Dynamic Analysis of Progressive Circular Ultrasonic Waves in Piezoelectric Motors of Photo Lenses

This paper presents a dynamic analysis of ultrasonic motors (USMs) used in camera lens systems, which achieve high-precision motion via piezoelectric stators rather than electromagnetic components. The study focuses on the coupling of radial and tangential vibrations that create elliptical particle trajectories, driving the rotor through friction. The methodology is divided into two stages: Stage I: A discrete mass-spring model simplifies the coupled motion to a single degree of freedom. This analytical approach approximates natural frequencies and identifies modal degeneracy and the upper limits of representable modes via the Nyquist–Shannon criterion. Stage II: Based on continuous ring elasticity theory, the research establishes the actual coupled modal shapes. This stage demonstrates the manner in which kinematically linked displacements result in an elliptical trajectory on the stator surface. The analytical findings are validated using Finite Element Analysis (FEA) in CATIA. The simulations confirm the degeneracy of natural modes, proving that biphasic excitation is strictly necessary to maintain the progressive waves required for USM operation.