Review of Hysteresis Models for Magnetic Materials

Abstract

There are several models for magnetic hysteresis. Their key purposes are to model magnetization curves with a history dependence to achieve hysteresis cycles without a frequency dependence. There are different approaches to handling history dependence. The two main categories are Duhem-type models and Preisach-type models. Duhem models handle it via a simple directional dependence on the flux rate, without a proper memory. While the Preisach type model handles it via memory of the point where the direction of the flux rate is changed. The most common Duhem model is the phenomenological Jiles–Atherton model, with examples of other models including the Coleman–Hodgdon model and the Tellinen model. Examples of Preisach type models are the classical Preisach model and the Prandtl–Ishlinskii model, although there are also many other models with adoptions of a similar history dependence. Hysteresis is by definition rate-independent, and thereby not dependent on the speed of the alternating flux density. An additional rate dependence is still important and often included in many dynamic hysteresis models. The Chua model is common for modeling non-linear dynamic magnetization curves; however, it does not define classical hysteresis. Other similar adoptions also exist that combine hysteresis modeling with eddy current modeling, similar to how frequency dependence is included in core loss modeling. Most models are made for scalar values of alternating fields, but there are also several models with vector generalizations that also consider three-dimensional directions.

Analysis of Higher-Order Bézier Curves for Approximation of the Static Magnetic Properties of NO Electrical Steels

“…During the preliminary analysis [31], we determined that the inverse hyperbolic sine function is promising, especially in the saturation region, because of its logarithmic character for higher input values. Therefore, the inverse hyperbolic sine of Function (6) was included in the presented analysis.…”

“…Because of its physical foundation, it is used in many models to describe the magnetization curves, e.g., in the Jiles-Atherton hysteresis model [5]. Further, in applied engineering, the so-called Frölich-Kennelly approximation is often used for the description of nonlinear properties, especially for extrapolation purposes [6,33]. The Frölich-Kennelly equation has an equivalent mathematical description in the Elliot function (Function (3)).…”

“…Examples of using the anhysteretic curve as input data are the widespread Jiles-Atherton hysteresis model and its variations [4,5] and various finite element simulation tools. Hysteresis models are used to describe nonlinear magnetization and power loss in iron cores, whereas the nonlinear behavior is indispensable in the design of electromagnetic machines and devices [6,7]. For these reasons, it is important to find adequate methods or analytic functions to describe such nonlinear curves with high accuracy and with low computational power.…”

Modeling Dynamic Hysteresis Curves in Amorphous Magnetic Ribbons

“…The value of the normalization constant K was equal to 0.0025 in this case. It is evident from the inspection of Figures 2 and 3 that hysteresis loops in quasi-static magnetization conditions for the considered core are regular and may be easily described, e.g., using the phenomenological description based on the arctangent function [31,32] or another convenient model [33,34]. However, in the present paper, we follow the approach outlined in [1] and take the experimentally determined H = H(B) curves as a reference in order to avoid additional errors inevitably introduced by the representations of quasi-static hysteresis curves.…”

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

“…The fitting accuracy of the J-A model in the unsaturated region can be improved by increasing the model parameters [16][17][18], but this also increases the computational burden. Another classic method for describing hysteresis loops is to use Fourier expansion to describe periodic B or H functions [19]. Under sinusoidal excitation, when material enters the magnetic saturation region, severe waveform distortion occurs in B or H, making it difficult to describe using Fourier series.…”