Nonlinear Dynamical Modeling And Analysis Of Rotary Traveling Wave Ultrasonic Motors

Ultrasonic motor (USM) is a new development in the field of small scale actuators, which has exhibited advantages of high holding torque, high torque at low speed, simple structure, compactness in size compared to conventional electromagnetic motors. Usually, USM shows strong nonlinear characteristics in the system, which has apparent effects on the performances of the system.Experiments and researches have proved that the piezoelectric material nonlinearities of the stator have become a remarkable factor affecting characteristics of USM. However, the researches of dynamical modeling and analysis of the USM in considering the nonlinearities of piezoelectric materials have not been fully developed up to now. In this paper, the nonlinear dynamic model of standing wave vibration, traveling wave vibration of the stator, movements of the rotor, as well as the integrated system of the USM were established by means of generalized Hamilton's principle and Rayleigh-Ritz method in considering the quadratic nonlinear constitutive relations of piezoelectric materials. Nonlinear dynamic theory and method were used to investigate the dynamic mechanism of the USM. The main parts included in the thesis are as follow:1. A review of the nonlinear dynamical modeling and analysis of USM at broad and homes was given;2. The nonlinear dynamic model of standing wave vibration of stator was established in considering the quadratic nonlinear constitutive relations of piezoelectric materials, the method of multiple scales was used to investigate the second order primary resonance of the stator, and the results show that the primary resonance has multi-solutions and jump phenomena in given conditions. Numerical integral results verified the validity of the analysis;3. The nonlinear dynamic model of traveling wave vibration of stator was established without considering the friction mechanism between the rotor and stator, the method of multiple scales was used to investigate the second order primary resonance of the stator. The results show that the primary resonance has some special phenomena such as modal separation, difference of the two modal amplitudes, multi-solutions and jump, and give the relationship between characters of the solution and the parameters of the system. Numerical integral results verified the stability of the primary resonance solution;4. The nonlinear dynamic model of the whole system (control system was excluded here) of the USM was established in considering the friction mechanism between the rotor and stator;5. Phase maps, time histories and spectrums of the two modal amplitudes of the stator, axial displacement and angular speed of the rotor were acquired by numerical method. The results give the relationship between inputs and outputs of the system. The behavior of the USM also presents jump phenomena in certain conditions.From the results of this thesis, the nonlinear dynamic behavior of USM due to quadratic nonlinearities of piezoelectric can be realized deeply. The results build a theoretical foundation for further study of nonlinear mechanism and control of rotary traveling wave ultrasonic motors.