Last modified: 2024-06-03
Abstract
This paper employs the alpha finite element method (αFEM) for the simulation analysis of electric machine electromagnetic fields. With the rapid advancement of power electronics and new energy industries, electric machines, particularly permanent magnet machines, have gained widespread adoption due to their high efficiency and environmental optimization advantages. As the electromagnetic finite element analysis (FEA) technology continues to evolve, the finite element simulation analysis of electric machine electromagnetic fields has become an essential aspect of machine design and optimization. Traditional finite element methods using linear triangular elements, however, often suffer from limitations in computational accuracy and efficiency when applied to complex electromagnetic field problems. To address these shortcomings, the αFEM approach has emerged as a promising solution.
Smooth finite element method (S-FEM) have been extensively studied as an improvement over traditional FEM since their inception. Approaches based on edge-based smooth finite element method (ES-FEM), node-based smooth finite element method (NS-FEM), and face-based smooth finite element method (FS-FEM), which leverage smooth gradient techniques, have been proposed and applied in various fields to enhance traditional FEM. To avoid the presence of spurious non-zero energy modes in the NS-FEM for dynamic problems, Liu et al. proposed an effective method to formulate numerical schemes with "correct" stiffness, known as the alpha finite element method (αFEM). In αFEM, by scaling the physical coordinates and/or the strain gradients in the Jacobian matrix using an adjustable factor "α", one can obtain an approximate yet accurate solution for a given problem. Several versions of αFEM have been developed, including those using FEM approximations for displacements and rotations, as well as the Aa-DSG3 method that approximates bending, geometric, and shear strains using NS-FEM. Due to its ability to alleviate locking issues and its good performance in dynamic problems, αFEM has been widely applied in vibration, acoustics, and plate analysis, and these methods have been proven to be stable and convergent. This paper applies αFEM to the simulation analysis of the electromagnetic field of a permanent magnet synchronous motor, investigating the computational performance of αFEM in the motor's electromagnetic field. The numerical examples demonstrate that αFEM has higher computational accuracy compared to traditional FEM in the calculation of the motor's electromagnetic field using the same mesh model.