具傾角與滑塊自調頻之拉伸式非線性壓電能量採集器

Abstract

本研究針對傳統壓電能量採集器頻寬狹窄、壓電材料拉伸量不均，以及發電效率受限的問題，設計並開發了一種具備自調頻功能的壓電能量採集機構。該機構主要由鋼體梁、壓電材料PVDF及可自由移動的滑塊組成，透過滑塊的運動來調整系統的共振頻率，以拓展頻寬並提升能量轉換效率。此外，本研究亦探討了機構在不同傾角條件下的能量採集效能，分析重力對滑塊運動行為的影響，以進一步提升系統穩定性與輸出效能。本研究基於拉格朗日方程式以及壓電本構方程式推導出完整的數學模型，包括鋼體梁運動方程式、滑動質量塊運動方程式與壓電材料的電學方程式，並透過MATLAB求解系統的運動行為。接著，進行一系列實驗驗證數學模型的準確性，包含掃頻測試與定頻測試，探討不同滑塊初始位置對系統頻率響應的影響。實驗結果顯示，當滑塊位置改變時，共振頻率可自適應調整，證實該機構具備拓展頻寬的能力。進一步分析發現，當系統處於有傾角狀態時，可藉由重力影響更順暢地進入高能階狀態，提高能量輸出。比較無傾角與有傾角實驗數據可知，適當的傾角設計能夠降低滑塊移動的慣性門檻，使系統更容易達到最佳能量採集狀態，進而提升輸出功率與穩定性。另一方面，模擬與實驗結果高度吻合，驗證了數學模型的準確性，並確認本研究所提出的設計在不同運行條件下皆具穩定的自調頻效能。加入傾角設計後，穩態輸出功率顯著提升，最大輸出電壓為6.63 V，比無傾角設計的能量採集器高出1.89倍，在頻寬上的大小也多出了3.08倍。

This study addresses the limitations of traditional piezoelectric energy harvesters, including narrow bandwidth, uneven strain distribution in piezoelectric materials, and restricted power generation efficiency. A piezoelectric energy harvester with self-tuning capability was designed and developed. The mechanism consists of a rigid beam, a piezoelectric PVDF material, and a freely movable sliding mass. By adjusting the sliding mass position, the system's resonance frequency can be tuned for broadening the bandwidth and enhancing energy conversion efficiency. Furthermore, this study investigates the energy harvesting performance under different inclination angles, and analyzes the effect of gravity on the sliding mass motion to further improve system stability and energy output. In this study, a complete mathematical model was derived based on Lagrange equation and the constitutive equations of piezoelectric materials. including the equations of motion for the rigid beam and sliding mass, and the electrical equations for piezoelectric material. And then the system dynamics were solved by MATLAB. A series of experiments were conducted to validate the accuracy of the mathematical model, including sweep frequency tests and fixed frequency tests, to investigate the effect of different initial positions of the sliding mass on the system's frequency response. Experimental results indicate that the system’s resonance frequency can adaptively adjust as the sliding mass moves, demonstrating its capability to broaden the bandwidth. Further analysis reveals that the inclined configuration allows the system to more smoothly enter high-energy orbits by the influence of gravity, leading to improved energy output. By comparing experimental data with inclination and without inclination, it is evident that an appropriate inclination design reduces the inertia for sliding mass movement, allowing the system to reach an optimal energy harvesting state more easily, thereby improving power output and stability. Moreover, the simulation and experimental results exhibit a high degree of agreement, validating the accuracy of the mathematical model and confirming that the design maintains stable self-tuning performance under various conditions. With inclination design, the steady-state output power was significantly enhanced. The maximum output voltage reached 6.63 V, which is 1.89 times higher than the energy harvester without inclination design. Additionally, the bandwidth was expanded by 3.08 times.