Modelling offset minor hysteresis loops with the modified Jiles–Atherton description

Abstract

The paper addresses the issue of modelling offset minor hysteresis loops within the framework of the Jiles–Atherton model. Two of the model parameters are expressed in terms of scaling power laws with respect to the magnetization level. The approach is consistent with earlier theoretical considerations on the effective ‘volume fraction’ by Professor D Jiles. The influence of eddy currents on hysteresis loop is taken into account using an additional term of magnetic field.

Minor Loops in the Harrison Model

“…A much more complex situation is with the JilesAtherton (JA) description, where both magnetization components are coupled through the eective eld term, but moreover through a magnetization dependent R(m) function in a recent model modication [36,43,44]. Anhysteretic magnetization is described in the JA formalism with the modied Langevin function with respect to the eective eld.…”

“…For a constant ambient temperature one obtains dierent oset anhysteretic curves, which correspond to dierent reversal curves, dened by magnetization values at the beginning and at the end of the magnetization process. This concept has been imple-mented for the modied JA description in [36], where two JA model parameters have been updated according to some power laws with respect to relative magnetization level. In the Harrison model the update of anhysteretic curve (and, what is more noticeable of the S-shaped hysteretic curve) for the minor loops is achieved by the normalization of model equations.…”

The effect of anisotropy in the modified Jiles-Atherton model of static hysteresis

“…is the so-called effective field, δ is the sign of time derivative of flux density, which is the input variable in the normalized measurement conditions (IEC60404), ( ) [4,[6][7]. 1 , 0 ∈ m denotes reduced magnetization, which is actual magnetization referred to saturation magnetization.…”

“…The latter impact should be pronounced for higher excitation levels. The modified Jiles-Atherton description has been developed to describe magnetization curves of electrical steels [2,4,[6][7]. For these soft magnetic materials the assumed values of J parameter could be equal to 0.5 (for grain oriented steels) or to 1 (for non-oriented steels).…”

Comparison of macroscopic descriptions of magnetization curves

“…At the same time several authors realized that in order to obtain a reliable representation of more complex magnetization cycles, including minor loops, reversal curves etc. it would be necessary to update the values of model parameters in accordance with certain functional dependencies [6,10,[17][18][19][20]. The abundance of different model versions and the focus set mostly on the advantages of one estimation method over another have blurred serious problems with the model equations themselves.…”