Optimal Profile Design for the Resonator Beam of an Ultrasonic Motor via Finite Element Modeling and Taguchi Methodology

Abstract

This study presents the optimal design for the resonator beam profile of a bimodal ultrasonic motor via finite element modeling and Taguchi experimental design method. General design goals of an ultrasonic motor are to maximize the output power while restraining the contact force in order to extend component lives. To achieve the aforementioned goals, based on recent studies, beam profile design could play an important role because geometric variants of profile lead to substantial changes in the output power of the motor and simultaneously affect the contact force significantly. To investigate the effect of various profiles on the performance of the ultrasonic motor, the dynamic equations of motion are first formulated by utilizing an extended Hamilton’s principle and the method of the Lagrange multiplier. The method of finite element modeling is meanwhile used to approximate the governing partial differential equations by a discrete, finite degree-of-freedom system. With the beam outer profile parametrized by cubic splines in terms of locations of two intercepts, the Taguchi experimental design method is finally applied based on the simulated dynamics of the derived finite system to distill generic design guidelines for beam profile of the ultrasonic motor. It is found that a general paraboliclike profile for beam outer shape is best suited for maximizing output power, while a vaselike profile leads to the worst performance.