旋轉磁激振位置最佳化之壓電混合共振能源擷取器

Abstract

本研究為探討壓電振子上磁激振位置之最佳化，進行理論分析與實驗驗證。從文獻回顧可知，以升頻轉換之特性，即當壓電振子之共振頻率 ω_n 與旋轉磁力之驅動頻率 ω_d 比值為正整數倍時，能以當前磁鐵之較低驅動頻率激振激發出壓電振子之較高自然共振頻率。另外透過雙點磁激振之特性、壓電振子之模態分析、以及對週期性磁外力進行傅立葉展開，發展出激發第一與第二模態混合之壓電振子理論。本研究以此理論為基礎，分析不同磁激振位置對發電功率之影響，進行理論與實驗驗證。 研究結果顯示，本研究發展之模型，可以分析出不同磁激振位置之輸出電壓，因此可以根據使用條件選取最佳的磁鐵位置。以本實驗式樣為例，第二顆磁鐵擺放於壓電振子全長之0.35~0.51比值的位置會有最佳發電效率。此外，根據實驗現象，當第二顆磁鐵擺放過於外側位置，使得等效第一模態力變為負值時，會導致阻尼比變大，造成電壓驟降。因此對等效模態力量與第二顆磁鐵位置進行解析，並透過回歸的方式得到等效模態力量與等效阻尼比之間的關係，為磁激振位置設計提供依據，能根據不同情況進行設計，增加其應用層面。

The thesis studies the optimal locations of placing magnets on a piezoelectric harvester beam under rotary magnetic plucking. Both the theoretical analysis and experimental validation are performed here. The operation principle is based on the frequency up-conversion, i.e., the high resonant frequency of the oscillator is induced by the low frequency of rotating environment whenever their frequency ratio is some multiples of integers. In addition, the first and second resonant modes of the mixed type can be induced simultaneously under the framework of two-point magnetic plucking. The analysis behind this phenomenon can be achieved by the standard modal analysis and Fourier expansions of the magnetic forces acted on two different locations of the beam. As a result, the effect of magnetic locations on harvested power can be analyzed with experimental justification. The result shows that the harvested power is optimized if the second magnet is placed at the ratio of 0.35~0.51 of the full beam length. Further, the analysis reveals that the sign of the modal force of the first mode is changed from being positive to negative when the second magnet is removed close to the beam tip. The experiment observes the increase of mechanical damping ratio, giving rise to the reduction of piezoelectric voltage. We propose to carry out the regression analysis by exploiting the relation between the modal force and mechanical damping. This provides a great advantage in design when various factors are under considerations.