Moment method based distributed multipoles for modeling magnetic materials in 2D and 3D magnetostatics

Abstract

This paper aims to develop a new modeling method, referred to as a moment method based distributed multipoles (MMDMP), for precise and fast computation of magnetic field and force involving various magnetic materials such as a permanent magnet (PM), an electromagnet (EM) and a ferromagnetic material (FM). The method decomposes the magnetic materials into local sources, consisting of volume and surface elements. Then, the magnetic field from the local sources is computed with the magnetization and demagnetization tensors of the elements. The demagnetization tensors are derived as a closed-form according to the geometry of the elements, which can be further converted into multipoles based on the distance between an observation point and the elements for computational efficiency. Additionally, the MMDMP is applied to the FM and EM by analyzing the magnetization of both materials due to existing magnetic fields. Magnetic interactions among the materials are computed by the sum of the elemental forces, which are forces on the local sources. The computational accuracy and efficiency are verified by field distribution and the force and torque interaction between the PM and an iron-core EM in 3D space. The results are compared to numerical solutions from a finite element method (FEM) and fundamental integral form equations such as Biot–Savart law. Finally, the MMDMP is applied to analyze the magnetic field of a brushless direct current (BLDC) motor and validated by the FEM and experiments. The results show that the MMDMP can provide fast and accurate analysis of magnetic characteristics of electromechanical systems.