A Methodology for Reconstructing Source Properties of a Conical Piezoelectric Actuator Using Array-Based Methods

Abstract

We investigated the force produced by a conical piezoelectric (PZT, lead zirconate titanate) transducer actuated by high voltage pulses (HVP) in contact with a steel transfer plate. Using elastic wave propagation theory in a semi-infinite plate, we aimed to quantify the magnitude and estimate the shape of the force-time function via the body waves produced in the transfer plate using the displacement field recorded on an array of 20 absolutely calibrated PZT receivers. We first calibrated the receiver array using glass capillary fracture. We proceeded to use a conical PZT transducer to actively produce a source at the origin, allowing us to study the displacement field produced on the now calibrated PZT receiver array. We studied two types of HVP: An impulsive and step source. The calibrated receiver array was used to estimate the general shape of the force-time functions for each type of HVP. From our hypothesized force-time functions we were able to estimate the peak force produced by the PZT actuator: The impulsive source generated a force of $f_{\mathrm{peak}}=2.90\pm 0.42$ N and the step source generated $f_{\mathrm{peak}}=1.79\pm 0.30$ N, respectively, for a peak applied voltage of 273 V. This translates to an applied force of $\sim$ 0.011 N/V and 0.007 N/V for the impulse and step force-time functions, respectively, which is similar to estimates found in the literature for other conical transducers in contact with metallic transfer media. This measurement was verified directly by independent measurements of the peak force $f_{\mathrm{peak}}$ using a dynamic force transducer. We found that our methodology correctly estimated the magnitude of the force but is limited to transducers with incident angles $\theta <$ 53 ${}^{\circ }$ . Beyond this angle, overestimates of the force were observed due to the lack of body wave energy produced by the source. These results allow us to quantitatively determine the forces produced by active PZT techniques using only the measurement of the displacement field captured on a calibrated conical PZT array. Quantitative understanding of active PZT sources additionally constrains the transfer functions approach, which is commonly used in the non-destructive testing of materials and in other fields, such as rock physics and laboratory seismology.

Keywords: Absolute calibration; Force–time function; Piezoelectric transducers; Spectral deconvolution; Waveform modeling.