Analytical model for magnetic anisotropy of non-oriented steel sheets

Purpose - Recent investigations on magnetic properties of non-oriented (NO) steel sheets enhance the comprehension of the magnetic anisotropy behaviour of widely employed electrical sheets. The concept of energy/coenergy density can be employed to model these magnetic properties. However, it usually presents an implicit form which requires an iterative process. The purpose of this paper is to develop an analytical model to consider these magnetic properties with an explicit formulation in order to ease the computations. Design/methodology/approach - From rotational measurements, the anhysteretic curves are interpolated in order to extract the magnetic energy density for different directions and amplitudes of the magnetic flux density. Furthermore, the analytical representation of this energy is suggested based on statistical distribution which aims to minimize the intrinsic energy of the material. The model is finally validated by comparing measured and computed values of the magnetic field strength. Findings - The proposed model is based on an analytical formulation of the energy depending on the components of the magnetic flux density. This formulation is composed of three Gumbel distributions. Every functional parameters of energy density is formulated with only four parameters which are calculated by fitting the energy extracted from measurements. Finally, the proposed model is validated by comparing the computation and the measurements of 9 H loci for NO steel sheets at 10 Hz. The proposed analytical model shows good agreements with an average relative error of 27 per cent. Originality/value - The paper presents an original analytical method to model magnetic anisotropy for NO electrical sheets. With this analytical formulation, the determination of H does not require any iterative process as it is usually the case with this energy method coupled with implicit function. This method can be easily incorporated in finite element method since it does not require any extra iterative process.