基於滑塊自調頻之拉伸式非線性壓電能量採集器

Abstract

壓電能量採集器是將環境中機械能轉化成電能的一種裝置。傳統懸臂梁壓電能量採集器具有應變分布不均，適用頻率範圍狹窄，導致發電效率低的缺點。本研究提出一種自調頻壓電振動能量採集裝置，其主要是包含一個薄梁加厚梁組合而成的兩段式梁結構、由PVDF壓電材料構成彈性梁以及一個安裝於厚梁上之滑塊。本研究推導之數學模型以尤拉伯努力梁理論、拉格郎日方程式以及壓電本構方程式為基礎，推導出梁的運動方程式、滑動質量塊運動方程式以及壓電材料的電學方程式。之後製作出壓電能量採集器原型進行實驗，並將實驗結果與先前的理論模型作比較與驗證。藉由此結構可使整段壓電材料應變分布更為均勻，使輸出電壓效率增加。此外，因彈性梁對兩段式梁施加非線性外力，使得系統的頻率響應有著明顯的非線性硬化的效果，擁有更高輸出電壓及更寬的採集頻寬。此外，當梁振動幅度較小時，滑動質量塊會因重力作用而從彈性梁連接端向固定端來回移動，在此同時系統的頻率響應會被轉換到更高的頻率範圍；當梁振動幅度較大時，滑動質量塊會獲得足夠的慣性力並向彈性梁連接端移動。透過上述自調頻行為，使得最終穩態下的輸出功率有著顯著的增加，最大輸出電壓為28.98 V，比非自調頻拉伸式非線性能量採集器高出2.71倍，在頻寬的大小上也多了2.83倍。

A piezoelectric energy harvester is a device that converts mechanical energy from the environment into electrical energy. Traditional cantilever beam piezoelectric energy harvesters suffer from uneven strain distribution and a narrow harvesting bandwidth, leading to low power generation efficiency. This study proposes a self-tuning piezoelectric energy harvester, primarily consisting of a two-segment beam formed by combining a thin stainless beam and a thick beam, an elastic beam made of PVDF piezoelectric material, and a sliding mass block. The mathematical model derived in this study is based on Euler-Bernoulli beam theory, Lagrange's equation, and piezoelectric constitutive equations, from which the motion equations of the beam, the sliding mass block, and the electrical equations of the piezoelectric material are derived. Subsequently, a prototype of the piezoelectric energy harvester was fabricated for experiment, and the experimental results were compared and validated against the previous theoretical model. This structure allows for a more uniform strain distribution across the entire piezoelectric material, increasing voltage output efficiency. Additionally, the elastic beam exerts a nonlinear force on the two-segment beam, resulting in a significant nonlinear hardening effect in the system's frequency response, leading to higher voltage output and harvesting bandwidth. Furthermore, when the beam's vibration amplitude is small, the sliding mass block moves back and forth from the elastic beam connection end to the fixed end due to gravity, simultaneously shifting the system's frequency response to a higher range. When the beam's vibration amplitude is large, the sliding mass block gains sufficient inertial force to move toward the elastic beam connection end. Through the aforementioned self-tuning behavior, the final steady-state output power is significantly increased, with a maximum output voltage of 28.98 V, which is 2.71 times higher than the non-self-tuning tensile nonlinear energy harvesters, and the frequency bandwidth is 2.83 times wider.