Phase difference optimization study on boundary reflection suppression of linear traveling wave piezoelectric actuator

Piezoelectric actuators (PEAs) find extensive applications in the ultra-precision industry due to their high precision and immunity to electromagnetic interference. Among these, ring-type ultrasonic motors exhibit highly stable traveling wave motion characteristics because of the absence of boundary wave reflections. Conversely, linear PEAs inevitably suffer from boundary wave reflections. This phenomenon degrades the stability of the traveling wave motion, thereby limiting further applications. Conventional perspectives generally consider a 90° phase difference as the optimal condition for generating traveling waves. However, based on wave interference theory and finite element method simulations, it is revealed that introducing non-standard phase differences (e.g., 75° or 80°) effectively suppresses parasitic standing waves. For quantitative evaluation, the coefficient of variation (CV) and the traveling wave ratio are introduced. The results indicate that, compared to the 90° phase difference, the optimized phase difference induces an amplitude loss of approximately 13.2% but expands the stable interval (CV ⩽ 5%) by 400%. This conclusion is verified across the flat beam, arc-shaped beam, and stepwise beam structures. Furthermore, the influence of system damping on the optimal phase difference is discussed. These findings expand the conventional understanding of phase control in traveling wave PEAs, revealing the unique advantages of non-standard phase differences in suppressing boundary reflections. Consequently, a more comprehensive theoretical framework is provided for the design of high-precision linear actuators. To ensure the transparency and reproducibility of this study, the complete finite element simulation source files have been open-sourced and are publicly available at: https://github.com/zhiwwu987-afk/Straight-Beam-Piezo-Actuator-FEA.