Mechanism of Ultra-Low-Speed Smoothness in Ultrasonic Motors Based on a Macro-Micro Multi-Scale Finite Element Model

The conventional microstepping driving method suffers from significant periodic speed oscillations under ultra-low-speed conditions, which fail to meet the stringent demand for smooth operation of ultrasonic motors in semiconductor packaging. Most existing theories and simulations of ultrasonic motors adopt a macroscopic mechanical perspective; after extensive linearization and idealization, they can only provide preliminary mechanism analysis and fail to achieve precise quantitative computation. Moreover, they neglect critical factors such as the microstructure of contact surfaces, preload distribution, and vibration mode transmission, making it difficult to reflect the true characteristics of the motor-including strong nonlinearity, multiphysics coupling, and complex interface behavior-resulting in considerable discrepancies between theory and experiment. In this paper, a macro-micro multi-scale finite element model of a traveling-wave ultrasonic motor is established using ADINA and HyperMesh, fully accounting for the strong nonlinearity and multiphysics coupling effects. Based on the ultrasonic friction reduction theory and the beat traveling wave mechanism, the stator deformation, interface zoning characteristics, and torque output of the superimposed pulse driving method and the microstepping driving method are systematically compared. The simulated stator mode shapes are validated by laser scanning vibrometry experiments, and multiple speed tests ranging from 200 to 320 arcsec/s are conducted. Simulation results show that at a target speed of 900 arcsec/s, the superimposed pulse driving method reduces the speed fluctuation rate from 228% to 32%. Experimental results confirm that the speed fluctuation rate of the superimposed pulse driving method is consistently much lower than that of the microstepping driving method across the entire tested speed range. This study reveals the low-speed smooth operation mechanism of the superimposed pulse driving method, characterized by single-peak dominance and smooth alternation between the driving and braking zones, thereby fundamentally overcoming the inherent shortcomings of the traditional microstepping driving method. The proposed model can effectively replace costly direct interface measurements, providing a new method and reference for ultra-low-speed precision control of ultrasonic motors and for investigating the driving mechanisms of similar motors.