Magnetic Field Calculation for Flat Permanent-Magnet Linear Machines Using a Hybrid Analytical Model


  • LADGHEM CHIKOUCHE Brahim University of M'Sila
  • Kamel Boughrara Ecole Nationale Polytechnique
  • Frédéric Dubas University of Bourgogne Franche-Comté
  • Lazhar Roubache University of M'Sila
  • Rachid Ibtiouen Ecole Nationale Polytechnique



Hybrid magnetic model, exact subdomain technique, finite difference method, finite-element analysis


This paper proposes an improved two-dimensional (2-D) hybrid analytical method (HAM) in Cartesian coordinates, based on the exact subdomain (SD) technique and the finite-difference method (FDM). It is applied to flat permanent-magnet (PM) linear machines with dual-rotor. The magnetic field solution is obtained by coupling an exact SD model, calculated in all regions having relative permeability equal to unity, with FDM in ferromagnetic regions. The analytical model and FDM 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. It is found that, whatever the iron core magnetic parameters, the developed HAM gives accurate results for no- and on-load conditions. Finite-element analysis (FEA) demonstrates excellent results of the developed technique.