Vector Hysteresis Model Research Articles

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.

Scalar and vector hysteresis simulations using HysterSoft

Hysteresis modeling has become an important research area with many applications in science and engineering. In this article we present a unified and robust simulation framework designed to perform scalar and vector hysteresis modeling. The framework is based on HysterSoft© which is a simulation platform that can be interfaced with other libraries and simulation programs to model various aspects of hysteresis. We describe the main features of our simulation framework by focusing on scalar and vector hysteresis modeling, direct and inverse modeling, dynamic hysteresis modeling, first-order reversal-curves analysis, identification of the scalar and vector Preisach distribution function using an experimental first- order reversal-curves, noise passage analysis through hysteretic systems, and thermal relaxation in scalar and vector hysteresis. The simulation modules, the user-defined features, and various parameter identification techniques are also presented.

NUMERICAL STUDY OF A TIME-DOMAIN FINITE ELEMENT METHOD FOR NONLINEAR MAGNETIC PROBLEMS IN THREE DIMENSIONS (Invited Paper)

In this work, numerical analysis of nonlinear ferromagnetic problems is presented using the three-dimensional time-domain flnite element method (TDFEM). Formulated with the second- order nonlinear partial difierential equation (PDE) combined with the inverse Jiles-Atherton (J-A) vector hysteresis model, the nonlinear problems are solved in the time domain with the Newton- Raphson method. To solve the ordinary difierential equation (ODE) representing the magnetic hysteresis accurately and e-ciently, several ODE solvers are speciflcally designed and investigated. To improve the computational e-ciency of the Newton-Raphson method, the multi-dimensional secant methods, aka Broyden's methods, are incorporated in the nonlinear TDFEM solver. A nonuniform time-stepping scheme is also developed using the weighted residual approach to remove the requirement of a uniform time-step size during the simulation. The capability and the performance of the proposed methods are demonstrated by various numerical examples.

THEORETICAL FORMULATION OF A TIME-DOMAIN FINITE ELEMENT METHOD FOR NONLINEAR MAGNETIC PROBLEMS IN THREE DIMENSIONS (Invited Paper)

In this work, a numerical solution of nonlinear ferromagnetic problems is formulated using the three-dimensional time-domain finite element method (TDFEM) combined with the inverse JilesAtherton (J-A) vector hysteresis model. After a brief introduction of the J-A constitutive model, the second-order nonlinear partial differential equation (PDE) is constructed through the magnetic vector potential in the time domain, which is then discretized by employing the Newmark-β scheme, and solved by applying the Newton-Raphson method. Different Newton-Raphson schemes are constructed and compared. The capability of the proposed methods is demonstrated by several numerical examples including the simulation of the physical demagnetization process, the prediction of the magnetic remanence in the ferromagnetic material, and the generation of higher-order harmonics.

Micromagnetic Hysteresis Model Dealing With Magnetization Flip Motion for Grain-Oriented Silicon Steel

This paper presents a vector hysteresis model based on micromagnetic theory. In this model, a magnetization state of a magnetic material is described by a collection of single-domain particles, and magnetic reversal processes due to domain-wall motions are treated approximately as a magnetization flip. The present model is applied to calculation of hysteresis properties of grain-oriented silicon steel. The simulation results show that the anisotropic hysteresis properties and iron loss can be reproduced accurately by the present model.

Identification and verification of a Preisach-based vector model for ferromagnetic materials

In many applications of ferromagnetic materials concerning sensors and actuators, magnetic fields are rotating. In order to precisely describe the behavior of ferromagnetic materials in rotating magnetic fields, vector hysteresis models are necessary. Therefore, much effort is being put into the development of efficient vector models. For the reason of computational efficiency, models have been developed that differ from the Preisach approach and are for example based on rotationally coupled step functions. We have proposed a very efficient Preisach-based model before, which we called the rotational vector Preisach model. In this paper, we propose an extension of the rotational switching function, which improves the model characteristics for arbitrary H-field trajectories. We also introduce a set of special vectorial minor loops for the general validation and comparison of vector models. We apply those H-field trajectories to isotropic materials such as sputtered FeCo thin films as used in micromechanical systems. The vectorial minor loops can readily be utilized to evaluate the model output, and the results agree well with vectorial measurements.

Design of High-Speed Hybrid Hysteresis Motor Rotor Using Finite Element Model and Decision Process

This paper aims at designing a high-speed hysteresis motor rotor with permanent magnets embedded in the magnetic system. The considered motor, due to the rotational magnetization and considerable impact of harmonic losses in the rotor, is an electrical machine whose design requires the involvement of a field model. A multicriteria design procedure consisting of a computer experiment, employing time-stepping finite element and vector hysteresis models and a search for the feasible design using the analytic hierarchy process, is conducted. The feasible design is found uniquely and a prototype motor is constructed and verifyingly tested.

Temperature-Dependent Vector Hysteresis Model for Permanent Magnets

Irreversible thermal demagnetization effects can sometimes play a significant role in, for instance, rotating Preisach model (PM) machines. Modeling such phenomena requires field simulation methods such as finite element (FE) analysis in combination with a temperature-dependent vector hysteresis model. This paper explores the feasibility of applying a formalism for temperature-dependent structural hysteresis to magnetics. The net magnetization is expressed as a superposition of contributions from plays. By allowing the anhysteretic curve and the coercivity to depend on temperature, irreversible thermal effects resembling experiments emerge automatically without additional assumptions or adjustable parameters. Incorporating this temperature dependence has negligible impact on the computational efficiency or complexity of the model.

A Benchmark Problem of Vector Magnetic Hysteresis for Numerical Models

In this paper, we present a benchmark problem for the validation of numerical models of vector magnetic hysteresis. The problem geometry and the measurement system are described. The materials considered are both oriented grain (OG) and not OG Si-Fe steels. A series of experimental data about magnetic field and magnetic induction loci under rotational magnetization are presented with the corresponding magnetic losses. The measured data can be useful as a reference for the numerical models testing, comparison, and development. In addition, we propose here a comparison of the experimental data with the numerical results computed using a vector hysteresis model based on the extension of the Preisach model in 2-D.

Improved Vector Play Model and Parameter Identification for Magnetic Hysteresis Materials

An improved vector play model for magnetic hysteresis materials is proposed, and its required parameters are identified from the input major hysteresis loop. Validation results show that this new vector hysteresis model improves the accuracy of core loss computation not only for rotating fields but also for alternating fields compared with the ordinary vector play models. The presented model has been successfully implemented in 2-D and 3-D transient finite element analysis (FEA). Some application results from the 2-D and 3-D transient FEAs are presented.

Vector magnetic property of electrical steel sheet and its influence on distributions of magnetic field and iron loss for electrical machines

Purpose – The purpose of this paper is to present the vector magnetic properties of the electrical steel sheet and investigate its influences on the magnetic field and iron loss distributions for the electrical machines. Design/methodology/approach – The vector magnetic property of the electrical steel sheet is measured by using a two-dimensional single sheet tester and modelled through an E&S vector hysteresis model to be applied to finite element analysis. Findings – The magnetic field and iron loss distributions are calculated by finite element analysis combined with the E&S vector hysteresis model for the three-phase transformer and induction motor models. Originality/value – The influences of the vector magnetic property on the electrical machines are verified by comparing with the numerical results from a scalar magnetic property.

Hysteresis parameters estimation using a modified harmony search

Purpose – The purpose of this paper is to introduce a chaotic harmony search (CHS) approach based on the chaotic Zaslavskii map to parameters identification of Jiles-Atherton vector hysteresis model. Design/methodology/approach – In laminated magnetic cores when the magnetic flux rotates in the lamination plane, one observes an increase in the magnetic losses. The magnetization in these regions is very complex needing a vector model to analyze and predict its behavior. The vector Jiles-Atherton hysteresis model can be employed in rotational flux modeling. The vector Jiles-Atherton model needs a set of five parameters for each space direction taken into account. In this context, a significant amount of research has already been undertaken to investigate the application of metaheuristics in solving difficult engineering optimization problems. Harmony search (HS) is a derivative-free real parameter optimization metaheuristic algorithm, and it draws inspiration from the musical improvisation process of searching for a perfect state of harmony. In this paper, a CHS approach based on the chaotic Zaslavskii map is proposed and evaluated. Findings – The proposed CHS presents an efficient strategy to improve the search performance in preventing premature convergence to local minima when compared with the classical HS algorithm. Numerical comparisons with results using classical HS, genetic algorithms (GAs), particle swarm optimization (PSO), and evolution strategies (ES) demonstrated that the performance of the CHS is promising in parameters identification of Jiles-Atherton vector hysteresis model. Originality/value – This paper presents an efficient CHS approach applied to parameters identification of Jiles-Atherton vector hysteresis model.

Study on the Vector Hysteron in Two-Dimensional Preisach-Stoner-Wohlfarth Model

A vector hysteresis model referred to as the Preisach-Stoner-Wohlfarth (PSW) model has been recently presented. The crux of the model is the definition of a vector hysteron. In this paper, the effects of interaction field and applied field angle on the magnetization of the vector hysteron are studied in detail. The center of the hysteresis loops of hysteron is displaced because of the effect of interaction field. The energy loss for each hysteron is verified when the critical surface is crossed.

Vector hysteresis measurements of not oriented grain SiFe steels by a biaxial hall sensors array

This work discusses the vector measurement of the effective magnetic field inside a not oriented grain SiFe steel sample, taking into account the effect of the demagnetizing field. We propose an array of biaxial Hall sensors, placed up to the sample surface. The calibration of the system and a suitable extrapolation data strongly reduce the uncertainties of the direct measurement and provide an accurate evaluation of the magnetic field inside the material sample. Although the approach proposed can be also used for industrial frequencies, 50–60Hz or more, the analysis is limited here to the static case, because we are mainly interested in static magnetic measurements. These measurements are especially useful for the vector characterization of soft magnetic materials and, in particular, for the identification and the experimental validation of vector hysteresis models. The experimental analysis presented in the paper deals with commercial not oriented grain SiFe steels. Experimental data about hysteresis loops and static power losses are given.

Genetic algorithm identification of a H-moving vector hysteresis model

In this work we present an identification procedure for a vector hysteresis model defined by a H-moving approach. The model parameters are identified by means of a suitable implementation of a genetic algorithm with a set of experimental data. The analytical formulation of the model and the characteristics of the genetic algorithm used are described. A comparison between computed data and experimental measurements for a not oriented grain Si–Fe magnetic steel with a weak lamination anisotropy are reported.

Validation of the rotational vector Preisach model with measurements and simulations of vectorial minor loops

In order to precisely describe the behavior of ferromagnetic materials in rotating magnetic fields, vector hysteresis models are necessary. The extension of the Preisach model with vector methods is well known. Much research in this field is based on the Mayergoyz vector hysteresis model. The drawback of this kind of model is the computational effort for the additional integral in the vectorial Preisach operator. Therefore, much effort is being put into the development of efficient vector models. For the reason of computational efficiency, models have been developed that differ from the Preisach approach and are, for example, based on rotationally coupled step functions. We have proposed a very efficient Preisach based model before, which we called the rotational vector Preisach model. Here, we propose an extension of the rotational switching function of the mentioned model, which improves the model characteristics for arbitrary H-field trajectories. We also introduce a set of special vectorial minor loops for the general validation and comparison of vector models. We apply those H-field trajectories to isotropic materials like FeCo thin films as used in our micromechanical systems. The vectorial minor loops can readily be utilized to evaluate the model output and the results agree well with vectorial measurements.

Iron Loss Analysis of a Permanent Magnet Rotating Machine Taking Account of the Vector Hysteretic Properties of Electrical Steel Sheet

This paper presents the iron loss prediction of rotating electric machines taking account of the vector hysteretic properties of electrical steel sheet. The E&S vector hysteresis model is adopted to describe the vector hysteretic properties of a non-oriented electrical steel sheet, and incorporated into finite element analysis (FEA) for magnetic field analysis and iron loss prediction. A permanent magnet synchronous generator is taken as a numerical model, and the analyzed magnetic field distribution and predicted iron loss by using the pro- posed method is compared with those from a conventional method which employs an empiri- cal iron loss formula with FEA based on a non-linear B-H curve. Through the comparison the effectiveness of the presented method for the iron loss prediction of the rotating machine is verified.

Convergence Stabilization of E&S Vector Hysteresis Model Incorporated With Finite Element Analysis of Electrical Machines

This paper presents a convergence stabilization method of E&S vector hysteresis model when it is combined with nonlinear finite element analysis (FEA). In order to ensure the stable convergence, an additional nonlinear iterative procedure with a relaxation method is incorporated with the conventional nonlinear FEA, and adaptive determination of relaxation factor during the nonlinear iteration is suggested. The effectiveness of the suggested method is verified through a comparison of the numerical results from the suggested and conventional methods.

전기강판의 벡터 자기특성을 고려한 전기기기의 손실특성 해석

This paper presents vector magnetic properties of an electrical steel sheet (ESS) employed for electric machine and iron loss analysis considering the vector magnetic properties of the ESS. The vector magnetic properties of the ESS are measured by using a two-dimensional single sheet tester and modeled by an E&S vector hysteresis model to be applied to finite element method. The finite element analysis considering the vector magnetic properties is applied to iron loss analysis of a three-phase induction motor model, and the influences of the vector magnetic properties on the iron loss distribution are verified by comparing with numerical results from a typical B-H curve model.

Mathematical Modelling of Magnetic Hysteresis in Exchange-Bias Spin Valves

In this work we present a physical-related model of vector hysteresis for magnetic simulation of nanometric structures. The mathematical formulation, based on a generalization of the Preisach and Stoner-Wohlfarth models, is very simple and elegant. The numerical implementation is very easy and the computation time required for the simulations is extremely fast. However the accuracy is not comparable with the codes based on the micromagnetic theory, but it is sufficient for the use as preprocessing of more accurate and more complex methods, in order to speed up the convergence. In this paper the model identification is performed for a nanoscale spin valve using the data generated by a 3D micromagnetic code.