Jiles-Atherton Hysteresis Model Research Articles

State Space Representation of Jiles-Atherton Hysteresis Model and Application for Closed-Loop Control.

Hysteresis is a fundamental characteristic of magnetic materials. The Jiles-Atherton (J-A) hysteresis model, which is known for its few parameters and clear physical interpretations, has been widely employed in simulating hysteresis characteristics. To better analyze and compute hysteresis behavior, this study established a state space representation based on the primitive J-A model. First, based on the five fundamental equations of the J-A model, a state space representation was established through variable substitution and simplification. Furthermore, to address the singularity problem at zero crossings, local linearization was obtained through an approximation method based on the actual physical properties. Based on these, the state space model was implemented using the S-function. To validate the effectiveness of the state space model, the hysteresis loops were obtained through COMSOL finite element software and tested on a permalloy toroidal sample. The particle swarm optimization (PSO) method was used for parameter identification of the state space model, and the identification results show excellent agreement with the simulation and test results. Finally, a closed-loop control system was constructed based on the state space model, and trajectory tracking experiments were conducted. The results verify the feasibility of the state space representation of the J-A model, which holds significant practical implications in the development of magnetically shielded rooms, the suppression of magnetic interference in cold atom clocks, and various other applications.

A Practical Hybrid Hysteresis Model for Calculating Iron Core Losses in Soft Magnetic Materials

Accurately calculating the losses of ferromagnetic materials is crucial for optimizing the design and ensuring the safe operation of electrical equipment such as motors and power transformers. Commonly used loss calculation models include the Bertotti empirical formula and hysteresis models. In this paper, a new hybrid hysteresis model method is proposed to calculate losses—namely, the combination of the Jiles–Atherton hysteresis model (J–A) and the Fourier hysteresis model. The traditional Jiles–Atherton hysteresis model is mainly suitable for fitting the saturation hysteresis loop, but the fitting error is relatively large for internal minor hysteresis loops. In contrast, the Fourier hysteresis model is suitable for fitting the minor hysteresis loops because the corresponding magnetic induction strength or magnetic field is lower and the waveform distortion is small. Moreover, Fourier series expansion can be expressed with fewer terms, which is convenient for parameter fitting. Through examples, the results show that the hybrid hysteresis model can take advantage of the strengths of each model, not only reducing computational complexity, but also ensuring high fitting accuracy and loss calculation accuracy.

Research on multi-scale hysteresis constitutive model of giant magnetostrictive materials considering multi-field coupling

The magnetization and magnetostrictive strain of giant magnetostrictive materials exhibit a complex nonlinear trend under the coupling of multiple fields, including magnetic field, temperature field, and prestress field. To enhance prediction accuracy, we propose a three-dimensional magnetic-thermal-force coupled nonlinear multi-scale hysteresis vector model. This model is derived from the principles of thermodynamics and continuum mechanics, taking into account the interactions among magnetic domains, grains, polycrystals, and macroscopic scales. It combines the volume-averaging principle of magnetic domain microscopy with the generalized Jiles-Atherton hysteresis model. The predicted hysteresis magnetization and magnetostrictive strain curves obtained from this model are in good agreement with experimental results. By analyzing the predicted hysteresis magnetization and magnetostrictive strain under different conditions, we demonstrate that our proposed model can comprehensively describe the effects of temperature and prestress on the multi-field coupled hysteresis behaviors of giant magnetostrictive materials. Moreover, it provides theoretical guidance for both macroscopic and microscopic optimization in designing active devices incorporating super magnetostrictive materials.

An improved dynamic magnetic hysteresis model in soft magnetic composites

In this paper, an improved static Jiles-Atherton (J-A) hysteresis model is proposed to simulate the hysteresis properties of soft magnetic composites (SMC) by introducing an excitation factor to control the rotational component of magnetic domains in the effective magnetic field based on the internal demagnetization effect and magnetization mechanism. On the other hand, Since SMC is usually applied in the mid-frequency band, an improved dynamic hysteresis model is necessary to be proposed. The analytical expression for calculating the intraparticle eddy current loss is proposed based on the microstructural parameters of the SMC. And the microstructural parameters are determined by discrete element method DEM. For the intraparticle eddy current loss, the squared term of the mean particle size in the expression is further clarified. Eventually, this improved dynamic J-A hysteresis model was derived through the theory of magnetic field separation. The results show that SMC hysteresis loops with magnetic flux densities up to 1.5 T and frequencies up to 1 kHz can be evaluated by the proposed model.

Analysis and Design of Adjustable-Gap Double-Side Axial Flux Permanent Magnet Hysteresis Damper

In this paper, a novel adjustable gap double-side axial flux permanent magnet hysteresis damper (AGDSAPHD) is proposed, of which the torque can be adjusted by changing the air gap and the magnetic field angle between the upper and lower stators at the same time. To analyze and design, a modified vector Jiles-Atherton (JA) hysteresis model is used for simulating the magnetic flux distribution and the hysteresis torque of AGDSAPHD. The eddy currents in the AGDSAPHD are analyzed, which have a great influence on the output torque when the rotational speed is fast. A splitting method used in the rotor of the AGDSAPHD is proposed to reduce the effect of eddy currents. The heat distribution of the AGDSAPHD is calculated to determine its slip power and operating mode. A prototype is built and tested to verify the reliability of the analysis. The experiments prove that the modified vector JA model has high computational accuracy in calculating the hysteresis effects of the AGDSAPHD. A splitting method used in the rotor can greatly reduce the eddy current torque. AGDSAPHD has a greater torque adjustment range and better temperature stability than the traditional one.

A new hysteresis model based on Weibull cumulative distribution function and Jiles–Atherton hysteresis model

A new hysteresis model based on Weibull cumulative distribution function and Jiles–Atherton hysteresis model

Numerical analysis of the frequency-dependent Jiles-Atherton hysteresis model using the example of Terfenol-D material

<p>The Jiles-Atherton model has been widely used in describing the hysteretic property of a magnetic material or device. However, the calculation errors are not so easily discovered. With a complex expression, the frequency-dependent Jiles-Atherton model should be solved numerically with appropriate settings. This paper proposes an effective solving method for this model and describes some necessary analysis built on the numerical results. In the numerical method proposed in this manuscript, the anhysteretic magnetization was calculated by the secant method, and the trapezoidal rule was utilized to form the implicit function, which can be calculated by the fixed-point iteration. Compared to the other common methods, the proposed one has a friendly expression and fast computation speed. The Terfenol-D material was taken as an example for the numerical analysis. The feasible region was determined and the commonly used approximation that neglects the term of the magnetic field when calculating the magnetic induction intensity was tested. At last, the required number of sampling points per period was reached to guarantee high precision from analyzing its influence on the computation precision. The proposed numerical method is helpful for high-precision solutions of the frequency-dependent Jiles-Atherton model. The results from the numerical analysis can also help users avoid some incorrect calculations when employing this hysteresis model.</p>

Hysteresis and loss characteristics of Fe-based nanocrystalline alloys based on a novel variable-temperature dynamic Jiles–Atherton hysteresis model

The magnetic characteristics of Fe-based nanocrystalline alloys can be influenced by temperature. The conventional dynamic Jiles–Atherton (J-A) hysteresis model does not take into consideration the impact that temperature has on magnetic characteristics. A novel variable-temperature dynamic J-A hysteresis model is proposed in this paper to effectively address the issue. Firstly, the hysteresis loops of Fe-based nanocrystalline are measured at −50 °C–130 °C and DC state. The five parameters of the J-A hysteresis model are identified at various temperatures using the particle swarm optimization algorithm, and five parameters are fitted as functions of temperature. Subsequently, the five parameters as functions of temperature are introduced into the conventional dynamic J-A hysteresis model to construct a novel variable-temperature dynamic J-A hysteresis model, which can not only reflect the impact of temperature but also accurately calculate the losses. Finally, hysteresis loops and losses of Fe-based nanocrystalline alloy are simulated and calculated at different temperatures and frequencies by the variable-temperature dynamic J-A hysteresis model. Meanwhile, this paper also investigates the trends and percentages of hysteresis loss, excess loss as well as eddy current loss with frequency and temperature. Compared to the results of measured data, the maximum average error of the variable-temperature dynamic J-A hysteresis model is 5.83%.

Analytical Inverse Preisach Model and Its Comparison With Inverse Jiles–Atherton Model in Terms of Accuracy and Computational Speed

Inverse hysteresis model with magnetic flux density and magnetic field intensity as input and output respectively is more preferred, compared with the forward one, for resolving the electromagnetic issues of electrical equipment in terms of magnetic vector potential or with voltage sources. And an inverse hysteresis model with high accuracy and high computation speed both has broader range of applications. However, the well known classical Preisach hysteresis model is formulated with the forward form, and has the double integration of its distribution function, making it inconvenient and unpractical in the electrical engineering. In this paper, an analytical inverse Preisach model is proposed for the first time. Firstly, the analytical expressions of permeability of initial magnetization curve, descending and ascending branches of the hysteresis loop are derived using one closed form of Everett integral function. Subsequently the analytical inverse Preisach model is derived by the difference method, considering the reversible magnetization component that classical Preisach model cannot simulate with an odd function analytically. The experiment of one grain oriented silicon steel sample and one non-oriented silicon steel sample, under different magnetic excitation levels is conducted, and the accuracy and efficiency of the proposed analytical inverse Preisach model are confirmed by comparing its simulated hysteresis loops with the experimental ones and that computed with the widely used inverse Jiles-Atherton hysteresis model.

Hysteresis characteristics prediction method of amorphous materials based on static Jiles-Atherton hysteresis model and Maxwell's equation

Establishing an accurate hysteresis prediction method is crucial for reliable numerical analysis, especially for the growing demand in industrial applications. Existing hysteresis prediction methods, unfortunately, suffer from high cost, time consumption, and inaccuracy, particularly for those under high frequency. For that, this paper proposes a dynamic Jiles-Atherton hysteresis method with practicality and effectiveness. Firstly, an analytical model is derived to predict the eddy current magnetic field strength under high-frequency excitation using Maxwell's equation. Secondly, a modified static hysteresis characteristics prediction approach considering the skin effect is proposed based on the static Jiles-Atherton hysteresis model. Finally, a dynamic Jiles-Atherton hysteresis method (DJAM) considering the influence of skin effect on hysteresis characteristics is presented under the statistical theory of losses. The comparison between the simulated and measured results not only confirms the accuracy and efficiency of the DJAM but also indicates that its prediction accuracy is superior to the traditional method, particularly for those under high frequency.

Modeling and Analysis of Wave Energy Harvester with Symmetrically Distributed Galfenol Cantilever Beams.

In response to the challenges of difficult energy supply and high costs in ocean wireless sensor networks, as well as the limited working cycle of chemical batteries, a cylindrical wave energy harvester with symmetrically distributed multi-cantilever beams was designed with Galfenol sheet as the core component. The dynamic equation of the device was established, and ANSYS transient dynamic simulations and Jiles-Atherton hysteresis model analysis were conducted to develop a mathematical model of the induced electromotive force of the Galfenol cantilever beam as a function of deformation. Experimental validation demonstrated that the simulated results of the cantilever beam deformation had an average error of less than 7% compared to the experimental results, while the average error between the theoretical and experimental values of the induced electromotive force of the device was around 15%, which preliminarily verifies the validity of the mathematical model of the device, and should be subject to further research and improvement.

Formulation of a Mechanical Stress Dependent Macroscopic Magnetic Model for Incremental Permeability Simulation

Electromagnetic based systems receive ever-growing interest for on-line assessment of steel strip properties for major manufacturers, especially when Advanced High Strength Steel (AHSS) products for automotive purposes are considered. Manufacturing AHSS need optimal control of the thermo-mechanical processing using in-line sensors for real time monitoring. IMPOC, 3MA and PropertyMon are some of the well-known electromagnetic sensors. Identification of a mechanical or metallurgical state from a magnetic signal is of great interest, requiring however sophisticated models to mimic the real behaviour and its sensitivity to many influencing parameters. Our paper presents a proposition to add the dependency of mechanical stress to the Jiles-Atherton hysteresis model. Experimental data consist of B(H) curves of carbon steels strips subjected to different levels of mechanical stress applied along the magnetic measurement direction. The JilesAtherton model has then been used to find out a set of stress-dependent coefficients. The variation of coefficients with stress is in close relationship with the variations of coercive field, remanent induction and permeability with stress. A coupled magneto-mechanical approach allows physics-based functions to be proposed to describe the evolution of JilesAtherton coefficients with stress. In this paper, experimental working conditions will be described, as well as the stressdependent Jiles-Atherton model. The model is finally implemented in FEM software, allowing more complex magneto-mechanical situations to be modelled. After matching with measurement, the new model is applied on 3MA modelling where magnetic transient analysis and magnetic AC steady state analysis are linked through incremental permeability.

Nonlinear dynamic characteristics of two-dimensional micro-positioning workbench based on giant magnetostrictive actuators

Studying the nonlinear dynamic characteristics of multi-field coupling of the giant magnetostrictive actuator (GMA) is one of the main ways to improve its output performance. Because of the problem that its multi-field coupling nonlinear dynamic characteristics are difficult to accurately describe, the multi-field coupled nonlinear dynamic model of GMA and two-dimensional micro-positioning workbench is established according to the Jiles–Atherton hysteresis model, magnetostrictive model, hysteresis nonlinear magnetic equation and the structural dynamics principle of GMA, respectively. The influence of equivalent damping coefficient, equivalent stiffness, and equivalent mass on the dynamic characteristics of each model is analyzed, and finally, the constructed model and the obtained law are experimentally verified. The results show that the displacement curve calculated by the model is consistent with the experimentally measured displacement curve, the influence of the equivalent damping coefficient, equivalent stiffness, and equivalent mass on the dynamic characteristics of the model measured by the experiment is consistent with the simulation analysis results, and the maximum error of the output displacement is 1.779 um, which verifies the correctness of the model. The research results provide a theoretical basis for improving the dynamic characteristics of GMA and improving the output performance of two-dimensional micro-positioning workbenches.

Theoretical and experimental analysis of the correlation between magnetic memory signals and cumulative ductile damage of butt weld under low cycle fatigue

Welded structures experiencing superimposed cyclic loads with large plastic strain during a strong earthquake can easily lead to ductile or fatigue fracture. A newly developed self-magnetic flux leakage (SMFL) nondestructive detection technology named metal magnetic memory (MMM) is a valid approach to monitoring the development of fatigue damage in ferromagnetic materials. To investigate the correlation between MMM signals and cumulative ductile damage for butt weld under low cycle fatigue (LCF), combining strain-based Jiles-Atherton hysteresis model, magnetic charge model, and cumulative damage mechanics model, the theoretical relations between normal component HSF(z) of MMM signals and cumulative ductile damage D for single V groove butt weld were established in this paper. Relevant monotonic tensile tests and strain-controlled LCF tests were conducted, and the HSF(z) signals on the surface of welding specimens under different cyclic loads were measured. Comparing with experimental results verified the feasibility and accuracy of the theoretical relations. The results indicated that the peak-valley gradient Kp-v on the HSF(z) signals curve was decreased monotonously as the cumulative ductile damage D increased and the rate of decrease also diminished gradually. A possible exponential descending tendency of Kp-v with increasing D was demonstrated. Besides, the influences of weld width and weld reinforcement on the correlation between Kp-v and D were discussed theoretically in detail. This research provided a potential possibility for the assessment of the cumulative ductile damage at the welding joints under LCF based on MMM technology.

The effect of temperature on giant magnetostrictive thin films in high pre-stress environment for sensor application

The high pre-stress environment arises in the manufacturing of amorphous thin films of Terfenol-D through sputtering techniques. The pre-stress thin film of Terfenol-D has been developed due to the mismatch in the thermal coefficient of deposited magnetostrictive film and substrate. In the presence of high pre-stress anisotropic energy has been changed and due to that magnetization and magnetostriction properties of the thin film are affected. A novel three-dimensional hyperbolically generalized constitutive model for giant magnetostrictive materials along with vector generalized Jiles-Atherton hysteresis model was considered for predicting the hysteretic responses precisely under thermo-elasto-magnetic field. The material constants for the generalized constitutive models are taken from calibrated physical and experimental evidence. A non-linear finite element model for the thin films made up of Terfenol-D has been developed for investigating the thermo-elasto-magnetic characteristics, using COMSOL Multiphysics software. The predicted thermo-elasto-magnetic results have been critically analyzed the effect of temperature, the orientation of the applied magnetic field, and in-plane stresses condition. Hence, the present study can be decisive for the development of a more reliable and robust design of magnetostrictive film-based intelligent devices.

Finite Element Analysis of Axial Flux Permanent Magnetic Hysteresis Dampers Based on Vector Jiles-Atherton Model

Some techniques are proposed to model axial flux permanent magnetic hysteresis damper (APHD) based on vector Jiles-Atherton (JA) model. These techniques improve calculation convergence and reduce calculation time. A fast identification method based on the numerical method and the genetic algorithm is used to obtain the parameters of the JA hysteresis model. The comparison between the measured and the calculated hysteresis curves proves that the identification method has the advantages of high accuracy and efficiency. The influence of the eddy current, dimensional parameters and the proportion of magnetization on the output torque of APHD is analyzed. A prototype is used to check the reliability of the simulation. The result shows that the 3-D FEM has high calculation accuracy.

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.

A dynamic magnetostrictive model based on the Jiles–Atherton hysteresis model and field separation approach

PurposeThe purpose of this paper is to combine the Jiles-Atherton (J-A) hysteresis model with the field separation approach to realize the accurate simulation of dynamic magnetostrictive characteristics of silicon steel sheet.Design/methodology/approachFirst, the energy loss of silicon steel sheet is divided into hysteresis loss Why, classical eddy current loss Wed and anomalous loss Wan according to the statistical theory of losses. The Why is calculated by static J-A hysteresis model, Wed and Wan are calculated by the analytical formulae. Then, based on the field separation approach, the dynamic magnetic field is derived. Finally, a new dynamic magnetostrictive model is proposed by means of the quadratic domain rotation model.FindingsComparison of simulation and experimental results verifies that the proposed model has high accuracy and strong universality.Originality/valueThe proposed method improves the existing method’s problem of relying on too much experimental data, and the method ensures the calculation accuracy, parameter identification accuracy and engineering practicability. Consequently, the presented work greatly facilitates further explorations and studies on simulation of dynamic magnetostrictive characteristics of silicon steel sheet.

Study of effective particle shape-dependent magnetization behavior of soft magnetic polymeric composites

This reports an investigation of the effect of magnetic particles with same chemical composition but different aspect ratios on the effective magnetization response of magnetorheological elastomers (MREs). MREs are composites that consist of magnetically permeable particles dispersed in a non-magnetic polymeric matrix. These materials are known for the tunability of their magnetoelastic properties. When subjected to an externally applied magnetic field, changes occur in their mechanical properties such as stiffness; this is the so-called magnetorheological (MR) effect. This is usually attributed to the magnetic interactions between the magnetic filler particles. Several factors significantly influence the MR effect. These are the polymer matrix, volume fraction, size, and shape of the magnetic particles. In this study, based on continuum formulation theory, microscale modeling using a finite element analysis (FEA) was used to determine the effect of the latter on the macroscopic magnetization of MREs. Using Jiles-Atherton hysteresis model parameters, the hysteresis loops of MRE were numerically resolved in the FEA software COMSOL Multiphysics. The model calculations were performed for randomly oriented (unaligned) and aligned microstructures with constant particle-volume fraction (φ= ∼20%) and varying particle-aspect ratios (AR=1, 2.5, 5 and 7.5). A computational homogenization scheme was used to relate the microscopic behavior to the macroscopic properties of these composites. From the analysis, it was found that for unaligned MRE the effective magnetization increased with increase in the particle aspect ratio, particularly in the linear region, while the saturation magnetization is seen to be independent of the particle shape. The effect is much more noticeable for particles aligned with the applied field, while for particles aligned perpendicular to the applied field an opposite effect is seen, where increasing aspect ratio results in decreased magnetization relative to the applied field.

Integral Methodology for the Multiphysics Design of an Automotive Eddy Current Damper

The present work reports an integrated (experimental and numerical) methodology that combines the development of a finite element multiphysics model with an experimental strategy to optimally design an eddy current damper for automotive suspensions. The multiphysics model couples the whole set of time-dependent electromagnetic, thermal, mechanical, and fluid–wall interaction (CFD) partial differential equations. The developed FE model was validated against both literature model predictions and in-house experimental data. The electromagnetic model takes into account the magnetic material characteristics of the ferromagnetic material and iron poles. Loss separation and the Jiles–Atherton hysteresis models were invoked to determine the heat generated in the soft iron parts. The computation of the fluid–wall interaction phenomena in the air gap allowed for the prediction of the temperature field across the solid materials, including the magnets. The design of the EC damper addresses the effects of the geometries of the stator and rotor, as they are the most critical geometries for maximizing the functions of an eddy current damper. The magneto-thermal simulations suggested that the heating of the permanent magnets remains within a safe region over the investigated operational frequency range of the eddy current damper.