O. de la Barriere

Analytical Approach for Air-Gap Modeling of Field-Excited Flux-Switching Machine: No-Load Operation

This paper presents a general and accurate approach to determine the no-load flux of field-excited flux-switching (FE-FS) machines. These structures are inherently difficult to model due to their doubly-slotted air gap. This analytical approach is based on magnetomotive force-permeance theory. The analytical model developed is extensively compared to field distribution obtained with 2-D finite element (2-D FE) simulations. The good agreement observed between analytical model and 2-D FE results emphasizes the interest of this general approach regarding the computation time. Hence, this analytical approach is suitable for optimization process in pre-sizing loop. Furthermore, based on the field model, classical electromagnetic performances can be derived, such as flux linkage and back-electromotive force (back-EMF) and also, unbalanced magnetic force. Once again, FE results validate the analytical prediction, allowing investigations on several stator-rotor combinations, or optimization of the back-EMF.

3-D Formal Resolution of Maxwell Equations for the Computation of the No-Load Flux in an Axial Flux Permanent-Magnet Synchronous Machine

This paper presents a 3-D analytical model of an axial flux permanent-magnet synchronous machine, based on formal resolution of Maxwell equations. This method requires much less computation time than conventional 3-D finite elements, and is therefore suitable for optimization purposes. In a first part, the mathematical procedure used to compute the machine no-load flux is described in detail. This method is 3-D, and then takes into account the radial edge effects of the machine, as well as the curvature effects by a resolution in cylindrical coordinates. Moreover, the originality of this method lies in the fact that it is totally analytical. The obtained results are verified using 3-D finite elements, and compared with simpler analytical models of axial flux machines, taken from the literature. This work puts in evidence the advantages of the proposed model. In particular, it is shown that the radial edge effects are important for a correct estimation of the no-load flux. On the contrary, the curvature effects are a second-order phenomenon.

Analytical Armature Reaction Field Prediction in Field-Excited Flux-Switching Machines Using an Exact Relative Permeance Function

In this paper, an analytical approach for the prediction of the armature reaction field of field-excited flux-switching (FE-FS) machines is presented. The analytical method is based on the magnetomotive force (MMF)-permeance theory. The doubly-salient air-gap permeance, developed here, is derived from an exact solution of the slot permeance. Indeed, the relative slot permeance is obtained by solving Maxwells equations in a subdomain model and applying boundary and continuity conditions. In addition, during a no-load study, we found that, regarding the stator-rotor teeth combination, phase distributions were modified. Hence, in this paper, phase MMF distributions, for q phases, several stator-rotor combinations and also phase winding distribution (single- or double-layers) are proposed. We compare extensively magnetic field distributions calculated by the analytical model with those obtained from finite-element analyses. Futhermore, the model is used to predict the machine inductances. Once again, FE results validate the analytical prediction, showing that the developed model can be advantageously used as a design tool of FE-FS machine.

Loss separation in soft magnetic composites

We report and discuss significant results on the magnetic losses and their frequency dependence in soft magnetic composites. Two types of bonded Fe-based materials have been characterized at different inductions from dc to 10 kHz and analyzed by extending the concept of loss separation and the related statistical theory to the case of heterogeneous materials. Starting from the experimental evidence of eddy current confinement inside the individual particles, the classical loss component is calculated for given particle size distribution. Taking then into account the contribution of the experimentally determined quasistatic (hysteresis) loss, the excess loss component is obtained and quantitatively assessed. Its behavior shows that the dynamic homogenization of the magnetization process with frequency, a landmark feature of magnetic laminations, is restrained in these materials. This results into a partial offset of the loss advantage offered by the eddy current confinement.

Computation of Eddy Current Losses in Soft Magnetic Composites

We compute the classical eddy current losses in soft magnetic composite (SMC) materials, taking into account the eddy current paths appearing at the scale of the sample cross-section because of random contacts between the grains. The prediction of this loss contribution is a challenging task, because of the stochastic nature of the associated conduction process. We start our study from an identification of the statistical properties of the contacts between grains, starting from resistivity measurements. We then develop a numerical loss model for random grain-to-grain conduction, by which we demonstrate that the classical loss in SMCs can be decomposed into a contribution deriving from the eddy currents circulating inside the grains and a contribution due to the macroscopic eddy currents flowing from grain to grain via random contacts. An experimental validation of this model is proposed for a representative SMC material, where the magnetic losses are measured in ring samples with a range of cross-sectional areas.

An Analytical Model for the Computation of No-Load Eddy-Current Losses in the Rotor of a Permanent Magnet Synchronous Machine

This paper describes an analytical model for computing the rotor eddy-current losses in the case of permanent magnet synchronous machines, based on a formal resolution of Maxwells equations. We focus on the computation of the eddy currents in the machine magnets, in which the diffusion equation is analytically solved, using an accurate electromagnetic model of the stator slotting. The model originality lies in its capacity of taking into account both the diffusion phenomenon and the magnets finite length over the pole pitch, imposing that the total current over the magnets surface should be zero at each instant. This important problem is studied by solving a Fredholm integral equation. A validation using a 2-D time-stepping finite-element model is also performed, and the obtained losses are shown to be in good agreement with those given by the analytical method, for a shorter computation time.

Classical eddy current losses in Soft Magnetic Composites

This paper deals with the problem of loss evaluation in Soft Magnetic Composites (SMCs), focusing on the classical loss component. It is known that eddy currents can flow in these granular materials at two different scales, that of the single particle (microscopic eddy currents) and that of the specimen cross-section (macroscopic eddy currents), the latter ensuing from imperfect insulation between particles. It is often argued that this macroscopic loss component can be calculated considering an equivalent homogeneous material of same bulk resistivity. This assumption has not found so far clear and general experimental validation. In this paper, we discuss energy loss experiments in two different SMC materials, obtained using different binder types, and we verify that a classical macroscopic loss component, the sole size-dependent term, can be separately identified. It is also put in evidence that, depending on the material, the measured sample resistivity and the equivalent resistivity entering the calculation of the macroscopic eddy currents may not be the same. A corrective coefficient is, therefore, introduced and experimentally identified. This coefficient appears to depend on the material type only. An efficient way to calculate the macroscopic classical loss in these materials is thus provided.

Extended frequency analysis of magnetic losses under rotating induction in soft magnetic composites

We present novel results on magnetic losses in soft magnetic composites (SMCs) excited with rotating field. Soft composites are very promising in electrical engineering applications, where new topologies of electrical machines with two- and three-dimensional induction loci are increasingly found. An experimental characterization of industrial SMC products has, therefore, been carried out, up to the kilohertz range, under alternating and circular flux loci, making use of a specifically designed and optimized loss measuring setup. The obtained results have been analyzed for all kinds of excitation, according to the loss separation concept, with the emphasis being placed on the relationship between the rotational and the alternating loss components. In particular, it is found that the ratio between the rotational and the alternating losses is, for any given peak induction, independent of frequency.

Skin effect in steel sheets under rotating induction

By means of a newly developed broadband measuring setup we have overcome the usual upper limit for the test frequency, around a few hundred Hz, which is encountered in the two-dimensional characterization of magnetic steel sheets at technical inductions and we have measured the rotational losses in low-carbon steels up to 1 kHz and peak induction 1.7 T. An important piece of information is thus retrieved upon a frequency range useful to predict the performance of high-speed electrical machines. Our experiments, performed on thick (0.640 mm) laminations, have brought to light the emergence of the skin effect under rotational fields. This is revealed by an abrupt deviation of the excess loss component, calculated under the conventional loss separation procedure, from its well-known linear dependence on the square root of the frequency. A simple magnetic constitutive law under rotating induction is proposed and introduced into the electromagnetic diffusion equation, which is solved by finite elements coupled to a non-linear algorithm. The classical rotational eddy current loss, largely prevalent with respect to the hysteresis and excess loss components on approaching the kHz frequencies in low-carbon steels, is then calculated in the presence of skin effect, permitting one to achieve full analysis of the rotational losses and good predicting capability upon a broad range of frequencies and peak inductions.

High-frequency rotational losses in different soft magnetic composites

The isotropic properties of Soft Magnetic Composites (SMC) favor the design of new machine topologies and their granular structure can induce a potential decrease of the dynamic loss component. This paper is devoted to the characterization of the broadband magnetic losses of different SMC types under alternating and circular induction. The investigated materials differ by their grain size, heat treatment, compaction rate, and binder type. It is shown that, up to peak polarization J p = 1.25 T, the ratios between the rotational and the alternating loss components (classical, hysteresis, and excess) are quite independent of the material structural details, quite analogous to the known behavior of nonoriented steel laminations. On the contrary, at higher inductions, it is observed that the J p value at which the rotational hysteresis loss attains its maximum, related to the progressive disappearance of the domain walls under increasing rotational fields, decreases with the material susceptibility.