纵扭复合型超声电机定子的非线性动力学特性研究OA北大核心CSTPCD

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 thefourth-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.