不同力電耦合強度壓電振子應用於能量擷取之研究

Abstract

本論文旨在設計與探討不同力電耦合強度之壓電振子應用於能量擷取，並提供一些方法可用於實驗量測壓電振子應用於能量擷取之系統等效材料參數。壓電振動懸臂樑數學模型以能量法為基礎，採用模態函數或均佈力負載兩種形狀函數來簡化壓電振子設計，亦可引入等效電路模型，將壓電振動懸臂樑數學模型比擬成RLC電路。並採用雷利阻尼的概念來假設振子的等效機械阻尼係數，最後定義壓電振子之力電耦合強度為無因次化力電耦合係數除以無因次化機械阻尼係數。 本論文第一部分是比較由不同系統等效參數之估計曲線的差異，實驗結果顯示由三種方法用於實驗所算出的估計值曲線，估計曲線在最佳阻抗下的功率誤差極小，在遠離最佳阻抗的電阻下之功率誤差則加大，但無論在何阻抗下，估計值曲線的趨勢皆與實驗曲線的趨勢吻合。其中，等效電路法較能量法好的原因是可在材料尺寸與參數未知的情況下作量測。 本論文第二部分是研究壓電層長度比對於力電耦合強度的影響，由理論、模擬、實驗得到以下結論，實驗結果與理論結果趨勢吻合，因此理論結果是可以當作預測壓電振子之物理行為的依據。分析發現強力電耦合振子與弱力電耦合振子有相似的物理行為，第一，皆為當壓電層長度比約為0.5時，力電耦合強度最強。第二，單位質量的發電功率並非隨著總質量的增加而增加，而是當壓電層長度比約為0.3時，單位質量的發電功率最小。有趣的是，單位成本的發電功率約在與前者相同的壓電層長度比下有最小值。第三，實驗結果顯示不同壓電層長度比之雷利阻尼的係數皆在同次序且可趨近定值，且強力電耦合振子的雷利阻尼係數小於弱力電耦合振子的雷利阻尼係數。

The goal of the present thesis is to design the piezoelectric energy harvesters with different magnitudes of electromechanical coupling. In addition, it also proposes several methods for measuring the effective system parameters of an energy harvester. The methodology is based on the energy approach where the shape function is chosen either by the standard modal analysis or by the method of uniform load. Besides, the effective system parameters can also be determined based on the equivalent RLC circuit model. The proposed criterion for measuring the strength of electromechanical coupling of an energy harvester is defined by the ratio of electromechanical coupling to the mechanical damping ratio. The damping coefficient is assumed to the type of Rayleigh damping here. The first part of the present thesis is to make comparisons among the different proposed estimates of effective parameters. It is found the estimation of harvested power frequency response measured at the optimal load agrees quite well with experimental observations. However, the disagreement increases in the case of attaching larger electric loads. It is also found the estimation based on the equivalent circuit model shows the least error compared to other methods. The second part is to study the effect of different lengths of piezoelectric layers on the magnitudes of electromechanical coupling. It is found both analytic estimates and experimental observations exhibit the similar trends. Hence, our proposed estimates are capable of performance evaluations. The first observation from our analysis is that the behavior of the case of strong electromechanical coupling is similar to that of the weak electromechanical coupling. The second result is the strongest coupling is achieved when the ratio of the length of the piezoelectric layer to that of the substrate is about 0.5.The third observation is the harvested power per unit mass is not monotone increasing as the increase of piezoelectric layer. Instead, it is minimized when the ratio of the piezoelectric layer to the substrate is around 0.3. Interestingly, the harvested power per unit price is also minimized at around the similar range. Finally, the experimental observations confirm that the coefficient of Rayleigh damping is approximate to be a constant in spite of different lengths of piezoelectric layers. In addition, it is observed the coefficient of Rayleigh damping in the case of weak coupling is larger than that in the case of strong coupling.