Page 430 - The Mechatronics Handbook

0066_Frame_C19 Page 52 Wednesday, January 9, 2002 5:27 PM

also be determined from Eq. (19.59). Requiring only noninvasive, observational measurements, this
method is especially useful for determining transitory torques; for example those associated with firing
events in multicylinder internal combustion engines [3].
Equations (19.63) and (19.64) are applicable only during rotation because, in the absence of motion,
no work is done and power transfer is zero. Equation (19.63) can be used to determine average torque
from calorimetric measurements of the heat generated (equal to the mechanical work W) during a totalized
number of revolutions (≡ θ/2π). Equation (19.64) is routinely applied in power measurement, wherein T
is determined by methods based on Eqs. (19.58), (19.60), (19.61), or (19.62), and ω is measured by any
suitable means [4].
F, T, and φ are sometimes measured by simple mechanical methods. For example, a “torque wrench”
is often used for the controlled tightening of threaded fasteners. In these devices, torque is indicated by
the position of a needle moving over a calibrated scale in response to the elastic deflection of a spring
member, in the simplest case, the bending of the wrench handle [5]. More generally, instruments, variously
called sensors or transducers, are used to convert the desired (torque or speed related) quantity into a
linearly proportional electrical signal. (Force sensors are also known as load cells.) The determination of
P most usually requires multiplication of the two signals from separate sensors of T and ω. A transducer,
wherein the amplitude of a single signal proportional to the power being transmitted along a shaft, has
also been described [6].

Torque Transducer Technologies
Various physical interactions serve to convert F, τ, γ, or φ into proportional electrical signals. Each requires
that some axial portion of the shaft be dedicated to the torque sensing function. Figure 19.47 shows
typical features of sensing regions for four sensing technologies in present use.
Surface Strain
Figure 19.47(a) illustrates a sensing region configured to convert surface strain (γ m ) into an electrical
signal proportional to the transmitted torque. Surface strain became the key basis for measuring both
force and torque following the invention of bonded wire strain gages by E. E. Simmons, Jr. and Arthur
C. Ruge in 1938 [7]. A modern strain gage consists simply of an elongated electrical conductor, generally
formed in a serpentine pattern in a very thin foil or film, bonded to a thin insulating carrier. The carrier
is attached, usually with an adhesive, to the surface of the load carrying member. Strain is sensed as a
change in gage resistance. These changes are generally too small to be accurately measured directly and
so it is common to employ two to four gages arranged in a Wheatstone bridge circuit. Independence
from axial and bending loads as well as from temperature variations are obtained by using a four-gage
bridge comprised of two diametrically opposite pairs of matched strain gages, each aligned along a
principal strain direction. In round shafts (and other shapes used to transmit torque), tensile and com-
pressive principal strains occur at 45° angles to the axis. Limiting strains, as determined from Eq. (19.61)
3
(with τ m equal to the shear proportional limit of the shaft material), rarely exceed a few parts in 10 .
Typical practice is to increase the compliance of the sensing region (e.g., by reducing its diameter or with
hollow or specially shaped sections) in order to attain the limiting strain at the highest value of the torque
to be measured. This maximizes the measurement sensitivity.
Twist Angle
If the shaft is slender enough (e.g., L > 5 d), φ, at limiting values of τ m for typical shaft materials, can
exceed 1°, enough to be resolved with sufficient accuracy for practical torque measurements (φ at τ m
can be found by manipulating Eqs. (19.60)–(19.62)). Figure 19.47(b) shows a common arrangement wherein
torque is determined from the difference in tooth-space phasing between two identical “toothed” wheels
attached at opposite ends of a compliant “torsion bar.” The phase displacement of the periodic electrical
signals from the two “pickups” is proportional to the peripheral displacement of salient features on the
two wheels, and hence to the twist angle of the torsion bar and thus to the torque. These features are
chosen to be sensible by any of a variety of noncontacting magnetic, optical, or capacitive techniques.

©2002 CRC Press LLC