Mode Optimization of Microelectromechanical-System Traveling-Wave Ultrasonic Motor Based on Kirigami

High-quality traveling waves in stators are critical for traveling-wave ultrasonic motors (TUSMs) to achieve good stability and efficiency. However, the modal splitting and shape distortion that is induced by the anisotropic elasticity induce severe traveling wave distortion. In this study, mode optimization based on kirigami is proposed to suppress modal splitting and shape distortion. Initially, the kirigami pattern on the inner boundary of the stator was built by linear interpolation. Subsequently, the optimization model for the orthogonal modes with even and odd nodal diameters was established. An extended Nelder-Mead Simplex Algorithm with the advantages of derivative-free and bound constraints was employed to search the solution. After optimization, the mode shape of the orthogonal modes with odd nodal diameters was much closer to the sine-style. For instance, the distortion of the B13 mode was significantly reduced to 0.003. Meanwhile, the intrinsic frequency matching was still retained after the optimization. In contrast, the optimization suppressed both the frequency splitting and shape distortion of the orthogonal modes, with even nodal diameters. For instance, the frequency splitting relating to the B14 mode was significantly reduced from 380 Hz to 1 Hz, and the shape distortion was as low as 0.004.