On-load magnetic field calculation for linear permanent-magnet actuators using hybrid 2-D finite-element method and Maxwell–Fourier analysis

Purpose The purpose of this study is to present a novel extended hybrid analytical method (HAM) that leverages a two-dimensional (2-D) coupling between the semi-analytical Maxwell–Fourier analysis and the finite element method (FEM) in Cartesian coordinates. Design/methodology/approach The proposed model is applied to flat permanent-magnet linear electrical machines with rotor-dual. The magnetic field solution across the entire machine is established by coupling an exact analytical model (AM), designed for regions with relative magnetic permeability equal to unity, with a FEM in ferromagnetic regions. The coupling between AM and FEM occurs bidirectionally ( x , y ) along the edges separating teeth regions and their adjacent regions through applied boundary conditions. Findings The developed HAM yields accurate results concerning the magnetic flux density distribution, cogging force and induced voltage under various operating conditions, including magnetic or geometric parameters. A comparison with hybrid finite-difference and hybrid reluctance network methods demonstrates very satisfactory agreement with 2-D FEM. Originality/value The original contribution of this paper lies in establishing a direct coupling between the semi-analytical Maxwell–Fourier analysis and the FEM, particularly at the interface between adjacent regions with differing magnetic parameters.