Excitation and distortion of elastic vibration of cylindrical ultrasonic stator

Abstract

This work examines the elastic vibration of the ultrasonic stator subjected to piezoelectric bending excitation by focusing on two fundamental issues: general driving rule and vibration distortion. An elastic model of a cylindrical ultrasonic stator is developed by using Hamilton’s principle and solved by analytical approach. The results imply that a desired vibration can be aroused provided that an algebraic relation is satisfied by a suitable parameter combination. Traveling/standing wave is excited by conventional time-spatial voltage ones or even other ones. The relationships between the duty ratio of input voltage and wave distortion are identified as closed-form expression of basic parameters. The excitation’s average creates a stationary deflection but it can be neglected thanks to the sufficiently small amplitude it causes relative to that at the resonance frequency. The rotation reversion is realized by changing the duty ratio or excitation frequency but remarkable distortion and amplitude decrease occur, leading to the asymmetry between the forward and inversion. Main results are validated by the superposition approach and comparisons against the existing ones. Discussions on phasing effect and vibration distortion relative to other symmetric systems are also made. Main contributions are the general driving rule with non-π/2 time-spatial phases and explanations on vibration distortion. These are achieved via the general time-spatial phasing in cyclically symmetric power-transmission systems.