Magnetic Hysteresis Model Research Articles

Stochastic model for magnetic hysteresis

A model of ferromagnetic hysteresis is presented, in which the different microscopic magnetization processes are reduced to the motion of a single domain wall in a random energy landscape. The equivalent pinning field acting on the domain wall is assumed to be a space-dependent stochastic process described by a set of coupled Langevin-type equations. The model is inspired by the one proposed by Néel for the description of hysteresis in the Rayleigh region, but it is more general, as it predicts both the static and the dynamic hysteresis loops, as well as their fine structure (Barkhausen effect). The model properties were investigated by computer simulations. In the low field limit, the Rayleigh law is verified, with coefficients depending on the stochastic properties of the pinning field, whereas at high fields the loop behavior is dominated by demagnetizing fields. The results obtained for the energy losses show that the separation of losses into the hysteresis and the dynamic components is a general property of this model. Furthermore, we numerically verified that in our model there is a complete decoupling of the dissipation effects due to the presence of the pinning field (inner disorder) and to the dynamics of the domain wall.

Computation of electromagnetic losses including stress dependence of magnetic hysteresis

An internal variable magnetic hysteresis model accounting for stress dependence is implemented in a 2D finite element model, in order to investigate the effect of an elastic stress on the field and eddy current distributions in electrical steels. Hysteresis and eddy current losses in a non oriented 3%FeSi lamination are computed and discussed for various excitation field magnitudes.

Identification of frequency effect on magnetic hysteresis and modelling with an internal variables model

In this paper, the first magnetisation response experimentally observed on 0.5 mm thick sheets made of a non-oriented silicon-iron alloy is given for different magnetic loading frequencies from 0.05 to 500 Hz. An internal variable magnetic hysteresis model is identified from the quasi-static response (from 0.05 to about 5 Hz). This model is used for finite element analyses performed to predict the electro-magnetic response of the material at higher frequencies. The comparison between the results of these structural analyses and the experimental results proves that in this case the macroscopic eddy currents are sufficient to explain the total frequency effect on the magnetic hysteresis measurements.

Modelling of quasi-static ferromagnetic behaviour

Modelling of magnetisation characteristics of magnetic materials is of great importance for magnetic field computation in electromagnetic devices. In this paper, a new scalar static magnetic hysteresis model which is based on the non-cquilibrium thermodynamics theory is presented. The model exhibits all the main features of ferromagnetism, such as nonlinearity, anhysteretic curve, first magnetisation curve, hysteresis loops and presence of minor loops.

Magnetic hysteresis modeling via feed-forward neural networks

A general neural approach to magnetic hysteresis modeling is proposed. The general memory storage properties of systems with rate independent hysteresis are outlined. Thus, it is shown how it is possible to build a neural hysteresis model based on feed-forward neural networks (NN's) which fulfills these properties. The identification of the model consists in training the NN's by usual training algorithms such as backpropagation. Finally, the proposed neural model has been tested by comparing its predictions with experimental data.

Magnetization process in a 2-D array of small magnetic particles

A model system of a regular square lattice of epitaxial garnet particles was used to investigate the magnetization process in two dimensions. Switching statistics of particles are treated in terms of the classical Preisach model of magnetic hysteresis. The dispersion of the coercivity, controlled by the technology of preparation of the medium, and the distribution of the magnetostatic interaction fields of the system of particles determine the hysteresis loop. However, the interaction fields depend on the magnetization distribution itself, i.e. on the actual information in a recording medium, and the non-ellipsoidal shape and size of the particles have a strong effect on the switching process.

Subharmonic ferroresonance in an LCR circuit with hysteresis

We use the Preisach model of magnetic hysteresis to model the inductance in a series LCR circuit. By introducing a hysteresis parameter into the Preisach functions used, we are able to continuously vary the width of the hysteresis loop and thereby investigate the effects of magnetic hysteresis on the circuit's behavior. In particular, it is shown that the stability region of a period-3 subharmonic ferroresonant solution can increase significantly as the hysteresis losses are reduced. The bifurcations leading to the appearance and disappearance of this subharmonic solution are examined. Also, strong numerical evidence is provided for the unsuitability of single-valued M-H curves in the analysis of ferroresonant phenomena.

Magnetic vector hysteresis model with dry friction-like pinning

A phenomenological model of magnetic vector hysteresis is described. Magnetization is expressed as a superposition from the contributions of a large number of pseudoparticles. The free energy of individual particles is assumed to be the sum of a convex component representing anhysteretic behaviour, and a small ripple representing the influence of pinning sites. The ripple component is found to give a dry friction-like hysteresis mechanism. Some comparisons with experiments are given.

Models of magnetic hysteresis based on play and stop hysterons

This paper deals with mathematical models of magnetic hysteresis implemented by assembling hysterons of play and stop type. A procedure for the identification of these models is described, and their behaviors are compared to experimental results. A comparison to the Preisach and Prandtl-Ishlinskii models is performed. It is shown that the Play-Type Model is a possible alternative to Preisach's algorithm, whereas the Stop-Type Model is apt to represent the inverse of Preisach's operator. Simulations adopting both models are reported and compared to experimental data. Moreover, an application to the analysis of a ferroresonant circuit is studied, both numerically and experimentally.

A neural network model of magnetic hysteresis for computational magnetics

A neural network to implement a hysteresis model for a magnetic material within a finite element program is described. It is shown that such a system can match the results produced by a Preisach model but the time overhead can be considerably reduced thus making feasible the solution of large problems involving hysteretic materials.

A new model of static scalar hysteresis

A new model of static magnetic hysteresis, based on Krasnoselskii operators of stop type, is studied experimentally. A novel feature of the model is the capability to describe clockwise-oriented loops in the input-output plane. Consequently, it can describe the H = H[ B] constitutive relationship of a ferromagnetic material. Some results are reported and discussed.

A new model of magnetic hysteresis, based on stop hysterons: an application to the magnetic field diffusion

A new model of scalar static magnetic hysteresis based on the superposition of Krasnoselkii hysterons of stop type is described. Unlike the magnetic hysteresis models known in literature, the present one naturally implements the constitutive relationship H=H[B]. In this respect it allows to formulate a field problem directly in terms of the vector magnetic potential. In the present work the new model has been applied to study the one-dimensional magnetic field diffusion in a hysteretic iron body by means of the Galerkin method.

Dependence of energy dissipation on annealing temperature of melt–spun NdFeB permanent magnet materials

A model of magnetic hysteresis which was developed originally for soft magnetic materials has been applied to melt–spun ribbons of Nd2Fe14B-based material. The crucial ideas in the model description of hysteresis center on a dissipation of energy due to hysteresis which is proportional to the change in magnetization. The Nd2Fe14B material was melt–spun amorphous and then annealed for a period of 24 h at temperatures ranging from 700 to 950 °C. This resulted in different grain sizes, depending on annealing temperature. Consequently the hysteresis curves represent the properties of the material as a function of both annealing temperature and grain size. It was found that the magnetic properties varied systematically with annealing temperature, and hence grain size, as would be expected. When modeling the magnetic properties it was found that the model parameters also varied systematically, in particular, the energy dissipation parameter k was to a first approximation a simple linear function of the annealing temperature and decreased with increasing annealing temperature as a result of grain growth. Therefore, this study revealed a basic relationship between materials processing conditions, microstructure, model parameters, and magnetic properties.

A generalized dynamic circuit model of magnetic cores for low- and high-frequency applications. II. Circuit model formulation and implementation

This paper describes the formulation and implementation of a generalized dynamic magnetic core circuit model suitable for both low- and high-frequency applications. The behavior of magnetic cores with any arbitrary flux waveforms is modeled by a simple ladder network consisting of nonlinear inductors and resistors. The nonlinear B-H loop and the hysteresis loss are incorporated in distributed nonideal inductors and calculated by the Preisach scalar model of magnetic hysteresis. The eddy current and anomalous losses are accounted for by the generalized nonlinear equivalent resistors reported in Part I of the paper. The transmission line modeling method is employed to solve the nonlinear state equations. Numerical aspects and software implementation of the model are discussed. The generalized model has been verified by simulations and measurements at both low- and high-frequency operations.

Hysteresis modeling based on transplantation

This paper describes a phenomenological model of scalar magnetic hysteresis which is based on the similarity of the processes taking place when a magnetic material is magnetized along the branches of both the main and any minor hysteresis loops. This allows one to form any reversal curve by means of conjugation of the portions which are transplanted from the main loop branches, and to fit the model to a given material.

Initial-vortex-entry-related magnetic hysteresis in thin-film SQUID magnetometers

We report measurements and modeling of magnetic hysteresis in SQUID magnetometers cycled in fields of 0.1 to 10 G peak to peak. We show that the observed hysteresis is caused by the penetration of magnetic vortices around the edges of the superconducting thin-film structures forming the SQUID. A threshold field for the onset of hysteresis is predicted and subsequently observed experimentally. The threshold corresponds to the situation when the Lorentz force driving a vortex into the SQUID washer first exceeds the sum of the surface barrier and pinning forces. The threshold field depends on the pinning strength of the superconducting material forming the edges of the device, and is thus distinguished from the lower critical field, ${\mathit{H}}_{\mathit{c}1}$, for flux entry in type-II superconductors. It is, to our knowledge, the first time a threshold field for flux entry is observed to relate to the local pinning strength of a structure. Comparison of our earlier experimental data with model calculations revealed the existence of a degradation in critical current density at edges of our devices. Subsequent optimization of our high-${\mathit{T}}_{\mathit{c}}$ device fabrication process lead to significant improvement in hysteresis characteristics. The threshold field in the improved devices is clearly observable, near which at 77 K a thousandfold reduction in hysteresis is obtained. We believe the mechanism of magnetic flux entry studied in this work is also relevant to the understanding of the hysteresis loss in high-${\mathit{T}}_{\mathit{c}}$ superconductors at microwave frequencies. Such hysteresis, resulting in a strongly power-dependent loss, is a major factor limiting the high-power applications of thin-film high-${\mathit{T}}_{\mathit{c}}$ microwave devices.

A new model of scalar magnetic hysteresis

In this paper the scalar quasi-static magnetic hysteresis is described by means of a new model based on a sequential algorithm, which appears to he a possible alternative to the classical Preisach model. A procedure leading to the identification of the model parameters is described. The hysteretic behavior obtained by using the new model is in good agreement with experimental measurements as well as with the predictions of the Preisach model. Finally, both models have been applied to study the dynamics of a circuit with an hysteretic inductor, driven by a sinusoidal voltage source. Good agreement between the two simulations was found, but our model appears computationally less cumbersome than that of Preisach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Measurement of the switching properties of a regular 2D array of Preisach-type particles (abstract)

The original Preisach model of magnetic hysteresis assumes an assembly of single domain particles, each having a rectangular hysteresis loop. The loops are characterized by up and down switching fields. The halfwidth of the loop is the coercivity Hc of the given particle. The loops might be shifted depending on the magnetic state of the environment, described by an effective interaction field, Hi. In the present work the switching properties of an artificially structured, highly uniaxial, magneto-optic garnet film (courtesy of R. Belt, AIRTRON), corresponding to the assumptions of the original Preisach model, are investigated. In this case the parameter identification is straightforward. The garnet film is etched into 42 μm rectangular pixels, separated by 15 μm grooves. Each pixel has a rectangular hysteresis loop. Up and down magnetized pixels give a black and white contrast due to Faraday effect. Magnetization can be measured by counting the number of pixels switched in a given field. The distribution of the coercive field has been obtained by measuring individual loops on each of several hundred pixels in an optical magnetometer. The average Hc=265±99 Oe, Hi=0±26 Oe. The interaction field has been measured on the same pixel, depending on the magnetization state of the nearest neighbor pixels. The contribution to Hi of oppositely magnetized pixels is dHi/dn=26 Oe/pixel. These data are compared to macroscopic hysteresis loops measured in VSM.

A possible alternative to Preisach's model of static hysteresis

A phenomenological model which represents a possible alternative to the well-known Preisach's model of magnetic hysteresis is here presented. The main feature of the proposed model, which differentiates it from Preisach's one, is that the individual elementary «particles» are not themselves hysteretic; it is the mechanism by which the state of these particles is modified that introduces hysteretic behaviour. The model appears to be computationally less cumbersome than Preisach's one, while having the same application range.

Application of a stress-dependent magnetic Preisach hysteresis model on a simulation model for Terfenol-D

A previously reported simulation model for the highly magnetorestrictive material. Terfenol-D has been extended by implementation of the recently developed stress-dependent magnetic Preisach hysteresis model. The model is based on static measurements of material characteristics combined with equations for the dynamic mechanical and magnetic behavior of the material. As a test of the model the authors have simulated the behavior of a Terfenol-D rod for different load conditions. The results show that the model is able to describe the influence of nonlinearities, eddy currents, and hysteresis on the magnetomechanical transduction process of magnetorestrictive materials.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>