Si-Fe Sheets Research Articles

A Novel Approach for Evaluating the Influence of Texture Intensities on the First Magnetization Curve and Hysteresis Loss in Fe-Si Alloys.

This paper examines the relationship between the magnetization behavior and crystal lattice orientations of Fe-Si alloys intended for magnetic applications. A novel approach is introduced to assess anisotropy of the magnetic losses and first magnetization curves. This method links the magnetocrystalline anisotropy energy of single crystal structures to the textures of polycrystalline materials through a vectorial space description of the crystal unit cell, incorporating vectors for external applied field and saturation magnetization. This study provides a preliminary understanding of how texture influences magnetic loss rates and the first magnetization curves. Experimental results from Electron Back-Scattered Diffraction (EBSD) and Single-Sheet Tests (SSTs), combined with energy considerations and mathematical modeling, reveal the following key findings: (i) a higher density of cubic texture components, whether aligned or rotated relative to the rolling direction, decreases magnetic anisotropy, suggesting that optimizing cubic texture can enhance material performance; (ii) at high magnetic fields, there is no straightforward correlation between energy losses and polarization; and (iii) magnetization rates significantly impact magnetization loss rates, highlighting the importance of considering these rates in optimizing Fe-Si sheet manufacturing processes. These findings offer valuable insights for improving the manufacturing and performance of Fe-Si sheets, emphasizing the need for further exploration of texture effects on magnetic behavior.

Domain Wall Structure Model of through the Thickness of Fe-Si Sheet Studied by X ray Topography

Domain Wall Structure Model of through the Thickness of Fe-Si Sheet Studied by X ray Topography

Magnetic Behavior of NO Fe-Si Sheets under Tensile and Compressive Stresses

Magnetic Behavior of NO Fe-Si Sheets under Tensile and Compressive Stresses

Iron loss evaluation method for SiFe sheet material under PWM inverter excitation

This study proposed an iron loss evaluation method for SiFe sheet material under high-frequency current ripple caused by pulse width modulation (PWM) inverter switching. The PWM inverter switching results in dynamic minor loops on the BH plane, leading to iron loss. Furthermore, in magnetic material with wide major loops, such as SiFe sheet material, the iron loss caused by one dynamic minor loop differs based on the flux density bias difference even for the same magnetic field bias. A previous study reported an iron loss calculation error because the conventional iron loss calculation method neglected the iron loss of the flux density bias characteristic in the same magnetic field bias. Therefore, we modified the previously developed iron loss measurement system to collect the iron loss of the flux density bias characteristic and proposed an iron loss calculation method for SiFe sheet material.

Decoupling the effects of texture and composition on magnetic properties of Fe-Si sheet processed by shear deformation

Soft magnetic Fe-Si alloys (electrical steels) possess exceptional functional properties such as high permeability, low coercivity, and low core loss, which generally improve with increasing Si content in the alloy. However, Fe-Si alloys containing > 3.5 wt% Si are also characterized by prohibitively low workability and poor ductility that have prevented their efficient commercial production in sheet form by rolling. This has limited their use for improving efficiency of motors and transformers. In this study, hybrid cutting-extrusion (HCE) is used as a single-step thermomechanical processing method to produce continuous Fe-Si alloy sheet with high Si compositions of 4 wt% to 6.5 wt%. HCE sheet is shown to have a homogeneous annealed grain structure and simple-shear crystallographic textures. By controlling the HCE deformation path, varied crystallographic shear textures are created in the sheet. Quasi-static magnetic properties of the HCE sheet are evaluated to decouple the effects of sheet texture and Si composition on resultant permeability and coercivity properties. The results suggest that HCE, with suitable process scaling, is a viable route for production of high-Si content electrical steel sheet for next-generation motors and transformers.

Magnetic loss in grain-oriented Fe–Si sheets under different harmonic excitation and high indication

This paper presents an improved loss calculation method that takes into account the effects of harmonics and skinning effects, thus extending the loss prediction of soft magnetic materials to a larger frequency and induction range. First, the first-order and second-order slew curves are concurrently fitted into a nonlinear Preisach model to determine the hysteresis loss. Then, integrating the effects of high frequency harmonics and high induction, the fixed-point technique based on the H–B magnetic intrinsic relationship is introduced into the finite element calculation in order to calculate the flux density distribution of the silicon steel sheet more accurately. Then, the classical loss at high flux density is further calculated more accurately. Finally, losses for soft magnetic materials in the 1 kHz range are computed under various harmonic excitations. This method is compared to the traditional method and the experimental results, and this method is closer to the experimental results.

Wideband magnetic losses and their interpretation in HGO steel sheets

The magnetic properties of high-permeability grain-oriented (HGO) Fe-Si sheets have been investigated in the frequency range 1 Hz-10 kHz, with attention devoted to the role of thickness on the behavior of the magnetic losses and the phenomenology of skin effect. The study is focused on the wideband response of 0.174 mm and 0.289 mm thick sheets, comparatively tested at peak polarization values ranging between 0.25 T and 1.7 T. The experiments associate fluxmetric measurements with direct Kerr observations of the dynamics of the domain walls. A picture of the magnetization process comes to light, where the dynamics of the flux reversal takes hold under increasing frequencies through the motion of increasingly bowed 180° walls, eventually merging at the sheet surface for a fraction of the semi-period. This effect can be consistently predicted, starting from the Kerr-based knowledge of the equilibrium wall spacing, by the numerical modeling of the motion of an extended array of 180° domain walls, subjected to the balanced action of the applied and eddy current fields, and the elastic reaction of the bowed walls. This model can be incorporated into the general concept of loss separation, by calculating the classical loss component through the solution of the Maxwell’s diffusion equation under a magnetic constitutive law identified with the normal DC curve. The numerical domain wall model and the loss decomposition consistently predict that the excess loss component, playing a major role in these grain-oriented materials at power frequencies, tends to disappear in the upper induction-frequency corner.

Effect of mechanical cutting on the energy loss of laser-scribed grain-oriented alloys

We investigate the effect of mechanical cutting on the magnetic properties of high permeability grain-oriented (HGO) laser-scribed Fe-Si sheets. Measurements have been performed on strips of different widths (5 to 60 mm) cut from 0.27 mm thick sheets. Normal magnetization curve and energy loss have been determined by means of a digitally controlled single strip tester from 1 Hz to 1 kHz at peak magnetic polarization values Jp = 1000 mT and 1700 mT. The results fit into a simple phenomenological model regarding the dependence of magnetization curve and energy loss on the strip width, in substantial continuity with the approach originally developed for non-oriented electrical steels. The hysteresis Wh and excess Wexc loss components are shown to depend on the strip width according to a hyperbolic law, with a limiting fully hardened strip predicted to occur for widths around 3.5 mm. It is then consistently observed that the mechanical cutting of standard 30 mm wide HGO Epstein strips is conducive to an increase of the energy loss at 50 Hz and 1.7 T of the order of 13 %.

Calculated versus measured iron losses and instantaneous magnetization power functions of electrical steel

Magnetic energy loss P of soft magnetic laminations like SiFe sheets tends to be expressed through an integral over the power product H · dB/dt. Already in earlier papers, we stressed that distinctions are needed for the quantities H and B. However, they are not considered in practically consistent ways, in the so far literature. Here, we discuss these distinctions in closer ways, comparing loss determination by calculation and measurement, respectively. A physically consistent procedure is described for the determination of loss and magnetization power functions through measurement of bi-located quantities HS and BC (S surface, C cross section). On the other hand, it is concluded that corresponding quantitative calculations—based on co-located quantities H and B—are impeded by the high amount of technological parameters of modern steel products. For example, they result from chemical additions, and—in particular—also from specific technologies of rolling, annealing, coating or scribing.

An Improved Cross-Yoke SST for Accurate 1-D and 2-D Magnetic Testing of Fe-Si Sheets

Single-sheet testers (SSTs) with asymmetrical yokes were developed for convenient measurement of 1-D and 2-D magnetic properties of Fe-Si sheets. An inherent drawback of such SSTs is that the magnetic properties in the central region of the specimen are affected by the planar eddy currents induced in the specimen plane facing the pole faces of the yokes, where the magnetic flux enters the specimen in the normal direction. Most relevant studies reported in the literature use large symmetrical double yokes to mitigate the influence of planar eddy currents on the magnetic properties. However, such configuration significantly increases the system complexity. This article proposes a compact cross-yoke SST with the novel arm-slotted specimen and the integrated 2-D B-H sensor to minimize the influence of the planar eddy currents and simplify the structure of the SST. The magnetic properties of non-oriented (NO) Fe-Si sheets of 50JN470 under 1-D and 2-D magnetizations are measured and analyzed. The experimental results from the proposed cross-yoke SST show the agreement with those measured by using the international standard SST.

Influence of a Laser Irradiation and Laser Scribing on Magnetic Properties of GO Silicon Steels Sheets Using a Nanosecond Fiber Laser

Improving the performance of electrical steels within the magnetic circuits is essential to save energy. The domain refinement through local surface treatment by laser is an effective technique to reduce the iron losses in grain-oriented iron silicon steels. To interpret the mechanism of this technique, we have quantitatively studied the impact of nanosecond pulse laser treatment on the magnetic properties of grain-oriented Fe(3%wt)Si sheets. We measured the total power loss and apparent permeability of the samples using a Single-Sheet Tester (SST). The laser treatment resulted in a loss reduction of up to 24% compared to the average power loss of standard samples at 50 Hz. At mid-induction levels, the reduction was also accompanied by an improvement in apparent permeability. A dynamic magnetic behavior law was used to identify a dynamic property Λ including information on density, surface area and wall mobility and another internal permeability property µ representative of static field and magnetization characteristics. Lastly, we presented the behavior of these properties under different laser treatment.

Anisotropy of losses in grain-oriented Fe–Si

Comprehensive assessment of the magnetic behavior of grain-oriented steel (GO) Fe–Si sheets, going beyond the conventional characterization at power frequencies along the rolling direction (RD), can be the source of much needed information for the optimal design of transformers and efficient rotating machines. However, the quasi-monocrystal character of the material is conducive, besides an obviously strong anisotropic response, to a dependence of the measured properties on the sample geometry whenever the field is applied along a direction different from the rolling and the transverse (TD) directions. In this work, we show that the energy losses, measured from 1 to 300 Hz on GO sheets cut along directions ranging from 0° to 90° with respect to RD, can be interpreted in terms of linear composition of the same quantities measured along RD and TD. This feature, which applies to both the DC and AC properties, resides on the sample geometry-independent character of the RD and TD magnetization and on the loss separation principle. This amounts to state that, as substantiated by magneto-optical observations, the very same domain wall mechanisms making the magnetization to evolve in the RD and TD sheets, respectively, independently combine and operate in due proportions in all the other cases. By relying on these concepts, which overcome the limitations inherent to the semi-empirical models of the literature, we can consistently describe the magnetic losses as a function of cutting angle and stacking fashion of GO strips at different peak polarization levels and different frequencies.

Analyzer-free, intensity-based, wide-field magneto-optical microscopy

In conventional Kerr and Faraday microscopy, the sample is illuminated with plane-polarized light, and a magnetic domain contrast is generated by an analyzer making use of the Kerr or Faraday rotation. Here, we demonstrate possibilities of analyzer-free magneto-optical microscopy based on magnetization-dependent intensity modulations of the light. (i) The transverse Kerr effect can be applied for in-plane magnetized material, as demonstrated for an FeSi sheet. (ii) Illuminating that sample with circularly polarized light leads to a domain contrast with a different symmetry from the conventional Kerr contrast. (iii) Circular polarization can also be used for perpendicularly magnetized material, as demonstrated for garnet and ultrathin CoFeB films. (iv) Plane-polarized light at a specific angle can be employed for both in-plane and perpendicular media. (v) Perpendicular light incidence leads to a domain contrast on in-plane materials that is quadratic in the magnetization and to a domain boundary contrast. (vi) Domain contrast can even be obtained without a polarizer. In cases (ii) and (iii), the contrast is generated by magnetic circular dichroism (i.e., differential absorption of left- and right-circularly polarized light induced by magnetization components along the direction of light propagation), while magnetic linear dichroism (differential absorption of linearly polarized light induced by magnetization components transverse to propagation) is responsible for the contrast in case (v). The domain–boundary contrast is due to the magneto-optical gradient effect. A domain–boundary contrast can also arise by interference of phase-shifted magneto-optical amplitudes. An explanation of these contrast phenomena is provided in terms of Maxwell–Fresnel theory.

Domain structure and energy losses up to 10 kHz in grain-oriented Fe-Si sheets

We investigate in theory and experiment the frequency dependence of magnetic losses in Grain-Oriented 0.29 mm thick high-permeability steel sheets up to 10 kHz. Such an unusually broad frequency range, while responding to increasing trends towards high-frequency regimes in applications, is conducive to a complex evolution of the magnetization process, as imposed by increasing frequencies to a non-linear high-permeability saturable material. We show that the concept of loss decomposition, supported by observations of the domain wall dynamics through Kerr experiments, is effective in the assessment of the broadband frequency dependence of the energy loss. By calculating, in particular, the instantaneous and time averaged macroscopic induction profiles across the sheet thickness through the Maxwell’s diffusion equation, the classical loss component Wclass, versus frequency f and peak polarization Jp, is obtained. A simplified theoretical approach is pursued in this case by identifying the normal magnetization curve with the magnetic constitutive equation of the material. While the hysteresis loss Whyst is shown to invariably increase with frequency, the excess loss Wexc, the quantity directly associated with the eddy currents circulating around the moving domain walls, tends to vanish upon increasing both frequency and induction values. The Kerr experiments actually show that, while the oscillating 180° domain walls can adjust to the depth of the induction profile by bowing at low Jp values, the magnetization reversal at high inductions and high frequencies occurs by inward motion of symmetric fronts originating at the sheet surface, according to a classical framework.

Physical Assessment of the Magnetic Path Length of Energy Loss Testers

Magnetic energy losses of SiFe sheets are determined by the standardized methods of single sheet tester (SST) or Epstein tester (ET). According to IEC standards, the total power consumption is measured in Watt-metric ways, and the portion that concerns the homogeneously magnetized region(s) is estimated on a nominal value l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> of the so-called conventional effective magnetic path length (PL). A clear definition of PL is lacking-a suggestion being provided here. Standards express l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> through the dependence between the magnetic field strength H and the magnetization current. However, they apply the same value l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> also for the determination of losses P. From the viewpoint of physics, two PL quantities l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m,H</sub> and l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m,P</sub> would be preferable. The problematic is enhanced by the fact that the flux distribution within the magnetic circuit of a tester may change dynamically during the period of time, with induction changes B(t). This means that the physical PL L is a function of time, according to a PL function L[B(t)]. Finally, dynamic changes in flux distributions prove to be distinctly influenced by hysteretic mechanisms which means that L[B(t)] exhibits loop character. The resulting complexity indicates that the concept of PL is not promising, if high accuracy of testing is demanded. However, for purposes of material comparisons, optimum PL values LOPT may be suitable that are determined for individual material families. Analyses of instantaneous loss power values p(t) indicate that energy dissipation is weak during high induction. Thus, determinations of LOPT should be focussed on moderate induction. The ET is characterized by strong modifications of 3-D flux distributions which means that individual values LOPT would be needed. On the other hand, the SST shows a clear design. For moderate induction, some energy dissipation is expected to occur within the yoke region. This indicates that LOPT exceeds the conventional value of 450 mm, in weak ways.

Experimental set up for magnetomechanical measurements with a closed flux path sample

AbstractIn this article, an experimental procedure is presented to handle magnetic measurements under uniaxial tensile stress reaching the plastic domain. The main advantage of the proposed procedure is that it does not require an additional magnetic core to close the magnetic flux path through the studied sample. The flux flows only in the sample, and no parasitic air gaps are introduced, thus avoiding the use of the H-coil to evaluate the magnetic field, which is often very sensitive and not easy to calibrate. A specimen of nonoriented FeSi (1.3%) sheet (M330-35A) is characterized under uniaxial tensile stress. To validate the proposed procedure, a comparison with the single sheet tester procedure is carried out. The results obtained by the two procedures are in good agreement. Moreover, to illustrate the possibilities offered by the proposed procedure, we confirm some results obtained in the literature. We show that the positive plastic strain leads to a significant degradation of magnetic behavior. An applied tensile stress on a virgin (unstrained) sample leads to a degradation of the magnetic behavior. However, on a pre-strained sample, an applied tensile stress results in reducing the deterioration caused by the plastic strain until a stress value called optimum is attained. Above this threshold, the magnetic behavior re-deteriorates progressively.

Use of Time-Frequency Representation of Magnetic Barkhausen Noise for Evaluation of Easy Magnetization Axis of Grain-Oriented Steel.

The paper presents a new approach to non-destructive evaluation of easy/hard magnetization axis in grain-oriented SiFe electrical steels based on the Barkhausen phenomenon and its time-frequency (TF) characteristics. Anisotropy in steels is influenced by a number of factors that formulate the global relationship and affect the Barkhausen effect. Due to the observed high variability in the dynamics of magnetic Barkhausen noise (MBN) over time, obtained for various directions in grain-oriented steel, it becomes justified to conduct MBN signal analyses in the time-frequency domain. This representation allows not only global information from MBN signal over entire period to be expressed, but also detailed relationships between properties in time and in frequency to be observed as well. This creates the opportunity to supplement the information obtained. The main aspect considered in the work is to present a procedure that allows an assessment of the resultant angular characteristics in steel. For this purpose, a sample of a conventional grain-oriented SiFe sheet was used. Measurements were made for several angular settings towards the rolling and transverse directions. A data transformation procedure based on short-time Fourier transform (STFT) as well as quantitative analysis and synthesis of information contained in the TF space was presented. Angular characteristics of selected TF parameters were shown and discussed. In addition, an analysis of the repeatability of information obtained using the proposed procedure under various measurement conditions was carried out. The relationship between the selection of calculation parameters used during transformation and the repeatability of the obtained TF distributions were demonstrated. Then the selection of the final values of the calculation parameters was commented upon. Finally, the conclusions of the work carried out were discussed.

3-D Printed Magnetic Field Coil for Medium Frequency Epstein Tester

For the determination of magnetic energy losses of SiFe sheets as applied for technical frequencies, the most effective tool is given by the standardized single sheet tester (SST). However, for measurements at elevated frequency, as becoming relevant in increasing ways, the SST fails due to strongly enhanced eddy currents. An alternative is given by the Epstein tester (ET). However, its results are affected by edge effects from sample slitting and strong inhomogeneity of flux distribution. Here, we propose the so-called Grand ET where these impacts are restricted through doubled strip width and through an extra-thin, precisely, 3-D printed tangential field coil of reduced edge height. Moreover, a restricted coil length yields concentration to the sample region of acceptable homogeneity. The coil is manufactured by the so-called 3-D-assembler that allows printing of all components, including the windings. Presentation of loss results is given for a medium frequency range of 1 kHz up to 20 kHz where losses reach the order of hundreds of W/kg. Rapid testing is favored by a restriction to just two sample strips.

The tensor magnetic phase theory for mesoscopic volume structures of soft magnetic materials – Quasi-static and dynamic vector polarization, apparent permeability and losses – Experimental identifications of GO steel at low induction levels

In this contribution, we propose to cope with the problem of soft magnetic materials heterogeneity and non-uniformity in terms of domains structure. This non-uniformity expresses itself with space variations of domains and walls geometry and characteristic properties from the bulk towards the surface. We investigate the possibility of describing and predicting these changes from a mesoscopic point of view. We begin with an introduction of typical subdivisions and define a tensor state variable [Λ2] to represent the diversity of magnetic structures with domains and walls. We then explain the material structuring thanks to an energy balance between the mesoscopic magnetic exchange, magneto-crystalline anisotropy, self-magnetostriction anisotropy, stress induced anisotropy and the dipolar demagnetizing energy. We write every contribution as a function of [V2] = [Λ2]−1. After minimizing the total energy, we derive a formulation compatible with classical numerical methods. [Λ2] is deduced thanks to a partial differential equation and surface boundary conditions. When a time varying field is applied to the material, damping effects occur either in the mass or at the surface. Eddy currents induced within domains lead to consider a volume dissipation energy. The surface magnetic field is also dampened by both the static hysteresis mainly due to defects and the dynamic hysteresis which stems from eddy currents around magnetic walls, added to the an-hysteretic field. The surface magnetic field, magnetic structure, and thus the polarization being known on the external surface, time variations of the volume magnetic structure can be calculated within the mass. Using the static or dynamic magnetic field coupling at the surface, the magnetic polarization can be rebuilt in the mass to calculate the apparent magnetic permeability. Finally, finding the geometry and frequency dependent vector magnetic behavior and iron losses becomes possible. The tensor magnetic phase theory is able to account for the sensitivity of the magnetic structure to the geometry, the macroscopic anisotropy partly influenced by the metallography, the residual or induced stress, some surface effects such as the texture, the rugosity or even any scribing patterns, at a mesoscopic scale. Two test cases for GO and NGO electrical steels are presented. Sensitivity analysis on the test case with GO steel are discussed. Results are then compared to static and dynamic measurements of GO SiFe sheet samples. This paper contributes to the investigations carried out on the geometry dependent magnetic behavior of soft magnetic materials.

Static and dynamic energy losses along different directions in GO steel sheets

Grain-oriented (GO) Fe-Si sheets are often preferred to non-oriented steels in large rotating machines, where the material response along directions different from the rolling one (RD) matters, both in terms of magnetisation curve and energy losses. The experiments show that the material properties depend in a complex fashion on the angle θ made by the applied field with respect to RD in the lamination plane, an effect that can be quantitatively interpreted in terms of evolution of the domain wall processes. It was shown that the pre-emptive knowledge of the material behaviour along RD (θ=0°) and the transverse direction TD (θ=90°) allows one to predict, under quasi-static excitation, the normal magnetisation curve, the hysteresis loop shape, and the energy loss dependence on θ in high-permeability GO sheets. The evolution of the quasi-static magnetic properties with θ has an obvious counterpart in the dynamic behaviour. In the present work we have therefore investigated, from the experimental and theoretical viewpoint, the behaviour of the magnetic energy loss W(f,Jp) versus frequency 1Hz⩽f⩽200Hz and peak polarisation (0.15T⩽Jp⩽1.6T) in high-permeability 0.29 mm thick GO Epstein samples, cut at 15° steps between RD and TD. We show that the predicting method developed for the quasi-static loss can be made general through loss decomposition and applied, in particular, to the determination of the excess loss term. This leads to a general description of W(f,Jp) as a function of the sheet cutting angle, without using arbitrary parameters.