This paper strives at getting deeper insight into possible methods to take anisotropy of magnetic properties of non-oriented steels into account. The first considered approach is derived from considerations from metallurgy and materials science. It offers a straightforward way to compute variations of magnetic properties from measurements defined for three cutting angles of the samples. The second method is based on some concepts from electromagnetic theory. This approach allows one to determine the relationships between vectors, and, thus, it is more useful from a perspective of an electrical engineer. One of the goals of the paper is to show the flexibility of the second approach, which offers a lot of information on the relationships between the above-mentioned vectorial quantities.
The approach based on orientation distribution functions is based on the assumption that many angular dependencies of physical quantities may be recovered from the knowledge of material behaviour in three well-defined directions. The method is directly applicable, e.g. to power losses, permeability at loop tip, coercive field strength, etc. The other method is derived from earlier research focused on approximating coenergy profiles. The modified elliptical model by Biró et al. (2010) used previously for material with more distinctive anisotropy (grain-oriented steel) is applied to non-oriented steel, which – in spite of its name – also exhibits a substantial anisotropy level.
The advantage of the first model is its simplicity. It offers a reasonable modelling accuracy; the discrepancies between the measured and the modelled values of the considered quantities did not exceed 10%. The second approach is more complicated; on the other hand, it provides information about spatial dependencies between vectors and . It was found that the value of exponent n in the relationship from which the magnitude of the vector is determined is somewhat higher for the considered material than the value proposed by Biró et al. This effect may be related to a different morphology of the examined materials. The discrepancies between model predictions and measurement values were below 15%. The computations in the present study were carried out in a wider range of working flux densities than were originally considered by Biró et al.
Anisotropy of magnetic properties may and should be taken into account also in the case of non-oriented electrical steels. This can be achieved during the design of magnetic circuits with the use of the presented models. In the present paper, we have used piecewise linear interpolation schemes to describe anhysteretic curves for two principal directions; however, more sophisticated approaches might be used instead, which in turn might improve the accuracy of the second model.
The modified elliptical model allows one to determine a number of important relationships for the considered non-oriented electrical steel. Therefore, it might be a useful tool at the design stage. A number of tedious measurements may be avoided. The authors believe that the method is also applicable to grain-oriented electrical steel.
