Prediction and suppression of inconsistent natural frequency and mode coupling of a cylindrical ultrasonic stator

Inconsistent frequency and mode coupling are primary concerns of ultrasonic motors. These modal properties are influenced by motor features, including piezoelectric ceramics, stator teeth, or other supports attached on a stator. While this influence is understood intuitively and has been studied numerically, they have not been clarified analytically. This work develops the analytical model of the example cylindrical stator and uses it to study the influence of the features on the modal properties. In this model, the stator is considered as a thin ring with equally spaced features. The analytical solution of the model is obtained by using the direct perturbation analysis, which connects the feature number and the wave number with the modal properties, and naturally provides an effective means to achieve the coincident frequency and suppress or even eliminate the predominant mode coupling only by optimizing the combination of the two numbers. Simulation results are well consistent with the analytical conclusions. The main feature of this work is that a quick and quantitative understanding of the effects of deviation from the perfect cylindrical stator is obtained. In addition, the derived analytical results contribute to the applications of common ultrasonic motor design choices. Furthermore, while the terminology of a cylindrical stator is used in this work, the analysis method applies for other stators, such as the disc-like or linear stator.