advantages
 Used for high power measurement at high speed
 Water supply serve two purpose as providing braking action and cooling.
 High absorption capacity in a small space and at low cost

28. Eddy-current Dynamometer
 Consist of toothed steel rotor fixed on engine shaft.
 Rotor rotates inside a smooth bored cast iron stator.
 Exiting coil is fitted into inner surface groove of stator.
 Principle of power loss produced on account of eddy current which generated
when rotating conductor cuts across magnetic flux.
 Eddy currents get dissipated in form of heat.

30. Working Eddy-current Dynamometer
 When dynamometer is operating, the rotor rotates which causes change in flux at
all point of the stator.
 Voltage is induced and local current (Eddy current) flow in a short circular path
within the conductor (stator).
 These tend to turn stator in direction of rotation of the engine shaft.
 This tendency is resisted by the brake arm balances system that measurement the
torque.
Range and Speed
Used for measure power upto 250 kW and Speed upto 6,000 rpm.
Advantages
 Small size for given capacity
 Suitable for large speed range
 Good control at low rotating speed

31. Torsion Bar Dynamometer

32.  Optical method of deflection measurement.
 The relative angular displacement of the two sections of the torsion bar can
be read from the Calibrated scales because of the stroboscopic effect of
intermittent viewing and the persistence of vision.
 A line of transmission dynamometers based on the principle is available in
the ranges up to 7500m kgf and 50,000 rpm, with error of ± 0.25%.
 By replacing the scales on disks 1 and 2 with sectored disks (alternate clear
and opaque sectors) and employing an electro-optical transducer in place of
the human eye, a version with electrical output May be obtained.
 For zero torque, the sectored disks are positioned to give a 50% light
transmission area.
 The positive torque increase the area proportionally while negative torque
decreases it, giving a linear and Direction sensitive electrical output.
Torsion Bar Dynamometer

33. Servo Controlled Dynamometer

34.  Tape recording of engine torque and speed, measured under actual
driving conditions for an automobile, are utilized to reproduce these
conditions in the laboratory engine test.
 Two feedback system control engine speed and torque.
 A tachometer generator speed signal from the dynamometer is compared
with the desired speed signal from the tape recorder; if the two are
different, the dynamometer control is automatically adjusted to change
speed until agreement is reached.
 Actual engine torque is obtain from a load cell on the dynamometer and
compared with the desired torque from the tape recorder.
 If these do not agree, the error signal actuates the engine throttle control
in the proper direction.
 Both systems operates simultaneously and continuously to force engine
speed and torque to follow the tape recorder commands.

35. What is Strain?
 Strain is the amount of deformation of a body due to an applied force.
More specifically, strain (ɛ) is defined as the fractional change in length.
 Strain can be positive (tensile) or negative (compressive). Expressed in
unit mm/mm (Unit less).
 In practice, the magnitude of measured strain is very small. Therefore,
strain is often expressed as micro 10–6.

36. The Strain Gauge
 There are several methods of measuring strain.
 The most common is with a strain gauge.
 A device whose electrical resistance varies in proportion to the amount
of strain in the device.
 The metallic strain gauge consists of a very fine wire or, more
commonly, metallic foil arranged in a grid pattern.
 The grid pattern maximizes the amount of metallic wire or foil subject
to strain in the parallel direction.

37. A strain gauge is a device which is used to measure dimensional changes
on the surfaces of a structural member under test.
Strain Gauge
Gauge factor (GF)
 A fundamental parameter of the strain gauge is its sensitivity to strain,
expressed quantitatively as the gauge factor (GF).
 Gauge factor is defined as the ratio of fractional change in electrical
resistance to the fractional change in length (strain)
 The Gauge Factor for metallic strain gauges is typically around 2.
 The Gauge Factor may range from 1.7 to 4 depending on the length of
gauge
ΔR = Change in resistance ΔL = Change in length
R = Initial resistance L = Initial length

38. Rosette Gauges
 More than two or more direction strain measure at the same point.
 More than one strain gauges bonded to the same supporting material in
definite relative positions, this configuration of gauges called rosette.

39. Advantages
Limitations
Application
 There is no moving part.
 It is small and inexpensive.
 It is non-linear.
 It needs to be calibrated.
 Residual stress
 Vibration measurement
 Torque measurement
 Bending and deflection measurement
 Compression and tension
measurement
 Strain measurement
Rosette Gauges

40. Mechanical Strain Gauges
 Change in length of test specimen is magnified using mechanical devices
like levers or gears.
 An extensometer of single mechanical lever type was introduced.
 Lever system is employed to obtain the magnification (10 to 1) of the
movable knife-edge of extensometer with respect to a fixed knife-edge.
 Extensometer employing compound levers (dial gauges) having
magnification of 2000 to 1 were introduced.
 Same time these operated over small gauge length.
 Most commonly used mechanical strain gauges are of Berry-type and
Huggen berger type.
 Used for static strain measurement only & point of measurement is
accessible for visual observation

41. Advantages
 Self contained magnification system
 No auxiliary equipment is needed as required in case of electrical
strain gauge.
Mechanical Strain Gauges
Disadvantages
 Comparatively larger in size & Suitable for sufficient area is
available.
 Unsuitable for dynamic & varying strains measurements
 No method of recording the reading

42. Electrical Strain Gauges
 A change in strain produces a change in some electrical output.
 Basic principle is changes in resistance, capacitance or inductance that are
proportional the strain transferred from the specimen to the gauge element.
 The output can be magnified by some auxiliary electronic equipment.
 Classifies as (1) Resistance gauge, (2) Capacitance gauge, (3) Inductance gauge,
(4) Piezoelectric or Semiconductor gauges.
 Resistance gauge – Resistance of Copper or iron wire changes when subjected to
tension as a function of strain, increasing with tension and reducing with
compression.
 Capacitance & Inductance types are only employed for special applications.
 Piezoelectric gauge for measurement of strain have limited application.
 Semiconductor have high sensitivity, small size and adaptability for both static
and dynamic measurements.

43. Advantages
Electrical Strain Gauges
 Simple in construction
 Less inertia effect and very sensitive.
 Small size
 Linear measurement is accomplished
 Output can be utilized for recording and indicating purpose
 Reliable and inexpensive

44. Theory of Resistance Strain Gauge
Longitudinal
Strain
Transverse
Strain

45. Theory of Resistance Strain Gauge

46. Metallic Strain Gauge Materials
Properties of Metallic Strain Gauge Materials
1. Gauge factor
2. Resistance
3. Temperature coefficient of gauge factor
4. Thermal coefficient of resistivity
5. Stability
Backing Material
 It portion of strain gauge to which the strain sensitive grid structure is
attached
 Primary electrical insulation backing
 Retain geometric shape of grid pattern and provide protection to the gauge
 Commonly used backing material with wire strain gauge are paper, Bakelite,
fiber glass, transfer gauges etc.

47. Metallic Strain Gauge Materials
 Constantan (Copper Nickel alloy)
(45 % Ni, 55 % Cu)
Most commonly used – low and controllable temp. coefficient – exhibit high
specific resistant – constant gauge factor – wide strain gauge range – good
stability over a reasonably large temp. range
 Karma (Nickel-Chrome alloy with perception forming additives)
(74 % Ni, 20 % Cr, 3 % Fe)
Wider temp. compensation range – minimum drift
 Nichrome (Nickel-Chrome alloy)
(80 % Ni, 20 % Cr)
Commonly used for high temp. static & dynamic strain measurement –
Measurement of Static 649° C & dynamic 982° C
 Isoelastic (Nickel-Iron alloy + other ingredients)
(36 % Ni, 8 % Cr, 0.5 % Mo, 55 % Fe)
Used for dynamic test – higher gauge factor – good sensitivity – poor stability
 479PT (Platinum-Tungsten alloy)
(92 % Pt, 8 % W)
High stability at elevated temp. – high gauge factor - Measurement of Static
649° C & dynamic 816° C

48. Material Composition Gage Factor
(Sensitivity)
Temperature
Coefficient of
Resistance
(10-6/C)
Constantan 45% Ni, 55% Cu 2.0 15
Isoelastic 36% Ni, 55% Fe, 8% Cr, 4%, 0.5 % Mo,
(Mn, Si, )
3.5 200
Karma 74% Ni, 20% Cr, 3% Fe, 3% Al 2.3 20
Monel 67% Ni, 33% Cu 1.9 2000
Silicon p-type 100 to 170 70 to 700
Silicon n-type -140 to –100 70 to 700
Metallic Strain Gauge Materials

49. Types of Resistance Strain Gauge
Resistance
Strain
Gauge
Unbonded Metallic wire
Bonded
Metallic
Flat Grid
Wrap
Around
Etched Foil
Woven Grid
Semiconductor

50. Bonded – Metallic Strain Gauge

51. Bonded – Metallic Strain Gauge

52. Bonded – Semiconductor Strain Gauge

53. Unbonded Strain Gauge

54. Assignment
Chapter – 3 Measurement of Force, Torque and Strain
1) Name the instrument used for force, torque (power) and strain
measurement.
2) Explain in brief Prony brake dynamometer with neat sketch.
3) Explain with neat sketch the arrangement for power measurement of a
given I.C. Engine by rope brake dynamometer. Also derive the equation
for power.
4) Describe strain gauge. Define gauge factor of strain gauge. What are
Rosette gauges explain with advantages, limitations & application?
5) Explain in brief Load cells and Proving rings with neat sketch.
6) Explain working principle of LVDT with advantages, disadvantages and
application.

56. Department of Mechanical Engineering
Shroff S.R. Rotary Institute of Chemical Technology