Vector Preisach Model Research Articles

Comparison between different models of magnetic hysteresis in the solution of the TEAM 32 problem

AbstractThe numerical modeling of magnetic materials in simulators is a difficult task, above all in real devices with specific excitation. The aim of this work is to compare the accuracy of scalar and vector Preisach models in a well know test benchmark: the TEAM 32 problem. The availability of measured data for this benchmark test and the simple geometry allow us to build hysteresis models and to test them in a 2D finite element analysis (FEA) scheme. The specific numerical formulation of each hysteresis model implemented is described, including the technique for the numerical identification of parameters starting from measured data. The comparison among the models is done in terms of accuracy, but also in terms of easy implementation in the FEA scheme and of computational cost.

Computation of rotational hysteresis losses by vector Preisach models based on rotational operators

PurposeA major purpose of vector hysteresis models lies in the prediction of power losses under rotating magnetic fields. The well-known vector Preisach model by Mayergoyz has been shown to well predict such power losses at low amplitudes of the applied field. However, in its original form, it fails to predict the reduction of rotational power losses at high fields. In recent years, two variants of a novel vector Preisach model based on rotational operators have been published and investigated with respect to general accuracy and performance. This paper aims to examine the capabilities of the named vector Preisach models in terms of rotational hysteresis loss calculations.Design/methodology/approachIn a first step, both variants of the novel rotational operator-based vector Preisach model are tested with respect to their overall capability to prescribe rotational hysteresis losses. Hereby, the direct influence of the model-specific parameters onto the computable losses is investigated. Afterward, it is researched whether there exists an optimized set of parameters for these models that allows the matching of measured rotational hysteresis losses.FindingsThe theoretical investigations on the influence of the model-specific parameters onto the computable rotational hysteresis losses showed that such losses can be predicted in general and that a variation of these parameters allows to adapt the simulated loss curves in both shape and amplitude. Furthermore, an optimized parameter set for the prediction of the named losses could be retrieved by direct matching of simulated and measured loss curves.Originality/valueEven though the practical applicability and the efficiency of the novel vector Preisach model based on rotational operators has been proven in previous publications, its capabilities to predict rotational hysteresis losses has not been researched so far. This publication does not only show the general possibility to compute such losses with help of the named vector Preisach models but also in addition provides a routine to derive an optimized parameter set, which allows an accurate modeling of actually measured loss curves.

A mixed multiscale FEM for the eddy current problem with T,Φ-Φ and vector hysteresis

PurposeThis work introduces an efficient and accurate technique to solve the eddy current problem in laminated iron cores considering vector hysteresis.Design/methodology/approachThe mixed multiscale finite element method based on the based on the T,Φ-Φ formulation, with the current vector potential T and the magnetic scalar potential Φ allows the laminated core to be modelled as a single homogeneous block. This means that the individual sheets do not have to be resolved, which saves a lot of computing time and reduces the demands on the computer system enormously.FindingsAs a representative numerical example, a single-phase transformer with 4, 20 and 184 sheets is simulated with great success. The eddy current losses of the simulation using the standard finite element method and the simulation using the mixed multiscale finite element method agree very well and the required simulation time is tremendously reduced.Originality/valueThe vector Preisach model is used to account for vector hysteresis and is integrated into the mixed multiscale finite element method for the first time.

Algorithms to reduce the computational cost of vector Preisach model in view of Finite Element analysis

The purpose of this work is to devise algorithms to reduce the memory consumption of the vector Preisach model in view of its usage in Finite Element analysis. Four algorithms, which all implement a vector Preisach hysteresis model, are presented and critically compared theoretically and by numerical experiments taken on with two materials and three signals. Several strategies are presented to reduce both the memory occupation and the computational cost of several orders of magnitude.

Numerical simulations of vector hysteresis processes via the Preisach model and the Energy Based Model: An application to Fe-Si laminated alloys

The paper presents the state of the art and the problems already open in modelling the hysteresis phenomenon in 2-D for laminated soft ferromagnetic materials. Firstly, a thorough experimental investigation has been carried out at a very low frequency by a single disk tester (SDT) for a specimen of innovative NGO electrical steel sheet. Scalar, rotational and elliptic magnetization processes have been experimentally measured under controlled waveforms of the magnetic induction vector thanks to an effective digital feedback algorithm. Two numerical model of hysteresis have been taken into account to reproduce the measured magnetization processes: the vector Preisach model (VPM) and the Energy Based Model (EBM). The main advantages and limitations in the use of the two hysteresis models are comprehensively analysed and discussed, taking into consideration both the problem of identification and the simulation results. In particular, the effective capability of the models to reproduce the vector field trajectories and to predict the hysteresis power losses has been shown. Conclusive considerations involve the memory usage and the computational time for the low level of abstraction implementation of the two hysteresis models.

An Improved Anisotropic Vector Preisach Model for Nonoriented Electrical Steel Sheet Based on Iron Loss Separation Theory

An improved anisotropic vector Preisach model is proposed in this paper to describe the hysteresis properties of nonoriented (NO) electrical steel sheet (ESS) under 50 Hz rotating magnetic fields. The proposed model consists of three components, static hysteresis component, eddy current component, and excess component, which is based on the iron loss separation theory. The static hysteresis component is constructed by the static vector Preisach model. The proposed model is identified by the measured hysteresis properties under 1 Hz and 50 Hz magnetic fields. Finally, the experimental results prove the effectiveness of the proposed anisotropic vector hysteresis model.

A Continuous Vector Preisach Model Based on Vectorial Relay Operators

This article introduces a new variant of a vector Preisach model. It is composed of vector relay operators, and discrete versions have already been used to model hysteretic material behavior in the finite-element analysis. Using a discrete hysteresis model thereby introduces several complications. The variant of the model proposed in this article enables continuous evaluation of the model, given that the model input can be approximated by a piecewise linear function. This is achieved by allowing infinitely many, however, not arbitrarily distributed vector relay operators. This article is limited to the case of relay operators with circularly or spherically shaped corresponding critical surfaces. Model parameters are identified for measured hysteresis loops, and the model is applied in a finite-element analysis.

Analytical formulation to estimate the dynamic energy loss in electrical steels: Effectiveness and limitations

This article aims to investigate the accuracy in modeling and characterization of the dynamic energy loss of modern laminated electrical steels in use for power electronics applications. Measurements by an Epstein Frame are performed in case of sinusoidal and non-sinusoidal waveform of the magnetic induction, at different frequencies and peak values. The Steinmetz and the time domain statistical loss theory, either in frequency domain are used, and the related parameters are fitted experimentally. The dynamic energy loss is also modeled and estimated by means of a finite element method (FEM) formulation in time domain, coupled with a vector Preisach model to represent the constitutive law of the magnetic material. The series of the results reported indicates effectiveness and limitations of the modeling approaches considered. Some considerations about the excess loss are also given.

Comparison of different vector Preisach models for the simulation of ferromagnetic materials

PurposeThe numerical computation of magnetization processes in moving and rotating assemblies requires the usage of vector hysteresis models. A commonly used model is the so-called Mayergoyz vector Preisach model, which applies the scalar Preisach model into multiple angles of the halfspace. The usage of several scalar models, which are optionally weighted differently, enables the description of isotropic as well as anisotropic materials. The flexibility is achieved, however, at the cost of multiple scalar model evaluations. For solely isotropic materials, two vector Preisach models, based on an extra rotational operator, might offer a lightweight alternative in terms of evaluation cost. The study aims at comparing the three mentioned models with respect to computational efficiency and practical applicability.Design/methodology/approachThe three mentioned vector Preisach models are compared with respect to their computational costs and their representation of magnetic polarization curves measured by a vector vibrating sample magnetometer.FindingsThe results prove the applicability of all three models to practical scenarios and show the higher efficiency of the vector models based on rotational operators in terms of computational time.Originality/valueAlthough the two vector Preisach models, based on an extra rotational operator, have been proposed in 2012 and 2015, their practical application and inversion has not been tested yet. This paper not only shows the usability of these particular vector Preisach models but also proves the efficiency of a special stageless evaluation approach that was proposed in a former contribution.

An Improved Anisotropic Vector Preisach Hysteresis Model Taking Account of Rotating Magnetic Fields

This paper presents an identification algorithm of the scalar Preisach model by using a set of symmetric minor hysteresis loops and suggests an improved vector Preisach model to describe the vector and anisotropic hysteresis behavior of a non-oriented (NO) electrical steel sheet (ESS) under rotating magnetic fields. Symmetric minor hysteresis loop is quite easy measured, so an identification algorithm based on symmetric minor hysteresis loop instead of first-order reverse curve is presented in this paper. The vector Preisach model employs a nonlinear coefficient, which is a function of magnitude and a direction of magnetic flux density, to describe the anisotropic property of the NO ESS and increases the numerical accuracy. The validity of the suggested vector Preisach model is investigated through comparisons with the experimental results under various magnetic field conditions.

Dynamic extension of vector Preisach model

The objective of the present paper is to generalize the vector Preisach hysteresis model to take dynamic effects into account. A comprehensive analysis of the vector behavior has been performed by a single sheet tester with a specimen of round shape. The locus of the magnetic flux density vector has been controlled by a digital measurement set up at different frequency. An inverse vector Preisach hysteresis model has been built up by viscous-type scalar models and an identification procedure has been developed to follow the measured data. Finally, the model has been inserted into a finite element procedure through the fixed point technique to simulate electrical engineering problems.

Stageless evaluation for a vector Preisach model based on rotational operators

PurposeThis paper aims to present a novel stageless evaluation scheme for a vector Preisach model that exploits rotational operators for the description of vector hysteresis. It is meant to resolve the discretizational errors that arise during the application of the standard matrix-based implementation of Preisach-based models.Design/methodology/approachThe newly developed evaluation uses a nested-list data structure. Together with an adapted form of the Everett function, it allows to represent both the additional rotational operator and the switching operator of the standard scalar Preisach model in a stageless fashion, i.e. without introducing discretization errors. Additionally, presented updating and simplification rules ensure the computational efficiency of the scheme.FindingsA comparison between the stageless evaluation scheme and the commonly used matrix approach reveals not only an improvement in accuracy up to machine precision but, furthermore, a reduction of computational resources.Research limitations/implicationsThe presented evaluation scheme is especially designed for a vector Preisach model, which is based on an additional rotational operator. A direct application to other vector Preisach models that do not rely on rotational operators is not intended. Nevertheless, the presented methodology allows an easy adaption to similar vector Preisach schemes that use modified setting rules for the rotational operator and/or the switching operator.Originality/valuePrior to this contribution, the vector Preisach model based on rotational operators could only be evaluated using a matrix-based approach that works with discretized forms of rotational and switching operator. The presented evaluation scheme offers reduced computational cost at much higher accuracy. Therefore, it is of great interest for all users of the mentioned or similar vector Preisach models.

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.

Hysteresis modeling of sequential application of orthogonal fields

In a cumulative effort to characterize the sizes, shapes, and distributions of the domains of the structurally superior high strength steels, a characteristic magnetization measurement and a Preisach model are presented to explain and model the distinctive trends observed in the data. The study investigates the effect of a constant transverse magnetic field and a cycling longitudinal magnetic field, applied sequentially, on the major hysteresis loop of solid cylinders of high strength steel. A coupled-hysteron vector Preisach model is extended to model the longitudinal magnetization of the samples under the effect of an applied transverse field. Insights about the microstructure of the rods and the contribution of different domains and magnetization mechanisms to the magnetic response are drawn.

Magnetostriction measurements of high strength steel under the influence of bi-axial magnetic fields

A detailed knowledge of a material's microscopic texture is required in order to produce a realistic model of the magnetization process under applied fields. Previous studies on the magnetostriction in high strength steels have ignored the internal anisotropies due to prior material handling. To this end, a measurement utilizing two perpendicular fields was designed to interrogate the magnetic texture and microstructure of high-strength steel rods. These magnetization and magnetostriction measurements were then fitted to an energy-based domain rotation model which had been altered to address vector fields and uniaxial anisotropies. Given the simplicity of the model it is surprising to see that it captures a number of the general trends in the Data, however the fit is generally poor. Improving upon this data set will allow us to determine general magnetic characteristics of microstructure in the steels. These measurements will be incorporated into a future Vector Preisach model allowing detailed predictions of the magnetic state after stress and field changes in multiple directions.

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.

Magnetostrictive Study of High Strength Steels With Respect to Angle From Rolling Direction

Many of the commonly used high strength steels have small amounts of magnetostriction. This magnetostriction can be utilized, for example to measure the torque on a rotating shaft. Previous studies on the magnetostriction in high strength steels have ignored the internal anisotropies due to previous material handling. This paper presents data taken on rods of a high strength steel that have been machined parallel, perpendicular and 45 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$^{\circ}$</tex></formula> to the rolling direction. Magnetization, magnetostriction, susceptibility, and stress-strain curves have been measured under various stresses and fields. In general, the parallel cylinders showed altered <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$B-H$</tex></formula> , susceptibility, and magnetostriction curves compared to the other two orientations. These measurements will be incorporated into a future Vector Preisach model allowing detailed predictions of the magnetic state after stress and field changes.

Stress Dependent Magnetization and Vector Preisach Modeling in Low Carbon Steels

Measurements of magnetic properties have been performed on commercially available low carbon steels (Armco and non-oriented electrical steels) in order to construct and test a Preisach model for materials under stress. The measurements include hysteresis loops of samples under tensile stress taken during loading and after unloading at given strain levels. A vector Preisach model using the SW model as the elementary operator, superposition to account for easy axes dispersion and a weighed mixture of normal distributions to account for the long-range interactions established through the magnetoelastic coupling is proposed. The model reproduces the effect of applied stress, verifying the experimental finding that the permeability of a material under tensile stress decreases. The Preisach density is constructed in such a way as to account for the strong magnetostatic interactions observed in the high induction regions in the case of built-in stresses, so the model is also able to capture the effect of the residual compressive stresses in unloaded materials. The use of the differential permeability and its first derivative are proposed as parameters to be monitored in NDT applications.

Model of laminated ferromagnetic cores for loss prediction in electrical machines

An iron-loss model for laminated ferromagnetic cores of electrical machines is presented and applied to estimate the core losses of an induction machine with finite-element analysis. Skin effect in the cross section of the core lamination is modelled using a set of sinusoidal basis functions while locally considering both the hysteretic material properties and the excess field caused by domain wall motion. After spatial and time discretisation, a single non-linear equation system is obtained. An accurate vector Preisach model, the differential reluctivity tensor and the Newton–Raphson method guarantee excellent convergence of the iteration procedure. Results from the model correspond well to iron-loss data obtained by measurements.

Hysteresis loss in vector Preisach models

PurposeThe magnetic modeling of materials has been focused on computing magnetization and forces in devices. With increasing efforts to make energy efficient devices, attention must now be paid to hysteresis losses in magnetizing processes. The purpose of this paper is to discuss the pertinent parameters that determine these losses and a method of identifying them.Design/methodology/approachA vector model was used that is designed to compute losses correctly, to focus on hysteresis losses in models that compute the same magnetization, but have different losses.FindingsThe model computes the same cyclic losses as expected.Research limitations/implicationsThe analysis of this paper is limited to isotropic media, but it can be generalized to anisotropic media. The accuracy of the Della Torre, Pinzaglia and Cardelli (DPC) model is also limited.Practical implicationsOnce the model has been validated, the designer can minimize the instantaneous as well as the average dissipation. This will permit the design of more reliable devices.Originality/valueThe DPC model used in this work has not been fully explored previously.