Force and torque measurements.pptx

1. Force and Torque
Measurement
1

2. Force and Torque Measurement
Force is defined as F = m  a N
m = mass kg,
a = acceleration m/s2.
Therefore a standard for force depends on standards for mass and
acceleration.
Mass is considered as a fundamental quantity, and its unit is
kilogramme.
Acceleration is not a fundamental quantity but is a derived quantity
from length and time. Both length and time are fundamental quantities
whose standards are defined. The acceleration due to gravity ‘g’, is a
convenient 'standard' for acceleration.
2

3. The measurement of torque is intimately related
to measurement of force. Therefore, torque
standards as such are not necessary, since force
and length are sufficient to define torque.
Similarly measurement of power transmitted by a
rotating shaft is related to measurement of torque
and the power is equal to the product of torque
and rotating angular velocity.
3

4. BASIC METHODS OF MEASUREMENT OF FORCE
An unknown force may be measured by the following methods.
1. Balancing the unknown force against the known gravitational
force either directly or indirectly using a system of levers.
2. Measuring the acceleration of a body of known mass to which
the unknown force is applied.
3. Balancing the unknown force against a magnetic force
developed on account of interaction current carrying coil and a
magnet.
4

5. 4. Transducing the unknown force to a fluid pressure and then
measuring the resulting fluid pressure, Hydraulic and
Pneumatic load cells are used for transducing the force into
pressure.
5. Applying the unknown force to an elastic member and
measuring the resulting deflection. The deflection of the elastic
member may be used directly to indicate the force or the
deflection be measured by using secondary transducers.
5

6. 6. Measuring the change in precession of a gyroscope caused by
an applied torque that is related to the unknown force.
7. Measuring the change in natural frequency of a wire which is
tensioned by the unknown force.
6

7. HYDRAULIC AND PNEUMATIC LOAD CELLS
The principle of operation on which hydraulic and pneumatic load cells
work is that
if a force is applied to one side of a piston or diaphragm, and a pressure,
either hydraulic or pneumatic, is applied to the other side, some
particular value of pressure is necessary to exactly balance the force.
This pressure is a measure of the applied unknown force.
7

8. Hydraulic Cell.
8

9. Figure shows the cross-section of a hydraulic cell.
This cell uses the conventional piston and
cylinder arrangement.
The piston does not actually come in contact with
the cylinder wall in the normal sense, but a thin
elastic diaphragm, or bridge ring, of steel is used
as the positive seal, which allows small piston
movement.
Mechanical stops prevent the seal from being
overstrained.
9

10. The cell is filled with oil . When the force acts on
the piston the resulting oil pressure is transmitted
to some pressure sensing device like a Bourdon
gauge.
Electrical pressure transducers can also be used to
obtain an electrical output.
If the load cell is completely filled with oil, very
small transfer or flow is required. Piston
movements maybe less than 0.05 mm at full
capacity. This feature is responsible for a good
dynamic response for the system.
10

11. However, the overall response is largely
determined by the response of the pressure
sensing element.
A problem with hydraulic cells using conventional
piston and cylinder arrangement is that the friction
between piston and cylinder wall and required
packings and seals is unpredictable, making good
accuracy difficult to obtain.
The use of a floating piston with a diaphragm seal
results in practically elimination of the problem.
11

12. Pneumatic Cells.
12

13. A pneumatic cell is shown in Figure. This cell
uses a diaphragm of a flexible material and is
designed to automatically regulate the balancing
pressure.
Air pressure is supplied to one side of the
diaphragm and is allowed to escape through a
position controlling bleed valve.
The pressure under the diaphragm is therefore
controlled both by source pressure and bleed
valve position.
13

14. The diaphragm tries to take up the position that
will result in just the proper air pressure to support
the load.
This naturally assumes that the supply pressure is
large enough so that its value multiplied by the
effective area will at least equal to the load.
The measuring diaphragm changes its position
slightly as the load changes in magnitude. This
may result in non-linearity unless care is taken in
design.
14

15. Simple pneumatic load cells tend to be
dynamically unstable. Therefore, in order to
prevent any instability most commercial cells use
some form of viscous damper. Also, additional
chambers and diaphragms may be used to
provide for tare adjustment.
Single units upto capacity of 350 kN are
available.
15

16. Proving Rings
They are steel rings which are used as force
standards.
16

17. 17

18. 18

19. They are particularly useful for calibration of material
testing machines in situations, where dead-weight standards
where dead-weight standards are impracticable to use on
account of their physical bulk.
A proving ring is a circular ring of rectangular cross-section
shown in Figure, which may be subjected to tensile or
compressive forces across its diameter.
In fact it is a thin ring whose force deflection relationship is
given by using Equation 1
19

20. 20

21. The deflection is small and hence the usefulness of the proving
ring as a calibration device depends on the accuracy with which
this small deflection is measured.
This is done by using precision micrometer as shown in figure.
In order to obtain precise measurements, one edge of micrometer
is mounted on a vibrating reed device, which is plucked to obtain a
vibratory motion.
The micrometer contact is then moved forward until a noticeable
damping of the vibration is observed.
21

22. Proving rings are normally used for force measurement within the
range of 2kN to 2MN.
The maximum deflection is typically of the order of 1per cent of the
outside diameter of the ring.
Although the deflection of the proving rings can be predicted
theoretically but for better accuracy they should be calibrated against
dead-weight standards.
22

23. Load Cells.
Elastic devices that can be used for measurement
of force through indirect methods i.e., through use
of secondary transducers are load cells.
Load cells utilize an elastic member as the primary
transducer and strain gauges as secondary
transducer.
23

24. Strain gauges may be attached to any elastic
member on which there exists a suitable plane
area to accommodate them. This arrangement
may then be used to measure loads applied to
deform or deflect the member, provided that the
resultant strain is large enough to produce
detectable output.
When the strain gauge-elastic member
combination is used for weighing it is called a
LOAD – CELL.
24

25. The factors which are considered in the design of
load cells using strain gauges are stiffness of
elastic element, optimum positioning of gauges on
the element and provision for temperature
compensation.
The stiffness of the elastic member should be such
that it produces a deflection which is compatible
with the range of the transducer.
Thus the gauges must be subjected to strains of
sufficient magnitude to give a measurable output
from the strain gauge bridge.
25

26. In order to obtain maximum sensitivity, a bridge
using four active gauges is used. An additional
advantage of this bridge provides complete
temperature compensation.
Strain gauge transducers can cover a very wide
range of forces. In fact, theoretically there is no
upper limit as the elastic member may be made as
robust as possible to withstand the load. The lower
limit is determined by the sensitivity of the gauges.
26

27. If the loads to be measured are large, the direct
tensile-compressive member may be used.
On the other hand, if the loads are small, strain
amplification provided by bending may be used
with advantage.
27

28. Tensile-Compressive Cell.
28

29. 29

30. Figure shows a tensile-compressive cell which is
a cylinder.
This arrangement uses four strain gauges each
mounted at 90° to each other. The bridge circuit
is also shown.
Two of strain gauges experience tensile stresses
while the other two are subjected to compressive
stresses.
The output of a bridge with equal arms and using
two strain gauges mounted 90° to each other is
 
1
4
i
o f
e
e G


 
2
30

31. In the present case, there are two sets of gauges
mounted 90° to each other, with one set
experiencing tensile stresses while the other
compressive stresses.
Output voltage of Wheatstone bridge is,
 
1
2
i
o f
e
e G


 
31

32. 32

33. The above relationship is clear from the following
explanation :
In the case of a cylinder, an axial compressive load
causes a negative strain in the vertical gauges and a
positive strain in the circumferential gauges. The two
strains are not equal. They are related to each other by a
factor, , the Poisson's ratio. Since the value of the strain
is of no interest, the objective is to produce a force
transducer. This force transducer is calibrated
empirically. In case all the gauges are similar,
temperature compensation is obtained as all the gauges
contribute equally to unbalance the bridge.
Compression cells of this type have been used with a
capacity of 300 MN.
33

34. MEASUREMENT OF TORQUE
Measurement of torque is carried out because:
i. it is of considerable interest for its own sake
ii. it is often associated with determination of
mechanical power. and
iii. it is required to obtain load information
necessary for stress and deflection analysis.
34

35. Torque is obtained by measuring force at a known
distance.
Torque is given by Nm ............ (2)
.
Fr
 
Where F is force in N and r is distance at which it
is measured in m.
Power
Where  = angular velocity; rad/s
The angular velocity  = 2n where n is speed in
rps.
Power is also expressed in horse power where on
horse power ----- h.p. = 735 W
W ............ 3)
.(
P 

35

36. MEASUREMENT OF TORQUE OF ROTATING SHAFTS
The methods of measurement of torque of
rotating shafts of machines may involve
1. Power Source: machine which supplies
power.
2. Power Sink: the machine which absorbs
power.
3. Power transmitter: the device that connects
the source and the sink and is responsible for
transmission of power from source to sink.
36

37. The arrangement showing source, sink and transmitter
37

38. MEASUREMENT OF SHAFT POWER
The conventional methods of determining the
power delivered to (or absorbed by) rotating
machinery require simultaneous measurements
of torque and shaft speed.
Machines used for torque measurements under
test-bed conditions are called dynamometers.
The word dynamometer comes from “dynamic
moment meter.”
38

39. The dynamometers are classified as :
1. Absorption dynamometers,
2. Transmission dynamometers, and
3. Driving dynamometers.
39

40. The type of dynamometer to be used depends on
the nature of the machine to be tested.
If the machine is a power generator the
dynamometer must be capable of absorbing its
power.
If the machine is a power absorber, the
dynamometer must be capable of driving it.
If the machine is power transmitter or transformer,
the dynamometer must provide both the power
source as well as the load.
40

41. Absorption Dynamometers
These dynamometers work on the principle that
the power measured is converted into heat by
friction or by other means. The power absorbed is
lost as heat and is dissipated to the surroundings
where it serves no useful purpose.
Absorption type of dynamometers are used in
measurement of power of generators, electric
motors, turbine and engines.
41

42. Dynamometers capable of power absorption
include various forms of
a) mechanical brakes employing dry friction
(Prony -brake)
b) fluid friction (air and water brakes) and
c) eddy current brake (inductor dynamometers).
42

43. Transmission dynamometers
The principle involved in transmission dynamometers is
that the power being transmitted either to or from the
dynamometer is not absorbed or dissipated.
The power after measurement is available in useful
mechanical or electrical form. However, a small power is
dissipated on account of friction.
They maybe thought as passive devices placed at an
appropriate location within a machine or between
machines simply for the purpose of measurement of torque
at that particular location.
43

44. They neither add nor subtract from the transmitted
energy or power and are referred to as
Torque Meters.
The dynamometers of this type are
1. torsion and belt dynamometers and
2. strain gauge dynamometers
44

45. Driving Dynamometers.
Applications which involve the machine under test
is one which absorbs power (such as a pump or a
compressor), the driving power must be supplied by
a driving dynamometer.
The requirement restricts the choice of the type of
driving dynamometer which can be used. Electric
motors are universally employed as driving
dynamometers.
The driving dynamometers are invariably d.c.
machines.
45

46. The major advantage using d.c. machines as
driving dynamometers is that their speed can be
controlled smoothly over a wide range by either
armature voltage control or field control or both.
The disadvantage of a d.c. driving dynamometer is
that the necessary d.c. supply is not easily
available and has to be obtained by using rectifier
cricuits to convert existing a.c. supply to d.c.
These devices are now in wide use and are cheap,
easy to operate and give a smooth control of
voltage.
46

47. Rope Brake
47

48. Rope Brake
The simplest form of absorption
dynamometer is the dry friction rope brake
shown in Figure.
A rope or a band is wound round a large wheel
called brake drum (pulley) coupled to the shaft
whose power is to be measured.
The rope or band is attached to a spring balance at
one end to a deadweight W at the other end.
48

49. The torque is,  = (W - S) r
Where S is the reading of spring
balance.
The power is,  
2
60
N
P W S r

 
Where N is the speed in r.p.m. and r is the
effective radius in m.
The effective radius is  / 2
r D d
 
Where D and d are respectively the diameters of
drum and rope.
 Horse Power (H.P.)
.
 
2
735 60
N W S r
 


49

50. The advantages of rope brake are that
1. It is simple in operation and easy to make.
2. Is suitable for measurement of wide range of
power, and
3. Is much more steadier in operation than a
prony brake and requires no lubrication
50

51. The disadvantages of rope brakes are that
1. The output of the driving machine is
dissipated as heat, and
2. The difficulty of dissipating the heat, without
exceeding temperatures which can be
withstood by the materials of the brake, place
a limit on the power which can be absorbed.
51

52. The brake arrangement does not stabilize the
speed of the machine under test, since there is no
automatic increase in torque with increase of
speed.
The rope type brake can be used for measurement
of power of low speed shafts having a large brake
drum (pulley). The power range of 0.1 to 50 h.p.
with speeds upto 4000 r.p.m.
52

53. PRONY BRAKE
53

54. 54

55. A rather old device like the rope brake for the measurement of
torque and power from machines is
prony brake. The schematic diagram of a Prony brake is
shown in Figure. Two wooden blocks are mounted
diametrically opposite on a pulley attached to the rotating
shaft whose power is to be measured.
One block carries a lever arm. Some arrangement is provided
to tighten the rope which is connected to the arm.
The rope is tightened so as to increase the frictional resistance
between the blocks and the pulley .
The torque exerted by the prony brake is,  = Fr.
55

56. The prony brake is inherently unstable. Its capacity
is limited by the following factors :
a) Due to wear of the wooden blocks, the co-efficient
of friction varies between the blocks and the
pulley. This requires continuous tightening of
clamp. Therefore, the system may become
unsuitable for measurement of large powers
especially when used for long periods.
b) The use of prony brake results in excessive
temperature rise which results in decrease in
coefficient of friction leading to brake failure. In
order to limit the temperature rise, cooling is
required. This is done by running water into the
hollow channel cross-section of the pulley.
56

57. c) When the machine torque is not constant, the
measuring arrangement is subjected to
oscillations. There may be changes in co-
efficient of friction and hence the reading of
force F may be difficult to take.
57

58. Hydraulic Dynamometers (water brake)
uses fluid friction rather than dry friction for
dissipating the input energy. Figure shows this type
of dynamometer in its simplest form.
58

59. Hydraulic Dynamometers (water brake)
59

60. Hydraulic absorption dynamometer is shown in
figure . Power is absorbed by fluid friction due to
the breaking action of the vortex produced by
flow of water along a helix. This brought about by
the relative motion of the rotor with respect to a
stator or the casing of the dynamometer.
60

61. The rotor and stator have cup shaped pockets such
that the path of water is a helix. The tendency of
the stator to rotate is opposed by an arm on the
stator with a balancing mass. The stator is freely
pivoted on the bearings. The load is controlled bu
control of sluice gates in the spaces between stator
and rotor pockets. This control can be effected
from outside and changes the braking effect
between the rotor and the stator.
61

62. Transmission Dynamometers
The principle involved in transmission
dynamometers is that power being transmitted
either to or from the dynamometer is not absorbed
or dissipated. The power after measurement is
available in useful mechanical or electrical form.
However, a small power is dissipated on account
of friction.
62

63. They maybe thought as passive devices placed at an
appropriate location within a machine or between machines
simply for the purpose of measurement of torque at that
particular location. They neither add nor subtract from the
transmitted energy or power and are referred to as
Torque Meters.
The dynamometers of this type are torsion and belt
dynamometers and strain gauge dynamometers.
63

64. Strain Gauge Torque Meters
64

65. The principle of this method is explained by
Figure. Two strain gauges are mounted on a shaft
at an angle 45° to each other. The torque is given
by :
 
4 4
2
G R r
L

 


G = modulus of rigidity; N/m2,
R = outer radius of shaft ; m,
r = inner radius of shaft ; m,
L = length of shaft ; m,
 = angular deflection of shaft ; rad.
65

66. The strain gauges attached at 45° degrees to the axis of the
shaft as shown will indicate strains of
 
45 4 4
R
G R r





The strain may be measured by electrical means to indicate the
torque. Multiple strain gauges may be
and connected in a bridge circuit configuration so that any
deformation due to axial or transverse is cancelled out in the final
readout.
66
Longitudinal strain in the shaft at 45º to the axis of the shaft,
ε45 = Shear strain / 2

67. The strain in the shaft may be measured by means of strain
gauges attached to its surface. The gauges
be so mounted that they give maximum sensitivity to the
strains produced by torsion. The theory of two-dimensional
stress systems shows that, for a shaft subjected to pure
torsion, the gauges will be strain in the directions of their
major axis if they are mounted at 45° to the axis of the shaft.
The normal method is to mount a complete strain gauge
bridge on the shaft. The strain bridge configuration generally
used for measurement of torque is shown in Figure.
67

68. 68

69. 69

70. In this arrangement two strain gauges are subjected to
tensile stresses while the other two experience compressive
stresses. The gauges must be precisely at 450 with the shaft
axis. Gauges 1 and 3 must be diametrically opposite, as
must gauges 2 and 4.
This arrangement has the advantages that it is fully
temperature compensated, provides auto compensation for
bending and axial loads and gives maximum sensitivity for
a given torque.
70

71. The main difficulty associated with the use of this
arrangement is the connection of the bridge to the
power source and display arrangement.
71

72. Electric Dynamometers
Almost any form of rotating electric machine can
be used as a driving dynamometer, or as an
absorption dynamometer, or as both. As expected,
those designed especially for the purpose are most
convenient to use. Four possibilities are:
(1)Eddy-current dynamometers,
(2)Cradled DC dynamometers,
(3) DC motors and generators,
(4) AC motors and generators.
72

73. “Cradled” DC dynamometer
73

74. “Cradled” DC dynamometer
74

75. “Cradled” DC dynamometer
Undoubtedly the most versatile of all types is the
cradled DC dynamometer, shown in Figure. This
type of machine is usable both as an absorption
and as a driving dynamometer in capacities to
5000 hp (3730 kW). Basically the device is a DC
motor generator with suitable controls to permit
operation in either mode.
75

76. When used as an absorption dynamometer, it
performs as a DC generator and the input
mechanical energy is converted to electrical
energy, which is dissipated in resistance racks.
This latter feature is important, for unlike the
eddy-current dynamometer, the heat is dissipated
outside of the machine.
76

77. Cradling in trunion bearings permits the
determination of reaction torque and the direct
application of Equation  = Fr
77
When the early electric motors were being developed about i884-'86, it is recorded that the cradle
dynamometer was devised by Professor Brackett as a more accurate means for ascertaining the "stray
power" factors than the Prony brake, and since this form of dynamometer consisted essentially of a
cradle upon which was mounted the electric motor to be tested, there can be little doubt as to the
approximate date of its origin.
It should be explained that the Brackett dynamometer, while embodying the principle of the modern
cradle type, differed in that the motor under test was supported bodily in a frame work which was
free to rock through an angle sufficient to per- mit measurement of pull at the end of an arm. A
leather belt was employed to transmit power from the motor pulley to a line shaft. It will readily be
seen that this method would be awk- ward and impracticable for the test of gasoline engines. The
principle was correct and the only change necessary was to con- sider the electric motor as a generator
to be used for loading the engine, which is connected by means of a flexible coupling to the shaft
rather than

78. 78