中文摘要：

在行波型超声波电机数学模型的基础上，研究了其稳定性。首先利用李雅普诺夫稳定性判据对超声电机驱动区间和制动区间的3种情况进行了分析，在研究数学模型基础上完成了超声电机的模型仿真、讨论和仿真验证；其次，在超声电机稳定性的分析基础之上，通过对驱动制动区间关系曲线和转速转矩关系曲线的分析得出了速度、转矩和预压力3者之间的关系，并做了超声电机运行稳定性的仿真讨论。研究表明：超声电机在满足李雅普诺夫平衡条件时，驱动区间的最大极限值是定子与接触层的边界接触点，即x1＝x0。对速度、转矩和预压力3者之间关系展开分析，为超声电机设计和控制提供借鉴。

英文摘要：

This article focuses on the stability of ultrasonic motor based on its mathematical model. Subjected to the condition that the running speed is satisfied with the Laypunov equation,three different driven interval of ultrasonic motors are analyzed at first. And then the simulation,discussion and verification work have been done after researching on the mathematical model of ultrasonic motor. Furthermore,according to the analysis of the driving-braking interval cure and speed-torque cure,the relationship among speed,torque and pre-pressure is obtained by a series of simulation studies.Research result shows that the maximum limit of the driving range is the boundary of the contact point of the stator and the contact layer x1 = x0 when the ultrasonic motor meets the Laypunov equilibrium conditions.It provides a reference for the design and control based on the relationship among speed,torque and pre-pressure.