Impedance method for determining the mounted resonant frequency of piezoelectric sensors

Abstract

We discuss reasons j'br determining the mounted resonant Aq'equencv of piezoelectric sensors by monitoring the frequency dependence of the electrical impedance of the sensors. We present data for experimental verification of the method.The mounted resonant frequency of a vibration monitoring transducer determines one of the limits of the working frequency range. A procedure using an electrodynamic or piezoelectric vibration tester is used to determine it as a required metrological parameter [ 1 ]. For a mounted resonant frequency higher than 8-i 0 kHz, the only suitable commercial vibration tester is the 4290 tester from Bruel & Kjaer with frequency range up to 50 kHz, maximum vibrational acceleration 1 m/sec 2, and permissible load up to 30 g. An adapter is required to test sensors not having a hole under the M5 stud; in this case the mounted resonant frequency changes, since the sensor together with the adapter is a mechanical system with different parmneters. All this limits the capabilities of this technique. Other devices, such as piezoelectric excitation sources or devices with shock excitation of damping vibrations, also have their disadvantages.In this comaection, we should note one more method suitable for the piezoelectric sensors which are part of most high-frequency devices for measuring mechanical quantities. This method is based on the reversibility of the piezoelectric effect: the electrical impedance of the transducer is a function of its mechanical state, abruptly changing at resonance as a function of frequency.This method is commonly accepted for testing piezoelectric resonators and determining the properties of piezocermnic materials [2]. The test object is included as a coupling element in a resistive four-terminal network powered by a generator with the required frequency range; the frequencies are determined at which the output voltage of the four-terminal network has an extremum, and the maximum corresponds to the resonant frequency. This technique is not effective when used with piezoelectric sensors, since because the mechanical Q of the sensor is small compared with the resonators, the resonant change in the impedance is also small and has a weak effect on the output signal of the tour-terminal network. But if the sensor is included in an ann of a capacitive bridge mad the latter is balanced at a frequency lower than the expected mounted resonant frequency, where the impedance of the sensor does not have any distinctive features, then the desired frequency can be clearly detected. Its value may be read from the maximum of the output signal of the bridge or from the phase shift of the latter relative to the bridge supply voltage as in [ 1]. The readings from both methods practically coincide.In Fig. 1, we show the results obtained when testing the impedance method on Bruel & Kjaer 4370 and 4384 accelerometers with certificate values for the mounted resonant frequency of respectively 17 kHz and 42 kHz. The lines of the spectrum belonging to the different accelerometers ai'e shown on the s...