Dynamic characterization of a threaded-rod linear ultrasonic motor considering preload-dependent contact behavior

Ultrasonic motors are widely used in aerospace, medical equipment and other fields through the inverse piezoelectric effect of piezoelectric ceramics. As a new structure of ultrasonic motor, the threaded-rod linear ultrasonic motor is different from other ultrasonic motors. It has the characteristics of low speed, high torque, high precision and good running stability. However, due to the lack of dynamic modeling and analysis of the threaded rod linear ultrasonic motor, it cannot be widely used. In order to solve this problem, this paper constructs a new type of motor model that can apply preload. Based on the three-dimensional Timoshenko beam, the analytical model of the stator is established, and integrates mover into a unified whole-machine model with a modal-pairing framework that clarifies elliptical traveling-wave formation and the energy-transfer chain. Based on a BP neural-network control algorithm, a self-learning PID controller with KP, KI, and KD is established for high-precision, fast intelligent control. Laser scanning vibrometry verifies the model: the main peak frequency is approximately 32.82 kHz with a relative error to theory of approximately 0.55 percent. Key input–output laws are identified: the no-load speed is approximately linear with voltage in the range of 75 to 200 V; the excitation frequency shows a single-peak response; and preload has an optimal value that raises both speed and bearing capacity. Introducing the relative contact time (RCT) further reveals that the motor maintains a high load-carrying capability when the RCT is in the range of 0.7–0.9, with the best performance near an RCT of approximately 0.75. Under the present experimental conditions, the highest measured stable load reaches approximately 23.5 N at a preload of 36 N, indicating an optimal balance between contact maintenance and braking reduction. These results provide a computable physical basis and engineering criteria for LUSM parameter optimization, rapid performance prediction, and BP-PID controller design.