In 1983 Toshiiku Sashida developed a new motor concept called Piezoelectric Traveling Wave Rotary Ultrasonic Motor (PTRUSM). The advantages of these motors include high torque at low speed, absence of a generated magnetic field, and high potential for miniaturization. Unfortunately PTRUSMs have some disadvantages that limit the areas of applications for these types of motors. The disadvantages are a short operating life (about 1000 hours), small output power, and the need of a complex motor controller.

On one hand, these motors have been used in satellites, mobile phones, photocopiers, robotic arms, telescopes, automobiles, and camera autofocusing. On the other hand, the use of the PTRUSM is still limited in its applications because of the previously mentioned disadvantages of these motors.

Modeling of the PTRUSM is a current challenge because the existing models of the motor are just focused in describing the behavior of certain parts of the motor, or the models have several assumptions that degrade the accuracy of these models. There is no accurate complete model of the PTRUSM capable of being implemented in a model-based control strategy to operate these motors.

This dissertation presents a complete and accurate mathematical model of the PTRUSM. The motivation of this work was the need of a complete and accurate model of the motor capable of being used as the backbone of a model-based control strategy.

A 2D model of the motor is presented. The PTRUSM stator is modeled using a finite volume discretization. Two models of the PTRUSM stator were proposed:​ a static and a dynamic one. A simple model of the rotor with the capability of being coupled with the stator model was developed as well.

The stator and rotor models are coupled to model the stator-rotor contact interface of the motor. Two algorithms were prosed to model the contact between stator and rotor. These algorithms provide the contact zone width, height, the normal force distribution, and the breaking and driving contact zones;​ these parameters define the horizontal rotor velocity.

The torque-speed characteristic of the USR60 is calculated with the proposed model. The results of the model are compared versus the real torque-speed of the motor. It was observed that this novel model accurately reflects the most important characteristic of the PTRUSM