Nonlinear Semianalytical Model for Axial Flux Permanent-Magnet Machine

Abstract

In this article, we propose a novel nonlinear semianalytical model (AM) for the magnetic field calculation of electric machines. The nonlinear properties and local saturation effect of the iron part are taken into consideration in Cartesian coordinates, which is the main contribution of the proposed model. Thus, high accuracy of electromagnetic field results can be obtained with the low computational time cost. The model is developed based on the harmonic modeling technique by solving Maxwell's equations. The detailed theoretical derivations, which use the complex Fourier series and the Cauchy product, are presented. To verify the proposed model, an axial flux permanent-magnet (PM) machine is selected to be investigated. Both finite-element model and experimental results agree well with that of the proposed model. Moreover, the nonlinear AM has potential application for other types of PM electrical motor in Cartesian coordinates, such as flat PM linear machines.

Full-Domain Harmonic Potential Balance Model for 2-D Magnetic Field Analysis of Electrical Machine

“…For instance, the relative permeance function, developed by conformal mapping [13], works as a multiplier to a predetermined field distribution of smooth air gap, in which way the real distribution in the presence of slots is calculated. To some extent, it explains the modulation effect of slots [12]- [14]. Similar interpretability can be achieved by MEC-based models as well [15].…”

“…In (1), the μ stk , μ pm , and μ cop are the relative permeability of stator/rotor stacks, PMs, and conductors of copper, respectively. In addition, define the permeability distribution function μ(p) and reluctivity distribution function ρ(p) in the annular domain as…”

“…While (12) specifies the boundary condition for γ-coordinate, the complex logarithm is a multivalued function and provides 2π-periodicity along θ-direction, so there is:…”

“…NALYTICAL models are essential for design and optimization of electrical machines. Proper analytical models not only provide predictions for electromagnetic quantities, but also enhance one's insight into the physical mechanism in electrical machines [1]. On the other side, numerical methods, such as finite-element (FE) analysis, hardly reveal illuminating relationship between design parameters and electromagnetic quantities of electrical machines [2].…”

“…Modeling electrical machines totally by composite conformal mappings is usually realized by cumbersome geometric transformations [9]- [11]. Nevertheless, an interesting feature about conformal mapping is it sometimes gives interpretation for the distribution of magnetic field in electrical machine [12]. For instance, the relative permeance function, developed by conformal mapping [13], works as a multiplier to a predetermined field distribution of smooth air gap, in which way the real distribution in the presence of slots is calculated.…”