Dynamics of Ultrasonic Motors

This thesis is treating theory, modeling, model analysis and experiments of traveling wave type ultrasonic motors. A framework to derive models for ultrasonic motors is given here, which is based on the continuum theory of electromechanical solids. This includes the modeling of the stator-rotor contact and the electromechanical behavior of piezoceramic stators. The principle of virtual power is stated for electromechanical systems, where the terms of virtual power due to normal and tangential contact stresses are expressed explicitly. Using this principle and a symbolic equation manipulation tool, a planar motor model based on BERNOULLI-EULER kinematics is derived. Subsequently, a scaling analysis is carried out. Then, a model analysis scheme is given, based on the derived motor model at steady-state. Contact boundary and transition conditions, continuity equations at the contact boundaries and contact search equations are stated. After that, a spatial discretization is carried out, using a GALERKIN discretization method with both, global and local Ansatz-functions. Compared to Finite-Element-Methods this reduces the number of degrees of freedom drastically, thus saving computer time. For the resulting algebraic equations, a contact algorithm is given. Using the computer code developed from this, numerical analyses are carried out. Particular resonance curves and speed-torque characteristics are computed and discussed. In the experimental part, the focus is on the resonance, the temperature and the steady-state motor operation behavior of a typical ultrasonic motor. Resonance curves of the electric admittances of stator and motor were measured and discussed as well as those of the velocity of surface points of both, stator and rotor. The resonance curves show a non-linear softening behavior. For sufficiently high stator vibration amplitudes this goes along with a jump phenomenon. It is found that material non-linearities in the piezoceramics may be the reason for this effect. Furthermore, the influence of the temperature rise due to the frictional contact mechanism is investigated. Speed-torque characteristics were measured and their dependence on various external parameters is investigated. At the same time, the time histories of different motor quantities like rotational speed, motor torque, electric current or velocity of surface points were recorded. Different effects in the motor behavior were observed, among them overhang speed-torque characteristics and hysteretic behavior. Finally, resistive and reactive power components as well as efficiencies along the speed-torque characteristics were computed