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研究生: 鐘培嘉
Chung, Pei-Chia
論文名稱: 應用於低轉速旋轉機構之壓電獵能器設計、分析與量測
Design, analysis and measurement of piezoelectric energy harvester for low-velocity rotational mechanism
指導教授: 陳重德
Chen, Chung-De
學位類別: 碩士
Master
系所名稱: 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年: 2023
畢業學年度: 111
語文別: 中文
論文頁數: 73
中文關鍵詞: 壓電獵能器振動非線性運動低轉速獵能磁力
外文關鍵詞: PEH, vibration, nonlinear motion, low-rotational energy harvester, magnetic force
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  • 本研究提出一個應用於低轉速旋轉機構之壓電獵能器之設計、分析、製作與量測,該獵能器包含一個偏心旋轉件、一個壓電樑以及兩個分別固定於壓電樑末端及偏心旋轉件上之磁鐵。獵能器之工作原理為旋轉機構轉動後帶動偏心旋轉件運動使其磁鐵靠近壓電樑磁鐵,並以非線性磁力激振壓電樑,使其產生暫態振動,並透過壓電效應將其機械能轉換成電能。
    為探查獵能器之運動狀態與發電性能,本研究以理論建構分析模型,並以實作及實驗平台量測。在理論分析部分,以能量法建構分析模型。首先以點磁鐵模型推導磁位能方程式,並結合偏心旋轉件之重力位能、動能代入拉格朗日方程,推導偏心旋轉件之運動方程式。此外以能量法推導壓電樑之分析模型,並以瑞利-里茲法將壓電樑等效成受磁力作用之一維自由度振動系統。由本研究所發展之模型,偏心旋轉件之運動可透過磁力影響壓電樑之振動位移。為簡化模型複雜度,假設壓電樑之振動位移很小,使其無法影響磁力大小,亦即壓電樑之振動狀態無法影響偏心旋轉件之運動。因此本研究所推導為單向耦合模型。
    在獵能器量測部分,使用高速攝影機量測偏心旋轉件之位置對時間之關係,將偏心旋轉件之運動模式分為轉動主導運動(revolution dominant motion)、擺動運動(swing motion)以及轉動/擺動混合運動(hybrid motion)三類。根據分析與量測比較結果,於轉動主導運動以擺動運動中,分析結果能夠準確的預測其行為。至於混合運動,因其行為屬於高度非線性運動,初始條件對分析結果相當敏感,亦即有混沌之現象發生,分析模型在短時間區間內雖可準確預測運動模式,但在較長時間尺度下,較難預測其行為。本研究亦探討偏心旋轉件於擺動運動達到穩態所需時間,並以此時間做為平均功率之計算依據。
    為使獵能器之功率輸出達到最佳化,本研究探討不同外接阻抗對平均功率的影響,結果顯示外接電阻為180kΩ時系統,最佳功率輸出為0.1 mW。本研究亦以實驗方式量測獵能器在不同特徵長度下、於不同轉速之平均功率輸出,並與分析數據比較。結果顯示,壓電獵能器於擺動運動時有較穩定且寬頻之能量輸出。最後本研究以分析模型模擬應用於風力發電機之可行性,結果顯示,由於風力發電機之葉片半徑遠大於實驗室設備,雖轉速極低,但仍可提供偏心旋轉件擺動運動之條件,過大之慣性力以及摩擦力造成其擺動角度過小,且極低轉速使壓電樑之運動趨於靜態響應,因此其功率輸出很低,未來可朝設計加速機構以及極低摩擦軸承方面發展。

    This study presents a piezoelectric energy harvester (PEH) designed for low rotational speed mechanisms. The PEH comprises an eccentric mechanism, a piezoelectric beam, and two magnets. It converts transient mechanical energy into electrical energy through vibration induced by magnetic forces. An analysis model based on energy methods is developed, considering gravitational potential energy, kinetic energy, and magnetic potential energy. A one-way coupling model is established due to the assumed small vibration displacements of the beam. Experimental measurements match theoretical predictions for revolution-dominant and swing motions, while hybrid motion remains highly nonlinear. The optimized PEH power output is 0.1 mW with an impedance of 180kΩ. The impact of eccentric mechanism length and rotational speed on power output is explored. Results indicate stable power generation during swing motion. Applying the PEH to large wind turbines suggests limitations due to low angular speed and swing angle. Future work will focus on mechanisms to accelerate PEH motion and integrate low-friction bearings.

    中英文摘要 I 致謝 XIII 目錄 XIV 表目錄 XVI 圖目錄 XVII 符號介紹表 XX 第1章 緒論 1 1.1 前言 1 1.2 研究背景與文獻回顧 1 第2章 運動分析及模型建立 6 2.1 機構設計原理 6 2.2 磁力模型 9 2.2.1 磁位能模型 9 2.2.2 永久磁鐵磁偶極矩模型 11 2.3 偏心機構件數值模型推導 13 2.4 壓電樑數值模型推導 19 2.5 求解聯立微分方程 23 第3章 實驗架設 24 3.1 獵能器原型製作 24 3.2 磁鐵參數量測 27 3.3 偏心機構件參數量測 30 3.4 壓電樑參數量測 36 3.5 MFC參數量測 39 3.6 壓電樑機械阻尼量測 44 第4章 實驗、分析結果討論 46 4.1 偏心機構件模型驗證 46 4.1.1.旋轉機構轉速與偏心機構件運動模式探討 46 4.1.2.轉動主導運動(revolution dominant motion) 48 4.1.3.混合運動(Hybrid motion) 50 4.1.4.擺動運動(swing motion) 53 4.1.5.穩態探討 55 4.2 最佳阻抗實驗 58 4.3 不同特徵長度下壓電樑功率輸出 60 4.4 應用於大型離岸風力發電機之數值探討 63 第5章 結論與未來展望 65 結論 65 未來展望 67 參考文獻 68

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