Piezoelectric travelling wave ultrasonic motors based on the shear effect with radially polarised annular stator

The present thesis is concerned with the mathematical-analytical model of a piezoelectric travelling wave ultrasonic motor (USM) based on the shear effect. USMs have been adopted in high precision applications such as in the robotics, automotive industry, medical devices and autofocus of camera lenses. They are characterised by compact size, low speed with high torque and zero backlash. Since the shear piezoelectric coupling factor and the shear piezoelectric constant are higher than for the other piezoelectric effects, a relative higher torque and a better efficiency are also attained. In this thesis, special attention is paid to the kinematics and the geometry of the motor parts and to characteristics that influence efficiency and torque. In the motor, the stator is of disc-type, made of piezoceramics and radially polarised. It is therefore modelled as an annular Reissner-Mindlin plate with piezoelectric terms. Rayleigh-Ritz discretisation is used to obtain eigenfrequencies and eigenmodes of the stator plate. In the laboratory, measured eigenfrequencies of the free vibrations of the plate corroborate the numerical method. Particularly, the generation of travelling waves requests the excitation of two degenerated vibration modes. This requires a specific electrode configuration and, in this case, the design of a voltage inverter. A suitable vibration mode is chosen as working mode for the motor, so that the energy loss through friction in the radial direction is minimised. The transmission of load from stator to rotor occurs through a ring of teeth over the stator. Instead of just estimating the influence of the teeth on the stator model, the kinetic energy of the teeth set is formulated and taken into account in the equations of motion. Additionally, the conditions for the symmetry of the stator are stated with respect to the disposition and the number of teeth. In the contact model, point contact with a rigid rotor is assumed. The present mathematical-analytical model, which is characterised by a few degrees of freedom, is able to deliver relevant characteristics of the considered USM. The transient behaviour can be numerically solved and performance parameters such as power and efficiency (at steady state) can be calculated. It allows a systematical optimisation of the motor with respect to its geometry, its size, the number and disposition of the teeth, as well as the electric excitation. The influence of the teeth and the electric excitation is depicted in performance curves such as speed-torque and efficiency-torque curves.