The physical assumptions underlying the static and dynamic Jiles-Atherton (JA) hysteresis models are critically analyzed. It is shown that the energy-balance method used in deriving these models is actually closer to a balance of coenergies, thereby depriving the resulting JA phenomenology of physical meaning. The non-physical basis of its dynamic extension is demonstrated by a sharp contrast between hysteresis loops predicted by the model and those measured for grain-oriented steel under conditions of controlled sinusoidal flux density at frequencies of 50, 100, and 200 Hz.

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.

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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.

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Even the so-called non-oriented steels used in electrical engineering reveal anisotropy of their magnetic properties. Anisotropy may have a substantial impact on the performance of magnetic circuits; therefore it is necessary to take this phenomenon into account already at the design stage. A simple formula useful for the description of magnetisation curves in two principal directions is proposed. The B(H) dependencies for other directions are determined using a model based on coenergy concept. The worst magnetic properties are obtained for the samples cut at approximately 60 degrees. The presented description may be useful for prediction of rotational loss in ferromagnetic sheets used as core material in electric machines.

An extension of the modified Jiles-Atherton description to include the effect of anisotropy is presented. Anisotropy is related to the value of the angular momentum quantum number J, which affects the form of the Brillouin function used to describe the anhysteretic magnetization. Moreover the shape of magnetization dependent R (m) function is influenced by the choice of the J value.