An Analytical Model for the Stiffness of Slotted Disk Springs

Abstract

The slotted disk spring is an important part of ultrasonic motors. Its mechanical properties directly affect the running stability of the motor. In this study, an analytical model is developed to solve the preload problem for slotted disk springs used in ultrasonic motors. The outer conical ring of the slotted disk spring is modeled using the conical shell theory. The inner separated teeth are modeled by the cantilever beam theory. An analytical mechanical model for the force-displacement relationship of the entire slotted disk spring is then developed. The results of the experiment based on a force-displacement transducer and the results from the analytical model, a finite element calculation, and the Schremmer formula are compared to validate the analytical model. The results show that the proposed model has the highest accuracy. Parameter-sensitivity analysis for the slotted disk spring is finally performed, and a new slotted disk spring with a long zero-stiffness interval is designed for a 40[Formula: see text]mm traveling wave rotary ultrasonic motor.