This article presents the simultaneous magnetic and structural topology optimization of a transverse laminated synchronous reluctance machine rotor using a solid isotropic with material penalization (SIMP)-based approach with the globally convergent method of moving asymptotes (GCMMA) optimization algorithm. Magneto-structural single and multi-objective optimization formulations are presented. The single objective formulation maximizes the average torque subject to constraints on torque ripple, Von Mises stress, and compliance. The multiobjective formulation simultaneously maximizes average torque and minimizes compliance subject to constraints on torque ripple and Von Mises stress. In both optimization formulations, the electrical steel densities in the rotor mesh elements are the control variables. Including stress and compliance in the optimization formulation ensures a structurally feasible design. The design-dependent centripetal force contributed by each element in the rotor mesh is considered dependent on its density and mass. An intermediate density material issue is observed where the density of the material in a mesh element does not converge fully to air or electrical steel. This issue is addressed through the use of a thresholding mass function which forces the convergence of the mass but not the density. The two optimization formulations are compared for rotors operating at 4000 and 12 000 r/min. An initial magnetic only topology optimization is used to seed the magneto-structural topology optimization to decrease the computational time. The impact of the magnetic only seed and rotor mesh density on the optimization outcomes is also examined.

中文翻译：

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同步磁阻电机转子的同时磁和结构拓扑优化

本文介绍了使用基于固体各向同性材料惩罚 (SIMP) 的方法和移动渐近线 (GCMMA) 优化算法的全局收敛方法对横向叠片同步磁阻电机转子进行同步磁和结构拓扑优化。提出了磁结构单目标和多目标优化公式。单一目标公式在受扭矩波动、Von Mises 应力和顺应性约束的情况下最大化平均扭矩。多目标公式同时最大化平均扭矩并最小化受扭矩波动和 Von Mises 应力约束的顺应性。在这两种优化公式中，转子网格单元中的电工钢密度是控制变量。在优化公式中包括应力和顺应性可确保结构上可行的设计。转子网格中每个元素贡献的设计相关向心力被认为取决于其密度和质量。当网格元素中的材料密度没有完全收敛到空气或电工钢时，会观察到中等密度材料问题。这个问题是通过使用阈值质量函数来解决的，该函数强制收敛质量而不是密度。将两种优化公式对以 4000 和 12 000 r/min 运行的转子进行比较。初始磁拓扑优化用于为磁结构拓扑优化提供种子以减少计算时间。