An acoustic/thermal model for self-heating in PMN sonar projectors

Dielectric hysteresis and a strong material temperature dependence uniquely couple the acoustic output and temperature of a sonar projector driven by electrostrictive Pb(Mg1/3, Nb2/3)O3 (PMN). Both the source level and the source of self-heating, i.e., dielectric hysteresis, dramatically decrease as the PMN driver heats. The final temperature delineates outstanding PMN transducers from mediocre PMN transducers, so accurate acoustic performance prediction requires accurate transducer temperature prediction. This study examined this self-heating phenomenon by combining an electro-acoustics model for a PMN flextensional transducer with a thermal finite element model. The sonar model calculated the source level and heat generation rate for the PMN driver as a function of temperature. This computed source level varied 12 dB over a 75 degrees C temperature range solely due to the temperature dependent ceramic. The heat transfer model used the computed heat rate to predict the transducer's transient thermal response. The results clearly demonstrate that the transducer reached a steady-state equilibrium temperature, where the heat generated by the PMN driver balanced the heat dissipated. While the transducer model predicted a significant temperature rise, the corresponding acoustic output still surpassed the output of an equivalent Pb(Zr,Ti)O3 (PZT) transducer by 8 dB. Good agreement with experiments made on a PMN flextensional transducer validated the model.