Modeling of hysteresis loops using rational and power functions

Abstract

Simple and precise hysteresis models with a small number of parameters allowing fast calculation are required for the magnetic analysis, as the field is calculated in a very large number of points. This paper presents a new simple method for modeling the hysteresis loops of soft magnetic materials using combined rational and power functions. Three approaches are used to model the hysteresis loops analytically. In the first approach, the upper and lower curves of the hysteresis loops are estimated and are calculated separately, using combined rational and power functions. In the second approach, the hysteresis loops are calculated using the DC magnetization curve and combined rational and power functions, applying a phase shift in the magnetic field strength variations relative to the magnetic flux density. The third approach presents a novel method for modeling hysteresis loops: first, the model is fitted to the “mean curve”, which is in the middle of the measured hysteresis curve, and as a second step the phase shift is calculated as in the second approach. A solid iron sample with a rectangular cross section is used for the measurements and the hysteresis modeling. The proposed method is also applied to model the hysteresis loops of a magnetic material with high magnetic permeability and grain-oriented steel, to show the generality of the proposed methods.