18.3 Torque measurement
Measurement of applied torques is of
fundamental importance in all rotating bodies to ensure that the design of the
rotating element is adequate to prevent failure under shear stresses. Torque
measurement is also a necessary part of measuring the power transmitted by
rotating shafts. The three traditional methods of measuring torque consist of
(i) measuring the reaction force in cradled shaft bearings, (ii) the ‘Prony
brake’ method and (iii) measuring the strain produced in a rotating body due to
an applied torque. However, recent developments in electronics and optic-fibre technology
now offer an alternative method as described in paragraph 18.3.4 below.
18.3.1 Reaction forces in shaft
bearings
Any system involving torque
transmission through a shaft contains both a power source and a power absorber
where the power is dissipated. The magnitude of the transmitted torque can be
measured by cradling either the power source or the power absorber end of the
shaft in bearings, and then measuring the reaction force, F, and the arm length
L, as shown in Figure 18.10. The torque is then calculated as the simple
product, FL. Pendulum scales are very commonly used for measuring the reaction
force. Inherent errors in the method are bearing friction and windage torques.
18.3.2 Prony brake
The principle of the Prony brake is
illustrated in Figure 18.11. It is used to measure the torque in a rotating
shaft and consists of a rope wound round the shaft. One end of the rope is
attached to a spring balance and the other end carries a load in the form of a
standard mass, m. If the measured force in the spring balance is Fs,
then the effective force, Fe, exerted by the rope on the shaft is
given by:
Fe = mg - Fs
If the radius of the shaft is Rs
and that of the rope is Rr, then the effective radius, Re,
of the rope and drum with respect to the axis of rotation of the shaft is given
by:
Re = Rs + Rr
The torque in the shaft, T, can then
be calculated as:
T = FeRe
Whilst this is a well-known method of
measuring shaft torque, a lot of heat is generated because of friction between
the rope and shaft, and water cooling is usually necessary.
18.3.3 Measurement of induced strain
Measuring the strain induced in a
shaft due to an applied torque has been the most common method used for torque
measurement in recent years. It is a very attractive method because it does not
disturb the measured system by introducing friction torques in the same way as
the last two methods described do. The method involves bonding four strain
gauges onto the shaft as shown in Figure 18.12, where the strain gauges are
arranged in a d.c. bridge circuit. The output from the bridge circuit is a
function of the strain in the shaft and hence of the torque applied. It is very
important that the positioning of the strain gauges on the shaft is precise,
and the difficulty in achieving this makes the instrument relatively expensive.
The technique is ideal for measuring
the stalled torque in a shaft before rotation commences. However, a problem is
encountered in the case of rotating shafts because a suitable method then has
to be found for making the electrical connections to the strain gauges. One
solution to this problem found in many commercial instruments is to use a
system of slip rings and brushes for this, although this increases the cost of
the instrument still further.
18.3.4 Optical torque measurement
Optical techniques for torque
measurement have become available recently with the development of laser diodes
and fibre-optic light transmission systems. One such system is shown in Figure
18.13. Two black-and-white striped wheels are mounted at either end of the
rotating shaft and are in alignment when no torque is applied to the shaft.
Light from a laser diode light source is directed by a pair of optic-fibre
cables onto the wheels. The rotation of the wheels causes pulses of reflected
light and these are transmitted back to a receiver by a second pair of
fibre-optic cables. Under zero torque conditions, the two pulse trains of
reflected light are in phase with each other. If torque is now applied to the
shaft, the reflected light is modulated. Measurement by the receiver of the
phase difference between the reflected pulse trains therefore allows the
magnitude of torque in the shaft to be calculated. The cost of such instruments
is relatively low, and an additional advantage in many applications is their
small physical size.
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