A mathematical model for the start-up of an ultrasonic bar-type motor

A simple mathematical model is presently being developed at TUD, modeling the transient behavior of an ultrasonic bar-type motor and in particular the start-up process. The model described is a further improvement on the earlier model formulated for steady state operation only. In the ultrasonic bar-type motor, stator vibrations are generated by means of piezoceramic elements. 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 here are modeled as rigid and are elastically supported. The kinematics is described taking into account all geometric nonlinearities. In modeling the start-up, special attention is given to differentiating between slip and stick contact conditions, as well as between contact and no-contact, since these conditions may change rapidly during the start-up process. These changes in the contact conditions have to be taken care of by the numerical integration procedure. 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. Reference is also made to experimental investigations.