复合型超声马达纵-扭振动固有频率简并研究

纵、扭振动固有频率简并是提高纵-扭复合型超声马达输出力矩的关键问题。然而同一弹性体内的纵振固有频率远高于扭振固有频率．目前对两种振动固有频率的简并缺乏深入的理论研究。纵一扭复合型超声马达振动分析模型都基于一维理论。在此提出了一种纵、扭振动固有频率简并的新方法。通过将纵一扭复合型超声马达设计成双定子对称结构．在定子上附加一个调整环改变定子的力学边界条件。实现纵、扭振动同频共振。应用Hamilton原理建立了考虑泊松效应的定子纵、扭振动理论模型，分析了定子的纵振与扭振第一阶固有频率随调整环质量和位置的变化规律，通过优化马达的几何结构参数获得了纵振与扭振的同频谐振点。

Study on eigenfrequency degeneration of longitudinal and torsional vibrations in a hybrid ultrasonic motor

Eigenfrequency degeneration of longitudinal and torsional vibrations is a key to enhance the output of a hybrid ultrasonic motor. However, the eigenfrequency of a longitudinal vibration is much greater than that of a torsional vibration within an identical elastic rod. The previous work lacked in damper theoretical study on matching the eigenfrequencies of such two vibrations. Furthermore, the analytical model of a hybrid ultrasonic motor is based on one-dimensional theory. In this paper, a new method to match the eigenfrequencies of longitudinal and torsional vibrations is proposed. A symmetrical structure with two stators is adopted in design of the present motor. Moreover, two adjusting rings are added to the stators for the purpose of changing the mechanical boundary conditions by which to make the eigenfrequencies of longitudinal and torsional vibrations coincide. Based on Hamilton's principle, the theoretical models of longitudinal and torsional vibrations are established, in which the Poisson's effect of the stator is taken into account. The influence resulted from the adjusting rings on the first order eigenfrequencies of longitudinal and torsional vibrations are investigated. An identical resonant frequency of longitudinal and torsional vibrations is obtained by means of optimizing the geometries of the motor.