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Magnetic Field Analytical Solution for Non-homogeneous Permeability in Retaining Sleeve of a High-Speed Permanent-Magnet Machine

Departamento de Engenharia Elétrica (DEE), Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG 31270-901, Brazil
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2018, 23(4), 72;
Received: 9 October 2018 / Revised: 6 November 2018 / Accepted: 7 November 2018 / Published: 10 November 2018
(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
PDF [1740 KB, uploaded 10 November 2018]


This work presents a novel solution for magnetic field calculation in two-dimensional problems in which one region is defined with space-varying magnetic parameter. The proposed solution extends the well-established Maxwell–Fourier method for calculating magnetic fields in surface-mounted cylindrical high-speed permanent-magnet machines. This contribution is effective to evaluate more realistic magnetic parameters, where measurements of a high-speed permanent-magnet generator prototype indicate saturation in the retaining sleeve due to pole-to-pole leakage flux. The saturation profile is a function of mechanical angle and can be modeled with the aid of a space-varying relative permeability, expressed in terms of a Fourier series. As an example, the presented solution has been applied to a surface-mounted PM machine at no-load condition. Magnetic field calculations show that a simple saturation profile, with low order space-varying permeability in the retaining sleeve significantly affects the magnetic flux density distribution in the air-gap. The analytical solution is confronted with finite-element method, which confirms validity of the proposed methodology. View Full-Text
Keywords: analytical model; high-speed; sleeve; non-homogeneous permeability; permanent-magnet analytical model; high-speed; sleeve; non-homogeneous permeability; permanent-magnet

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Mendonça, G.A.; Maia, T.A.C.; Cardoso Filho, B.J. Magnetic Field Analytical Solution for Non-homogeneous Permeability in Retaining Sleeve of a High-Speed Permanent-Magnet Machine. Math. Comput. Appl. 2018, 23, 72.

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