以有限元素法模擬並聯陣列式壓電振動子之機電行為

Abstract

本論文提出一個「等效阻抗」想法為基礎之分析模型，用以研究壓電能量擷取系統。首先，將非線性整流電路，諸如標準整流電路、同步開關能量擷取介面電路(Parallel Synchronized Switch Harvesting in Inductor、Series Synchronized Switch Harvesting in Inductor)，將其替換成相對應之等效負載阻抗。接下來，利用「阻抗匹配」的觀念，來獲得系統最佳功率輸出之條件，其結果顯示，當機械阻尼比等於電致阻尼比時，壓電能量擷取系統會有最佳的功率輸出。此外，對於SSHI電路而言，必會存在一個最佳等效阻抗使得弱力電耦合形式材料也會有最佳的功率輸出。 將「等效阻抗」分析模型運用於並聯陣列式壓電振動子搭配不同介面電路之分析，而我們所提出「等效負載阻抗」模型成功解決現有商用有限元素軟體，對於壓電元件搭配非線性整流電路之功率輸出時，數值計算上的困難。此外，也提供了對於系統參數差異之壓電振動子的分析方法。考慮並聯陣列式的系統，其中三個壓電振動子彼此系統參數有所差異，當為強力電耦合型式材料，可以很明顯發現標準電路搭配一個較大的最佳阻抗時，其功率的衰減併不明顯；然而，對於中、弱力電耦合型式材料，就會發現其功率輸出會有很明顯的衰減現象。接著，對於Parallel-SSHI電路而言，對功率輸出有著明顯的改善，當為中力電耦合型式材料，Parallel-SSHI電路呈現著寬頻之效果；對於弱力電耦合型式材料則呈現功率提升之效果。 最後，我們提出一個修改的方式，由最初3D有限元素模擬中所獲得之功率輸出，可由2D模組(Plane-stress、Plane-strain)之模擬結果的二次方來近似，其呈現令人滿意之結果。

The present thesis proposes a model based on the idea of equivalent impedance to study piezoelectric energy harvesting. First, several nonlinear interface circuits, including the standard and parallel-/series-SSHI (Synchronized Switch Harvesting on Inductor) electronics, are replaced by several equivalent load impedances. Next, using the concept of impedance matching, the optimal power and the conditions to achieve it are derived. It is shown that the optimal condition refers to the case that electrically induced damping ratio is equal to the mechanical damping ratio. In addition, there always exists an optimal load such that the optimal condition is achieved for an SSHI system with weakly coupled electromechanical coupling. The model of equivalent load impedance is applied to the case of multiple piezoelectric oscillators connected in parallel and attached to distinct interface circuits. As the present commercial finite element softwares are unable to simulate the electrical response of power generators connected to nonlinear interface circuits, our proposed approach successfully resolves such a numerical difficulty. In addition, the parametric study provides a way for analyzing the system response under various imperfect conditions. To see it, we consider a model problem consisting of three oscillators with different system parameters. For a system with strong electromechanical coupling, it is remarkably found that the drop in power is not significant for the standard system operated at the large optimal load. However, there is a significant drop in harvested power for the medium and weak electromechanical coupling systems. However, the parallel-SSHI system exhibits a significant improvement in bandwidth for the case of medium electromechanical coupling and boots harvested power significantly for the case of weak electromechanical coupling. Finally, we present a modification such that harvested power obtained originally from a 3D finite element simulation is approximated by quadratic interpolation of results obtained by 2D plane-stress and plane-strain simulations. It shows satisfactory results.