An analytical solution of the nonlinear eddy-current losses in ferromagnetic materials

The present analysis is concerned with the determination of the electromagnetic field and losses in a cylinder of ferromagnetic material. The method consists of finding a linear solution for the diffusion equation governing the field and then applying the method of variation of parameters to take the nonlinearity into account. The application of the method of averaging reduces the problem to the solution of two first-order ordinary differential equations governing the amplitude and phase variations with depth. The equation governing the averaged phase is readily integrable, while that governing the averaged amplitude is integrated numerically. The results are in excellent agreement with experimental data and with finite-difference numerical solutions.