單頻雙彎曲模態驅動旋轉壓電馬達之分析與最佳化

Abstract

本研究旨在開發一使用單頻驅動二彎曲模態以疊加產生旋轉行進波之二維壓電馬達，不同於以往以雙彎曲模態疊加產生單一方向行進波於結構上，本研究透過空間與時間上之理論設計，產生反向行進波於結構x方向及y方向上，進而產生旋轉行進波。本研究設計四片12×20×0.2mm3壓電致動器於100×77×0.5 mm3一不鏽鋼薄板上，以單頻分別驅動其中兩片壓電片使所要激發之雙彎曲模態可以分開驅動，並進行雙彎曲模態之最佳化驅動參數設計，使雙彎曲模態疊加出菱形形狀之旋轉行進波，並於壓電馬達結構上方驅動載物旋轉，透過改變驅動訊號之電壓比及相位差，以達到精確控制載物之旋轉效果。本研究透過壓電片之間對稱位置黏貼於不鏽鋼薄板上，並設計夾具以於x方向模擬雙簡支端之邊界條件，並於y方向邊界產生雙自由端。在驅動方法上，將四片壓電片分成兩組做驅動，以分別激發雙彎曲模態之Ф34 與 Ф43模態陣型。本研究開發分析方法將菱形旋轉行進波切分成四段行進波，分別以希爾伯特轉換理論，及成本函數定量得到最佳化的驅動參數，以數值模擬分析在不同電壓比及相位差驅動下的四段行進波之效率及振幅一致性，再以有限元素模擬分析並驗證其可行性。最後本研究以實驗驗證所設計之壓電馬達旋轉行進波之驅動效率。當輸入2.757kHz作為單頻驅動頻率，輸入電壓16Vpp，相位差為73.35°，荷重為1.187g之載物，可達平均角速度為22.49deg/s之順時鐘旋轉，在改變相位差為253.85°，即可產生平均角速度為15.4deg/s的逆時針旋轉，當增加載物荷重為1.903g，其平均角速度降為7.39deg/s及6.18deg/s，當提高輸入電壓為24Vpp，其平均角速度即可提高到12.12deg/s，及15deg/s。本研究成功地在有限之二維結構上 開發以雙向行進波驅動旋轉功能之壓電馬達，並證明可以改變輸入訊號之電壓比及相位差來控制載物之旋轉方向及速度，達到控制載物旋轉之研究目標。

In this study, bi-directional traveling waves are generated to create a rotational piezoelectric motor. It is different from previously reported piezoelectric motors that only can generate linear traveling waves. The present rotational piezoelectric motor is constructed by four 12×20×0.2mm3piezoelectric actuators that attached symmetrically to the surface of a 100×77×0.5 mm3 stainless steel plate. The fixture are designed to simulate the boundary conditions of double simply-supported in the x-direction and double free ends in the y-direction. The 34-th and 43-th bending modes are stimulated to generate rotational traveling waves propagate on a rectangular plate. To analyze the vibration profile, an analytical solution is developed. The generated rotating traveling wave is separated into four segments, and the driving parameters are optimized using the Hilbert transformation and the cost function. The performance of the traveling waves is analyzed by numerical simulation and finite element analysis, and it is verified with experimental studies. The experimental results demonstrated that driving at 2.757kHz, 16Vpp, and 73.35° phase difference, a 1.187g object can be rotated at an average velocity of 22.49deg/s. Its direction can be changed using a phase difference of 253.85°,with an average angular velocity is 15.4deg/s. When the load is increased to 1.903g, the average angular velocity decreased to 7.39deg/s and 6.18deg/s. When the input voltage is increased to 24Vpp, the average angular velocity reached 12.12deg/s and 15deg/s. The experimental results demonstrate that by changing the voltage ratio and phase difference of the input signal, the rotating direction and velocity of the load can be controlled. These results demonstrated the feasibility of this piezoelectric rotational motor.