Revisiting Piezoelectric Sensor Calibration Methods Using Elastodynamic Body Waves

Abstract

The application of absolutely calibrated piezoelectric (PZT) sensors is increasingly used to help interpret the information carried by radiated elastic waves of laboratory/in situs acoustic emissions (AEs) in nondestructive evaluation. In this paper, we present the methodology based on the finite element method (FEM) to characterize PZT sensors. The FEM-based modelling tool is used to numerically compute the true Green’s function between a ball impact source and an array of PZT sensors to map active source to theoretical ground motion. Physical-based boundary conditions are adopted to better constrain the problem of body wave propagation, reflection and transmission in/on the elastic medium. The modelling methodology is first validated against the reference approach (generalized ray theory) and is then extended down to 1 kHz where body wave reflection and transmission along different types of boundaries are explored. We find the Green’s functions calculated using physical-based boundaries have distinct differences between commonly employed idealized boundary conditions, especially around the anti-resonant and resonant frequencies. Unlike traditional methods that use singular ball drops, we find that each ball drop is only partially reliable over specific frequency bands. We demonstrate, by adding spectral constraints, that the individual instrumental responses are accurately cropped and linked together over 1 kHz to 1 MHz after which they overlap with little amplitude shift. This study finds that ball impacts with a broad range of diameters as well as the corresponding valid frequency bandwidth, are necessary to characterize broadband PZT sensors from 1 kHz to 1 MHz.

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

“…We observed a similar deviation in the previous calibration work using the ball drop [ 40 , see Fig. 9b therein].…”

“…Figure 2 a gives a schematic representation of the steel plate (350 mm 350 mm 50 mm) in an extruded aluminium frame. Small rubber pads (30 mm 30 mm 3 mm) are used to isolate the vibrations in the steel plate from the frame [ 40 ]. The material properties of the steel plate that are required to model the wave propagation, are given in Table 1 .…”

“…This simplifies ( 1 ) to The voltage signal measured by the PZT transducers can be viewed using the convolution integral of the displacement field with the instrument response , shown here: The instrument response depends on the position (contact conditions, sensor and preamplifier, cables, digitization, etc.) but also position since the incident angle of the incoming waves affects the instrument response [ 40 ]. Similar to assumptions in the force, the recorded signals on the receivers are only measured in the 3-direction simplify the instrument response to and equation ( 3 ) to Combining ( 2 ) and ( 4 ), we can represent the measured voltage from the force that produced it, for the problem described in Fig.…”

“…This code has been validated with theoretical studies [e.g. 17 , 33 ] and finite element models [ 25 , 37 , 39 , 40 ]. Since we only considered the high-frequency behavior of the body waves induced in the plate (between 100 kHz to 1 MHz), we assumed that the plate is semi-infinite; reflections from the sides of the plate were ignored and only those from the top and bottom surfaces were modeled.…”

“…Therefore, they also suffer from similar problems, such as site (coupling) effects, electronic errors and the influence of the internal components of the seismometer/PZT transducer. Improved calibration methods have been employed in experimental laboratory work [ 4 , 6 , 11 , 23 , 26 , 32 , 34 , 37 , 40 ] to give a better understanding for modeling of the source that produced the elastic waves.…”