Dynamical Analysis Of Rotary Traveling Wave Ultrasonic Motors In Considering Hysteretic Nonlinearities Of Piezoelectric Material

Ultrasonic motor (USM) is a new developed mini-motor in recent decades. The USM converts a piezoelectrically excited resonant vibration of the stator into a movement of the rotor by frictional forces. Generally, there are many nonlinear factors in different parts of USM, in which the hysteretic nonlinearities of piezoelectric material affect the performance of the motor. But now few scholars have studied the nonlinear dynamic characteristics in considering hysteretic nonlinearities of piezoelectric material.In this paper, the hysteretic nonlinearities of piezoelectric materials were described by a cubic polynomial firstly. Then the nonlinear dynamic models of standing wave vibration, travelling wave vibration of the ring-type stator of ultrasonic motor, along with the whole USM were developed by considering elastic hysteretic nonlinearities of piezoelectric material, without considering the interface forces, based on Hamilton theory and Rayleigh-Ritz method. At last the nonlinear dynamic models were analyzed using some nonlinear dynamic theories and methods. The contents are summarized as follows:1. Current studies of hysteretic nonlinear constitutive relations of piezoelectric material and USM were summarized.2. The cubic polynomial model was introduced to establish nonlinear constitutive relations of dielectric hysteresis, piezoelectric hysteresis and elastic hysteresis, which describes the hysteretic nonlinear characteristics of piezoelectric material.3. The nonlinear dynamic model of standing wave vibration of a ring-type stator of ultrasonic motor was developed by considering the dielectric hysteresis, piezoelectric hysteresis and elastic hysteresis, without considering frictions between the stator and rotor. The results show that the elastic hysteresis is the direct reason which makes stator present dynamical nonlinearity.4. The nonlinear dynamic model of travelling wave vibration of ring-type stator of ultrasonic motor was developed by considering the elastic hysteresis, without considering frictions between the stator and rotor. The method of multiple scales was used to research the first approximate primary resonance of the model, and the results show that the primary resonance is with two different modal amplitudes, soft characteristic and multi-solutions phenomena. The influences of hysteresis of piezoelectric materials on responses of the stator were analyzed in detail.5. Interface forces between the stator and rotor were simulated by the linear springs contact model. The model of whole system of USM was developed by considering interface forces between stator and rotor.This thesis has successfully solved the problem of dynamically modeling piezoelectric constitution in considering hysteretic nonlinearities of piezoelectric material, and particularly studied how the elastic hysteresis nonlinearity affects the responses of thin ring-type stator in standing and travelling wave vibration, The results given in this thesis provide a theoretical foundation for further analysis of dynamic mechanism and control of the whole system USM.