Self-heating phenomenon of piezoelectric elements excited by a tone-burst electric field

Highlights

• A self-heating model of a piezoelectric disc element excited by a tone-burst electric field was proposed.

• Analytical solution of the model was obtained by Laplace transform method.

• High-field dielectric loss properties of piezoelectric samples can be obtained by multiparameter fitting to the theoretical model.

• We found that the strategy of reducing heat dissipation by using different pulse repetition frequency is not feasible if the duty cycle of the electric field is a constant.

Abstract

Tone-burst excitation is often used for ultrasonic transducers of specific operation modes or for overcoming transducer overheating problems associated with continuous wave (CW) excitation. In this study, a theoretical model for the self-heating phenomenon of a piezoelectric disc element is established to estimate the temperature rise induced by a tone-burst electric field. An analytical solution for the temperature rise of the piezoelectric element is obtained by using Laplace transform method. Numerical simulations and experimental measurements are performed to investigate the influence of different excitation parameters on the temperature rise. By comparing the experimental results with the simulation results, the temperature-rise difference between tone-burst and CW excitations is quantified, and the validity of the theoretical model is verified. Furthermore, a multiparameter estimation method is proposed for the heat convection coefficient and dielectric properties under high-field operating conditions. These results are useful in both optimization of heat dissipation performance and characterization of high-power ultrasonic transducers.

Introduction

In recent years, high power ultrasound field is growing fast, such as ultrasonic cleaning [1] and ultrasonic welding [2], so that the demand for high-power piezoelectric transducers has been steadily increasing [3]. However, with the increase of electric power, the heat generation within piezoelectric elements will increase accordingly due to the intrinsic electrical and mechanical losses of piezoelectric materials [4], [5], [6]. This self-heating phenomenon can be detrimental to device performance. If the structure of a power ultrasonic device is not designed properly and the heat energy cannot be efficiently dissipated, the temperature of the piezoelectric components will continue to rise, leading to performance degradation or even causing device failure in severe cases [7]. In the field of high power ultrasonic medical applications, such as high intensity focused ultrasound (HIFU) therapy, the self-heating of piezoelectric ceramic components under high-field may cause ultrasonic transducer failure due to severe temperature rise [8]. In particular, ultrasonic transducers operating under high-power for an extended period of time, such as transcranial probes, pose alarming safety issues due to high temperature [9]. Therefore, the study of self-heating mechanism of piezoelectric ceramic components is very important for industrial power ultrasound and medical therapeutic ultrasound [10], [11].

In the literature, there are considerable amount of theoretical and experimental investigations on the self-heating phenomenon of piezoelectric elements or devices under a continuous sinusoidal wave (CW) excitation. R. Ramesh et al. [12] studied the self-heating phenomenon of piezoelectric ceramic polymer composites under low frequency resonance and non-resonant CW excitation and discussed its heating mechanism. M.S. Senousy et al. [13] studied the self-heating in soft lead zirconate titanate (PZT) stack actuator at different dynamic operating conditions relevant to the fuel injection process. Z. Wu et al. [14] investigated the temperature rise phenomenon and loss characteristics of multilayer piezoelectric ultrasonic transducers with adhesive layers, in which the effect of temperature rise to material properties of the transducer elements was considered. Finite element methods were also utilized to analyze the self-heating effect for sonar transmitters [15] and Langevin piezoelectric transducers devices [16]. M. Stewart et al. [7] summarized current research status of self-heating simulations and measurements of piezoelectric materials and devices and pointed out that most investigations on the self-heating phenomenon of piezoelectric materials and devices focused on CW excitation. Up to date, there is little research done on non-CW excitation cases.

In reality, due to the necessity of a specific operation mode, or to overcome overheating problems associated with CW operation, non-CW excitations of piezoelectric devices are often used. A diesel injector valve is an example of pulse excitation, in which the duty cycle is very small but its working power is very high. By contrast, in order to suppress the temperature rise, the operation of a resonant-driving high-power ultrasonic cleaning bath may be limited to a duty cycle below 10%. For color doppler applications, medical ultrasonic transducers are often driven by high-frequency pulses with a certain pulse number rather than CW driving field [17]. In addition, in the accelerated life test of medical ultrasound equipment, the pulse repetition rate used is usually high in order to speed up the test efficiency, which often cause obvious heat generation [18]. Therefore, the study of self-heating under burst excitation is very important not only for the predication of the temperature rise of ultrasonic elements but also for the characterization of high-power properties of piezoelectric ceramics. H. N. Shekhani et.al. [19] suggested a unique method for characterizing high-field mechanical loss in piezoelectric materials using temperature and vibration measurements. However, under high-power conditions, significant heat can be generated, causing a large temperature rise in the piezoelectric elements. As a result, it is difficult to separate the effects of temperature rise and property changes under the CW driving field. In contrast, the advantage of the burst driving method is that the temperature rise is relatively low so that the temperature dependence of material properties can be ignored, allowing us to more accurately evaluate of the properties of piezoelectric elements under a high-power electric field. In this work, we have carried out theoretical and experimental studies on the self-heating phenomenon of piezoelectric elements excited by a tone-burst electric field, which can give useful guidance for many practical applications.

A simplified theoretical model of self-heating is proposed to evaluate the temperature rise of a piezoelectric ceramic disc under the excitation of a single-frequency pulse train (sine-wave tone-burst) electrical field. The method of Laplace transform was used to solve the transient heat conduction equation, and the influence of different excitation parameters on the temperature rise were analyzed by numerical simulations. Moreover, a self-heating measurement system excited by a tone-burst electric field was designed and built, and the temperature rise characteristics under different experimental conditions were measured and analyzed. The validity of the analytical model was verified by the comparison between simulation results and experimental results.