Contact modelling by the finite element method : Application to the piezoelectric motor

Abstract
The operating principle of the piezoelectric motor is based upon various physical phenomena, among which one could mention the acoustic vibration and the friction between the stator and the rotor. In our laboratory a finite element code called ATILA has been developed. ATILA is efficient to perform static, modal or harmonic analysises for elastic structures. During the last two decades, the contact modeling drew the attention of numerous research groups, suggesting numerical approach by the finite element. However, most of these numerical studies require heavy programming techniques. In this paper we suggest an algorithm in order to treat the problem of contact with or without friction. This algorithm is based on a technique of mathematical simple programming using the method of static condensation. Finally, an application to the piezoelectric motor is presented. The present study focused on the interface between the stator and the rotor, where the acoustic energy is converted into the spinning of the rotor through the friction mechanism. The contact algorithm presented in this paper allows the contact surface, the normal and tangential stresses to be determined as a function of the interface parameters. The results are validated by comparing with piezoelectric motor experimental data.