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

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, the standard non-linear solvers would either diverge or converge toward the closest local minimum. Thus, we propose two different specific solvers: 1) a combined particle swarm optimization with a relaxed Newton-Raphson and 2) a modified Newton method.