Page 403 - The Mechatronics Handbook

high-frequency applications. The roll-off typically starts near 100 Hz. These active devices have no DC
response. Since piezoelectric accelerometers have comparatively low mechanical impedances, their effect
on the motion of most structures is negligible.
Mathematically, their transfer function approximates a third-order system that can be expressed as

e 0 s() K q τs
----------- = --------------------------------------------------------------------------------- (19.22)
as() Cω n τs +( 1 ) s /ω n + 2ζs/ω n + 1)
2
2
2
(
where K q is the piezoelectric constant related to charge (C cm), τ is the time constant of the crystal, and
s is the Laplace variable. It is worth noting that the crystal itself does not have a time constant τ, but the
time constant is observed when the accelerometer is connected to an electric circuit, for example, an RC
circuit.
The low-frequency response is limited by the piezoelectric characteristic τs/(τs + 1), while the high-
frequency response is related to mechanical response. The damping factor ζ is very small, usually less
than 0.01 or near zero. Accurate low-frequency response requires large τ, which is usually achieved by
use of high-impedance voltage amplifiers. At very low frequencies thermal effects can have severe influ-
ences on the operation characteristics.
In piezoelectric accelerometers, two basic design configurations are used: compression types and shear-
stress types. In compression-type accelerometers, the crystal is held in compression by a preload element;
therefore the vibration varies the stress in compressed mode. In a shear-stress accelerometer, vibration
simply deforms the crystal in shear mode. The compression accelerometer has a relatively good mass to
sensitivity ratio and hence exhibits better performance. But, since the housing acts as an integral part of
the spring-mass system, it may produce spurious interfaces in the accelerometer output if excited around
its natural frequency.
Piezoelectric accelerometers are available in a wide range of specifications and are offered by a large
number of manufacturers. For example, the specifications of a shock accelerometer may have 0.004 pC/g
in sensitivity and a natural frequency of up to 250,000 Hz, while a unit designed for low-level seismic
measurements might have 1000 pC/g in sensitivity and only 7000 Hz natural frequency. They are man-
ufactured as small as 3 × 3 mm in dimension with about 0.5 g in mass, including cables. They have
excellent temperature ranges and some of them are designed to survive the intensive radiation environ-
ment of nuclear reactors. However, piezoelectric accelerometers tend to have larger cross-axis sensitivity
than other types, about 2–4%. In some cases, large cross-axis sensitivity may be minimized during
installations by the correct orientation of the device. These accelerometers may be mounted with threaded
studs, with cement or wax adhesives, or with magnetic holders.

Piezoresistive Accelerometers
Piezoresistive accelerometers are essentially semiconductor strain gauges with large gauge factors. High
gauge factors are obtained since the material resistivity is dependent primarily on the stress, not only on
the dimensions. This effect can be greatly enhanced by appropriate doping of semiconductors such as
silicon. Most piezoresistive accelerometers use two or four active gauges arranged in a Wheatstone bridge.
Extra precision resistors are used, as part of the circuit, in series with the input to control the sensitivity,
for balancing, and for offsetting temperature effects. The sensitivity of a piezoresistive sensor comes from
the elastic response of its structure and resistivity of the material. Wire and thick or thin film resistors
have low gauge factors, that is, the resistance change due to strain is small. The mechanical construction
of a piezoresistive accelerometer is shown in Fig. 19.24.
Piezoresistive accelerometers are useful for acquiring vibration information at low frequencies, for exam-
ple, below 1 Hz. In fact, they are inherently true non-vibrational acceleration sensors. They generally have
wider bandwidth, smaller nonlinearities and zero shifting, and better hysteresis characteristics compared to
piezoelectric counterparts. They are suitable to measure shocks well above 100,000g. Typical characteristics

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