Modeling the dynamic behavior of laminated steels using a Fourier-based approach

A new magneto-dynamic model is proposed to approximate the dynamic hysteresis effect in laminated steels considering the static hysteresis, eddy-current field, and excess field. An accurate congruency-based hysteresis model is used to predict the static hysteresis field. The eddy-current is determined from the 1D diffusion equation and the well-known Bertotti empirical equation is utilized to model the excess-field effect. The dynamic lamination model obtained from coupling three field components is solved using a Fourier-based approach. In this approach, the flux density across the lamination thickness is approximated by a cosine-based Fourier series. The coefficients of the Fourier series are determined by solving a system of nonlinear equations through an iterative procedure. Owing to the employed congruency-based static hysteresis model, the proposed magneto-dynamic model offers high accuracy for arbitrary magnetization regimes. To validate the model accuracy, the model results are compared with sinusoidal and multi-harmonic measurements. The comparison shows that the proposed model predicts the dynamic hysteresis phenomenon in laminated steels with a relative energy error of less than 7%.