Instrumentation & Measurement Magazine 26-4 - 53

The damping rate suitable for the piezoelectric sensor
according to Table 3 and Fig. 3 to minimize the error of measurement
to 0.28% is of 0.68.
The simulation of new relation of relative sensitivity is presented
in Table 4 and Fig. 5. Table 4 lists the results of relative
sensitivity according to the relative frequency for five damping
rate values.
From the results obtained in Table 4 and Fig. 5, we notice
that:
◗ The relative sensitivity is equal to 0.0159 mV / g ± 0.5%, if
ζ =0.6 and the relative frequency variation of 0 to 4200 Hz.
◗ The relative sensitivity is equal to 0.0159 mV / g ± 0.3%,
if ζ =0.63 and the relative frequency variation of 0 to
4200 Hz.
Fig. 4. Measurement error according to relative frequency for five damping
ratios values (from [21], ©2018 Springer, used with permission).
◗ For a relative frequency variation of 0 to 4200 Hz and a
damping rate choice equals to 0.63, the error does not
exceed a value which equals 2.15%.
◗ For a relative frequency variation of 0 to 4200 Hz and a
damping rate choice equals to 0.65, the error does not
exceed a value which equals 1.2%.
◗ For a relative frequency variation of 0 to 4200 Hz and a
damping rate choice equals to 0.68, the error does not
exceed a value which equals 0.28%.
◗ For a relative frequency variation of 0 to 4200 Hz and
a damping rate choice equals to 0.7, the error does not
exceed a value which equals 1.18%.
◗ The relative sensitivity is equal to 0.0159 mV / g ± 0.15%,
if ζ =0.65 and the relative frequency variation of 0 to
4200 Hz.
◗ The relative sensitivity is equal to 0.0159 mV / g ± 0.1%,
if ζ =0.68 and the relative frequency variation of 0 to
4200 Hz.
◗ The relative sensitivity is equal to 0.0159 mV / g ± 0.25%, if
ζ =0.7 and the relative frequency variation of 0 to 4200 Hz.
We deduce that the damping rate which equals 0.68 makes
it possible to obtain a constant sensitivity, which implies that
the sensor is more sensitive and precise.
Influence of the Resonance
Phenomenon on the Accelerometer
Operation
Vibrations are generally undesirable. Resonance is a phenomenon
that presents itself in various aspects; it manifests by
an amplification of the response or the vibrations amplitude
Table 4 - Relative sensitivity results
Relative sensitivity (mV/g)
Frequency (Hz)
300
600
900
1200
1500
1800
2100
2400
2700
3000
3300
3600
3900
4200
June 2023
ζ = 0.6
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0160
0.0160
0.0161
0.0161
0.0162
0.0163
0.0163
0.0164
0.0164
ζ = 0.63
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0160
0.0160
0.0160
0.0161
0.0161
0.0161
0.0162
0.0162
ζ = 0.65
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0160
0.0160
0.0160
0.0160
0.0160
0.0160
0.0160
IEEE Instrumentation & Measurement Magazine
ζ = 0.68
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0158
0.0158
ζ = 0.7
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0159
0.0158
0.0158
0.0158
0.0158
0.0158
0.0158
0.0157
0.0157
53
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