Modes and tip motions in ultrasonic motors using torsional/ longitudinal vibration

Ultrasonic motors using combined torsional/longitudinal vibration rotate at frequencies where the stator tip has a large rotational velocity when the axial tip acceleration is high. Frictional contact with the rotor imparts a torque impulse to the rotor. Various geometries have been proposed that produce the required combination of torsional and longitudinal vibration. The resulting stator tip motions are complex and it is not obvious which frequencies will yield effective operation. We report here on simulations of the tip motion in such motors and use the simulations to predict the driving frequencies that result in rotation.