Transient behavior of an ultrasonic wobbling-disk motor

Stationary behavior of a wobbling-disk ultrasonic motor has already been studied in a previous publication with the help of a simple mathematical model. The model is able to capture basic motor features both quantitatively and qualitatively. The mathematical model presented in this paper describes the transient behavior of an ultrasonic wobbling-disk motor. Bending stator vibrations are generated in the ultrasonic motor with the help of a piezoceramic element. Two phase-shifted bending modes cause the upper plate of the stator to undergo a wobbling motion. The rotor is pressed against the stator and driven by frictional forces at the contact point. Both, stator and rotor are modeled as rigid and are elastically supported. The kinematics is described taking into account all geometric nonlinearities. In modeling the transient motion, special attention is given to differentiating between slip and stick contact conditions. Further improvements will include modeling the piezoceramic excitation in more detail. It is presently described by a rotating torque, generating the wobbling motion of the stator.