Li Rong, Ran Longqi, Wang Cong, He Jiangbo, Zhou Wu
School of Mechanical Engineering, Xihua University, Chengdu 610039, China.
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China.
Micromachines (Basel). 2025 Feb 19;16(2):239. doi: 10.3390/mi16020239.
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.
定子中的高质量行波对于行波超声电机（TUSM）实现良好的稳定性和效率至关重要。然而，各向异性弹性引起的模态分裂和形状畸变会导致严重的行波畸变。在本研究中，提出了基于折纸术的模态优化方法来抑制模态分裂和形状畸变。首先，通过线性插值在定子内边界构建折纸图案。随后，建立了具有偶数和奇数节径的正交模态的优化模型。采用具有无导数和边界约束优点的扩展Nelder-Mead单纯形算法来搜索解。优化后，奇数节径的正交模态的模态形状更接近正弦形式。例如，B13模态的畸变显著降低至0.003。同时，优化后仍保留了固有频率匹配。相比之下，该优化抑制了偶数节径的正交模态的频率分裂和形状畸变。例如，与B14模态相关的频率分裂从380 Hz显著降低至1 Hz，形状畸变低至0.004。
