縱-扭模態耦合之三角形超音波馬達

Abstract

本研究改良蔡慶芳學長設計之三角形超音波馬達，希望以不同方形 壓電片分別致振縱向模態與扭轉模態來驅動馬達，三角形馬達定子的三 頂點設為與轉子之接觸點，並在頂角接近底座處切割橫向孔縫，減損定 子的軸向剛性。定子的三個側面各黏貼三片方形壓電陶瓷材料，施予電 極固定相位差之交流電壓，以相同工作頻率、振幅激發定子的縱向與扭 轉共振模態。兩共振模態的耦合振動致使定子接觸點作橢圓軌跡運動， 定子與轉子間存在的摩擦力致使轉子轉動。調整輸入電壓的相位差，可 控制轉子轉動方向。本文採用有限元素分析軟體進行數值模擬，以三角 形定子水平孔縫長度與位置為主要設計參數，依據模態耦合與模態隔離 程度，找出可同時激發縱向與扭轉模態的幾何模型，分析馬達定子作動 時接觸點的運動軌跡。超音波馬達原型機的定子材質為鋁合金，轉子為 不銹鋼，進行馬達性能曲線測試，最大轉速為59rpm，最大扭矩為 2.91N-cm。

This thesis presents an improvement of the triangular ultrasonic originally designed by Tsai. The longitudinal mode and torsional mode of the stator are excited to drive the rotor by distinct rectangular elements of PZT-4. The stator looks like a triangular tube machined with three horizontal slots in the apexes, which are set as contact points. The short tube is used to have a higher natural frequency for longitudinal mode than the torsional mode. Both longitudinal mode and torsional mode can have the same natural frequency if the axial stiffness is degraded by the horizontal slots. The PZT-4 element with segmented electrodes is adhered to each peripheral surface of the stator. The AC signals with constant phase difference are applied to the electrodes to excite both vibration modes. Every contact point experiences an elliptical trajectory in response to a harmonic excitation of the coupled modes, which are used to propel the ultrasonic motor through frictional force between the rotor and stator. The revolution direction of the rotor can be controlled by adjusting the phase difference of input signals. A finite element analysis code is used to calculate the resonant frequencies of the stator with various design iii parameters, including the length and position of the horizontal slots in the stator. In the probably optimal trial, both longitudinal and torsional modes can be simultaneously excited in a numerical model of the stator at the same frequency in accordance with modal separation and dual mode coupling theory. The trajectory of a contact point between the stator and rotor has been analyzed. The prototypes of the presented ultrasonic motors were fabricated and tested. The stator and rotor are made of aluminum alloy and stainless steel, respectively. The maximum measured revolution speed is 59 rpm without payload, and the maximum measured torque is 2.91 N-cm.