弓形壓電能量採集器之設計與分析

Abstract

傳統的壓電懸臂梁採集器具有採集頻寬窄、電壓輸出小等問題，為了進一步改善能量採集效率，本研究提出弓形梁採集器，弓形主體由PVDF壓電片及不鏽鋼基梁所組成。藉由末端質量將基梁及壓電片兩端相互固定，兩者的長度差異使不鏽鋼基梁受到軸向預力並發生挫曲，而壓電片則會被基梁的抗彎力繃直，形成弓形結構。在此結構下，系統受到的軸向預力使頻率響應產生非線性的特性，進而拓展採集頻寬。由於挫曲梁末端的位移會比基底激振更大，連帶使壓電片受到的垂直激振提高，可以達到力量放大的效果。且透過挫曲梁的幾何關係，會將垂直方向所受到的基底激振轉為水平方向的軸向力，拉伸壓電片來進行能量採集。本研究的動態模型以古典梁理論及Lagrange’s equation為基礎，將壓電片視為等效彈簧，並加入軸向預力的影響；電學模型的部分則是以壓電本構方程式為基礎，僅考慮壓電片軸向位移來計算力電耦合方程式，以此建立理論模型。本研究也針對弓形梁採集器的各項參數進行實驗驗證，探討不同基梁厚度、末端質量、壓電片偏移量、基梁等效長度以及不同加速度對採集器性能所帶來的影響，最後與傳統懸臂梁採集器相互比較。實驗結果顯示，弓形梁採集器與懸臂梁採集器相比，最大電壓將提高2倍，且具有較寬的採集頻寬及較小的末端位移，節省工作空間的同時也使採集器性能得到提升。由最佳阻抗實驗結果得知弓形梁採集器於10 MΩ的外接阻抗下具有最佳輸出功率0.86 mW。

Conventional cantilever piezoelectric energy harvester have problems such as narrow bandwidth and low voltage output. To enhance efficiency, this study proposes a bow-shaped energy harvester composed of PVDF piezoelectric sheet and a stainless steel beam. The introduction of axial preload in this design results in nonlinear characteristics in the frequency response, expanding the bandwidth. Due to the greater displacement at the end of the buckled beam compared to the base excitation, the vertical excitation of PVDF is increased, leading to force amplification. By utilizing the geometric relationship of the buckled beam, the vertical force is converted into a horizontal force, thereby stretching the piezoelectric sheet. The dynamic model in this study is based on beam theory and Lagrange’s equation, considering PVDF as an equivalent spring and accounting for the influence of preload. The electrical model is based on the piezoelectric constitutive equation, focusing solely on the axial displacement of PVDF to establish a theoretical model. Experimental verification of our design's parameters is also conducted. The influence of beam thickness, tip mass, PVDF offset, beam length, and acceleration on performance is discussed and compared with the conventional cantilever energy harvester. The experimental results show that the maximum voltage of bow-shaped PEH is twice higher than that of cantilever PEH. Furthermore, it exhibits a wider bandwidth and smaller terminal displacement. According to the impedance experiment results, the bow-shaped PEH achieves a maximum output power of 0.86 mW with an external impedance of 10 MΩ.