Inverse Model of the Magnetic Hysteresis Based on Exponential Function

Abstract

Very often in numerical calculations of magnetic field distribution in ferromagnetic materials it is necessary to take into account a certain model of the magnetic hysteresis presenting changes of the flux density as a function of the magnetic field strength. However, in many cases it is profitable to apply an inverse model of the magnetic hysteresis describing the relationship between the field strength and the flux density. This paper presents a relatively simple method of approximation of field strength changes during magnetization of electrical steel sheets. It is assumed that the field strength changes are a sum or a difference of a function which describes one curve of the limiting hysteresis loop and a certain "transient" component. A method of the determination of functions describing changes of the field strength for assumed changes of the flux density is discussed in the paper. Theoretical considerations have been confirmed by comparison between measured and calculated hysteresis loop for chosen dynamo and transformer steel sheets.