Page 385 - Mechatronics with Experiments

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JWST499-c06
JWST499-Cetinkunt
SENSORS 371 254mm×178mm
Diaphragm F = PA
F
Force
- - - - - F = MA
+ + + + +
- - - - - V out + + + + +
+ + + + + - - - - - - - - - -
+ + + + +
+ + + + +
- - - - - + + + + +
- - - - -
V out
Base
V out
Object whose acceleration is measured
Piezoelectric force sensor Piezoelectric pressure sensor Piezoelectric acceleration sensor
FIGURE 6.41: Piezoelectric principle and its usage in force, pressure, and acceleration sensors.

Notice that although the piezo element has a finite stiffness and acts as a stiff spring, the
actual deformation of the piezo element is very small due to its large stiffness. Therefore,
it can be considered almost as if there is no deformation. Piezoelectric based acceleration
sensors have a range as high as 1000 g, with sensor bandwidth up to 100 kHz. The limiting
factor in the frequency response of the sensor is the charge amplifier bandwidth, which is
much slower than the sensor element. The bandwidth of the sensor element plus the charge
amplifier can be up to a few kHz range. Piezoelectric based sensors are most appropriate
for measuring signals that are time varying. They are not appropriate for measuring static
or low frequency signals since the charge due to the load will slowly discharge.
The design principles of piezoelectric based sensors for pressure, force, strain, and
acceleration measurements are very similar. The external force (in the case of a force sensor
it is the force sensed, in case of a pressure sensor it is the pressure times the surface area of
the diaphragm, in the case of acceleration sensor it is the inertial force, m sensor ⋅ ̈ x) induces
a strain on the piezoelement of the sensor. The output charge is proportional to the strain
(Figure 6.41).
As a example, the accelerometer Model-339B01 by PCB Piezotronics has the fol-
lowing characteristics: voltage sensitivity K = 100 mV∕g, frequency range up to 2 kHz,
amplitude range up to 50 g with a resolution of 0.002 g.

6.6.3 Strain-gauge Based Accelerometers
The operating principle of a strain-gauge based accelerometer is very similar to an inertial
accelerometer. The only difference is that the spring function is provided by a cantilever
flexible beam (Figures 6.42–6.45a). In addition, the strain in the cantilever beam is mea-
sured, instead of the displacement. The strain is proportional to the inertial force, hence the
acceleration. The voltage output from the sensor, proportional to strain, is obtained from
the standard Wheatstone bridge circuit.
̈ x → F → → → ΔR → V out (6.125)
where F = m̈ x, = F∕A, = (1∕E) , ΔR = G , m is inertia, A is the cross-sectional area
of deformation, E Youngs’ Modulus of elasticity constant, G the strain-gauge factor.
V (t) = K ⋅ ̈ x(t) (6.126)
out
The range of the accelerations this type of sensor can measure is very similar to those of
piezoelectric type accelerometers, that is up to 1000 g. The bandwidth of the sensor can be
as high as a few kHz.