Page 402 - The Mechatronics Handbook

the motor and magnet combination. The accuracy of the servo-type accelerometers is ultimately limited
by consistency and stability of scale factors of coupling and cup-and-magnet devices as a function of
time and temperature.
Another accelerometer based on induction design uses the eddy-current induction torque generation.
The force-generating mechanism of an induction accelerometer consists of a stable magnetic field, usually
supplied by a permanent magnet, which penetrates orthogonally through a uniform conduction sheet.
The movement of the conducting sheet relative to the magnetic field in response to acceleration results
in a generated electromotive potential in each circuit in the conductor. This action is in accordance with
Faraday’s principle. In induction-type accelerometers, the induced eddy currents are confined to the
conductor sheet, making the system essentially a drag coupling. Since angular rate is proportional to
acceleration, angular position represents change in velocity. This is a particularly useful feature in navi-
gation applications.
A typical commercial instrument based on the servo-accelerometer principle might have a microma-
chined quartz flexure suspension, differential capacitance angle pick-off, air-squeeze film plus servo-lead
compensation for system damping. Of the available models, as an example, a typical 30g unit has a
threshold and resolution of 1 µg, a frequency response that is flat to within 0.05% at 10 Hz and 2% at
100 Hz, a natural frequency of 1500 Hz, a damping ratio from 0.3 to 0.8, and transverse or cross-axis
sensitivity of 0.1%. If, for example, the output current is about 1.3 mA/g, a 250 W readout resistor would
give about ±10 V full scale at 30g. These accelerometers are good for precision work and used in many
applications such as aircraft and missile control systems, measurement of tilt angles for borehole navi-
gation, and axle angular bending in aircraft weight and balance systems.

Piezoelectric Accelerometers
Piezoelectric accelerometers are widely used for general-purpose acceleration, shock, and vibration mea-
surements. They are basically motion transducers with large output signals and comparatively small sizes
and they are self generators not requiring external power sources. They are available with very high
natural frequencies and are therefore suitable for high-frequency applications and shock measurements.
These devices utilize a mass in direct contact with the piezoelectric component or crystal as shown in
Fig. 19.23. When a varying motion is applied to the accelerometer, the crystal experiences a varying force
excitation (F = ma), causing a proportional electric charge q to be developed across it. So,

q = d ij F = d ij ma (19.21)

where q is the charge developed and d ij is the piezoelectric coefficient of the material.
As this equation shows, the output from the piezoelectric material is dependent on its mechanical
properties, d ij . Two commonly used piezoelectric crystals are lead-zirconate titanate ceramic (PZT) and
crystalline quartz. They are both self-generating materials and produce a large electric charge for their
size. The piezoelectric strain constant of PZT is about 150 times that of quartz. As a result, PZTs are
much more sensitive and smaller in size than quartz counterparts. These accelerometers are useful for

FIGURE 19.23 A compression type piezoelectric accel-
erometer arrangement.

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