基於懸臂梁並結合磁力之拉伸式壓電能量採集器設計與分析

Abstract

傳統的懸臂式壓電能量採集器因為彎曲變形的緣故，使得壓電材料的應變分布不均，導致發電效率低下，且具有頻寬窄的問題。為了要解決這個問題，本研究提出一種基於懸臂梁結構並搭配非線性磁力，對PVDF壓電材料進行拉伸變形的採集器結構，壓電材料僅受到軸向拉伸，因此應變分布均勻，可以有效的提升採集器的輸出電壓。此外，本結構也可以利用兩磁鐵間距離來調整系統剛性，從而實現頻率諧調。理論模型基於尤拉梁理論、壓電本構方程式及Charge Model進行推導，由於PVDF的抗彎曲剛性遠小於整體系統的剛性，因此將其視為一個等效彈簧計算。研究也針對基於懸臂梁並結合磁力之拉伸式壓電能量採集器的各項參數進行驗證，探討不同參數對採集器性能的影響，最後與懸臂式採集器互相比較，相較於懸臂式採集器，本研究所提出的採集器在最大輸出電壓為懸臂式的4.86倍，頻寬為6.62倍，經過最佳阻抗匹配後，在2.8 MΩ外接阻抗下最佳輸出功率為2.53 mW。

Traditional cantilever beam piezoelectric energy harvesters face challenges with uneven strain distribution in the piezoelectric material due to bending deformation, leading to low power generation efficiency and narrow bandwidth issues. To address these problems, this study proposes an energy harvester structure based on a cantilever beam combined with nonlinear magnetic force to induce tensile deformation in PVDF piezoelectric materials. The piezoelectric material is subjected to only axial tension, resulting in uniform strain distribution, which significantly enhances the output voltage of the harvester. Additionally, the structure can adjust system stiffness by varying the distance between two magnets, achieving frequency tuning. The theoretical model is derived based on Euler beam theory, piezoelectric constitutive equations, and the charge model. Since the bending stiffness of PVDF is much smaller than the overall system stiffness, it is treated as an equivalent spring in the calculations. The study validates the various parameters of the proposed tensile-mode piezoelectric energy harvester based on a cantilever beam with magnetic interaction, analyzing the impact of different parameters on the harvester's performance. Finally, the proposed harvester is compared to a conventional cantilever beam harvester. The results show that the maximum output voltage of the proposed harvester is 4.86 times that of the cantilever beam harvester, and the bandwidth is 6.62 times wider. After optimal resistance matching, the maximum output power under an external load resistor of 2.8 MΩ is 2.53 mW.