用有限元模拟超声电机起动到稳态的摩擦驱动过程，提升控制精度。

Finite element modeling (FEM) is a critical tool in the design and analysis of piezoelectric devices, offering detailed numerical simulations that guide various applications. While traditionally applied to eigenfrequency analysis and time-dependent studies for predicting excitation eigenfrequencies and estimating traveling wave amplitudes, FEM's potential extends to more sophisticated tasks. Advanced FEM applications, such as modeling friction-driven dynamic motion and reaction forces, are essential for accurately simulating the complex behaviors of piezoelectric actuators under real-world conditions. This paper presents a comprehensive motor model that encompasses the coupling dynamics between the stator and rotor in a piezoelectric ultrasonic motor (USM). Utilizing contact theory, the model simulates the complex conditions encountered during the USM's initial start-up phase and its transition to steady-state operation. Implemented in COMSOL Multiphysics, the model provides an in-depth analysis of a rotary piezoelectric actuator, capturing the dynamic interactions and reaction forces that influence its performance. The introduction of this FEM-based model represents a significant advancement in the simulation and understanding of piezoelectric actuators. By offering a more complete picture of the motor's behavior from start-up to steady state, this study enables more accurate control and optimization of piezoelectric devices, enhancing their efficiency and reliability in practical applications.