Approximation of Hysteresis Changes in Electrical Steel Sheets

Witold Mazgaj,Zbigniew Szular,Michal Sierzega

doi:10.3390/en14144110

Abstract

This paper describes a simple method of approximating hysteresis changes in electrical steel sheets. This method is based on assumptions that flux density or field strength changes are a sum or a difference of functions that describe one curve of the limiting hysteresis loop and a certain ‘transient’ component. Appropriate formulas that present the flux density as functions of the field strength and those that present inverse dependencies are proposed. An application of this approximation requires knowledge of the measured limiting hysteresis loop and a few minor loops. Algorithms for determining changes in the flux density or field strength are proposed and discussed. The correctness of the proposed approximation of hysteresis changes was verified through a comparison of measured hysteresis loops with the loops calculated for several different excitations of the magnetic field occurring in dynamo and transformer steel sheets. Additionally, an example of the application of the proposed approximation of hysteresis changes is discussed in the paper. The proposed approximation of hysteresis changes is recommended for numerical calculations of the magnetic field distribution in dynamo and transformer steel sheets.

Highlights

IntroductionThe hysteresis phenomenon is a characteristic feature of any magnetic circuit containing a ferromagnetic material
Hysteresis Changes in Electrical SteelThe hysteresis phenomenon is a characteristic feature of any magnetic circuit containing a ferromagnetic material
The original equation formulated by Landau–Lifschitz was modified by Gilbert to take into account the damping conditions of the magnetic moment rotation, which in the steady state will occupy a position along the direction of the magnetic field strength

Summary

Introduction

The hysteresis phenomenon is a characteristic feature of any magnetic circuit containing a ferromagnetic material. This phenomenon is related to a certain delay in changes in the magnetic flux density in relation to changes in the magnetic field strength in this material. The hysteresis mechanism is quite well known [1,2,3,4,5,6,7]; the formulation of an appropriate mathematical model based on the knowledge of the phenomena describing the magnetization process is still a complex issue. As stated in a previous study [9], the calculation results obtained on the basis of the Landau–Lifschitz–Gilbert equation “can be averaged to provide hysteresis curves of material”. It should be mentioned that hysteresis curves of ferromagnetic materials are often described by different empirical fitting procedures

Objectives

Methods

Conclusion