Page 406 - The Mechatronics Handbook

0066_frame_C19 Page 28 Wednesday, January 9, 2002 5:17 PM

The device so far described can measure acceleration in one direction only, and the output is quadratic
in character, that is,

( V 1 – V 2 ) = Da (19.29)

where D is the constant of proportionality.
The output may be linearized in a number of ways, one of which is the quarter-square method. If the
servo controller applies a potential −V 2 to the other fixed electrode, the force of attraction between this
electrode and the movable electrode becomes

ekV 1 +( V 2 ) S
2
a = ----- = ---------------------------------- (19.30)
F 2
2
m 2h m
and the force-balance equation of the movable electrode when the instrument experiences a downward
acceleration a now is

ekS V 1 + V 2 ) – ( V 1 – V 2 ) ]
[
(
2
2
ma = F 2 – F 1 = ----------------------------------------------------------------------
2h 2
or
ma = F 2 – F 1 = 2ekSV 1 V 2 (19.31)
------------------------
h 2

Hence, if the bias potential V 1 is held constant and the gain of the control loop is high so that variations
in the gap are negligible, the acceleration becomes a linear function of the controller output voltage V 2 .
The principal difficulty in mechanizing the electrostatic force accelerometer is the relatively high
electric field intensity required to obtain an adequate force. Damping can be provided electrically or by
viscosity of the gaseous atmosphere in the inter-electrode space if the gap h is sufficiently small. The
scheme works best in micromachined instruments. Nonlinearity in the voltage breakdown phenomenon
permits larger gradients in very small gaps.
−3
A typical electrostatic accelerometer has the following characteristics: range ±50g, resolution 10 g,
−4
sensitivity 100 mV/g, nonlinearity <1% FS, transverse sensitivity <1% FS, thermal sensitivity 6 × 10 /K,
mechanical shock 10,000g, operating temperature −45°C to 90°C, supply voltage 5 V DC, and weight
45 g. The main advantages of electrostatic accelerometers are their extreme mechanical simplicity, low
power requirements, absence of inherent sources of hysteresis errors, zero temperature coefficients, and
ease of shielding from stray fields.
Differential-Capacitance Accelerometers
Differential-capacitance accelerometers are based on the principle of the change of capacitance in pro-
portion to applied acceleration. In one type, the seismic mass of the accelerometer is made as the movable
element of an electrical oscillator. The seismic mass is supported by a resilient parallel-motion beam
arrangement from the base. The system is set to have a certain defined nominal frequency when undis-
turbed. If the instrument is accelerated, the frequency varies above and below the nominal value depend-
ing on the direction of acceleration.
The seismic mass carries an electrode located in opposition to a number of base-fixed electrodes that
define variable capacitors. The base-fixed electrodes are resistances coupled in the feedback path of a
wideband, phase-inverting amplifier. The gain of the amplifier is predetermined to ensure maintenance

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