旋轉式週期性磁力應用於壓電振能擷取之研究

Abstract

本研究旨為探討壓電振子受到旋轉磁鐵激振下之自主發電研究，並發展理論模型及其實驗驗證。由文獻回顧可知，壓電振能擷取研究幾乎都集中在單軸線性激盪壓電振子發電，而在旋轉環境下的振能擷取研究則較少。而本論文則利用磁鐵旋轉給予貼在壓電懸臂樑端點的另一顆磁鐵斥力，產生類似週期性脈衝波形的激振力，而此週期磁力經過傅立葉展開可得到多項等同於垂直式之線性激振力，能夠在旋轉轉速為壓電振子共振頻除上整數倍時，激發壓電振子在第一模態下的共振。另在實驗部分，本文開發適用於本研究之LabView 實驗介面，並且設計出實驗架構及其實驗流程，成功做出AC交流輸出以及搭配標準介面電路的DC 直流輸出之實驗，使實驗與理論可以相互驗證。結果顯示，(1)兩磁鐵的間距較小時雖然磁力係數會變大，但強耦合壓電振子會出現非線性現象，而弱耦合壓電振子則否；(2)實驗結果顯示有高達數十多項磁力係數可維持一常數，故可在一固定轉速區間均有功率輸出，但之後便會明顯開始下降；(3)發現採用阻尼比較大之弱力電耦合壓電振子，並搭配較小之磁鐵間距，可以得到功率波形重疊之掃頻圖；(4)最後實驗結果顯示，在5-14Hz之旋轉轉速下，壓電振子之平均直流功率輸出可達到1mW之高。

The thesis aims to develop a theoretical framework together with experimental validation to investigate the piezoelectric energy harvesting under rotational environment. Much work has been done on the study of vibrational energy harvesting under translational excitation along certain directions. However, little work has been done for rotational energy harvesting. Instead, the present thesis studies the energy harvesting from a cantilever piezoelectric bimorph attached to a magnet on its tip which is excited by a rotational movement of another magnet. As a result, such an excitation is similar to the case of periodic impulsive force. In addition, The Fourier expansion of such an impulsive force indicates that the cantilever bimorph is able to be resonantly excited at its first flexural mode as long as the rotational frequency is equal to the integer fraction of the natural frequency of the oscillator. In addition, an experimental setup with LabView interface is developed for validating the proposed model. Both AC and DC harvested power are recorded and found in good agreement with theoretical predictions. The result shows that the driving force increases as the distance between two magnets decreases. However, under this circumstance, the frequency response shows nonlinearity for strongly coupled oscillators while the response remains linear for weakly coupled oscillators. Second, the there is a range of rotational speeds such that power remains accumulated within this period. It is attributed to the non-vanishing Fourier coefficients of the magnetic impulsive force up to tens of terms in its Fourier expansion. But the subsequent coefficients drop to zero when the rotation speed is small. Third, there are a number of peaks of harvested power located at the integer fraction of the natural frequency of the oscillator in the power-frequency plot. But the interactions between two adjacent power curves remain sufficiently high in a wide range of rotational speeds for the case of weakly coupled oscillators. Finally, the experiment shows that the average harvested DC power can be up to 1mW with the rotational frequency range between 5-14Hz.