This paper proposes a smooth finite element method (S-FEM) for efficient and accurate analysis of motor magnetic fields. The edge-based smooth finite element (ES-FEM) formulations are derived for two-dimensional triangular element meshes suitable for multi-material motor structures, and then a magnetic flux density calculation method appropriate for S-FEM to calculate nonlinear electromagnetic fields is introduced. In the calculation of motor magnetic field, ES-FEM has a proper softening effect on the stiffness matrix of the finite elements, which makes the calculation more accurate and more efficient than FEM. The magnetic flux intensity calculation method introduced in this paper is not only appropriate for ES-FEM to calculate the nonlinear electromagnetic field of motor, but also can improve the calculation accuracy of magnetic flux density. In the calculation of nonlinear magnetic field of motor, ES-FEM can also improve the calculation accuracy of magnetic field analysis compared with FEM. Several numerical examples demonstrate the improving effect of the ES-FEM discussed above on the motor's magnetic field calculation.

中文翻译：

---

使用基于边缘的平滑有限元法 (ES-FEM) 进行电机磁场分析

本文提出了一种平滑有限元方法（S-FEM），用于高效、准确地分析电机磁场。推导了适用于多材料电机结构的二维三角形单元网格的基于边缘的平滑有限元（ES-FEM）公式，然后介绍了适合S-FEM计算非线性电磁场的磁通密度计算方法。在电机磁场计算中，ES-FEM对有限元的刚度矩阵有适当的软化作用，使得计算比FEM更准确、更高效。本文介绍的磁通强度计算方法不仅适用于ES-FEM计算电机非线性电磁场，而且可以提高磁通密度的计算精度。在电机非线性磁场计算中，ES-FEM相比FEM还可以提高磁场分析的计算精度。几个数值例子证明了上述ES-FEM对电机磁场计算的改进效果。