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The paper presents a model for a standing wave piezoelectric motor with a two bending mode resonator. The resonator is modelled using Hamilton’s principle and the Rayleigh-Ritz method. The contact is modelled using the Lagrange Multiplier method under the assumption of slip and it is showed how to solve the set of differential-algebraic equations. Detailed simulations show resonance frequencies as function of the piezoelement’s position, tip trajectories and contact forces. The paper demonstrates that contact stiffness and stick should be included in such model to obtain physically realistic results and a method to include stick is suggested. INTRODUCTION Most two mode standing wave piezoelectric motors excites a longitudinal mode and a bending mode to generate elliptical trajectories. This paper presents a method where both first and second bending modes are excited. A sketch of the motor which is currently being constructed is shown in Figure 1. The principle used in this motor is taken from the design of a spherical piezoelectric motor (Andersen et al. 2000). To predict the performance of a piezomotor an important issue is the contact model. The contact problem for travelling wave motors has been analysed by many authors (Wallaschek 1998) whereas the contact for the intermittent contact type motor has been analysed in smaller extent. Zharii (1996) proposed a method based on Hertz theory and Fung et al. (1999) solved the contact problem using the Lagrange Multiplier method. Gear et al. (1985) proposed a method for a numerical solution to this problem, Hatman et al. (1996) extended the method to include friction at the contact interface. In this paper the resonator is modelled using Hamilton’s principle together with a Rayleigh-Ritz representation of the assumed modes. The effect of the piezoelement’s position on the tip trajectories and resonance frequencies are studied. The contact constraint is modelled using the Lagrange multiplier method under the assumption of slip. Using earlier methods (Hatman et al. 1996) and (Fung et al. 1999) to solve the system equations, simulation results are presented. The quality of the results are discussed, and it is shown that the contact force can hardly be correct. The indication is that the commonly accepted way of using the Lagrange Multiplier method falls short on this problem. The remedial is inclusion of contact stiffness in the model. Also stick is included to improve the slip-stick model. The paper presents these enhancements of a new piezomotor model. DERIVATION OF BENDING VIBRATIONS FOR THE RESONATOR Figure 1 shows the piezoresonator with piezoelements attached to the beam. The poling direction of the piezoceramic is indicated by the arrow P and causes the upper piezoelements to expand when the applied voltages are positive relative to ground whereas the lower elements will contract for the same voltage. When the applied voltage becomes negative relative to ground the situation is reversed. The voltages UA and UB are formed by

Two-Mode Resonator and Contact Model for Standing Wave Piezomotor