An Analytical Approach of Magnetic Diffusion in a Plate Under Time-Varying Flux Excitation

A new analytical computation of magnetic flux distribution and eddy currents is proposed in this paper. Equations are set down for a plate subjected to a time-varying flux excitation. This method consists of using Neumann´s boundary conditions in the flux-density diffusion equation to consider the instantaneous variations of the imposed flux waveform. The diffusion equation is solved by separation of variables and Duhamel´s theorem. Different cases of imposed magnetic flux are studied: sinusoidal flux, flux ramp, and arbitrary time-varying flux. This new analytical method is a complement of the classical approach (with Dirichlet´s boundary conditions) where induction at boundary needs to be corrected to fit the instantaneous total flux. In this paper, a distinctive method allows to compute the instantaneous distributions and corresponding losses directly from the experimental flux measurements on electromagnetic devices. The analytical expressions of magnetic flux density and eddy current distributions are explicitly given. The comparison between analytical and finite-element simulation results shows the validity of the new analytical method.