The importance of rotor flexibility in ultrasonic traveling wave motors

In the simulation of a typical ultrasonic traveling wave motor, usually at least four topics have to be considered: modeling the stator, the piezoceramic ring bonded to the stator, the rotor and the contact problem between stator and rotor. Although from experimental observations it is well known that rotor flexibility strongly affects the motor behavior, this has so far not been taken into account in modeling these motors. The aim of this paper is to point out the importance of rotor flexibility in an electromechanical model of an ultrasonic traveling wave motor. A motor of the plate type with one piezoceramic ring is modeled. The simulation is based on the approach suggested by Hagood, where we however incorporate rotor flexibility. The geometrical and material parameters for the model are taken from data of an industrial prototype motor. The coefficient of friction between the contact layer of the rotor and the stator is obtained from the stall torque, and the damping of the disk spring is adjusted to measured torque-speed characteristics of the motor. The steady state dynamical behavior of the model is simulated in the frequency domain. Such an analysis can be carried out much faster than the numerical integration of the equations of motion in the time domain, as originally done by Hagood. It turns out that the measured torque-speed characteristic can not be fitted if rotor flexibility is ignored, while good results are obtained if the flexibility of the rotor is included in the model.