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This paper aims to propose a semianalytical model of a squirrel-cage induction machine (SCIM), considering local magnetic saturation and eddy-currents induced in the rotor bars.

The regions of the rotor and stator are divided into elementary subdomains (E-SDs) characterized by general solutions at the first harmonic of the magneto-harmonic Maxwell’s equations. These E-SDs are connected in both directions (i.e., along the r- and θ-edges).

The calculation of the magnetic field has been validated for various values of slip and iron permeability. All electromagnetic quantities were compared with those obtained using a two-dimensional finite-element method. The semianalytical results are satisfactory compared with the numerical results, considering both the amplitude and waveform.

Expansion of the recent analytical model (E-SD technique) for the full prediction of the magnetic field in SCIMs, considering the local saturation effect and the eddy-currents induced in the rotor bars.

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.

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.

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.

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.