臺灣博碩士論文加值系統

在振動能源轉換成電能的研究領域中，壓電振動獵能器是很常被討論及研究的系統，藉由壓電材料結合懸臂樑並加入磁鐵提供磁力產生非線性振動的行為，依擺放磁鐵的個數可以形成雙穩態或三穩態的非線性獵能系統，來放大振動機械能；再利用壓電片的正壓電效應將機械能轉換成電能，達到回收環境振動能源的效用，由於環境中的振動頻寬是隨機且大範圍的，所以在設計壓電振動獵能器時能讓系統的有效頻寬加大並讓系統響應較容易出現snap-through現象來提高發電效率是主要的目標。
此篇論文之研究將動態系統方程簡化成Duffing Equation，利用磁化電流法計算非線性磁力，並利用材料力學理論計算系統剛性，透過積分後計算出壓電獵能器系統的位能位移曲線，從繪製的位能位移圖中，計算出穩定與不穩定平衡點的距離、位能井的勢壘深度，再經由基因遺傳演算法做最佳化運算，找出磁鐵間最佳的水平距離、垂直距離及不對稱的偏移距離等參數。本研究結果顯示透過結構參數最佳化以及實驗驗證，當壓電獵能器使用最佳化結果的結構參數後，能在較低的頻率進入snap-through行為，且在較高的頻率離開snap-through現象，提升了有效的頻寬，且提升壓電獵能器的發電效率。

In the research of converting the vibration energy into electrical energy, the piezoelectric vibration energy harvester has been discussed and studied. The cantilever beam with piezoelectric material combines the magnetic force to produce a nonlinear vibration behavior. According to the number of magnets, the energy harvesting system can form a nonlinear bistable or tristablestructure to enlarge the mechanical vibration energy. The positive piezoelectric effect is used to convert the mechanical energy into the electrical energy achieving the recycling of environmental vibration energy. Since the environmental vibration frequency may be random and the bandwidth may be large, the main objective is to increase the system effective bandwidth and to make the system more prone to the snap-through state, such that the efficiency of electric energy harvesting can be enhanced.
The research in this paper simplifies the system dynamic equation into the Duffing Equation. The magnetizing current method is employed to determine the nonlinear magnetic force. The system stiffness is estimated based on the material mechanics theory. The system’s curve of displacement-potential energy is calculated by integrating the displacement-force relationship. From the plot of displacement-potential energy, all the distance between the stable and unstable equilibrium points and the barrier depth of the potential energy well are calculated. The optimal structural parameters, including the horizontal and vertical distances between the magnets and asymmetric offset, are found through the genetic algorithm of optimization. With the optimized structural parameters, the experimental verification shows that the piezoelectric energy harvesting system can begin having the snap-through behavior at lower frequencies and stop the state at higher frequencies. It demonstrates that the efficiency of the piezoelectric vibration energy harvester can be enhanced by increasing the effective bandwidth.

摘要 i
Abstract iii
目錄 v
圖目錄 vii
表目錄 xiv
第一章 前言 1
1.1 研究動機 1
1.2 研究目標 1
1.3 文獻回顧 2
1.3.1 壓電獵能文獻回顧 2
1.3.2 電磁感應線圈文獻回顧 4
1.3.3 電路設計文獻回顧 5
1.4 論文大綱 6
第二章 理論 7
2.1 Duffing equation 7
2.2 系統模型 9
2.3 壓電效應 11
2.4 磁力模型 14
2.5 壓電懸臂樑模型 16
2.6 複合懸臂樑理論 17
2.6.1 等效質量meq 17
2.6.2 系統阻尼c 19
2.6.3 等效剛性keq 19
2.6.4 位移轉換常數 22
2.7 實驗數據訊號處理與分析 23
2.7.1 經驗模態分解法(Empirical Mode Decomposition) 24
2.7.2 訊號處理流程 25
2.8 遺傳演算法 27
第三章 實驗設備與架構 28
3.1 實驗流程 28
3.2 實驗架設 30
3.3 實驗設備及平台 31
第四章 實驗結果與討論 34
4.1 磁鐵間距參數之最佳化 34
4.2 實驗一:對稱之磁鐵間距參數對於獵能系統頻率響應以及獵能效果之影響 39
4.3 實驗二:探討對稱與非對稱磁鐵間距對三穩態獵能系統的影響 72
第五章 結論與未來展望 92
5.1 結論 92
5.2 未來展望 94
參考資料 95
附錄A-壓電主結構三視圖 97

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