Page 405 - The Mechatronics Handbook

0066_frame_C19 Page 27 Wednesday, January 9, 2002 5:17 PM

Bonded-strain-gauge accelerometers generally use a mass supported by a thin flexure beam. The strain
gauges are cemented onto the beam to achieve maximum sensitivity, temperature compensation, and
sensitivity to both cross-axis and angular accelerations. Their characteristics are similar to the unbonded-
strain-gauge accelerometers but have greater sizes and weights. Often silicone oil is used for damping.
Semiconductor strain gauges are widely used as strain sensors in cantilever-beams and mass types of accel-
erometers. They allow high outputs (0.2–0.5 V full scale). Typically, a ±25g acceleration unit has a flat
response from 0 to 750 Hz, a damping ratio of 0.7, a mass of about 28 g, and an operational temperature
of −18°C to +93°C. A triaxial ±20,000g model has a flat response from 0 to 15 kHz, a damping ratio
3
of 0.01, and a compensation temperature range of 0–45°C, and is 13 × 10 × 13 mm in size and 10 g
in mass.

Electrostatic Accelerometers
Electrostatic accelerometers are based on Coulomb’s law between two charged electrodes; therefore, they
are capacitive types. Depending on the operation principles and external circuits they can be broadly
classified as (a) electrostatic-force-feedback accelerometers, and (b) differential-capacitance accelerometers.
Electrostatic-Force-Feedback Accelerometers
An electrostatic-force-feedback accelerometer consists of an electrode, with mass m and area S, mounted
on a light pivoted arm that moves relative to some fixed electrodes. The nominal gap h between the
pivoted and fixed electrodes is maintained by means of a force-balancing servo system, which is capable of
varying the electrode potential in response to signals from a pickoff mechanism that senses relative
changes in the gap. Mathematically, the field between the electrodes may be expressed by

Q
E = -------- (19.24)
ekS
where E is the intensity or potential gradient (dV/dx), Q is the charge, S is the area of the conductor, and
k is the dielectric constant of the space outside the conductor.
2
From this expression, it can be shown that the force per unit area of the charged conductor (in N/m )
is given by

2 2
F Q ekE
--- = -------------- = ----------- (19.25)
S 2ekS 2 2
Consider one movable and one stationary electrode and assume that the movable electrode is main-
tained at a bias potential V 1 and the stationary one at a potential V 2 . The electrical intensity E in the gap,
h, can be expressed as

E 1 = V 1 – V 2 (19.26)
-----------------
h
so that the force of attraction may be found as
2
2
F 1 = ekE S ekV 1 –( V 2 ) S (19.27)
-------------- =
----------------------------------
2h 2 2h 2
In the presence of acceleration, if V 2 is adjusted to restrain the movable electrode to the null position,
the expression relating acceleration and electrical potential may be given by
(
2
ekV 1 – V 2 ) S
a = ----- = ---------------------------------- (19.28)
F 1
2
m 2h m
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