This paper presents a multi-material topology optimization for the design of permanent magnet synchronous motors (PMSMs). Specifically, structural shapes of permanent magnet (PM) and iron core in a PMSM rotor are simultaneously designed together with the orientation of PM magnetization. For a co-design of PM and iron core, relative permeability and residual magnetic flux density are interpolated by the three-field density approach based on the Helmholtz filtering and regularized Heaviside step function. Here, the Helmholtz filtering aims to attain smooth border in design results, and the Heaviside function enables us to acquire a clear border (i.e. zero-one design) without intermediate densities. The optimization goal is set as maximizing the average torque of PMSMs. The average torque is calculated by Maxwell stress tensor (MST) method considering a maximum torque per ampere (MTPA) control. To validate the effectiveness of the proposed multi-material topology optimization approach, a PMSM rotor with 4 poles and 12 slots is designed. In addition, design results at various settings of input current amplitude and PM strength are compared and discussed. When the input current is stronger than the PM strength, rotor PM and iron core are designed for utilizing both PM and reluctance torque components like V-shape interior PMSMs. On the other hand, in the case of stronger PM strength, PM is designed near the air-gap, which utilizes only PM torque component like surface PMSMs.

中文翻译：

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永磁同步电机多材料拓扑优化

本文提出了一种用于永磁同步电机 (PMSM) 设计的多材料拓扑优化。具体而言，PMSM转子中的永磁体（PM）和铁芯的结构形状与PM磁化方向一起设计。对于 PM 和铁芯的协同设计，相对磁导率和剩余磁通密度通过基于亥姆霍兹滤波和正则化 Heaviside 阶跃函数的三场密度方法进行插值。这里，亥姆霍兹滤波的目的是在设计结果中获得平滑的边界，而Heaviside函数使我们能够获得没有中间密度的清晰边界（即零一设计）。优化目标设置为最大化 PMSM 的平均扭矩。平均扭矩是通过麦克斯韦应力张量 (MST) 方法计算的，考虑到每安培的最大扭矩 (MTPA) 控制。为了验证所提出的多材料拓扑优化方法的有效性，设计了具有 4 极和 12 槽的 PMSM 转子。此外，还比较和讨论了不同输入电流幅度和 PM 强度设置下的设计结果。当输入电流大于 PM 强度时，转子 PM 和铁芯设计为同时利用 PM 和磁阻转矩分量，如 V 形内部 PMSM。另一方面，在 PM 强度更强的情况下，PM 设计在气隙附近，它像表面 PMSM 一样仅利用 PM 扭矩分量。设计了一个4极12槽的永磁同步电机转子。此外，还比较和讨论了不同输入电流幅度和 PM 强度设置下的设计结果。当输入电流大于 PM 强度时，转子 PM 和铁芯设计为同时利用 PM 和磁阻转矩分量，如 V 形内部 PMSM。另一方面，在 PM 强度更强的情况下，PM 设计在气隙附近，它像表面 PMSM 一样仅利用 PM 扭矩分量。设计了一个4极12槽的永磁同步电机转子。此外，还比较和讨论了不同输入电流幅度和 PM 强度设置下的设计结果。当输入电流大于 PM 强度时，转子 PM 和铁芯设计为同时利用 PM 和磁阻转矩分量，如 V 形内部 PMSM。另一方面，在 PM 强度更强的情况下，PM 设计在气隙附近，它像表面 PMSM 一样仅利用 PM 扭矩分量。