Model of Magnetic Anisotropy of Non-Oriented Steel Sheets for Finite-Element Method

Abstract

Even non-oriented steel sheets present a magnetic anisotropic behavior. From rotational flux density measurements at 5 Hz, the model of magnetic anisotropy is derived from two surface Basis-cubic splines with the boundary conditions matching with ferromagnetic theory. Furthermore, the investigation of the magnetic anisotropy shows that the H(B) characteristic is not strictly monotonous due to the angle difference between the field and the flux density. Hence, standard non-linear solvers would either diverge or converge towards the closest local minimum. Thus, we propose two different specific solvers: a combined Particle Swarm Optimization with a relaxed Newton-Raphson and a Modified Newton Method.

Modelling anisotropy in non-oriented electrical steel sheet using vector Jiles–Atherton model

“…The unidirectional alternating magnetic field measurements are shown in Figures 2 and 3, and Figure 6 depicts the rotational measurements. Thus, the silicon steel sample of grade M400-50A reveals weak magnetic anisotropy (Figure 6) as compared to the measurement done on an NO electrical steel sample at 5 Hz by Martin et al (2016).…”

“…The unidirection alternating magnetic field measurements are shown in Figure 2, and Figure 6 depict the rotational measurements. Thus, the silcon steel sample of grade M400-50A reveals weak magnetic anisotropy ( Figure 6) as compared to the measurement done on a NO electrical steel sample at 5 Hz by Martin et al (2016). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59…”

“…The contours of the coenergy/energy density can be modelled with a Vector Jiles-Atherton model modified ellipse for improving the accuracy of the anisotropic anhysteretic model. Although this approach can be easy to implement, the interpolation of every component of the field with respect to all the components of the magnetization can significantly improve the accuracy of the anhysteretic curve (Enokizono and Soda, 1995;Martin et al, 2016). The aim of this paper is to present a further improvement of the original anisotropic vector J-A model for modelling NO electrical steel sheets.…”

Finite Element Level Validation of an Anisotropic Hysteresis Model for Non-Oriented Electrical Steel Sheets

“…However, the results they predict disagree with the measurement data. Instead of using the magnetic energy, [11] employs bicubic splines to represent the anhysteretic characteristics identified from the rotational measurements. The method based on the surface bicubic spline is easier to integrate with the FEM and it is more accurate than the energy-density method.…”

Tensorial permeability microstructure model considering crystallographic texture and grain size for evaluation of magnetic anisotropy in polycrystalline steels

“…There is an important implicit assumption in the scalar permeability models that the magnetic flux density B always parallels with the applied field H, which is only a valid approximation at low and uniform fields. Some tensor permeability models [13][14][15][16] have been reported to be able to address this limitation, which also facilitates finite element modelling [17][18][19] to solve problems that involve rotational fields and complex geometry. Nevertheless, tensor models require prior knowledge of the permeability for principal directions, along which B parallels with H, to formulate a permeability tensor.…”