Analytical formulation for magnetic shields taking into account hyteresis effects in the Rayleigh region
Purpose - To study the magnetic shielding and the losses of non-linear, hysteretic multilayered shields by using fast to evaluate analytical expressions. Design/methodology/approach - In order to evaluate the shield in the frequency domain, the non-linear shield is divided into a sufficient number of piecewise linear sublayers. Each sublayer has a permeability that is constant (space independent) and complex (to model hysteresis). This expression for the permeability is found from the Preisach model by a Fourier transform. Once H is known in the entire shield, analytical expressions calculate the eddy current losses and hysteresis losses in the material. The validity of the analytical expressions is verified by numerical experiments. Findings - In the Rayleigh region, the shielding factor of perfectly linear material is better than the one of non-linear metal sheets, but also the eddy Current losses are higher. The results of the optimization show that steel is only a useful shielding material at low frequencies. Research limitations/implications - The analytical method is valid for infinitely long shields and for weak imposed fields in the Rayleigh region. Practical implications - As the analytical expressions can be evaluated very fast (in comparison with slow finite elements models), many magnetic shields can be compared in parametric studies. Originality/value - Analytical expressions exist for the shielding factor and the losses of linear materials. In this paper, the method is extended for non-linear hysteretic materials. The effects of several parameters (material parameters, incident fields parameters) on the shielding and the losses are shown.
electromagnetism optimization techniques numerical analysis electrical conductivity