有限元素法於壓電變壓器的熱壓電分析

Abstract

在本文中，我們發展一套三維有限元素法的壓電分析程式NTUPZE-T來分析壓電變壓器。這套軟體包含可以分析壓電元件的熱效應。為了要得到壓電元件的溫度分布，我們計算了因為阻尼效應所產生的能量損耗，將這些能量損耗當作熱源帶入熱傳方程式用來計算壓電元件的溫度分布。壓電材料參數通常跟溫度有關。溫度變化常常會影響壓電材料的參數，所以在本研究中需要一個自我一致(Self-consistent)的熱與壓電分析程序。鬆弛演算法(Relaxation algorithm)在本研究中被使用來偶合熱分析與壓電分析。經過計算後可得在不同頻率不同外加負載下的壓電變壓器升壓比、相位差、效率比也和溫度分布一樣可以由這套軟體可以求得。在NTUPZE-T中，我們採用20個節點的三次元有限元素(20-node brick element)來建立模型。使用NTUPZE-T，我們分析了Rosen-modal-type壓電變壓器，包含不同負載下的最高升壓比、效率、共振頻、升溫，並且與實驗進行比較。

In this work, we develop a 3-D FEM solver, NTUPZE-T for analyzing piezoelectric transformers. This solver is capable of estimating the device thermal effects. In order to estimate the device temperature distribution when the device operates, we calculate the dissipation of energy based on the internal damping effects. The dissipated energy is considered as the heat source of the heat transfer equation for calculating the temperature distribution of a device. Material constants of piezoelectric materials are usually dependent on temperature. Therefore, a self-consistent thermo-piezoelectric analysis procedure is proposed. In this work, we employ the relaxation algorithm for self-consistently computing the solutions in the piezoelectric domain and the thermal domain. Then the voltage gains, phase difference, efficiencies, as well as the temperature distribution of the device at difference frequencies and loadings can be obtained by the solver. The solver employs 20-node brick-element formulation for the discretization. We analyzed Rosen -modal-type piezoelectric transformer. The simulated results of voltage gains, efficiencies, resonant frequencies, and temperature increase of the device were also verified with the measured results.