Rotational Single Sheet Tester Research Articles

Basic properties of ferromagnetic vector hysteresis play models and their validation by finite element method

PurposeMagnetic hysteresis holds significant technical and physical importance in the design of electromagnetic components. Despite extensive research in this area, modeling magnetic hysteresis remains a challenging task that is yet to be fully resolved. The purpose of this paper is to study vector hysteresis play models for anisotropic ferromagnetic materials in a physical, thermodynamical approach.Design/methodology/approachIn this work, hysteresis play models are implemented to interpret magnetic properties, drawing upon classical rate-independent plasticity principles derived from continuum mechanics theory. By conducting qualitative and quantitative verification and validation, various aspects of ferromagnetic vector hysteresis were thoroughly examined. By directly incorporating the hysteresis play models into the primal formulations using fixed point method, the proposed model is validated with measurements in a finite element (FE) environments.FindingsThe proposed vector hysteresis play model is verified with fundamental properties of hysteresis effects. Numerical analysis is performed in an FE environment. Measured data from a rotational single sheet tester (RSST) are validated to the simulated results.Originality/valueThe results of this work demonstrates that the essential properties of the hysteresis effects by electrical steel sheets can be represented by the proposed vector hysteresis play models. By incorporation of hysteresis play models into the weak formulations of the magnetostatic problem in the h-based magnetic scalar potential form, magnetic properties of electrical steel sheets can be locally analyzed and represented.

Measurement and simulation of a rotational single sheet tester

Measurement and simulation of a rotational single sheet tester

Effects of simultaneous loading of temperature and biaxial stress on the 1&2D magnetic properties of non-oriented electrical steel sheets

As the effect of factors like temperature and stress on the magnetic properties of electrical steel materials are gradually being emphasized, many research teams are carrying out related tests. Currently, most studies focus only on the effect of a single factor on the magnetic properties, while in reality, multiple factors exist simultaneously in electrical equipment. Therefore, accurate data of alternating (1D) and rotational (2D) magnetic properties under simultaneous loading of temperature and stress are very important. In this paper, a system based on a vertical rotational single sheet tester (VRSST) with temperature and stress loading parts is designed and constructed. Then, the 1D and 2D magnetic properties under many combinations of different temperatures, uniaxial and biaxial stress are measured and analyzed.

Influence of the geometric parameters of a vertical rotational single-sheet tester on sample field homogeneity

PurposeThe horizontal rotational single-sheet tester (RSST) suffers from weaknesses such as the reduced size of test samples, measurement disturbances due to magnetic flux leakage and nonhomogeneity of field in the measurement area. Although the vertical RSST allows to overcome the first two aforementioned drawbacks, the heterogeneity of the field in the test sample remains an issue. In addition, there is still a lack of device standardization to ensure test repeatability, as already is well established with the Epstein frame. This paper aims to investigate the influence of several parameters on the field homogeneity in the test sample.Design/methodology/approachA fully 3D finite element model of a vertical RSST is developed and used to perform a sensibility study on several geometrical parameters.FindingsThe influence of several parameters on the field homogeneity in the test sample, such as the geometrical dimensions of the yokes, the presence or not of holes drilled inside the test sample for B-coil placement as well as the size of the H-coils and B-coils, is addressed.Originality/valueIt is expected that this study will contribute to the optimization and standardization vertical RSSTs.

Finite element level validation of an anisotropic hysteresis model for non-oriented electrical steel sheets

This paper presents the finite element level validation of the anisotropic Jiles–Atherton hysteresis model. Numerical analysis of a round rotational single sheet tester is performed using the 2D finite element method. Anisotropic extension of the Jiles–Atherton hysteresis model is coupled with the 2D finite element method. The finite element simulations are performed for the cases when the magnetic field alternates and rotates in the lamination plane. The simulated results for alternating and rotational flux density excitations agree with the measured data. The measured data used in this paper corresponds to the M400-50A nonoriented silicon steel.

Modeling of Magnetic Anisotropy in Electrical Steel Sheet by Means of Cumulative Distribution Functions of Gaussians

This article proposes a methodology for modeling magnetic anisotropy in ferromagnetic materials. This approach was initially used to represent the isothermal remanent magnetization (IRM) acquired by natural mineral assemblages and based on the use of the cumulative distribution function (CDF) of a probability density function (PDF). For the purpose of this work, the anisotropy of electrical steel sheets is modeled by means of CDFs of Gaussians. The methodology is validated by comparisons between numerical and experimental data obtained from an Epstein frame and a Rotational Single Sheet Tester. The outcomes of the study are twofold: first, the parameters defining the CDF follow a polynomial trendline, and second, they can easily be calculated from a limited amount of experimental data which is a key point from an engineering point of view.

Prediction of hysteresis losses by an advanced vector hysteresis stop model with threshold surfaces

PurposeThe ordinary vector hysteresis stop model with constant threshold values is not able to prohibit the hysteretic property after the saturation correctly. This paper aims to develop an improved vector hysteresis stop model with threshold surfaces. This advanced anisotropic vector hysteresis stop model can represent the magnetic saturation properties and the hysteresis losses under alternating and rotating magnetizations.Design/methodology/approachBy integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model, the anisotropy of the permeability of an electrical steel sheet can be represented. Instead of the commonly used constant threshold value for plastic elements of the hysteresis model, threshold surfaces are applied to the stop hysterons. The threshold surfaces can be derived directly from measured alternating major loops of the material sample. By saturated polarization, the constructed threshold surfaces are vanishing. In this way, the reversible magnetic flux density is in the same direction of the applied magnetic flux density. Thus, the saturation properties are satisfied.FindingsAnalyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows that the clockwise (CW) and counter-CW (CCW) rotational hysteresis losses decrease by saturated flux density. At this state, instead of the domain wall motion, the magnetization rotation is dominant in the material. As a result, the hysteresis losses, which are related to the domain wall motion, are vanished near the saturation. In one stop operator, the plastic element represents the hysteresis part of the model. Integrating threshold surface into the plastic element, the hysteresis part can be modified to zero near the saturation to represent the saturation properties.Originality/valueThe results of this work demonstrate that the presented vector hysteresis stop model allows simulation of anisotropic hysteresis effects, alternating and rotating hysteresis losses. The parameters of the hysteresis model are determined by comparing the measured and modeled minor loops in different alternating magnetization directions. With the identified parameters, the proposed model is excited with rotated excitations in CW and CCW directions. The rotated hysteresis losses, derived from the model, are then compared with those experimentally measured. The modified vector stop model can significantly improve the accuracy of representing hysteresis saturations and losses.

Modeling anisotropic magnetic hysteresis properties with vector stop model by using finite element method

PurposeThis paper aims to use a history-dependent vector stop hysteresis model incorporated into a two dimensional finite elements (FE) simulation environment to solve the magnetic field problems in electrical machines. The vector stop hysteresis model is valid for representing the anisotropic magnetization characteristics of electrical steel sheets. Comparisons of the simulated results with measurements show that the model is well appropriate for the simulation of electrical machines with alternating, rotating and harmonic magnetic flux densities.Design/methodology/approachThe anisotropy of the permeability of an electrical steel sheet can be represented by integrating anhysteretic surfaces into the elastic element of a vector hysteresis stop model. The parameters of the vector stop hysteresis model were identified by minimizing the errors between the simulated results and measurements. In this paper, a damped Newton method is applied to solve the nonlinear problem, which ensures a robust convergence of the finite elements simulation with vector stop hysteresis model.FindingsAnalyzing the measurements of the electrical steel sheets sample obtained from a rotational single sheet tester shows the importance to consider the anisotropic and saturation behavior of the material. Comparing the calculated and measured data corroborates the hypothesis that the presented energy-based vector stop hysteresis model is able to represent these magnetic properties appropriately. To ensure a unique way of hysteresis loops during finite elements simulation, the memory of the vector stop hysteresis model from last time step is kept unchanged during the Newton iterations.Originality/valueThe results of this work demonstrates that the presented vector hysteresis stop model allows simulation of vector hysteresis effects of electrical steel sheets in electrical machines with a limited amount of measurements. The essential properties of the electrical steel sheets, such as phase shifts, the anisotropy of magnetizations and the magnetization characteristics by alternating, rotating, harmonic magnetization types, can be accurately represented.

Design issues of Rotational Single Sheet Tester for Fe-Based Nanocrystalline Alloys at High Frequencies

Measuring the vector magnetic properties of nanocrystalline soft magnetic materials at high frequencies is of great significance to the optimal design and energy saving of the electrical equipment. In this paper, some key design issues are discussed for a rotational single sheet tester (RSST) to further studied the Two-Dimensional (2D) magnetic properties of nanocrystalline alloys in the kilohertz range. Firstly, the magnetization uniformity of the testing sample is analyzed and discussed considering the stray field. Secondly, the magnetizer

Analysis of vector hysteresis models in comparison to anhysteretic magnetization model

The design of electrical machines and magnetic actuators requires accurate models to represent hysteresis effects in ferromagnetic materials. The magnetic nonlinearity of the iron core is usually considered by an anhysteretic magnetization curve. With this assumption, hysteresis’ effects in the field computation are completely neglected. This paper presents a comparative study of different hysteresis models, particularly Pragmatic Algebraic Model (PAM) and vector stop model, with regard to a vector anhysteretic anisotropic model. The PAM turns out to be an efficient model implemented with one mathematical equation. The multi cells stop model relies on a consistent thermodynamic formulation, whose dissipation corresponds to a dry friction-like element. Both models implement a constitutive relationship, in which the magnetic flux density vector as independent input and magnetic field strength as output. With a rotational single sheet tester (RSST), various tests for a sample of material FeSi24-50A (FeSi) with a silicon proportion of 2.4 wt% can be proceeded under the application of relevant field distribution. The obtained measured data are applied to parameterize and validate the models. Following numerical experiments the results are compared with those obtained by means of an anhysteretic anisotropic model.

Rotational Single Sheet Tester for Multiaxial Magneto-Mechanical Effects in Steel Sheets

A detailed design of a new rotational single sheet tester device which allows comprehensive multiaxial magneto-mechanical analysis of ferromagnetic sheets is proposed. The challenges that arose during the mechanical and magnetic design phases are addressed. The applicability of the device is tested by performing magneto-mechanical measurements on an M400-50A electrical steel sheet. Results under several multiaxial magneto-mechanical loadings with circular and alternating magnetic flux densities are reported. It is shown that the effect of multiaxial stress on iron losses can be much more significant than that of uniaxial stress.

Numerical and Experimental Determination of Local Building Factors of a Three-Phase Transformer Core Package

The analyses of flux distributions and losses in transformer cores need highest expenditure if performed in experimental ways. This paper presents a novel combined methodology for the evaluation of local and global loss building factors BF. As a first step, the local patterns of the dynamic induction vector B(t) were calculated, by means of a novel numerical “magnetic anisotropic circuit calculation (MACC) methodology. The latter considers the core materials non-linear permeability functions in rolling direction and transverse direction, as well as non-linear effects of overlaps in corners and T-joints. In a second step, the calculated induction patterns were exactly simulated on the hexagonal Vienna rotational single sheet tester and the corresponding local losses p were measured electrodynamically. Finally, the values p were allocated to the corresponding core positions, taking into account the entire core geometry. BF of the core was estimated from the total of loss values weighted to the corresponding volume portions. The method was applied for a three-phase core of highly grain-oriented material, magnetized with BNOM = 1.7 T. The procedure shows the local distributions of losses, yielding also information on those of eddy currents and rotational magnetization (RM). As an example, the T-joint, as the area of highest RM, yields a local loss increase of about 50%. Apart from RM, the local induction variations-including waveform distortions, caused mainly by circulating magnetization-prove to have a high impact on losses, locally yielding 50% as well. These highly convincing results indicate that the complicated sensor studies of cores can partly be replaced by: 1) numerical modeling of induction distributions and 2) subsequent allocations of loss values as detected by RSST simulations.

Waveform Conditioning Problems of Nanocrystalline Alloys Under One/Two-Dimensional High-Frequency Magnetization

The problem of waveform distortion in high-frequency magnetization of nanocrystalline alloys has been discussed and analyzed in this paper. By measuring the sample in a rotational single sheet tester, the distortion caused by the dc bias field is largely reduced. A robust control algorithm based on model-free control is developed to keep the magnetic flux density sinusoidal when the materials are magnetized to saturated at high frequencies. Finally, the vector magnetic properties of nanocrystalline alloys are measured after adjusting the waveforms. The losses from 2 to 10 kHz in the casting direction and the transverse direction are calculated and compared.

Rotating magnetizations in electrical machines: Measurements and modeling

This paper studies the magnetization process in electrical steel sheets for rotational magnetizations as they occur in the magnetic circuit of electrical machines. A four-pole rotational single sheet tester is used to generate the rotating magnetic flux inside the sample. A field-oriented control scheme is implemented to improve the control performance. The magnetization process of different non-oriented materials is analyzed and compared.

Vector Magnetic Hysteresis Measurement of Nonoriented Electrical Steel Sheets Under Unidirectional Compressive Stress Applied by Piezoelectric Actuators

This paper presents the vector magnetic hysteresis measurement of nonoriented electrical steel sheets under unidirectional compressive stress applied by piezoelectric actuators. We used a round rotational single sheet tester system to measure the vector magnetic hysteresis, where a stator of an induction motor was used to magnetically excite a sample in the in-plane orthogonal directions. To apply stress to the sample, we used commercial film-type piezoelectric actuators, which were directly glued on both surfaces of the sample. The experimental results showed that the compressive stress in the sample was proportional to the dc voltage applied to the actuators and that the loci of the magnetic field in the stress application direction were extended when increasing the compressive stress.

Implementation of the Single Hysteron Model in a Finite-Element Scheme

The single hysteron model is identified to reconstruct the magnetization processes of a grain-oriented electrical steel and it is implemented in a finite-element scheme. The model involves the Zeeman energy and the anisotropy energy of the material and an interaction field to take into account others terms, such as the magnetoelastic energy, the exchange energy, inclusions, and crystallographic discontinuities. The interaction field is evaluated experimentally using a round rotational single sheet tester, where a disk sample of the material is excited for several rotational magnetization processes. Details about the finite-element scheme, the computational time, and the memory allocations involved in the simulations are presented and discussed.

Energy-Based Magnetization and Magnetostriction Modeling of Grain-Oriented Silicon Steel Under Vectorial Excitations

The assembled domain structure model (ADSM) is an energy-based macroscopic magnetization model of a core material. In this paper, we used the ADSM to simulate the magnetization curves and magnetostriction of a grain-oriented (GO) silicon steel sheet under vectorial excitations, and we measured the same sheet using the rotational single-sheet tester with a three-element strain gage rosette. In the simulation, the target value of the average magnetization vector representing unidirectional or rotational magnetic flux is given as a known parameter. We obtained the magnetization state by finding the external magnetic field vector and state vectors, satisfying the criteria that the average magnetization vector equals the target value and that the total magnetic energy is locally minimized. The simulation reconstructed the magnetostriction produced by the 90° domain-wall motion under unidirectional magnetization as well as the vectorial contraction and extension under rotational magnetization.

Shielding of the <italic>Z</italic>-Component of the Magnetic Field in a 2-D Magnetizer With a Deep Yoke

Compact round rotational single sheet testers (RRSSTs) can achieve very high flux densities ( $\sim\!2 \text{T}$ at 60 Hz), owing to sinusoidal distribution of the magnetizing magnetomotive force (MMF), equalization of reluctance, a reduction in their diametrical size and longer stack lengths (deep yokes). The last two measures result in an increase in the magnetic field $z$ -component $(H_{z})$ , which is often reduced by shielding. This paper shows that a given shield distance is not effective in minimizing $H_{z}$ over the entire flux density range. The impact of the magnetizer diametrical size and the yoke depth on $H_{z}$ is also compared with shielding. Finally, this paper shows that magnetic properties contribute significantly to $H_{z}$ at very high flux densities, whereas the magnetic interaction of the sample and shields, reduce the effectiveness of shielding in deep saturation at 2 T.

Comparison of rotational single sheet testers for evaluating 2-D magnetic properties of electrical steel sheet

Evaluating magnetic properties accurately under various flux conditions is necessary to reduce iron losses in designing motors and transformers. Particularly, two-dimensional (2-D) magnetic property is one of the most important factors for highly eff

Anisotropic Generalization of Vector Preisach Hysteresis Models for Nonoriented Steels

A Preisach-type vector hysteresis model is developed to represent anisotropic material characteristics under static and dynamic conditions. Bi- and uniaxial anisotropy are incorporated by generalizing the input projection of the vector model. Frequency-dependent eddy current and excess effects are considered by an additional field strength component. The model is applied to simulate the magnetic properties of weakly anisotropic nonoriented magnetic steel. The simulation results are successfully validated against measurements under alternating and circular flux carried out on a rotational single-sheet tester.