Jiles-Atherton Hysteresis Model Research Articles

Prediction Model of Hysteresis Characteristics of Non-Oriented Silicon Steel Under DC Bias

Accurate simulation of the hysteresis loop is challeng-ing, especially using manufacturer data. Traditional parameter extraction methods (e.g., using optimization algorithm and solving transcendental equation) can extract the static Jiles-Atherton (JA) hysteresis model parameters under an arbitrary condition, but it requires fitting parameters because the model parameters vary with flux density. To reduce the dependence on measurement data, this paper proposes a simple but effective parameter extraction method. Firstly, an identification procedure of minor loop is presented using only static B - P loss curves by investigating the influence of model parameters on hysteresis loop, where the average root-mean-square error of the hysteresis loop is decreased by 4. To estimate the dynamic loss coefficients under DC bias, a calculation method based on the Statistical Theory of Losses (STL) is established by investigating the law of influence of DC bias on hysteresis loss and dynamic loss. The effectiveness of the proposed method is verified.

Hysteretic response of bulk magnetostrictive material employing a novel hyperbolic vector generalized magneto-thermoelastic constitutive model

Taylor series expansion of Gibbs free energy density function for elastic deformation, the physics of demagnetization and the Weiss molecular field coupled with the thermodynamic relations have been used to develop a generalized nonlinear hysteretic thermo-magneto-elastic vector model with potential application for the development of sensors and actuators. The nonlinear elastic strains in the magnetostrictive material are induced due to the magnetic domain rotation caused by tensile and compressive stresses in giant magnetostrictive materials. A vector function of the hyperbolic tangent is defined to take into account this nonlinear characteristic validating the elastic stress field boundary condition. The vector generalized Jiles-Atherton hysteresis model with modified Langevin equation is employed to incorporate the pinning of magnetic domain walls in the mathematical model. Thus, derived macroscopic model is put to the test for 1D, 2D and 3D nonlinear magnetostriction, magnetization and elastic constitutive relation with Terfenol-D (giant magnetostrictive materials) as a potential candid material. Finite element analyses for rods and films have been conducted using the general H(B) relation coded in the C programming language, as shown in the solution algorithm (Fig. 2). Employing the calibrated physical and experimental parameters (Tables 2 and 3), the confidence of the model is checked with existing analytical and experimental models. The magnetization and magnetostriction hysteresis responses have been evaluated considering the variation of a broad range of the prestress (up to 110 MPa), temperature (0 °C–80 °C) and applied magnetic field (0 kA/m–193.2 kA/m). The numerical simulation of this fully coupled phenomenological model demonstrates good agreement with the experimental data. The theoretical modelling error obtained from averaging the normalized root mean square error for each experimental data set is found to be maximum of 2.8 % and hence vindicates the efficacy of the present model.

A novel 3D simulation prediction model of mechanical properties of ferromagnetic materials via incremental permeability method

Ferromagnetic material is one of the basic materials in industrial production and whose mechanical properties are key indicators to evaluate quality. At present, incremental permeability (IP), one method of nondestructive testing, is used in the mechanical properties testing field of ferromagnetic materials, but its 3D simulation prediction model and method have not been established. To solve this problem, a finite element simulation method for mechanical properties of ferromagnetic materials based on Jiles-Atherton (JA) hysteresis model was proposed in this paper, which is established on the basis of the experimental method of electromagnetic nondestructive testing via incremental permeability. In this paper, the finite element 3D simulation prediction model based on IP method is proposed. Besides, the difficulty in JA hysteresis model parameter measurement is solved by combining magnetic-force method and artificial fish swarm algorithm. The 3D simulation prediction model is applied to the yield strength prediction of ferromagnetic materials for the first time. By testing the yield strength of the material, the simulation method and 3D simulation prediction model proposed in this paper can accurately reflect the incremental permeability characteristics of real materials and can provide a simulation platform for testing the mechanical properties of ferromagnetic materials via IP method.

Modeling and analysis of a single-phase core-type transformer under inrush current and nonlinear load conditions

In this paper, a transformer model based on the equivalent electrical circuit considering the nonlinearity of the iron core has been developed. The nonlinear behavior of the iron core was taken into account by using the inverted Jiles–Atherton hysteresis model. The single-phase core-type transformer was analyzed under different energization, remnant flux for inrush current and nonlinear load conditions. Illustrative and remarkable simulation and experimental results related to inrush current along with the primary and secondary currents under nonlinear load conditions were demonstrated. In addition, magnetic flux in the iron core and the hysteresis curve as a consequence of the relation of the magnetic flux and magnetizing inrush current were demonstrated. Operation of the transformer under various nonlinear load conditions have been demonstrated with simulation and experimental results. Variation of peak value of the inrush current for different levels of remnant flux in the iron core and different switching-on angles of the voltage applied to the primary was further indicated.

An efficient dynamical model of reluctance actuators with flux fringing and magnetic hysteresis

This paper presents an efficient and accurate dynamical model of reluctance actuators, suitable for prediction and control applications. It is a hybrid lumped-parameter state-space model that takes into account the mechanical and electromagnetic dynamics, including eddy currents, flux fringing, magnetic hysteresis and saturation. Special emphasis is placed on the hysteresis model, which is based on the Jiles–Atherton theory. The novel parts of the model – the gap reluctance expression and the modified Jiles–Atherton hysteresis model – are identified, showing that the simulated results fit very well the experimental data. Furthermore, its potential application for control is exemplified with a feedback strategy, in which the design of the controller and observer are based on the proposed dynamical model.

Alternating and rotational loss prediction accuracy of vector Jiles-Atherton model

In this paper, the vector extension of the Jiles-Atherton hysteresis model is modified to predict both alternating and rotational field strength variations observed in a nonoriented silicon steel sheet. The model parameters are changed to be functions of the magnitude and direction of flux density, and the anhysteretic magnetic characteristics are identified from several unidirectional alternating B(H)measurements. We demonstrate that the modified vector Jiles-Atherton model can predict both alternating and rotational field strength variations with better accuracy than the “basic” approach.

Quantitative evaluation of cumulative plastic damage for ferromagnetic steel under low cycle fatigue based on magnetic memory method

AbstractCumulative plastic damage caused during the low cycle fatigue (LCF) regime may seriously undermine the safety of the steel members and even lead to serious industrial accidents. Magnetic memory method (MMM), as a novel nondestructive testing technology, has been developed to evaluate the fatigue damage for the ferromagnetic material, but there is the lack of a quantitative description exists for the relationship between magnetic memory signals and cumulative plastic damage yet. In this paper, the strain‐based Jiles–Atherton hysteresis model under cyclic load during the LCF regime was established. Meanwhile, the LCF tests for S355 steel were performed, and the HSF signals on the surface of the specimen were collected under different loading cycles. Finite element (FE) simulations for coupling magnetic memory signals and cumulative plastic strain were carried out by the strain‐based Jiles–Atherton hysteresis model. Comparing with experimental results verifies the feasibility and accuracy of the FE method. The results indicate that the slope of the HSF signals fitting curve, K, as a characteristic parameter, has an exponential decrease as the cumulative plastic damage D increases. A general quantitative expression of the magneto‐damage model was built by discussing the influences of different factors on the K–D relation curves. It can be proved by verification that the magneto‐damage model provides a direct way for the quantitative evaluation of the cumulative plastic damage for the low‐carbon steel under LCF.

Finite-Element Modeling and Characterization of Iron Losses in 12 mm Thick Steel Laminations Including the Effect of Cutting

Iron losses in laser-cut toroidal samples of 12 mm thick steel laminations used in large synchronous motors are studied. Eddy currents in the lamination cross-section are solved with the 2-D finite element method while applying a constitutive law based on the Jiles-Atherton hysteresis model. The effect of cutting on the material properties is included by a continuous local material model approach, which enables to express the material properties as a function of distance from the cutting edge. The accuracy of the model is validated by comparing the simulations and experimental measurements of five toroidal samples assembled from concentric rings with different widths. Highly accurate results are obtained in terms of both the matching of B-H loops and the total loss values with an average relative error less than 2.9%. The results show that the hysteresis loss under quasi-static excitation increases up to 20.4% due to the effect of cutting. It is observed that the eddy-current loss becomes dominant over the hysteresis loss even at 5 Hz, and this eddy-current loss decreases up to 72.5% as the number of concentric rings increases. The presented model and the results accurately show how iron losses occur in thick materials and how they are affected by the cutting process.

Neural Network Model for Magnetization Characteristics of Ferromagnetic Materials

The magnetic characteristics of silicon steel sheet 30Q120 under different AC frequencies were measured by an Epstein frame in order to analyze the effects of frequency variation on the hysteresis loop of ferromagnetic materials and compare the differences of such materials at different frequencies. First, the forecasting method of the magnetic properties of ferromagnetic materials under the influence of frequency using neural network was proposed based on the measured experimental data. Hysteresis loops at different frequencies were obtained. Then, the obtained results were compared with the measured results. Second, the dynamic Jiles–Atherton hysteresis model was established based on the Jiles–Atherton hysteresis theory, and hysteresis loops at different frequencies were obtained. The accuracies of the neural network model and Jiles-Atherton hysteresis model were verified by comparing the simulation results with the measured data. Upon comparing the dynamic Jiles–Atherton hysteresis and the neural network hysteresis models, results show that the latter has better accuracy. Furthermore, the correctness and effectiveness of the proposed method are verified.

An Integrated Model of Magnetic Hysteresis, the Magnetomechanical Effect, and the Barkhausen Effect

This article reviews the ferromagnetic hysteresis, magnetomechanical, and Barkhausen properties of magnetic materials and presents an integrated model to describe these effects and the underlying mechanisms that cause these effects. Hysteretic properties of ferromagnets, such as permeability, coercivity, remanence, and hysteresis loss are known to be sensitive to external factors including applied stress, temperature, and heat treatment, and internal factors like residual strain, microstructure, grain size, and anisotropy and the presence of precipitates of a second phase, such as iron carbide in steels. It thus becomes imperative to characterize the effect of these factors on the hysteresis parameters. Currently, several models such as Preisach, Stoner-Wohlfarth, and Jiles-Atherton are used to describe the magnetic hysteresis of ferromagnetic materials. We review here the quasistatic Jiles-Atherton hysteresis model which describes hysteresis in terms of domain wall motion enabling a connection to be made to the physical response of the magnetic material. This model has been extended to include the magnetomechanical effect and the Barkhausen effect in ferromagnetic materials. Theoretical work presented here provides a conceptual framework linking together these magnetic property measurements with model parameters and to the structure of the material.

A constraint-based optimization technique for estimating physical parameters of Jiles – Atherton hysteresis model

PurposeImproperly fitted parameters for the Jiles–Atherton (JA) hysteresis model can lead to non-physical hysteresis loops when ferromagnetic materials are simulated. This can be remedied by including a proper physical constraint in the parameter-fitting optimization algorithm. This paper aims to implement the constraint in the meta-heuristic simulated annealing (SA) optimization and Nelder–Mead simplex (NMS) algorithms to find JA model parameters that yield a physical hysteresis loop. The quasi-static B(H)-characteristics of a non-oriented (NO) silicon steel sheet are simulated, using existing measurements from a single sheet tester. Hysteresis loops received from the JA model under modified logistic function and piecewise cubic spline fitted to the average M(H) curve are compared against the measured minor and major hysteresis loops.Design/methodology/approachA physical constraint takes into account the anhysteretic susceptibility at the origin. This helps in the optimization decision-making, whether to accept or reject randomly generated parameters at a given iteration step. A combination of global and local heuristic optimization methods is used to determine the parameters of the JA hysteresis model. First, the SA method is applied and after that the NMS method is used in the process.FindingsThe implementation of a physical constraint improves the robustness of the parameter fitting and leads to more physical hysteresis loops. Modeling the anhysteretic magnetization by a spline fitted to the average of a measured major hysteresis loop provides a significantly better fit with the data than using analytical functions for the purpose. The results show that a modified logistic function can be considered a suitable anhysteretic (analytical) function for the NO silicon steel used in this paper. At high magnitude excitations, the average M(H) curve yields the proper fitting with the measured hysteresis loop. However, the parameters valid for the major hysteresis loop do not produce proper fitting for minor hysteresis loops.Originality/valueThe physical constraint is added in the SA and NMS optimization algorithms. The optimization algorithms are taken from the GNU Scientific Library, which is available from the GNU project. The methods described in this paper can be applied to estimate the physical parameters of the JA hysteresis model, particularly for the unidirectional alternating B(H) characteristics of NO silicon steel.

Accounting for dynamic losses in the Jiles-Atherton model of magnetic hysteresis

When designing semiconductor pulse converters of power systems operating in peak load conditions, it is necessary to calculate their characteristics and parameters, taking into account the magnetization reversal processes in the magnetic circuits of transformers and chokes. Magnetic materials of magnetic cores exhibit nonlinear, hysteretic, and dynamic properties due to the presence of classical vortex and additional losses. Various dynamic models, based on the classical Jiles–Atherton (JA) approach, are presented in the literature, however, they are unstable for textured materials and cannot be explained from a physical point of view. These models show certain non-physical situations expressed by the deformation of the hysteresis loop in the saturation region. In this paper, the direct and inverse dynamic hysteresis models are presented, based on the application of the theory of field separation. This approach explains some of the energy aspects of the JA model.

Representation of anisotropic magnetic characteristic observed in a non-oriented silicon steel sheet

This article presents a modified Jiles–Atherton hysteresis model for a weakly anisotropic non-oriented silicon steel sheet. In a toroidal inductor, the magnetic flux density can point toward any direction compared to the sheet orientation, and the hysteresis model should take this into account. We identify the model parameters independently for unidirectional alternating B(H)-characteristics in seven different directions. Then, we construct an anisotropic hysteresis model, where the model parameters can depend on the magnitude and direction of the applied magnetic flux density. We demonstrate that the parameters identified in the rolling and transverse directions of the silicon steel sheet (M400-50A) are sufficient to describe the hysteresis losses in other directions.

Parameter Estimation for the Jiles–Atherton Model in Weak Fields

The purpose of this article is to estimate the parameters of the Jiles–Atherton hysteresis model, based on minor-loop measurement data in weak applied fields. The well-known hysteresis model by Jiles and Atherton serves as a basis of this article with an extension for the closure of minor loops. In order to represent minor loops correctly, a dissipative factor is introduced. A methodology to obtain the initial magnetization of a specimen is defined, based on an expansion in terms of higher order Gaussian functions. The methodology is implemented within a finite-element method using an interconnection between MATLAB and COMSOL. This interconnection allows the investigation of potentially large ferromagnetic objects to be calibrated to the proposed ferromagnetic model in weak fields. The proposed methodology was verified using an original approach. The approach relies on the use of a sensor array that makes it possible to detect local variations of magnetic properties in steel plates. Material parameters for our test specimen are successfully obtained by means of experimental data, using the shuffled frog leaping optimization algorithm. An analysis of the obtained results shows that the calibrated model is able to represent the measurement data accurately.

A Dynamic Magnetostriction Model of Grain-Oriented Sheet Steels Based on Becker–Döring Crystal Magnetization Model and Jiles–Atherton Theory of Magnetic Hysteresis

Grain-oriented (GO) sheet steels are widely used as the core material in large power transformers. The strong magnetostriction in GO sheet steels, however, causes undesirable vibrations and acoustic noises, and is difficult to estimate in the design optimization of power transformers. This article proposes a new magnetostriction model of GO sheet steels by combining the Becker-Doring crystal model and the dynamic Jiles-Atherton hysteresis model. Incorporated in the finite-element analysis (FEA), the new model can correctly simulate the butterfly loops of magnetostriction in GO sheet steels. The effectiveness and accuracy of the proposed model are verified by the experimental measurement results on a single sheet sample in a free state with no external stress.

Parameter estimation of extended Jiles–Atherton hysteresis model based on ISFLA

This study introduces an extended Jiles–Atherton (JA) hysteresis model, which considers dynamic loss and anisotropy. The two considerations facilitate an accurate non-linearity representation of electromagnetic devices, thereby resulting in a precise agreement between the simulated and measured hysteresis loops. To achieve this goal, JA hysteresis model parameters must be estimated by an optimisation algorithm. Therefore, an improved shuffled frog-leaping algorithm (ISFLA) is proposed in this study. Differential evolution (DE) mutation operator, adaptive step size factor, and inertia weight factor are considered. Then, the implementation of the ISFLA is discussed using MATLAB. The proposed ISFLA is verified by the measured hysteresis loops of grain-oriented silicon toroidal core. The comparison between genetic algorithm, simulated annealing, DE, and ISFLA is discussed. Results show that the proposed ISFLA demonstrates better global optimum ability, lower computational burden, and faster convergence rate than the other three methods.

Magnetic Hysteresis Under Compressive Stress: A Multiscale-Jiles–Atherton Approach

Based on multiscale modeling of the anhysteretic magnetization considering mechanical stress and crystallographic texture effects, an extension of the Jiles-Atherton (J-A) hysteresis model is proposed. The magnetization and the volume fractions given by the multiscale approach are advantageously used in the J-A model to modify the anhysteretic magnetization and the pinning parameter. The parameters of the proposed model are identified in order to fit with the characterization results under compressive stress using two sets of experimental data. Using the same optimized parameters, the model is tested for the representation of loops under other stress conditions to evaluate its prediction capabilities.

Bifurcation and chaos characteristics of hysteresis vibration system of giant magnetostrictive actuator**Project supported by the Science Fund from the Ministry of Science and Technology of China (Grant No. 2017M010660) and the Major Project of the Inner Mongolia Autonomous Region, China (Grant No. 2018ZD10).

Chaotic motion and quasi-periodic motion are two common forms of instability in the giant magnetostrictive actuator (GMA). Therefore, in the present study we intend to investigate the influences of the system damping coefficient, system stiffness coefficient, disc spring cubic stiffness factor, and the excitation force and frequency on the output stability and the hysteresis vibration of the GMA. In this regard, the nonlinear piezomagnetic equation, Jiles–Atherton hysteresis model, quadratic domain rotation model, and the GMA structural dynamics are used to establish the mathematical model of the hysteresis vibration system of the GMA. Moreover, the multi-scale method and the singularity theory are used to determine the co-dimensional two-bifurcation characteristics of the system. Then, the output response of the system is simulated to determine the variation range of each parameter when chaos is imposed. Finally, the fourth-order Runge–Kutta method is used to obtain the time domain waveform, phase portrait and Poincaré mapping diagrams of the system. Subsequently, the obtained three graphs are analyzed. The obtained results show that when the system output is stable, the variation range of each parameter can be determined. Moreover, the stability interval of system damping coefficient, system stiffness coefficient, and the coefficient of the cubic stiffness term of the disc spring are obtained. Furthermore, the stability interval of the exciting force and the excitation frequency are determined.

Design and analysis of a nested structure micro-displacement amplification mechanism for a galfenol-based actuator

In this paper, two galfenol rods are arranged in a nested structure to amplify the micro-displacement of an actuator. First, a finite element model of the actuator is developed to analyze the magnetization process of the actuator for different material of the sleeves. Secondly, the mathematical model of the actuator is established using the theory of magnetization, magnetostriction, and structural dynamics to describe the output displacement characteristics of the actuator at different frequencies; the hysteretic behavior of the actuator is taken into consideration and is modeled according to Jiles–Atherton hysteresis model. The experiments and results show that the output displacement of the dual galfenol rods-based actuator is significantly larger than that of a single galfenol rod-based actuator under the same experimental conditions, in addition to that, the proposed nested structure exhibits the advantages of occupying small volume and maintaining response dynamics even at high frequencies. Finally, using the established mathematical model, studies are carried out to analyze the feasibility of further amplification of the output displacement using more than two galfenol rods in a nested structure.

Saturation and Hysteresis Characteristics Analysis of a HTS Controllable Reactor With Orthogonally Configured Core

The saturated controllable reactor is developed in order to compensate the reactive power in the power system. The traditional reactors have some limitations in the regulation range or induced voltage of control winding. A high temperature superconducting controllable reactor (HTSCR) with orthogonally configured core was proposed and studied, which can overcome some shortcomings of traditional reactors. However, simulation accuracy of the saturation characteristic of the iron core poses a major challenge in the reactor. In this paper, the structure of the reactor is explained and a precise finite element method (FEM) model aims to analyze the saturation and hysteresis characteristics has been modified. The anisotropic feature of the orthogonally configured core has been fully considered. Finite-element analysis simulations based on the anisotropic core model and Jiles-Atherton hysteresis model are performed using COMSOL Multiphysics and compared with verification experiments, proving that the HTS controllable reactor is efficient in reactance regulation, harmonic suppression, and induced voltage reduction.