Self-heat generation in piezoelectric stack actuators used in fuel injectors

Multilayer piezoelectric actuators are used in fuel injectors due to their quick response, high efficiency, accuracy, low power consumption, and excellent repeatability. Experimental results for soft lead zirconate titanate (PZT) stack actuators have shown that a significant amount of heat is generated when they are driven under high frequency and/or high electric-field magnitudes, both of which occur in fuel injectors. Self-heat generation in these actuators, mainly caused by losses, can significantly affect their reliability and piezoelectric properties, and may also limit their application. Other studies have demonstrated that at large unipolar electric-field magnitudes, displacement-electric-field loss (displacement hysteresis) shows a direct relation with polarization-electric-field loss (dielectric hysteresis). In this paper, a simplified analytical self-heating model is presented. The model directly relates self-heating in multilayer piezoelectric actuators to displacement-electric-field loss (displacement hysteresis). The model developed is based on the first law of thermodynamics, and accounts for different parameters such as geometry, magnitude and frequency of applied electric field, duty cycle percentage, fuel type, and environmental properties. The model shows reasonable agreement with experimental results at low and high electric-field magnitudes.