壓電能量擷取系統之分析研究

Abstract

本論文主要從事壓電能量擷取系統之研究與開發，利用壓電懸臂梁將外界振動能量轉化為電能並且儲存。模型之建立則結合壓電力學與電路概念，探討壓電振動子和外部電路之力電耦合行為，並找出最佳化力電耦合機制及介面。 一般文獻在描述壓電振動行為和外部電路之關係時，主要是將壓電振動子簡化成一電流源和電容並聯之簡易模型，然而此方法卻忽略了可能有的力電耦合效應；本論文則應用力平衡原理結合壓電統御方程式推導出一包含壓電效應之偏微分方程式，並藉由模態近似得到一完整之壓電力電耦合統御方程式，再配合商用軟體做完整數值模擬；除此之外，本論文亦用簡易模型推導出全壓電能量擷取系統穩態解，並配合模擬和實驗結果一同比較分析。 實驗部分則利用阻抗分析儀量得統御方程式之各項係數，並連接各種不同的外部電路，和理論模擬比較之後可歸納出：面對力電耦合性質強的材料，完整模型比簡易模型有更高的準確性並解釋了之前用簡易模型所不能解釋的非理想特性。針對於力電耦合性質弱的材料，不論是簡易模型或是穩態解均和完整模型有著相當高的吻合性。

The thesis is to study the development of piezoelectric power harvesting system. The idea is to transfer the vibrating energy of a piezoelectric cantilever beam into the electric energy which can be stored using a series of harvesting circuits. To do it, we develop a harvesting model based on the transformation of the electromechanical coupling energy and use it to find out the key parameters for the optimal design. The conventional model for piezoelectric power harvesting in literature is to replace the piezoelectric vibrating element with a current source in parallel with its internal electrode capacitance. Such a simplification is questionable since the piezoelectric coupling effect is neglected. On the other hand, we develop a model in this thesis accounting for such coupling effect. We use the technique of eigen-function expansion to derive the governing equations of the piezoelectric vibrator. The whole system is not solvable until the external circuit conditions are included into the vibration equations. In addition, we derive a series of analytic solutions of the model equations and use them to predict the performance of the whole harvesting system. We also design a series of experiment to validate the harvesting model: the vibrator is connected with several different external loads such as resistance, diodes-capacitance and diodes-capacitance-resistance. Experimental results show that the electromechanical coupling effect has to be taken into account for piezoelectric materials which have large coupling coefficient. The conventional model is suitable only for materials with small piezoelectric coupling coefficient. Finally, we conclude with discussions on the several future directions.