Classical Eddy Current Loss Research Articles

The excess loss analysis of an easy-plane FeSiAl@SiO2 soft magnetic composite with high permeability

The loss coming from the special eddy current caused by the inhomogeneous domain wall motion is usually used to explain the complex mechanisms of the excess loss below 200 kHz. In this work, an easy-plane FeSiAl@SiO2 SMC was fabricated to analyze the core loss. The prepared easy-plane FeSiAl@SiO2 SMC exhibits an initial permeability of 816 at 1 MHz and a domain wall resonance peak of 5.9 MHz. The core loss was measured up to 3 MHz and was separated into hysteresis loss, classical eddy current loss and excess loss. The excess loss was deeply analyzed by the theory of G. Bertotti. The results show the excess loss caused by localized eddy curreny is the main component of core loss in the range of 200 kHz to 3 MHz, and the domain wall resonance also exhibits the contribution on the core loss in the MHz band.

Effect of grain size on the core loss of nanocrystalline Fe86B13Cu1 prepared by ultra-rapid annealing

Nanocrystalline alloy samples with the same chemistry (Fe86B13Cu1) but with a range of mean grain sizes were prepared in order to investigate the effect of the grain size (D) on the core losses in nanocrystalline alloys. The core loss was measured on an Epstein frame in a frequency range between 10 Hz and 30 kHz. The measured core loss was separated into 3 parts, i.e. the hysteresis loss, classical eddy current loss and the excess loss. The classical eddy current loss is only a minor component due to the small thickness and moderately high electrical resistivity of the samples. Both the coercivity and the cycle hysteresis loss are found to follow roughly a D3 dependence. The excess loss at the maximum polarization (Jm) between 0.6 and 1.0 T is described universally by a simple power dependence of (Jm·f)n with an exponent of about 1.4 over a wide frequency (f) range between 10 Hz to 30 kHz. The excess loss at low frequencies appears almost independent of the grain size. Thus, the grain size effect on the total loss at low frequencies is attributable to the change in the hysteresis loss which reflects the static coercivity. However, the excess loss at 30 kHz shows a clear increase with an increase in D, indicating that the excess loss also becomes influential to the grain size dependence of the total core loss at high frequencies.

A dynamic magnetostrictive model based on the Jiles–Atherton hysteresis model and field separation approach

PurposeThe purpose of this paper is to combine the Jiles-Atherton (J-A) hysteresis model with the field separation approach to realize the accurate simulation of dynamic magnetostrictive characteristics of silicon steel sheet.Design/methodology/approachFirst, the energy loss of silicon steel sheet is divided into hysteresis loss Why, classical eddy current loss Wed and anomalous loss Wan according to the statistical theory of losses. The Why is calculated by static J-A hysteresis model, Wed and Wan are calculated by the analytical formulae. Then, based on the field separation approach, the dynamic magnetic field is derived. Finally, a new dynamic magnetostrictive model is proposed by means of the quadratic domain rotation model.FindingsComparison of simulation and experimental results verifies that the proposed model has high accuracy and strong universality.Originality/valueThe proposed method improves the existing method’s problem of relying on too much experimental data, and the method ensures the calculation accuracy, parameter identification accuracy and engineering practicability. Consequently, the presented work greatly facilitates further explorations and studies on simulation of dynamic magnetostrictive characteristics of silicon steel sheet.

Fractional derivatives for the core losses prediction: State of the art and beyond

The core losses prediction in laminated magnetic circuits has generated relentless scientific research efforts. In this domain, the almost forty years old Statistical Theory of Losses (STL) is still prevailing. Modern electrical energy conversion exposes laminated magnetic circuits to higher frequencies and larger excitation fields. STL, which requires a full flux penetration, poorly considered these intense stimuli. Recent studies proposed upgrading STL by modifying the classical eddy current loss term using fractional derivative operators. Excellent predictions were observed, but the lumped aspect inherent to STL means working with averaged quantities which constitutes a limitation. Alternatively, local predictions and good simulation trajectories were obtained for the frequency dependence of hysteresis by replacing the classic magnetic diffusion equation with a fractional one. Still, the physical origin of the fractional diffusion equation remains questionable. In the light of these results, we propose in this new study to review the use of the fractional derivative operators for the core losses prediction. We eventually revealed an alternative way to combine the classic diffusion equation to a fractional material law, leading to the ultimate fractional method, with physical fundaments, few parameters, and accurate results on significant frequency bandwidths.

Analytical Prediction Model of Energy Losses in Soft Magnetic Materials Over Broadband Frequency Range

Accurately and efficiently estimating the energy losses in electrical steels over a large frequency bandwidth, particularly in the high-frequency regimes, is of great significance for the optimal design of magnetic components. However, the traditional loss models, e.g., Steinmetz equations, have intrinsic drawbacks of being empirical and thereby require large amount of measured data to identify models' coefficients. Base on the fact that 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, and conventional applications of STL are limited to low-frequency range where the skin effect is negligible, a novel broadband analytical loss model is devised by introducing the fractional derivative concept into the simulation of classical eddy current loss in both low- and high-frequency domains, and proposing the energetic model to calculate the hysteresis loss component analytically under the framework of STL. Using such model, a few measured data are required, and the solving of the coupled nonlinear diffusion problem for high-frequency loss is thereby circumvented. The simulation and experimental results confirm the accuracy and efficiency of the proposed method.

Conductivitylike Gilbert Damping due to Intraband Scattering in Epitaxial Iron.

Confirming the origin of Gilbert damping by experiment has remained a challenge for many decades, even for simple ferromagnetic metals. Here, we experimentally identify Gilbert damping that increases with decreasing electronic scattering in epitaxial thin films of pure Fe. This observation of conductivitylike damping, which cannot be accounted for by classical eddy-current loss, is in excellent quantitative agreement with theoretical predictions of Gilbert damping due to intraband scattering. Our results resolve the long-standing question about a fundamental damping mechanism and offer hints for engineering low-loss magnetic metals for cryogenic spintronics and quantum devices.

Modeling of multi-axial stress dependent iron losses in electrical steel sheets

Modeling the effect of multi-axial mechanical stress on the iron losses of an M400-50A grade non-oriented electrical steel sheet is studied. By utilizing the statistical loss theory, the total measured iron losses are first segregated to hysteresis, classical eddy current and excess losses. Then, the stress dependency of the excess losses is modeled by correlating them to the hysteresis losses under multi-axial stress. This correlation, coupled with a magneto-elastic invariant based loss model, can be used to predict the iron loss evolution with reasonable accuracy under multi-axial stress when only iron loss data under no applied stress at various excitation frequencies and under only two uniaxial stress levels at quasi-static excitation are available. Consequently, this approach significantly reduces the required measurement data for estimating the iron losses under multi-axial stress.

A unified explicit analytical expression for considering anomalous eddy-current losses of ME laminate

Based on the equivalent circuit approach, a unified explicit analytical expression for RME field and voltage coefficients, taking into account the anomalous eddy-current losses of domain magnetization rotation (DMR) and domain wall displacements (DWD) in the magnetic phase, is established for ME laminate. For slabs with bar domains, the combination of classical eddy-current model and Polivanov’s eddy-current model in derivation achieved the consideration of microstructure of magnetic domains influencing the anomalous eddy-current losses. The proposed expressions are capable of reduction to some existing models, in which only the classical eddy-current losses or anomalous eddy-current losses of DWD are considered. The results prove that (1) the proposed novel expressions unified the previous analytical models on investigations of the anomalous eddy-current losses of ME laminate. (2) The prediction accuracy of the resonant ME (RME) coefficients corresponding to ME coupling effect has been increased due to considering the anomalous eddy-current losses. (3) The present investigations offer analytical expressions for obtaining the lower and upper boundary values of anomalous eddy-current losses for the specific ME laminate under intermediate values of and appropriate The numerical results provide theoretical guidance in design, manufacturing and application of smart structures with ME laminate.

Use of quasi-static loops of magnetic hysteresis in loss prediction in non-oriented electrical steels

One of the most important factors taken into account in the design and optimization of magnetic circuits of electronic and electric devices are energy losses. Therefore, it is necessary to have accurate models of energy losses in magnetic materials. At present, the most popular model describing excess losses in material Pexc is the semi-empirical model proposed by Bertotti. An important source of error in its application is the methodology of determining hysteresis losses Ph, that are part of total losses expressed in the form of the following formula Ptot=Ph+Pc+Pexc. The second component of this expression Pc is defined as classical eddy-current losses. The paper proposes a new approach to calculate hysteresis losses by using the Warburg theorem in which B(H) is expressed in the form of parametric equations. The proposed solution allows one to reduce the loss prediction error significantly.

The Microstructural Characterization, Physical and Dynamic Magnetic Properties of (Ni49Fe51)100−xCrx (x = 0,3,7) Thin Sheets

In this work, the effects of Cr on the microstructure, physical, and AC magnetic properties of the Ni49Fe51 alloy was studied. In this respect, three series of thin sheets of (Ni49Fe51)100−xCrx (x = 0, 3, and 7 at. pct) alloys with a final thickness of 120 µm were prepared by means of severe cold rolling and an 1150 °C annealing process at H2 atmosphere. Optical microscopy (OM), scanning electron microscopy (SEM), X-ray diffraction (XRD), (200) X-ray pole figure, and magnetic force microscopy (MFM) were employed to study microstructure, texture, and magnetic domain structure of the alloys. The magnetic characteristics of the samples were evaluated using BH-hysteresis loop tracer at a frequency range of 0.5 to 300 Hz. Based on the results obtained, it was shown that the mean magnetic domain width was increased from 1.006 to 1.398 μm for 0 Cr and 7 Cr samples, respectively. Furthermore, the magnitude of the static hysteresis loss increased and the excess and classical eddy current loss decreased for the Cr-added thin sheets.

Relevance of microstructure and texture to the accuracy and interpretation of 1 and 2 directional characterisation and testing of grain-oriented electrical steels

This paper is intended to stimulate discussion of some effects of not properly accounting for material microstructure in some established methods of measurement and prediction of losses in electrical steel laminations. Aspects of methods which have been used for many years are briefly discussed and some constraints or pitfalls are raised which users should be aware of. The basic cause of losses is summarised in order to set the scene for discussion of the analysis of losses into classical eddy current, hysteresis and anomalous loss. The possible presence and consequences of transverse flux in grain-oriented (GO) steels is raised followed by an explanation of some effects of the strong anisotropy of GO steel on flux density, magnetic field and loss measurement in stacks and single strips of GO steel. The presentation concludes with some questions on how circular rotational magnetisation can be made and precautions needed when assessing the effect of flux harmonics on the losses.

Magnetic Circuit Model combined with Play Model Obtained from Landau-Lifshitz-Gilbert Equation

This paper presents a novel magnetic circuit model considering magnetic hysteresis behavior, in which dc hysteresis is expressed by a play model while classical and anomalous eddy current losses are calculated by magnetic circuit elements. We describe an efficient method for obtaining the play model from the minimum measured B-H loops. It is proved that the proposed magnetic circuit model can calculate hysteresis loops under Pulse Width Modulation (PWM) excitation with high accuracy in a short time.

Perturbation Finite Element Method for Efficient Copper Losses Calculation in Switched Reluctance Machines

Copper losses dissipated in the windings of electric machines are the sum of classical ohmic dc losses and additional ac eddy current losses. In fact, the level of eddy current losses is strongly correlated with the manner of disposition of coil conductors in machine slots. Then, to improve the efficiency in electric machines, the selection of an optimal winding configuration becomes substantial. Since eddy current losses derive from the strong electromagnetic coupling between current density and time-dependent magnetic field, which cannot be solved easily, numerical analyses, such as particularly the one using the finite element (FE) method, are often used. As for the FE modeling, it can employ moving band technique to perform the rotor motion and Newton-Raphson iterations to deal with the nonlinear behavior of magnetic circuits. It leads then to a substantial computational time that hinders any process of conception or optimization of winding geometries. To overcome this issue, a 2-D FE model reduction based on the perturbation method is proposed. It starts from one approximate FE solution of a simplified complete machine modeling to find fast but accurate solutions in slots subdomains when any variation of geometrical or physical data occurs. It allows adapting nonconforming meshes and provides clear advantages in repetitive analyses when we search the optimized winding configuration for a given number of turns.

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圧縮応力下における電磁鋼板古典渦電流損の検討

Comprehensive Magnetic Properties Analysis of the Silicon Steel Considering the Laminated Direction

Comprehensive magnetic properties of the laminated silicon steels are key factors in magnetic core design, which should be measured and modeled by using a new testing method. Comparing with traditional Epstein frame and single sheet tester, a new method of three-dimensional magnetic properties measurement is used for complex magnetic properties of the laminated silicon steels. The comparison of magnetizations between the rolling or transverse direction and the laminated direction are illustrated. Both magnetic hysteresis and core loss features of the silicon steels specimen are measured and analyzed considering the laminated direction. The hysteresis loss, classical eddy current loss, and excess loss are analyzed and compared in different directions. This study can provide dynamic and comprehensive data to design and evaluate performance of electrical machines and power transformers.

Dynamic Experiments of Strain and Magnetic Field for Galfenol Rod and Its Modeling

Dynamic actuation experiments of an Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">83</sub> Ga <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">17</sub> (Galfenol) rod sample were conducted by the authors. A permanent magnet was used to apply a 2.25-kA/m bias field. Dynamic current through the excitation coils was applied to obtain a dynamic magnetic field. The frequencies of the dynamic field are 1, 10, 20, 40, 60, 100, 200, and 300 Hz. Hysteresis between the strain and dynamic magnetic field increases with increasing frequency. The power losses consist of hysteresis loss, classical eddy current loss, and anomalous (or excess) loss when Galfenol is excited by a dynamic field. To describe the hysteresis, a dynamic hysteresis model of Galfenol based on the energy-weighted average hysteresis equation, eddy current loss, and anomalous loss was used. The hysteresis loss was calculated using incremental volume fractions, which was evaluated using the energy-weighted average formula. The experimental results and model calculations agree well for frequencies below 200 Hz. The model can be used to guide the design of Galfenol dynamic applications in low frequency such as actuators and vibrators.

Influence of the Induction Shape on Hysteresis and Loss Measurements of Soft Magnetic Materials

The frequency dependence of the hysteresis loop of high-pressure torsion treatment (HPT)-deformed Fe75Al25, industrial steel Fe–3wt%Si, bulk Fe–3wt%Si plates, and nanocrystalline VP800 was measured on ring-shaped samples. Applying a sinusoidal or triangular $H(t)$ delivers a strong frequency dependence of the losses. A sinusoidal or triangular $B(t)$ reduces the total loss [this reduction is larger for triangular $B(t)$ ] and the dependence of loss on frequency becomes smaller. Our results are discussed in terms of Bertotti’s loss separation model. For HPT-deformed Fe75Al25, the total loss $W$ linearly varies with the square root of frequency when a triangular $H(t)$ is applied; however, no significant change in the total loss was found for a triangular induction $B(t)$ up to 500 Hz. The hysteresis, classical, and excess loss values of the Fe–3wt%Si steel plates are different from those of bulk Fe–3wt%Si for all $H(t)$ and $B(t)$ shapes due to different microstructures. In nanocrystalline VP800, the contribution of classical eddy current loss to the total core loss is very small due to high resistivity and small ribbon thickness.

Angular Properties of Specific Total Loss Components Under Axial Magnetization in Grain-Oriented Electrical Steel

Electrical steel (ES) plays an important role in the design of magnetic circuit cores of electrical machines. Separating specific total loss into components is an excellent tool for loss analysis in ES. As is commonly accepted, the specific total loss is separated into three components: hysteresis and both classical and additional eddy current loss components. In addition, the conventional grain-oriented (GO) ES presents the strong anisotropy of magnetic properties, due to the (110) [001] Goss texture, with [001] the easiest direction [parallel to rolling direction (RD)], with intermediate [011] and magnetically worst [111] directions, at angles x = 0°, 90°, and about 54° to RD, respectively. However, magnetization angles 0° <; x <; 54° and 54° <; x <; 90° also play a very important role in the research of specific total loss components. The angular properties of specific total loss under axial magnetization in GO ES should be most preferably evaluated by the use of single-sheet tester with specimens cut at different angles with respect to RD. This paper demonstrates, in the quantitative way, the dependence of hysteresis P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> and additional eddy current Pa specific total loss components on Goss texture. In addition, the results obtained justify the division of specific total loss and its components in two flux density regions: below B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> ≤ 1 T (the lower region) and above B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> > 1 T (the upper region). This paper is intended to offer a better understanding of phenomena that cause magnetic anisotropy, i.e., different Goss textures.

Low power loss in Fe65.5Cr4Mo4Ga4P12B5.5C5 bulk metallic glasses

Power loss – one of the important application-oriented magnetic properties of ferromagnetic metallic glasses – has been well studied in glassy ribbons rather than bulk metallic glasses. This paper studies the influence of frequency, induction, annealing, and specimen thickness on the total power loss – which is divided into hysteresis loss, classical eddy current loss, and excess eddy current loss – of bulk ferromagnetic Fe65.5Cr4Mo4Ga4P12B5.5C5 glasses. The total power loss of bulk glasses increases with frequency and peak induction and follows a power relation, similar to what has been observed in glassy ribbons. Annealing decreases both the hysteresis loss and the classical eddy current loss, resulting in a lower total power loss. The ratio of excess eddy current loss to classical eddy current loss deceases with increasing specimen thickness. The excess eddy current loss is negligible for our thickest glass and comparable to the classical eddy current loss for our thinner glasses. In contrast, the excess eddy current loss is often at least one to two orders of magnitude greater than the classical eddy current loss in glassy ribbons. The low total power loss achieved in bulk ferromagnetic glasses should be beneficial to their practical applications in energy conversion devices.

3-D Eddy Current and Fringing-Flux Distribution in an Axial-Flux Permanent-Magnet Synchronous Machine With Stator in Laminated Iron or SMC

This paper compares the iron losses generated by the concentrated excitation windings of an axial-flux permanent-magnet synchronous machine (AFPMSM) in the stator core elements constructed with laminated silicon steel sheets (LSSS) or with soft magnetic composite (SMC). As the flux mainly flows in one direction, we use grain-oriented LSSS. In order to provide a very accurate comparison, individual laminations are modeled in the 3-D finite-element model, including the coating layer. The model accounts for the magnetic stray field (fringing field) that causes eddy currents in the plane of the sheets, in addition to the main flux causing the classical eddy-current loss. The losses caused by the 3-D eddy-current pattern, as well as hysteresis and excess losses, are computed and measured for a test setup. A comparison of losses is made for the SMC mounted in the same setup. SMC does not suffer from eddy currents due to fringing flux. Although SMC has a 16 times higher loss than the LSSS at 1 T and 50 Hz as measured with an Epstein frame, it was shown that the iron losses in the SMC in the AFPMSM setup are only 1.5 times higher than for the LSSS.