剛體梁與懸臂梁結合之拉伸式非線性壓電能量採集器分析

Abstract

傳統的懸臂梁式壓電能量採集器以彎矩的方式來傳遞機械能給予壓電材料，這樣的方式使得梁體應變分布不均，造成發電效率低落之情況，且採集頻寬也相對狹窄。因此為改善上述情況，本研究提出剛體梁與懸臂梁結合之拉伸式壓電能量採集器，可將其視為一組由剛體梁、懸臂梁組成之兩段式懸臂梁以及PVDF壓電材料構成之彈性梁結合之採集器。彈性梁之一端與兩段式懸臂梁接合，另一端與基座以夾持方式固定，而彈性梁因其抗彎剛性遠小於整體系統，因此其兩端皆視為旋轉接頭。本研究推導之數學模型將以古典尤拉梁理論配合壓電本構方程式為基礎進行推導，並加入非線性外力項以及調整系統各參數來探討其性能影響及趨勢。藉由這樣的結構，可使整段壓電片受到兩段式懸臂梁帶來的軸向拉伸力，使壓電材料應變分布更為均勻，使其電壓輸出效率獲得增長，並且同時，因彈性梁施以兩段式懸臂梁之非線性拉伸力，使得系統位移以及電壓響應有著非線性硬化效果，而擁有更大的頻寬以及電壓輸出。兩段式懸臂梁之設計為使兩段式懸臂梁側有更大的剛性，使其不因彈性梁外力而影響懸臂梁之末端位移與懸臂梁之假設，並且同時保有懸臂梁固定端之彎曲特性。最後實驗與模擬結果顯示，本文之拉伸式壓電能量採集器之最大電壓輸出是懸臂梁式壓電能量採集器的4.54倍，並且頻寬達到3.54倍，且經過最佳阻抗實驗後，顯示本採集器在10MΩ下，最大輸出功率1258 μW。

The traditional cantilevered piezoelectric energy harvester transmits mechanical energy to the piezoelectric material through bending moment, which results in uneven strain distribution in the beam and leads to low power generation efficiency and collection bandwidth. To solve this problem, this study proposes a stretching-type piezoelectric energy harvester that combines a rigid beam and a cantilevered beam. It can be regarded as a harvester composed of an elastic beam made of PVDF piezoelectric material and a two-segment cantilevered beam combined with a rigid beam. One end of the elastic beam is connected to the two-segment cantilevered beam, while the other end is fixed to the base by clamping, and both ends of the elastic beam are treated as resolute joints because its bending stiffness is much smaller than that of the whole system. With this structure, the entire piezoelectric material can be stretched by the axial tensile force brought by the two-stage cantilevered beam, making the strain distribution of the piezoelectric material more uniform, and improving its voltage output efficiency. Additionally, due to the non-linear tensile force generated by the elastic beam, the system displacement and voltage response have non-linear hardening effects, resulting in a wider bandwidth and larger voltage output. The design of the two-segment cantilevered beam is to increase its rigidity on both sides to prevent the maximum displacement of the cantilevered beam from decreasing due to external forces acting on the elastic beam while maintaining the bending characteristics of the fixed end of the cantilevered beam. The mathematical model derived in this study will be based on the classical Euler beam theory combined with the piezoelectric constitutive equation, and non-linear external force terms will be added, along with the adjustment of various system parameters to investigate their performance impact and trends. Finally, the experimental and simulation results showed that the maximum voltage output of the stretchable piezoelectric energy harvester proposed in this paper is 4.54 times that of the cantilever beam piezoelectric energy harvester. Additionally, the bandwidth reached 3.54 times. After conducting the optimal impedance experiment, it was shown that the maximum output power of this harvester is 1258 μW at 10MΩ.