Analyses Of Several Dynamic Problems In Rotary Travelling Wave Ultrasonic Motors

Rotary travelling wave ultrasonic motor is a classical type of driving device.It is widely used and concerned due to the merits such as high torque at low speed,simple and compact structure and silence.This work approaches the effects of the teeth geometry and machining error of the stator,the parametric excitation from the piezoelectric elements and the vibration of the rotor through mathematical analyses,software simulations and experiments.Following are the main contents:(1)Effects of the teeth on stator vibration.Stators with teeth lose axisymmetry such that the vibration mode can be contaminated.The contaminations result in distorted travelling wave response and reduce the efficiency and stability of the motor.Considering the perturbation mass and bending stiffness from the teeth,the natural frequency splitting and mode contamination are analyzed.The travelling wave response is obtained through mode superposition,and then the relationship between the wave distortion and three parameters are discussed including the teeth count,teeth height and teeth occupation.Further,the optimized teeth height for higher driving speed is found.(2)Effects of machining error on forced response.Besides the teeth,machining errors also lead to nonuniform geometry of the stator.Periodic structures consisting of a stepped plate and several mass blocks are studied focusing on the problem of mass nonuniformity.It is predicted that the resonance frequency varies with the excitation phase and then verified by experiment.Accordingly,the response of standing wave couple is studied and the optimized phase of the bonding angle of piezoelectric elements is found.(3)Contact mechanics considering the piezoelectric parametric effect.The stretch of the piezoelectric elements bends the stator,while it creates forces along the stator,and actually these forces are parametric excitation.Considering the parametric forces,the unstable regions and the distorted travelling wave are analyzed.The contact model is established based on the distorted wave shape,and then the effects from pre-pressure and stimulating frequence on the pressure at stator surface and torque-speed curve are studied.(4)Nonlinear axial vibration of the rotor.Due to the travelling wave,the gap and the top of the stator teeth move to the wave crest alternatively.This alternation excites axial vibration of the rotor and then arouses fluctuation of the rotor speed.Based upon the dynamic model with quadratic nonlinearity,the amplitude-frequency characters and approximate responses for the resonance,subhamonic resonance and superharmonic resonance are analyzed.Further,the speed fluctuation is calculated based on the contact model.(5)Dynamics of ring-type periodic structures in ultrasonic motor.In essence,lots of stators and rotors of travelling wave ultrasonic motors belong to ring-type periodic structures.Based on the in-plane vibration model from Hamilton's principle,the rules of natural frequency splitting and mode contamination are solved by perturbation method.Two new phenomena are recognized for the case of splitting natural frequency,that are(a)the resonance frequency varies with the phase of wave crest for non-rotating structure;(b)the effect of dynamic stiffening due to the attached mass can be strengthened for rotating structure.