Analytical magnetic field calculation for flat permanent-magnet linear machines with dual-rotor by using improved two-dimensional hybrid analytical method

Abstract

This paper aims to propose an improved two-dimensional hybrid analytical method (HAM) in Cartesian coordinates, based on the exact subdomain technique and the magnetic equivalent circuit (MEC). The magnetic field solution is obtained by coupling an exact analytical model (AM), calculated in all regions having relative permeability equal to unity, with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff’s current law) in ferromagnetic regions. The AM and MEC are connected in both axes (x, y) of the (non-)periodicity direction (i.e. in the interface between the tooth regions and all its adjacent regions as slots and/or air-gap). To provide accuracy solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead of the MEC characterized by an equivalent magnetomotive force (MMF) located in slots, teeth and yokes. It is found that whatever the iron core relative permeability, the developed HAM gives accurate results for no- and on-load conditions. The finite-element analysis demonstrates excellent results of the developed technique. The main objective of this paper is to make a direct coupling between the AM and MEC in both directions (i.e. x- and y-edges). The current density distribution is modeled by using Maxwell’s equations instead of the MEC and characterized by an MMF.