METHOD FOR MEASURING MECHANICAL PRESSURES

I. G. Minaev, A. I. Trofimov

(Presented by the Department of Computer Engineering)

At present, various methods are used for converting the measured nonelectrical quantity of pressure into an electrical one by means of capacitive, inductive, carbon, magnetoelastic, strain-gauge, and piezoelectric sensors.

The choice of one method or another is determined by the specific conditions. The known piezoelectric method for measuring pressure is applicable only for measuring rapidly varying in time, i.e., dynamic pressures, since the charge arising at the moment the force is applied disappears as a result of leakage according to the exponential law (1)

\[ U_t = U \cdot e^{-\frac{t}{T}} \]

with time constant \(T\), equal to

\[ T = R \cdot C, \]

where

\(R\) is the leakage resistance formed by the surface and volume resistances of the piezoelement and the input resistance of the measuring device;

\(C\) is the capacitance between the faces of the piezoelement (including the input capacitance of the measuring device).

In view of the finite values of the quantities \(R\) and \(C\), there also exists a finite value of the lower, or minimum, frequency \(f\) of the recorded variation of the measured pressure, with \(f\) being determined by condition (1)

\[ f \gg \frac{1}{T}. \]

The use of electrometric measuring amplifiers having high-ohmic input resistance, but also low stability, makes it possible to extend the frequency range of pressure measurement only down to tenths of a hertz, with a considerable decrease in accuracy. The authors have developed a piezoelectric method for measuring mechanical pressure that made it possible to extend the frequency range of measurement into the low-frequency region, including the limiting case when \(f = 0\) (static pressure).

The measuring circuit is shown in Fig. 1. As the sensitive element, a piezoelement (PE) made of piezoceramic material is used.

with two electrode systems formed by one common electrode and two electrodes on the face opposite to it.

An exciting voltage from an electric-oscillation generator (EOG) is applied to one electrode system. Owing to the inverse piezoelectric effect, the alternating electric field applied to the left half of the crystal causes mechanical oscillations of the entire crystal. At the resonant frequency for the given crystal, oscillations of maximum amplitude arise in it; these create an electric charge in the right half of the crystal (direct piezoelectric effect), leading to the appearance of a potential difference on the second electrode system, i.e., the piezoelectric element operates in transformer mode.

Fig. 1. Diagram for implementing the proposed method: EOG—electric-oscillation generator; PE—piezoelectric element; MI—measuring instrument; \(P\)—measured pressure

When the pressure acting on the piezoelectric element is increased (decreased), the amplitude of the oscillations observed on the screen of an oscilloscope connected to the right-hand electrode system decreases (increases). The magnitude of the measured pressure is determined from the change in amplitude. In practice, instead of an oscilloscope, a measuring instrument (MI)—a voltmeter—is connected.

Thus, in the general case, the measured electrical signal is an amplitude-modulated oscillation with a carrier frequency equal to the frequency of the exciting generator or to the resonant frequency of the oscillations of the piezoelectric element, and with an envelope whose shape corresponds to the change over time of the applied pressure, which in the particular case (\(f = 0\)) may also be static.

In Figs. 2–3, graphs are presented of the dependence of the voltage at the output of the piezoelectric element on the static pressure \(P\), obtained in testing piezoelectric elements made of TsTS-19 piezoceramic (lead zirconate titanate). They show that the range of measured pressure increases with an increase in the excitation voltage applied to the piezoelectric element (radiation power) (Fig. 2) and with the volume of the piezoelectric element (Fig. 3).

Fig. 2. Graph of the dependence of the output signal on the measured pressure at different excitation voltages

However, the increase in the range of measured pressure occurs up to a certain value of the excitation voltage, at which saturation of the piezoelectric element sets in. For this piezoelectric element, with a diameter of 28 mm and a thickness of 3 mm (Fig. 2), saturation occurs at \(U_{\mathrm{e}} = 30\ \text{V}\).

The sensitivity of the sensor decreases as the excitation voltage is increased.

At \(U_{\mathrm{в}} = 10\ \mathrm{V}\), the slope of the characteristic increases (Fig. 2), but the pressure-measurement range narrows to \(4\ \mathrm{kgf}\).

At \(U_{\mathrm{в}} = 30\ \mathrm{V}\) (Fig. 2), its sensitivity is considerably lower, but the measurement range expands to \(11\ \mathrm{kgf}\).

Fig. 3. Plot of the dependence of the output signal on the pressure being measured for piezoelements of different volumes

The magnitude of the measurement range is proportional to the volume of the piezoelement (Fig. 3).

At the same excitation voltage (\(30\ \mathrm{V}\)), the pressure-measurement range varies from \(20\ \mathrm{kgf}\) for a piezoelement of diameter \(20\ \mathrm{mm}\) and thickness \(18\ \mathrm{mm}\), to \(8\ \mathrm{kgf}\) for a piezoelement of diameter \(24\ \mathrm{mm}\) and thickness \(3\ \mathrm{mm}\), and to \(4\ \mathrm{kgf}\) for a piezoelement of diameter \(24\ \mathrm{mm}\) and thickness \(1.2\ \mathrm{mm}\).

Conclusions

1. Laboratory tests confirmed the fundamental feasibility of the proposed method for measuring static pressures.

2. The pressure-measurement range and sensitivity can be varied by changing the magnitude of the excitation voltage and the dimensions of the piezoelement.

References

1. D. I. Ageikin, E. I. Kostina, I. N. Kuznetsova, Sensors for Monitoring and Regulation. Moscow, Mashinostroenie Publishing House, 1965.