Instrumentation & Measurement Magazine 26-4 - 54

Fig. 5. The relative sensitivity of sensor according to relative frequency
for different damping rate values (from [21], ©2018 Springer, used with
permission).
of any system as a function of the excitation frequencies. In
piezoelectric accelerometers, if the vibratory movement frequency
approaches the natural frequency of the sensor, the
phenomenon of resonance appears. To reduce the effect of this
phenomenon, a relationship must be found between the movement
frequency and the natural frequency, which allows the
suitable frequency margin to be determined for the piezoelectric
sensor.
To simulate the piezoelectric accelerometer model in the
presence of resonance phenomenon, it is necessary to vary the
relative frequency from 0 up to 10,000 Hz knowing that the
sensor natural frequency is equal to 10,000 Hz. The simulation
results of displacement and measurement error are illustrated
in Fig. 6 and Fig. 7.
The results of Fig. 6 and Fig. 7 illustrate that the piezoelectric
accelerometer loses its performance in the case where the
movement frequency approaches to the natural frequency (the
Fig. 7. Error according to frequency ratio in the resonance phenomenon.
measurement error takes the maximum values). We see that
the reduction in the resonance phenomenon effect and the
measurement error of the accelerometer occurred if we take a
frequency ratio less than or equal to 0.35, as shown by:


 0.35
Then the maximum frequency of the motion is given by:

max
0.35
(21)
(22)
This relation makes it possible to choose the suitable accelerometer
and to protect it.
The obtained results showed that the appropriate choice of
the damping rate which equals to 0.68 makes it possible to reduce
the measurement error to a reduced value equal to 0.28%,
to increase the accuracy to an optimal value equal to 99.72%
and to improve the sensitivity of the piezoelectric sensor on
the one hand. On the other hand, the appropriate choice of the
frequency margin makes it possible to protect the sensor and
reduce the effect of the resonance phenomenon.
Table 5 shows a comparison between our results obtained
in this work and the results obtained in the two recent works
[24] and [25]. The piezoelectric sensor proposed in this work is
more precise, more stable and sensitive compared to the two
sensors proposed in [24] and [25].
Conclusion
Fig. 6. Displacement according to frequency ratio in the resonance
phenomenon.
54
In this work, the piezoelectric sensor is studied to present a
mathematical model of its operating principle. The model
developed is an equation related to the displacement with
the sensor parameters, as well as the new relationship that
expresses the relative sensitivity according to different parameters
of the sensor. By simulation tests, this developed model
is validated and the results obtained have shown that ζ =0.68 is
chosen in order to minimize the measurement error to a value
IEEE Instrumentation & Measurement Magazine
June 2023
Instrumentation & Measurement Magazine 26-4

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