Olivier De La Barriere

Magnetic Field Solution in Doubly Slotted Airgap of Conventional and Alternate Field-Excited Switched-Flux Topologies

A general solution of the magnetic field in the airgap of conventional and alternate field-excited switched-flux (FE-SF) machines is proposed in this paper. The analytical model is based on the subdomain method. It involves the solution of governing field equations in a doubly slotted airgap using the variable separation method. The complete model is derived and described in a general manner so that it can be easily extended to unconventional FE-SF topologies. By means of example, analytical predictions of airgap field are extensively compared and validated using 2D FE results. FE simulations were performed on a 24-10 classical FE-SF structure and also on a novel 18-11 FE-SF machine with additional spacer teeth.

A Multiscale Approach to Predict Classical Losses in Soft Magnetic Composites

This paper presents the application of a finite element multiscale method, based on the homogenization technique, to the prediction of classical losses in soft magnetic composite materials. The experimental results, obtained for a wide range of frequencies and for various toroidal samples with different cross sections, are explained by using the considered model. It has been found that the classical losses are influenced by the dimensions of the sample, as well as by the conductivity and the length of the random contacts between the grains.

Alternating and Rotational Losses Up to Magnetic Saturation in Non-Oriented Steel Sheets

A three-phase magnetizer has been developed, by which non-oriented Fe-Si steel sheets can be characterized under alternating and rotational flux up to a polarization value Jp ≈ 0.98 Js, where Js is the saturation magnetization. The loss measurements, performed in the frequency range 2 Hz-1 kHz, require the combination of field-metric and thermometric methods, besides fine control of the induction wave-shape/loci under the required demanding exciting conditions. By exploiting the loss separation concept, it is observed that under rotational flux, both the hysteresis and excess loss components monotonically decrease with Jp, to disappear at saturation. The measured losses then become equal to the calculated classical losses. This could actually be predicted, because of the expected disappearance of the domain walls under saturating rotational field, but it has never been previously verified by the experiments.

Prediction of Energy Losses in Soft Magnetic Materials Under Arbitrary Induction Waveforms and DC Bias

The statistical theory of losses (STL) provides a simple and general method for the interpretation and prediction of the energy losses in soft magnetic materials. One basic application consists, for example, in the prediction of the loss under arbitrary induction waveform, starting from data available from conventional measurements performed under sinusoidal flux. There are, however, persisting difficulties in assessing the loss when the induction waveform is affected by a dc bias, because this would require additional experimental data, seldom available to machine designers. In this paper, we overcome this problem applying, with suitable simplifications, the dynamic Preisach model. Here, the parameters of the STL model are obtained exploiting preemptive conventional measurements only. By this new simplified method, analytical expressions for the loss components are obtained under general supply conditions, including dc-biased induction waveforms.

A novel magnetizer for 2D broadband characterization of steel sheets and soft magnetic composites

The magnetic materials used in embedded applications need characterization and modeling in the kilohertz range. This problem is well addressed under conventional alternating induction, but with rotational and two-dimensional induction loci, which are ubiquitous in electrical machines, there is lack of results, because of the difficult task of reaching such high frequencies at technically interesting induction values with the conventional laboratory test benches. To overcome this difficulty, a novel three phase magnetizer has been designed, exploiting 3D finite element calculations, and applied in the lab. This device permits one to measure magnetization curve and losses in soft magnetic steel sheets and soft magnetic composites under alternating and circular induction up to about 5 kHz. We provide a few significant examples of loss measurements in 0.20 mm thick Fe-Si and Fe50Co50 laminations, and in soft magnetic composites. These measurements bring to light the role of skin effect under one-and two-dimensional fields.

Rotational Magnetic Losses in Nonoriented Fe-Si and Fe-Co Laminations up to the kilohertz Range

Literature data on the energy loss behavior of steel sheets under rotating induction are restricted to quite low frequencies, i.e., up to a few hundreds of hertz. This is not sufficient to predict the loss in high-speed electrical machines, where frequencies in the kilohertz range are commonly encountered. We have overcome this difficulty by making loss measurements under alternating and circular induction in 0.2 mm thick Fe-(3 wt%)Si and Fe49Co49V2 sheets using a specially designed experimental setup. Peak polarization levels and frequencies up to 1.6 T at 2 kHz have been reached in the Fe-Si laminations, whereas the Fe-Co alloy, endowed with much higher permeability, has been characterized up to 2.1 T at 5 kHz. In the first part of this paper, the measured loss behavior versus peak polarization and magnetizing frequency is presented. In the second part, a loss model for circular induction is proposed, considering the skin effect. To this end, we have derived a simple magnetic constitutive law for the material, assumed to be isotropic, and we have introduced it into the electromagnetic diffusion equation. The solution of this equation by an iterative algorithm provides the induction profile across the sample thickness and eventually the classical loss component, which represents the major contribution to the total loss at high frequencies. Good agreement with the experiments is obtained.

Semianalytical and Analytical Formulas for the Classical Loss in Granular Materials With Rectangular and Elliptical Grain Shapes

Granular soft magnetic materials, such as ferrites or soft magnetic composites, are widely spread in modern electrical engineering applications. An important loss contribution is the classical one. It is known that in these materials, two kinds of classical loss must be distinguished: eddy currents flowing at the scale of the whole sample (therefore called macroscopic), and current lines inside the grains (called microscopic). For the macroscopic eddy currents computation, the sample cross sections are often square or rectangular. For eddy currents prediction inside the grains, two cases can be distinguished: 1) the case of low density materials, for which circular or elliptical grain shapes are often realistic and 2) the case of high density materials. In this last class of granular materials, it is more difficult to identify a precise grain shape, because the deformations occurring during the compaction process often give to the grains a random shape. For carrying out the eddy current computation, rectangular shapes are often considered, because they allow a complete filling of the available space. To our knowledge, analytical eddy current formulas only exist for cylindrical or spherical regions. For other shapes, such as squares, rectangles, or ellipses, the finite element method must be used to compute the eddy current distribution, which can be time consuming. This paper overcomes this difficulty by proposing respectively a semianalytical formula for classical loss in rectangular geometries, and an analytical formula for elliptical cases.

Loss decomposition in non-oriented steel sheets: the role of the classical losses

The concept of loss separation based on the statistical theory of losses (STL) provides complete and accurate description of the frequency dependence of the energy losses in non-oriented soft magnetic sheets under the assumption of uniform magnetization reversal through the sheet cross-section. This assumption, implying a simple standard formulation for the classical loss component, has been recently challenged in the literature, in favor of a non-uniform reversal mechanism, expected to prevail in highly non-linear materials, where saturation magnetization wavefronts are deemed to symmetrically propagate across the sheet thickness (saturation wave model, SWM). Different conclusions regarding the dynamic loss analysis and its decomposition into the classical and excess loss components correspondingly emerge. In this letter, we discuss detailed investigations on the broadband energy loss versus frequency behavior in different non-oriented Fe-Si and low-carbon steel sheets. The experiments can be fully and consistently described by the STL. This occurs, in particular, for high-induction values and near-squared hysteresis loops, a predictable condition for adopting the SWM, which, however, fails to account for the experiments.

Uni- and Bidirectional Flux Variation Loci Method for Analytical Prediction of Iron Losses in Doubly-Salient Field-Excited Switched-Flux Machines

Field-Excited Flux-Switching machines are doubly-salient machines with complex flux-density waveforms in the core. Hence, prediction of iron losses is difficult. In this article, we propose a method to determine flux loci in iron parts in an analytical manner, accounting for bidirectional field in back-irons of stator and rotor. The analytical model for flux-density prediction in the core at no-load was first validated with 2D FE simulations. Then measured iron losses on a prototype machine were used to calibrate an iron loss model. It was shown that in FE-SF machines rotor iron losses are not negligible and represent 28% of total iron losses. This model could be advantageously used in a design optimization procedure.

Magnetic Loss Versus Frequency in Non-Oriented Steel Sheets and Its Prediction: Minor Loops, PWM, and the Limits of the Analytical Approach

The pulsewidth modulation (PWM) technique is commonly used to supply modern high-speed electrical machines. The fundamental frequency is typically in the kilohertz range, with switching frequencies of several tens of kilohertz, as determined by the new SiC- or GaAs-based power transistors modules. Switching introduces minor loops in the major hysteresis cycle, with durations of the order of