This article presents an improved analytical spatial harmonics subdomain (SHSD) model for analyzing the influence of individual spatial harmonics, in stator magneto-motive forces (MMFs), on the performance of multiphase cage rotor induction motors (CRIMs). The proposed SHSD model is an extension of conventional techniques that consider each MMF spatial harmonic, caused by stator slots with tooth-tips, to be individual excitations when quantitatively analyzing the resulting physical effects. The solution domain was divided into four subdomains (SDs) in 2-D polar coordinates, including 1) rotor bars described by the Helmholtz equation; 2) air gaps; 3) slot openings described by Laplace’s equation; 4) stator slots represented by pure forced vibration equations. Current density in the stator structure was decomposed in a Fourier series of position angles to obtain MMF spatial harmonics. This produced a set of pure forced vibration equations in the stator slots, which were first solved in 2-D polar coordinates rather than the typical Poisson’s equation. This approach establishes a relationship between electromagnetic performance and stator parameters, for further optimization of IMs and analysis of electromagnetic vibrations. The proposed analytical model was validated using a series of finite element simulations, which exhibited high accuracy and computational efficiency.

中文翻译：

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多相笼式转子感应电机MMF空间谐波感应磁场的解析计算


本文提出了一种改进的分析空间谐波子域 (SHSD) 模型，用于分析定子磁动势 (MMF) 中的各个空间谐波对多相笼式转子感应电机 (CRIM) 性能的影响。所提出的 SHSD 模型是传统技术的扩展，在定量分析所产生的物理效应时，将由带齿尖的定子槽引起的每个 MMF 空间谐波视为单独的激励。解域在二维极坐标中被分为四个子域（SD），包括 1）由亥姆霍兹方程描述的转子条； 2）气隙； 3)拉普拉斯方程描述的槽口； 4) 定子槽由纯受迫振动方程表示。定子结构中的电流密度被分解为位置角的傅里叶级数，以获得 MMF 空间谐波。这在定子槽中产生了一组纯受迫振动方程，这些方程首先在二维极坐标而不是典型的泊松方程中求解。该方法建立了电磁性能和定子参数之间的关系，以便进一步优化 IM 和电磁振动分析。所提出的分析模型通过一系列有限元模拟进行了验证，显示出较高的精度和计算效率。