纵扭复合型超声电机定子的非线性动力学特性研究  

Research on nonlinear dynamic characteristics of the stator of a longitudinal-torsion composite ultrasonic motor

作　　者：周天洋[1] 陶征[1] 赵丹[1] ZHOU Tianyang;TAO Zheng;ZHAO Dan(School of Mechanical and Power Engineering,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]郑州大学机械与动力工程学院,郑州450001

出　　处：《重庆理工大学学报（自然科学）》2024年第9期135-142,共8页Journal of Chongqing University of Technology：Natural Science

基　　金：郑州市普通科技攻关计划项目(131PPTGG409-1)。

摘　　要：纵扭复合型超声电机的非线性动力学特性是影响电机运行的稳定性和可靠性的重要因素。基于广义Hamilton能量变分原理、Rayleigh-Ritz假设模态法以及非线性压电本构关系,建立纵扭复合型超声电机定子的非线性动力学模型,采用四阶Runge-Kutta法和Lyapunov指数等方法仿真分析纵向激励下电机定子的非线性振动响应特性。结果表明:电机定子的固有模态频率和实验值误差仅为1.8%,证明了所建立的纵扭复合型超声电机定子的非线性动力学模型的准确性。超声电机具有频率漂移、振幅跳跃等非线性行为特性,而实际工作时通常将定子的共振频率(即λ=1处)作为工作激励频率,此时位于稳定的周期运动区域。通过数值仿真分析得到不同频率激励下系统的发展趋势,以及系统稳定与不稳定运动的参数匹配区间,可为开展纵扭复合型超声电机的非线性动力学特性研究提供参考。The nonlinear dynamic characteristics of the longitudinal torsional composite ultrasonic motor are important factors affecting the stability and reliability of the motor operation,limiting its further application.Therefore,building a reasonable nonlinear dynamic model to reveal the nonlinear dynamic characteristics of the motor is of great significance for the design and performance improvement of the motor.A nonlinear dynamic model of the stator of a longitudinal torsional composite ultrasonic motor is built based on the generalized Hamilton energy variational principle,Rayleigh-Ritz assumption modal method,and nonlinear piezoelectric constitutive relationship.The nonlinear vibration response characteristics of the motor stator under longitudinal excitation are simulated and analyzed by employing the fourth-order Runge-Kutta method and Lyapunov exponent method.Our results show the error between the natural mode frequency of the motor stator and the experimental value is only 1.8%,proving the accuracy of the nonlinear dynamic model of the longitudinal torsional composite ultrasonic motor stator.Ultrasonic motors exhibit nonlinear behavior characteristics such as frequency drift and amplitude jump during operation.In practice,the resonance frequency of the stator(i.e.λ=1 point)is usually employed as the excitation frequency,which is located in a stable periodic motion region.The development trend of the system under different frequency excitations and the parameter matching range of stable and unstable motion of the system are clarified through numerical simulation analysis.Our research results may provide some references for the systematic study of the nonlinear dynamic characteristics of longitudinal torsional composite ultrasonic motors.

关 键 词：超声电机 压电陶瓷 定子 HAMILTON原理 

分 类 号：TM35[电气工程—电机] TM359.6