旋轉環境下壓電能量擷取系統之研究

Abstract

本研究主旨為探討旋轉環境下壓電振能擷取系統之應用，運用其被動調頻的性質，使壓電振子共振頻在一定的頻率範圍內保持接近外界轉速頻率，以達到頻寬增幅的效果。有別於過往本團隊研究的單軸式往復振動發電，本文將壓電懸臂樑徑向安裝於旋轉體上，並分為三種安裝方式，接著基於漢米爾頓原理建立數學模型，同時搭配分佈參數法與瑞利-里茲近似法推導出單一模態方程式。本文採用MATLAB SIMULINK對簡化方程式進行數值求解，並依此定性分析系統行為，由模擬結果觀察到離心力對於系統勁度的影響，其中，考慮的離心力分為兩個方向，一沿軸向，另一力則平行於側向振動方向。我們可觀察到軸方向之離心力若使樑拉伸，則系統勁度增加，反之，在壓電樑朝旋轉中心安裝的原型中，軸向離心力在樑內部產生壓縮應力，使得系統共振頻降低。另一方面，當懸臂樑之側向振動方向垂直於旋轉軸時，旋轉時產生平行側向之離心力會使系統勁度下降，是以整體共振頻曲線斜率較小。最後，將壓電懸臂樑徑向朝外安裝於旋轉體，利用其離心力調頻的特性，可應用於寬頻需求的環境，並以參數分析的結果作為設計準則，壓電能量擷取運用於胎壓偵測系統時，我們在模擬結果中呈現極佳的寬頻效果以及足夠的輸出功率。另外，朝內安裝的旋轉模型則成功地應用於降低基礎共振頻較高之壓電振子，以符合操作頻率較低的環境，而不影響其輸出功率。

This study is to investigate on the piezoelectric vibration energy harvesting system for rotational motion applications. Based on the characteristic of passive self-tuning, the resonance frequency of optimized piezoelectric resonator can track and match the driving frequency over a wide frequency range to perform broadband mechanism. Instead of our group’s research in piezoelectric energy harvester under translational motion, the piezoelectric cantilever beam is mounted radially on a rotating body in three ways, such as case A, B and C. The distributed parameter and Rayleigh-Ritz method are proposed to derive the ordinary differential equations in the first mode using Hamiltonian principle. This article also presents numerical simulation to comprehend the piezoelectric system behavior by using MATLAB SIMULINK. According to the simulation results, we find that the resonance frequency of energy harvester passively tunes due to centrifugal force, which are divided into two types. One is along the axial direction of beam, and the other is parallel to transverse direction. The centrifugal force along the axis leading to tensile stress effectively stiffens the composite beam. The results of softening characteristic attributed to compressive stress has been observed in inward rotation. On the other hand, the centrifugal force parallel to transverse direction existed in the prototype of transverse vibration perpendicular to the rotation axis, actually decreasing the resonance frequency. The simulation results also provide the guidelines for design of the piezoelectric energy harvester outwardly mounted on rotating body, which is utilized in the tire pressure monitoring system, and demonstrate significant improved bandwidth and sufficient power output. Further more, the model of inward rotation is successfully applied to lower the resonance frequency of piezoelectric beam to satisfy the environment with low operation frequency.