Arch-shaped axially magnetized bodies tend to appear frequently in electrical machine analysis such as in the overhang parts of the classical radial-flux machines as well as in the main parts of the axial-flux machines. The calculation of the 3-D fields originating from these bodies is demanding. The 3-D FEA suffers from high computational burden as well as no knowledge of the field origin. Analytic techniques involve the use of elliptic integrals and complex numbers for numerical evaluation, which makes them significantly slower than the 3-D FEA. In this article, a new analytical technique is proposed to speed up the computation by a factor of 20 for the global magnetic field created by a generic magnetized body by removing complex numbers and reducing the analytic equations significantly without any loss of precision. As a result, it can compete with the conventional 3-D FEA. In addition, integral methods may contribute to the wider use of parallel processing techniques. The original expressions for the vector potential are also provided, which has its own benefits and applications. Finally, the showcased magnetized body is assessed against 3-D FEA and discussed in terms of practical applications.

中文翻译：

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电机中拱形轴向磁化体超快速 3D 场和矢量势计算的广义和简化分析公式


拱形轴向磁化体经常出现在电机分析中，例如经典径向磁通电机的悬垂部分以及轴向磁通电机的主要部件。来自这些物体的 3D 场的计算要求很高。 3-D FEA 面临着高计算负担以及不了解场源的问题。分析技术涉及使用椭圆积分和复数进行数值评估，这使得它们比 3-D FEA 慢得多。在本文中，提出了一种新的分析技术，通过删除复数并显着减少解析方程，将通用磁化体产生的全局磁场的计算速度提高 20 倍，而不会损失任何精度。因此，它可以与传统的 3-D FEA 竞争。此外，积分方法可能有助于并行处理技术的更广泛使用。还提供了矢量势的原始表达式，它有其自身的优点和应用。最后，根据 3-D FEA 评估展示的磁化体，并根据实际应用进行讨论。