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Schematics of the eddy-current models. Only a segment of the infinitely wide and long slab is drawn in (a)–(d). (a) Classical model. (b) Polivanov (DWD) model. (c) DMR model.
Source publication
A systematic description of theoretical eddy-current permeability
spectra of infinitely long and wide slabs with 180° bar domains is
made for the classical model, the Pry-Bean and Polivanov model
concerning the eddy-current anomaly owing to domain wall displacements
(DWD), as well as a model dealing with the anomalous low-frequency
eddy-current los...
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Citations
... we obtain the anomaly factor η(RB = 0) = 59 and 28 for 50W470 and 30Q130, respectively. Since the modeling η = 1.63w d /ts, where w d is the bar domain width, 48 this gives w d = 18 and 5 mm for 50W470 and 30Q130, respectively, indicating that there is only one or a few moving walls during magnetic reversal at B ∼ 0. It can be seen in Fig. 12(a) that H c,mid < Hc,cur occurs systematically, which corresponds to an effective magnetic path length lm = 0.22 m for Hc calculated by ...
... (17) and (19) being used, with η between f 1 and f 2 to be calculated and compared with eddy-current modeling. On the other hand, Eq. (32) is justified because h and Ke correspond to the two terms in Eq. (33), and K = (E/E f ) 2 is the consequence of a constant anti-eddy parallel equivalent resistance Rp. 46,48 For mathematical fitting of the experimental relation Ws(Bp, f ) vs f , Ws(Bp, f ) is expressed as the addition of static hysteresis loss, classical eddy-current loss, and excess loss, corresponding to P h , Pe, and Pr defined in ASTM A340-21, ...
The dc and ac flux density vs magnetic field B(H) loops of Epstein electrical strips are measured in an IEC type-A permeameter with a high-quality electrical strip wound double yokes of inside length l0 = 0.2 m and inside height h0 = 0.1 m and in a long solenoid. The relevant demagnetizing and eddy-current effects are analyzed, modeled, and discussed. It is concluded that demagnetizing corrected solenoid measurement developed for determining dc B(H) loops of the material cannot be used for the ac case, owing to complicated eddy-current demagnetizing effects. Permeameter-measured ac B(H) loops with H detected by a flat H-coil of length less than l0/2 touching the strip’s middle surface may be considered representative of the actual material because H is very uniform along the strip within 3l0/4. Strips with ac B(H) loops thus determined should be used to calibrate the effective magnetic path length lm of Epstein measurements, where a very nonuniform field is applied to the strips.
... Moreover, at high enough induction level, the DMR process becomes significant. Comparisons of the DMR and the DWD processes and corresponding eddy currents as a function the induction level and frequency can be found in several references [25,31], and they all lead to the same conclusion: the description of magnetization dynamics and losses at high induction levels must take the whole mechanisms including the DWD with bowing (DWB), multiplication (DWM), fusion (DWF), nucleations (DWN) and the DMR process. ...
... Microscopic eddy currents jw and jd are induced around moving domain walls w and inside domains d with rotating magnetization [4,25,31] (see Figure 1). Accurate calculations of the latter are impossible. ...
... For Fields HM < 25 A.m -1 , i.e. for induction levels B < 1.25 T, the anti eddy field due to the DMR mechanism is negligible in front of the anti eddy field due to the DWD mechanism. In references [25,31] for example, comparison is made between the characteristic time constants: ...
The definition and development of a dynamic or transient magnetic formulation compatible with the Finite Element Method, able to take the dynamic hysteresis and classical and extra losses into account (not a posteriori but a priori), and using the most adapted state variable that makes the problem well defined and easily convergent requires the knowledge of dynamic behavioral properties of soft magnetic materials whatever the thickness and the working conditions. The dynamic hysteresis of soft magnetic materials corresponds to excess iron losses, due to dynamic magnetization reversal processes within magnetic domains and especially to microscopic eddy currents around the magnetic walls in motion and inside rotating domains. The model properties used are the internal quasi-static permeability μ and the dynamic magnetization property Λ that lumps the magnetization mechanisms (domain walls displacement, bowing, fusion, nucleation and multiplication). The latter are involved in the magnetic field damping due to microscopic eddy currents within the field diffusion that renders the magnetic behavior geometry dependent. This model does not separate the field diffusion process from the magnetization reversal mechanisms. In this paper, the sheet thickness ζ dependence of the dynamic magnetization property Λ(ζ) for a Grain Oriented Electrical Steel (GOES: steel made of 3% Silicon and Iron: SiFe) is analyzed in the Rolling Direction (RD). To this extend, it is proposed to carry out and interpret magnetic measurements on GOES samples with the Epstein frame for four different thicknesses (ζ = 0.23, 0.27, 0.30 and 0.35 mm), but with similar metallurgical and crystallographic properties for the whole specimens. Magnetic properties are first identified at low induction with linear assumptions and at higher induction with non-linearities. It makes it possible to re-compute the dynamic hysteresis loops of the material and to predict the losses whatever the working conditions with frequencies from 50 to 800 Hz. It is found that μ does not depend significantly on the sheet thickness whereas Λ depends on it significantly. Microscopic observation of the magnetic domains width are then performed thanks to the MOIF (Magneto-Optical Indicator Film) technique. It helps us discriminate between three simultaneous origins for the dependence of iron losses to the sheet thickness: a skin-like effect, a domains’ refinement and changes on the walls’ mobility. Results are discussed taking the dipolar magnetic effects, closure domains, the grains and texture and the manufacturing and coating residual stress on the metal surface into account.
... In this study, we do not take either the effects of the demagnetizing field or the eddy current into account. However, based on the analysis in [34], we observe that the power loss caused by the eddy current is negligible for thin, small-scale devices and can be disregarded. The demagnetizing field H d is always opposed to the externally applied field H 0 . ...
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... The physical meaning of a is the initial permeability, and its value should be 1 for Ag/SiO 2 composites, in good agreement with the calculation results (in Table S7). The parameter b is an intrinsic parameter, which is closely related to the composition, microstructure and electromagnetic property of composites [34,35]. The magnetic loss was also studied to reveal the influence of eddy current on negative susceptibility/permeability. ...
The mechanism of negative permittivity/permeability is still unclear in the random metamaterials, where the precise control of microstructure and electromagnetic properties is also a challenge due to its random characteristic. Here silver was introduced into porous SiO 2 microsphere matrix by a self-assemble and template method to construct the random metamaterials. The distribution of silver was restricted among the interstices of SiO 2 microspheres, which lead to the precise regulation of electrical percolation (from hoping to Drude-type conductivity) with increasing silver content. Negative permittivity came from the plasma-like behavior of silver network, and its value and frequency dispersion were further adjusted by Lorentz-type dielectric response. During this process, the frequency of epsilon-near-zero (ENZ) could be adjusted accordingly. Negative permeability was well explained by the magnetic response of eddy current in silver micronetwork. The calculation results indicated that negative permeability has a linear relation with ω0.5 , showing a relaxation-type spectrum, different from the “magnetic plasma” of periodic metamaterials. Electromagnetic simulations demonstrated that negative permittivity materials and ENZ materials, with the advantage of enhanced absorption (40dB) and intelligent frequency selection even in a thin thickness (0.1 mm), could have potentials for electromagnetic attenuation and shielding. This work provides a clear physical image for the theoretical explanation of negative permittivity and negative permeability in random metamaterials, as well as a novel strategy to precisely control the microstructure of random metamaterials.
... The physical meaning of a is the initial permeability, and its value should be 1 for Ag/SiO 2 composites, in good agreement with the calculation results (in Table S7). The parameter b is an intrinsic parameter, which is closely related to the composition, microstructure and electromagnetic property of composites [34,35]. The magnetic loss was also studied to reveal the influence of eddy current on negative susceptibility/permeability. ...
The mechanism of negative permittivity/permeability is still unclear in the random metamaterials, where the precise control of microstructure and electromagnetic properties is also a challenge due to its random characteristic. Here silver was introduced into porous SiO 2 microsphere matrix by a self-assemble and template method to construct the random metamaterials. The distribution of silver was restricted among the interstices of SiO 2 microspheres, which lead to the precise regulation of electrical percolation (from hoping to Drude-type conductivity) with increasing silver content. Negative permittivity came from the plasma-like behavior of silver network, and its value and frequency dispersion were further adjusted by Lorentz-type dielectric response. During this process, the frequency of epsilon-near-zero (ENZ) could be adjusted accordingly. Negative permeability was well explained by the magnetic response of eddy current in silver micronetwork. The calculation results indicated that negative permeability has a linear relation with ω0.5 , showing a relaxation-type spectrum, different from the “magnetic plasma” of periodic metamaterials. Electromagnetic simulations demonstrated that negative permittivity materials and ENZ materials, with the advantage of enhanced absorption (40dB) and intelligent frequency selection even in a thin thickness (0.1 mm), could have potentials for electromagnetic attenuation and shielding. This work provides a clear physical image for the theoretical explanation of negative permittivity and negative permeability in random metamaterials, as well as a novel strategy to precisely control the microstructure of random metamaterials.
... In linear descriptions of MS materials, the eddy-current can be described in terms of a complex permeability by multiplication of the static permeability l S with the eddy-current loss factor v. 21 According to the study on the eddy-current effect in a ferromagnetic conductive plate in Ref. 22, the complex permeability l à of the MS alloy plate with a given electric conductivity r can be expressed as ...
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... A model, based on physical properties of the material, is presented in [19] and [20] to consider both phenomena of domainwall movement and magnetization rotation inside the domains for rectangular slabs and cylindrical samples, respectively. In this model, a dc magnetic field is applied perpendicular to the domain structure to rotate the magnetization vector inside the domains. ...
... One can write (19) It should be noticed that and components are related together through the angle by and , i.e. is equivalent to . One can write the relation between the two coordinate systems which are connected to the domain magnetization direction and rolling direction: (20) Additional subscript is related to the rolling direction coordinate system, as shown in Fig. 4. ...
... Since there is no field perpendicular to the rolling direction, and terms have no effect on the system. In order to have a complete description of the material, the susceptibility matrix (19) should be determined. First, the lowfrequency behavior is investigated: -, parallel susceptibility when there is no perpendicular field, is the susceptibility of the material calculated by the domain wall model [12], [16] and is denoted by subscript. ...
Ultrasoft magnetic materials, such as amorphous, nanocrystalline, and polycrystalline alloys, have been successfully used for power electronic applications during recent years. However, enhancements are needed for the integration of power electronic features, which involves high power densities and operating frequencies up to a few megahertz. Complex permeability spectra, which are used to describe material behavior in these applications, depend mainly on domain-wall motions and coherent magnetization rotation mechanisms. In this paper, we present a model describing these mechanisms, in terms of magnetic anisotropies and domain structure of the material. To validate the model, we measured permeability spectra of polycrystalline Ni-Fe alloys under mechanical stress using a specific setup. These measurements are suitable for comparing the physical model according to different magnetoelastic anisotropies. Results are useful for correlating high-frequency magnetic behavior and the annealing process of materials.
... The model used for the magnetic laminates is referred to as the classical eddy current model [22]. As in previous high-frequency models of steel laminates used for power applications [16,[23][24][25][26], it neglects anomalous effects, which are related to domain rotations and displacements [22]. ...
... The model used for the magnetic laminates is referred to as the classical eddy current model [22]. As in previous high-frequency models of steel laminates used for power applications [16,[23][24][25][26], it neglects anomalous effects, which are related to domain rotations and displacements [22]. Hysteresis is also neglected. ...
This paper presents a coupled FEM and lumped circuit modelling approach that is primarily intended for high-frequency and overvoltage simulations of rotating electric machines with coaxially insulated windings, such as Powerformer and Motorformer. The magnetic fields and their interaction with the conductors of the winding are simulated with the aid of a FEM-program. The displacement current and its losses are modelled with an external lumped circuit. To consider eddy current losses, the stranded conductors and the laminated steel cores are replaced by homogeneous bodies with similar losses over a wide frequency range. The approach is illustrated and experimentally verified for a set-up with a cable wound around two slot cores. The model agrees well with measurements up to 1 MHz. Copyright © 2007 John Wiley & Sons, Ltd.
... Un siècle plus tard, de nombreux physiciens s'affairent de nouveau à l'étude des processus dynamiques induits dans les matériaux ferromagnétiques (doux). Parmi eux, de nombreux italiens ( [WSK_1], [NEE_3], [GAL_1], [BEA_3], [BIS_1], [SLO_1], [CAR_1], [DEL_3], [BER_1], [BER_3], [MBM_1], [CHE_1]), dont Giorgio Bertotti [ [BER_2], [BER_4], [BER_5], [BER_6]] qui a laissé son nom à un modèle prédictif toujours basé sur une séparation entre pertes par hystérésis statique, pertes classiques et pertes en excès ( [BER_7], [BER_8], [BER_9]). Ces dernières sont alors expliquées à l'aide d'une étude statistique de pertes locales par courants induits microscopiques autour des divers objets magnétiques en mouvement tels que les parois (nous préciserons ces termes dans le chapitre 3). ...
... Lorsque la structure magnétique naturelle ne contient pas de domaines orientés parallèlement au champ d'excitation, mais perpendiculaires; ou lorsque le maté-riau est au bord de la saturation parallèle; il ne reste plus que la rotation cohérente des moments au sein des domaines non-parallèles ( [CHE_1], [OSH_1]). On peut reconstruire cette réponse sur le même esprit que précédemment et imaginer superposer les deux mécanismes DWD et DMR. ...
... Ceci reste le cas tant que les obstacles (défauts involontaires ou volontaires (aimants)) au mouvement des frontières restent minoritaires; c'est à dire justement pour les matériaux dits doux. Cependant, il peut exister des situations, où la direction ou l'intensité du champ imposé et de l'induction d'expérimentation rendent le mécanisme de rotation inévitable (exemple: induction perpendiculaire à l'axe de facile aimantation ou d'intensité élevée ne laissant plus que la rotation possible jusqu'à saturation), ou complémentaire du processus plus accessible du déplacement de parois [CHE_1]. ...
Soft magnetic materials (Fe, Ni, Co, ... amorphous, crystal or poly-crystal) are used in power electrical engineering to convert energy, to guide flux lines and to transmit information. Their main characteristic is to be easilly magnetised. They are also conducting and free currents are induced with time harmonics and transient signals. These last can be classicaly diffused at the macroscopic scale but also and
mainly locally induced in a moving microscopic magnetic structure. These damping effects and dynamic losses have got several consequences: power losses, time delay, signal distortion, remanence. We are interested in faithful models in order to understand soft
materials static and dynamic properties and to compute power electrical devices with accuracy. We have chosen to focus on microscopic eddy currents in addition to macroscopic ones, because they are at the origin of the dynamic hysteresis which is observed and measured.
After introducing the set of problems, stakes and state of the art; we began to build a theoretical material representation at the mesoscopic scale, between the microscopic and macroscopic ones, usable in material science and numerical simulation tools. So Matter-
Field Equations have been derived again with the physics of dynamic magnetisation reversal processes.
Then we tried to analyse the relevance and limits of our representation thanks to analytical calculations on simple and academic problems. We also carried out some calculations, measurements and experimental characterisations to confront theory and reality.
Finally, we have written, with the Finite Element Method, some dedicated electromagnetic formulations in 3-D and 2-D. We have confirmed them with simple test cases always comparing with standard and previous results, analytical calculations and experimental observations. First simple configurations of circuit breaking applications have also been investigated, studied and computed.
... Here, as in the similar models and the models with frequency-dependent parameters, the eddy current losses in the electric sheets are dealt with in the classical way. Hence, the anomalous effects, domain wall displacements, and domain magnetization rotations that are significant for the transient response of electric sheets [32] are neglected. ...
The polyphase model can be used to simulate the terminal and internal electromagnetic response of, for example, Powerformer™: a new power generator. The circuit parameters are based on geometrical and material data. The slot leakage is modeled by means of a reluctance circuit, which is coupled to the electric circuit by means of winding templates. The capacitive current and its losses in the outer semiconducting layer of the cable are modeled with a simplified version of an RC model that has been used previously for other coaxially insulated windings. The eddy current losses were neglected; however, it is presented how they can be included in the model. The simulated frequency and transient response of the lumped circuit is compared with measurements on an 11-MVA/45-kV, 600-r/min hydro Powerformer. With exception of the damping, the agreement is good, qualitatively, up to 100 kHz.
