Abstract
A new hybrid Laplace transform/finite element method is proposed to solve the dynamic problem of a bimodal ultrasonic motor, which used a piezoelectric beam to drive the rotor. Two modes, longitudinal and flexural, of the piezoelectric beam are simultaneously excited by only one power amplifier. A set of differential equations is derived by finite element formulation for this oscillating beam. A proper similarity transform technique is used to decouple the Laplace transformed equations governing the vibration of the beam without contact and to make the inverse Laplace transformation easier. The contact problem between the beam and the rotor is also formulated and numerically solved. It is found that the simulation results obtained by using this hybrid method are almost identical with those by the Runge–Kutta method, but the former is able to avoid an excessive amount of computation time. Some important factors affecting the behavior of this motor are studied, including structure design, amplitude of input voltage, phase displacement, exciting frequency, gap between beam tip and rotor, and contact phenomena.
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