Analyses of the temperature field in a bar-shaped piezoelectric transformer operating in longitudinal vibration mode

In this study, a theoretical model of the steady-state temperature field in a bar-shaped piezoelectric transformer operating in longitudinal vibration mode is developed, and the characteristics of the temperature field are analyzed numerically. Being different from previous work, the effects of the stress distribution and the relative positions of input and output parts on the internal loss distribution are taken into account in this model. Using this model, the temperature rise and its distribution are calculated, and the effects of ambient temperature, internal loss distribution, size, heat dissipation coefficient, and heat conductivity of the transformer on the temperature rise are estimated. The calculated temperature rise and its distribution agree quite well with the experimental data. It is found that the allowable output power of the transformer should be reduced markedly when the ambient temperature increases to maintain a reasonable working temperature for the piezoelectric material of the transformer. It also is found that decreasing wavelength, making internal loss distribution uniform, and increasing the ratio of perimeter to area of the cross section (for example, decreasing the cross-sectional area and using a thin plate structure), decrease the temperature rise for a given internal loss per unit volume. Furthermore, it is revealed that the heat dissipation coefficient has a remarkable effect on the temperature rise at a large internal loss, and the variation in the heat conductivity of the piezoelectric material has little effect on the temperature rise.