Figure 2
Source publication
The most significant assumptions in the subdomain technique (i.e., based on the formal resolution of Maxwell's equations applied in subdomain) is defined by: “The iron parts (i.e., the teeth and the back-iron) are considered to be infinitely permeable so that the saturation effect is neglected”. In this paper, the author presents a new scientific c...
Contexts in source publication
Context 1
... shown in Figure 2, the problem domain is divided into 7 subdomains with µ = C st . The vacuum around to the air-or iron-cored coil is defined by 4 regions, i.e., ...
Context 2
... the outer boundaries for (x 1 ∧ x 6 , ∀y) and (∀x, y 1 ∧ y 4 ) [see Figure 2], the component of the magnetic vector potential satisfies the Dirichlet boundary condition, i.e., (3c). By applying (3) and using (A.2) [see Appendix A], the respective boundaries at the interface between the various regions are illustrated in Figure 4. ...
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The most significant assumptions in the subdomain technique (i.e., based on the formal resolution of Maxwell's equations applied in subdomain) is defined by: “The iron parts (i.e., the teeth and the back-iron) are considered to be infinitely permeable so that the saturation effect is neglected”. In this paper, the author presents a new scientific c...
Citations
This article presents the process of building a hybrid analytical model (HAM) for surface-mounted permanent-magnet machines. The HAM couples a reluctance network (RN) model in the stator region with a magnetic scalar potential analytical model in the air gap and magnets regions. This hybrid model can deal with the slotting effect with straight teeth, and takes magnetic saturation into account in the stator iron material using the RN model. It is calculated under open-circuit and loaded conditions. The magnetic flux density, flux linkage, back electromotive force (EMF), and torque of the machines are also calculated. This hybrid model is compared with the subdomain method. It is also compared with the finite element method (FEM) both in terms of the size of the matrix that needs to be calculated and in terms of the torque error. We analyzed this method for two surface-mounted permanent-magnet machines, one with a symmetry factor of four and another with a symmetry factor of three. In both cases, HAM reduced the size of the matrix that needed to be solved compared to FEM. In the machine with a symmetry factor of three, when the matrix size of both FEM and HAM was around 1700 × 1700, the torque error of FEM was 2.62% compared to the high-mesh-density FEM simulation, while the torque error of HAM was only 0.17% compared to the same simulation. HAM also had significant advantages over the subdomain method, as it reduced the torque error from 16.8% to 0.08% in the case of high magnetic saturation. The HAM can, hence, play a significant role in the design and optimization of surface-mounted permanent-magnet machines, especially in cases where magnetic saturation is present.
This paper presents a two-dimensional analytical model of outer rotor permanent magnet machines equipped with surface inset permanent magnets. To obtain the analytical model, the whole model is divided into the sub-domains, according to the magnetic properties and geometries. Maxwell equations in each sub-domain are expressed and analytically solved. By using the boundary/interface conditions between adjacent sub-regions, integral coefficients in the general solutions are obtained. At the end, the analytically calculated results of the air-gap magnetic flux density, electromagnetic torque, unbalanced magnetic force (UMF), back-electromotive force (EMF) and inductances are verified by comparing them with those obtained from finite element method (FEM). One of the merits of this method in comparison with the numerical model is the capability of rapid calculation with the highest precision, which made it suitable for optimization problems.
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.
This paper presents a two-dimensional (2D) exact subdomain technique in polar coordinates considering the iron relative permeability in 6/4 switched reluctance machines (SRM) supplied by sinusoidal waveform of current (aka, variable flux reluctance machines). In non-periodic regions (e.g., rotor and/or stator slots/teeth), magnetostatic Maxwell's equations are solved considering non-homogeneous Neumann boundary conditions (BCs). The general solutions of magnetic vector potential in all subdomains are obtained by applying the interface conditions (ICs) in both directions (i.e., r-and θ-edges ICs). The global saturation effect is taken into account, with a constant magnetic permeability corresponding to the linear zone of the nonlinear B(H) curve. In this investigation, the magnetic flux density distribution inside the electrical machine, the static/dynamic electromagnetic torques, the magnetic flux linkage, the self-/mutual inductances, the magnetic pressures, and the unbalanced magnetic forces (UMFs) have been calculated for 6/4 SRM with two various non-overlapping (or concentrated) windings. One of the case studies is a M1 with a non-overlapping all teeth wound winding (double-layer winding with left and right layer) and the other is a M2 with a non-overlapping alternate teeth wound winding (single-layer winding). It is important to note that the developed semi-analytical model based on the 2D exact subdomain technique is also valid for any number of slot/pole combinations and for non-overlapping teeth wound windings with a single/double layer. Finally, the semi-analytical results have been performed for different values of iron core relative permeability (viz., 100 and 800), and compared with those obtained by the 2D finite-element method (FEM). The comparisons with FEM show good results for the proposed approach.
This paper presents a new scientific contribution to the two-dimensional red(2-D) subdomain technique in polar coordinates taking into account the finite relative permeability of the ferromagnetic material. The constant relative permeability corresponds to the linear part of the nonlinear B(H) curve. As in the conventional technique, the separation of variables method and the Fourier series are used for the resolution of magnetostatic Maxwell equations in each region. The general solutions of the magnetic field in subdomains, as well as the boundary conditions (BCs) between regions are different from the conventional method. In the proposed method, the magnetic field solution in each subdomain is a superposition of two magnetic quantities in the two directions (i.e., r-and Θ-axis), and the BCs between two regions are also in both directions. For example, the scientific contribution has been applied to an air-or iron-cored coil supplied by a constant current. The distribution of local quantities (i.e., the magnetic vector potential and flux density) has been validated by a corresponding 2-D finite-element analysis (FEA). The obtained semi-analytical results are in very good agreement with those of the numerical method.
