Calculation and evaluation of the magnetic field air gap in permanent magnet synchronous machine BELLAL ZAGHDOUD 1 , SAADOUN ABDALLAH 2 Department of electrical engineering University of Annaba, ALGERIA 1 [email protected], 2 [email protected]Abstract: - The best way to understand the phenomena in any investigated motors is to get inside and to see magnetic field distribution. In this paper we will determine and evaluate the air gap field in a permanent magnet synchronous machine (PMSM) using finite element method (FEM). At first a numerical calculation of the magnetic field distribution is applied. Then a harmonic analysis of the air gap flux density waveform is carried out. The results are presented by diagrams. They discussed and compared with experimentally obtained ones, under no load and full load conditions. They show a very good agreement. Key-Words: - Finite element, harmonic analysis, magnetic flux density, air gap, permanent magnet synchronous machine. 1 Introduction Prediction and performance analysis of electrical machines depend mainly on the accuracy in the evaluation of the magnetic field linking the different parts of the machine [1-2]. During the last century several approaches have been used to solve this problem. The formulation of the magnetic field by Maxwell's equations using the vector potential is described by the Poisson differential equation [1-3]. Although its formulation is relatively easy to obtain, resolving the equation is virtually impossible in the case of electrical machines, mainly because of the complexity of the geometry and the nonlinearity of the various media of the domain’s solution. In the case of permanent magnet machines the problem becomes insurmountable because of the lack of an analytical formulation of the magnetomotive force (mmf) magnets. The only alternative to solve this problem is to use numerical methods [4-6]. During the last two decades the finite element method proved to be the most appropriate numerical method in terms of modeling, flexibility and accuracy to solve the nonlinear Poisson’s equation governing the magnetic field in electric machines [5,6]. Currently, several modeling of electrical machines softwares are available. The finite element package FEMM 4.2 (Finite Element Method Magnetic) developed by D. Meeker available for free on its website was used for the modeling of the PMSM model and to solve the Poisson’s equation governing the magnetostatic field. 2 Notations A(x,y) magnetic potential vector Ω(Г) domain solution bounded by the contour Г v x reluctivity of the media in the x direction v y reluctivity of the media in the y direction J current density of the carrying current conductors J m equivalent current density of the magnets v peripheral speed of the rotor B flux density H field intensity M magnetization M 0 magnetization constant μ permeability of medium μ 0 permeability of free space 3 Poisson equation of magnetic field The formulation for magnetic field in quasi-static regime formulated using the magnetic vector potential is represented by Maxwell's equations: The relation (2) states that the magnetic field is solenoidal, while the relationship (3) which represents the Ampere in differential form defines Recent Advances in Electrical Engineering ISBN: 978-960-474-318-6 98
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Calculation and evaluation of the magnetic field air gap in permanent