Permanent-magnet (PM) motors have been widely used in industrial applications and automobiles. However, owing to the design tolerances, manufacturing uncertainties, and material inconsistency, deviations from the ideal motor inevitably occur with parasitic effects, such as additional cogging torque and vibration. One of the most significant obstacles for evaluating these uncertainties is the large computational burden caused by the countless uncertain combinations, which must be computed via the finite-element method (FEM). Herein, a worst-uncertain-combination-analyze (WUCA) method is proposed to significantly reduce the computational cost. A widely used analytical method is modified to identify the origin of additional cogging-torque harmonics caused by uncertainties. Different types of uncertainties for the surface-mounted PM machine and interior PM machine can be analyzed simultaneously. With the WUCA method, the worst-case combinations can be confirmed theoretically; thus, FEM calculations for only a few combinations of uncertainties are required, rather than thousands. Compared with the widely adopted design of experiments based uncertain combining methods, the worst-case cogging torque obtained from the WUCA is higher. FEM verification of different pole/slot configurations revealed that the WUCA method was a general and effective method for quickly estimating the worst-case cogging torque under manufacturing uncertainties.

中文翻译：

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一种评估制造不确定性下最坏情况齿槽转矩的方法

永磁 (PM) 电机已广泛用于工业应用和汽车。然而，由于设计公差、制造不确定性和材料不一致，与理想电机的偏差不可避免地会产生寄生效应，例如额外的齿槽转矩和振动。评估这些不确定性的最重要障碍之一是无数不确定组合造成的巨大计算负担，必须通过有限元方法 (FEM) 进行计算。在此，提出了一种最坏不确定性组合分析（WUCA）方法来显着降低计算成本。修改了一种广泛使用的分析方法，以识别由不确定性引起的附加齿槽转矩谐波的来源。可以同时分析表面贴装 PM 电机和内部 PM 电机的不同类型的不确定性。使用 WUCA 方法，可以从理论上确认最坏情况的组合；因此，只需要对几种不确定性组合进行 FEM 计算，而不是数千种。与广泛采用的基于不确定组合方法的实验设计相比，从 WUCA 获得的最坏情况的齿槽转矩更高。不同极/槽配置的 FEM 验证表明，WUCA 方法是一种通用且有效的方法，可用于在制造不确定性下快速估计最坏情况下的齿槽转矩。只需要对几种不确定性组合进行 FEM 计算，而不是数千种。与广泛采用的基于不确定组合方法的实验设计相比，从 WUCA 获得的最坏情况的齿槽转矩更高。不同极/槽配置的 FEM 验证表明，WUCA 方法是一种通用且有效的方法，可用于在制造不确定性下快速估计最坏情况下的齿槽转矩。只需要对几种不确定性组合进行 FEM 计算，而不是数千种。与广泛采用的基于不确定组合方法的实验设计相比，从 WUCA 获得的最坏情况的齿槽转矩更高。不同极/槽配置的 FEM 验证表明，WUCA 方法是一种通用且有效的方法，可用于在制造不确定性下快速估计最坏情况下的齿槽转矩。