Measurement of Mechanical Parameters

1. Measurement of force and
torque

2. Measuring devices
Measurands Measuring instruments
Force, load Analytical balance
Platform balance
Proving ring
Torque Prony brake
Hydraulic dynamometer
Pressure Bridgeman gauge
Mcload gauge
Pirani gauge

3. Introduction
 Force: It is defined as the reaction between the two
bodies or components.
 The reaction can be either tensile force (Pull) or it can be
Compressive force (Push).
 Measurement of force can be done by any two methods:
◦ Direct Method: This involves a direct comparison with a known
gravitational force on a standard mass. Example: Physical
Balance.
◦ Indirect Method: This involves the measurement of effect of
force on a body. E.g. Force is calculated from acceleration due
to gravity and the mass of the component.

4. Linear Mechanical Power
 Linear Power
 To summarize: Work is force times the change in distance
 W = f x Δd
 Where W is work, f is the force and Δd is the change in distance.
If work = force x distance
then power = force x distance/time
then P = f x d/t or
Power = force x rate or
Power = force x speed

5. Rotational Power
 Torque causes objects to spin or rotate.
 Torque = force x lever arm
 Power is the rate of doing rotational work. Work is the product of
torque x swept angle in radians.
 W = T x Θ
 T is Torque and Θ is swept angle in radians. Power = rotational
work/time
 Power = T x Θ/t
 Since Θ/t = ω angular speed in radians/second, so
 Power = T x ω
 ω is angular velocity. The unit we use is revolutions per minute
(rpm). The conversion of ω (angular velocity) from radians/sec to
rev/min:
 ωrad/sec = ωrpm x (2π/60)
 ωrpm = ωrad/sec x (60/2π

6. Rotational Power
 An encoder disk with four slots is mounted on the motor shaft. The
revolution of the motor shaft is measured by counting the slots of
an encoder disk as they pass through an optical switch.
 The force applied to the motor shaft is weight in ounces (oz.) and
the lever arm distance from the shaft is in inches. Therefore, the
units of torque are oz. x in. or oz-in. Therefore, rotational power is
defined by:
 Power = T oz-in x rpm
 When doing power calculations the units involved are
important. The torque speed product needs to be converted to
power watts. Torque units of oz-in and speed units of rpm can be
converted to power watts by use of the following conversion factor:
0.00074. . The efficiency E of the energy conversion process is
defined by:
 E = Pmech / Pelect or Pelect / Pmech

7. Direct Method: Analytical Balance
(Equal arm balance)

8. Unequal arm balance:

9. Unequal arm balance:

10. Unequal arm balance:
• For balance of
moments,
Ft * a = Fg * b
or test force,
Ft = Fg * (b / a)
Therefore, the test
force is proportional
to the distance ‘b’ of
the mass from the
pivot.

11. Platform Balance: (Multiple Lever System)

12. Platform Balance: (Multiple Lever
System)
• Large weight W may be measured in
terms of smaller weights Wp and Ws.
• Weight Wp is called the poise weight
and Ws the pan weight.
• The weight W1 and W2 is may be
substituted for W.
• With W on the scale platform and
balanced by a pan weight Ws, the
relation is given by
T*b = Ws * a (1)
T*c = W1 (f/d) e + W2 * h (2)
Now if we proportion the linkage such the

13. Proving ring
 The proving ring is a device used to measure force. It
consists of an elastic ring of known diameter with a
measuring device located in the center of the ring.
 They are made of a steel alloy.
 manufactured according to design specifications
established in 1946 by the National Bureau of
Standards (NBS).
 Proving rings can be designed to measure either
compression or tension forces.

14. Proving ring
 Standard for calibrating material testing machine.
 Capacity 1000 N to 1000 kN.
 Deflection is used as the measure of applied load.
 This deflection is measured by a precision micrometer.
 Micrometer is set with a help of vibrating reed.
P = force or load
M = Bending moment
R = Radius of proving
ring

15. Proving Ring:
 A ring used for calibrating
tensile testing machines. It
works on the principle of LVDT
which senses the displacement
caused by the force resulting in
a proportional voltage.
 It is provided with the
projection lugs for loading. An
LVDT is attached with the
integral internal bosses C and
D for sensing the displacement
caused by application of force.
 When the forces are applied
through the integral external
bosses A and B, the diameter
of ring changes depending
upon the application which is
known as ring deflection.

16. Proving Ring:
• The resulting deflection of the ring is measured by LVDT
which converts the ring deflection or displacement in to
voltage signal.
• An external amplifier may be connected to provide direct
current to drive the indicators or the measured value of
force.
• In place of LVDT micrometer can also be provided for
accurate measurement of force or deflection, which is given
by formula
Where,
• F is the force, E is the young's modulus, I is the moment of

17. Damage to Force Sensor
 Because force transducers are
expensive, preventing them from being
damaged should be a high priority. There
are many ways to damage a transducer.
Shock, overloading, lightning strikes or
heavy surges in current, chemical or
moisture ingress, mishandling (dropping,
pulling on cable, etc.), vibration, seismic
events, or internal component
malfunctioning to name a few. If your
sensor becomes damaged, don't just re-
calibrate it. Mechanical failure may have
catastrophic effects and you will no longer
have a reliable sensor.

18. Torque Measurement:
 Torque: Force that causes twisting or turning moment.
E.g. the force generated by an internal-combustion engine
to turn a vehicle's drive or shaft.
 Torque measuring devices are called as dynamometers.
 The torque may be computed by measuring the force ‘F’
at a known radius ‘r’, given by the formula
in N - m

19. Torque Measurement:
 Torque measurement is usually associated with
determination of mechanical power, either power required
to operate a machine or to find out the power developed
by the machine.
Where,
N = Speed in rpm.
T =Torque developed due to load “W”, (N-m)
R = Radius from the center to the point of application of
force (m)
kw
NT
power
1000
*
60
2


20. Horsepower
 Measurement of an engine’s ability to
perform work in a specified time
◦ One horsepower equals 33,000 foot-
pounds of work per minute
 Amount of work required to life 550
pounds one foot in one second
◦ One horsepower equals 0.746 kilowatts
 Gross horsepower
◦ Power produced at crankshaft
 Several measurements

22. Horsepower (cont'd.)
 Accessories that rob power in vehicle (absorb
about 25%)
◦ Alternator
◦ Air conditioning
◦ Water pump
◦ Cooling fan
◦ Power steering
◦ Smog pump
 Net power is what remains
 Power is also lost through friction

24. Types of Dynamometers:
 Absorption dynamometers:
◦ They are useful for measuring power or torque
developed by power source such as engines or electric
motors.
 Driving dynamometers:
◦ These dynamometers measure power or torque and as
well provide energy to operate the device to be tested.
◦ These are useful in determining performance
characteristics of devices such as pumps and
compression.
 Transmission dynamometers:
◦ These are the passive devices placed at an appropriate
location within a machine or in between the machine to
sense the torque at that location.

26. Dynamometer Safety
Concerns in vehicle
 Engine dynamometer
◦ Concerns: fire, part failure, and noise
 Chassis dynamometer
◦ Concerns: carbon monoxide, keeping the
vehicle secured and connected to rollers, part
failure, and noise
 Other dynamometer types
◦ Towing dynos
◦ Cycle dyne

27. Mechanical Dynamometer (Prony
Brake):
Rope

28.  Consists of wooden cleats
or blocks mounted
diametrically opposite on a
flywheel attached to the
rotating shaft whose
power is to be determined.
 One wooden block carries
a lever arm and an
arrangement is made to
tighten the rope to
increase the frictional
resistance between the
blocks.
 The torque exerted by the
Prony brake is T = F . L

29. Hydraulic Dynamometer:
 This is a power sink which uses fluid friction for dissipation of
the input energy and there by measures the input torque or
power.
 The capacity of hydraulic dynamometer is a function of two
parameters speed and the water level.
 The torque is measured with the help of reaction arm or
shaft.
 The power absorption at a given speed may be controlled by
adjustment of water level in the housing.

30.  This dynamometer may be used in larger capacities
than the simple Prony brake dynamometer because
heat generated can be can be easily removed by
circulating the water in and out of the housing.
 The force acting on the shaft is then measured by
using the force measuring device or strain gauges.
 Then by using the relation, T = F . r, we can find the
torque acting on it.

31. Hydraulic Dynamometer:

32. Hydraulic Dynamometer
Characters
 Small in size. Easy installation
 Simple dynamometer structure and easy for
maintenance
 High brake torque
 High measurement accuracy
 Reliable and stable working condition
 High real-time speed measurement accuracy with
EM sensors
 Fast loading control by electronic-control butterfly
valve
 High reaction speed which is suitable on dynamic
testing Tuning of in-use engines, typically at
service centers or for racing applications

33. Case Study – Application of Sensors
in measuring torque produced by propellers in small unmann
quad-rotor helicopter

34. ???
Propeller Thrust, Torque & RPM
Thrust (N) / Lift force by propeller
Torque (N-m)

35. Measuring Torque

36. Measuring Thrust & Torque
Thrust
Torque

39. Calibration of Sensors

42. Calibration of Sensors
y = 8E-06x3
- 0.0006x2
+ 1.0108x
y = -4E-06x3
- 0.0027x2
+ 2.1242x
0
20
40
60
80
100
120
140
160
180
200
220
240
260
280
0 40 80 120 160 200
MEASURED RESPONSE (A/D COUNT)
APPLIED
WEIGHT
(gm)
Torque Calibration Curve
Thrust Calibration Curve

59. Strain measurement on
aircraft