以單頻雙模態驅動彎曲扭曲複合模態壓電馬達之研究

Abstract

本研究旨在開發一使用單頻雙模態(One-Frequency Two-Modes, OF-TM)驅動之壓電馬達，有別於過去單頻雙模態驅動方法在兩片壓電片上分別驅動相同頻率且相位差90度之訊號來激發相鄰兩彎曲模態來產生行進波，本研究在同一片壓電片上設計雙電極並藉由改變兩電極之輸入電壓比以及相位差，同時激發相互正交之彎曲模態與扭曲模態，並使所產生之行進波方向以及速度皆可進行調控，進而達到控制載物移動速度與方向之效果。本研究透過設計結構、壓電片、電極之尺寸以單一頻率激發出第八彎曲模態與第四扭曲模態之複合模態，並於結構中產生旋轉形之行進波。在結構設計上以不銹鋼作為傳遞行進波之基板並使用壓電陶瓷材料作為致動器，而夾具由鋁合金所製且使用雙定位銷夾持法，以利用線接觸的形式來模擬簡支端邊界條件。本研究並透過等效長度理論模型求得其解析解，及使用希爾伯特轉換數值模擬分析評估波形振幅均勻度，再透過分析波形之斜率與平均振幅得到最佳化行進波驅動參數，再以有限元素模擬驗證分析方法之可行性。本研究藉由理論設計不同壓電馬達結構以驗證單頻雙模態驅動法之條件，以實驗驗證雙電極壓電馬達結構之驅動效率，以輸入電壓比為13V：5V、相位差70度的2.073kHz單頻率驅動參數，可將重量為2.4g之載物向-y方向移動8.67mm，平均速度為0.83mm/s；在輸入電壓比為6.5V：10V、相位差為288度的參數下可將載物向+y方向移動9.06mm，平均速度為-0.85mm/s；而在輸入電壓比為13V：10V、相位差21度的參數下，載物可以向-y方向移動9.29mm，平均速度為2.03mm/s；最後在輸入電壓比為13V：10V、相位差為336度的參數下，載物可以向+y方向移動10.54mm，平均速度為-2.17mm/s，實際驗證了透過改變輸入訊號之電壓比與相位差具有控制載物移動速度與方向之效果，以及以單一壓電片產生穩定傳遞波之功能驗證。

This study aims to develop a piezoelectric motor driven by one-frequency two-modes (OF-TM) method using a bending and a twisting mode. In the past, most OF-TM motors were driven by two piezoelectric sheets at the same frequency with a 90 deg phase difference for generating traveling waves. Unlike this traditional method, we use one piezoelectric sheet with two electrodes to generate and control the direction and speed of traveling waves. The driving performance can be controlled by adjusting the input voltage ratio and phase difference between the two electrodes. Using this design configuration, a composite wave of the 8th bending mode and the 4th twisting mode can be simultaneously excited to generate a rotary traveling wave by designing motor structure, piezoelectric sheet, and electrode size. In the structural design, stainless steel is used as the substrate, and a piezoelectric PZT ceramic is used as the actuator. An aluminum fixture is designed to simulate the simply supported boundary condition. To describe the vibration profile, an analytical solution is derived using the concept of equivalent length. The waveform is designed using the numerical simulation and the Hilbert transform. The optimized driving parameters are obtained by analyzing the slope and average amplitude of the waveform. The feasibility of this method is verified through finite element simulation analysis. Finally, the present study is verified experimentally using a scanning laser Doppler vibrometer to monitor generated traveling waves. The driving efficiency is studied and compared. The experimental results demonstrate that objects in different weight can be moved in both +y and -y directions. For a 2.4g object, it can be moved in -y direction at a speed of 0.83mm/s and a distance of 8.67mm under a condition of 13V: 5V and 70 deg phase difference. In +y direction, the average speed is 0.83mm/s and moved 9.06mm under a condition of 6.5V: 10V and 288 degrees. The speed increased to 2.03mm/s and -2.17mm/s in +y and -y directions under the conditions of 13V: 10V and 21 deg and 336deg, respectively. These experimental findings verify that changing the input voltage ratio and phase difference can control the moving speed and direction. It also verifies that using a single piezoelectric actuator, a rotary piezoelectric motor can be developed using the OF-TM method.