Modelling dynamic hysteresis loops in steel sheets

Abstract

PurposeThe aim of the paper is to present a simple approach to modelling minor hysteresis loops in grain‐oriented steel sheets under quasi‐static and dynamic conditions. The hysteresis phenomenon is described with a recently developed hybrid model, which combines ideas inherent in the product Preisach model and the Jiles‐Atherton description. The dynamic effects due to eddy currents are taken into account in the description using a lagged response with respect to the input.Design/methodology/approachIt is assumed that some model parameters might be dependent on the level of relative magnetization within the material. Their dependencies could be given as power laws. The values of scaling coefficients in power laws are determined.FindingsA satisfactory agreement of experimental and modelled quasi‐static and dynamic hysteresis loops is obtained.Research limitations/implicationsThe present study provides a starting point for further verification of the approach for other classes of soft magnetic materials, which could be described with the developed model. At present, the approach to model minor loops by the update of model parameters is verified for the B‐sine excitation case.Practical implicationsThe “branch‐and‐bound” optimization algorithm is a useful tool for recovery of the values of both model parameters and scaling coefficients as well.Originality/valueThe recently developed hybrid description of hysteresis phenomenon can be successfully extended to take into account symmetric minor loops. The developed approach could be a framework to develop a comprehensive description of magnetization phenomena in the future.

Description of Henkel plots by the magnetization-dependent Jiles–Atherton model

“…k, describes the distribution of pinning sites, whereas the other one, namely a, is related to the average size of domains aligned with the applied field. The proposed relationships are envisaged in the form of power laws [17,18] …”

“…The values of other model parameters a; b and M s are kept constant during the estimation process. The detailed descriptions of the approach are given elsewhere [17,18,26].…”

“…This difficulty has been successfully overcome in a recent modification of the model [17,18]. Values of some model parameters are updated upon the level of magnetization.…”

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).…”