Magnetic Fields, Eddy Currents, and Losses, Taking the Variable Permeability into Account

Abstract

An analog method is described in which a network, consisting of semiconductor diodes, capacitors, and resistors, is used to solve the partial differential equations. The magnetization curves of electrical sheet steels and solid iron are simulated to a high degree of accuracy by specially selected silicon zener diodes. With constant permeability any two-dimensional region, consisting of solid or laminated iron, copper, brass, air, etc., may be considered. With variable permeability, the one-dimensional case has been treated for three different boundary conditions. The equations necessary for the determination of the quantities flux, power, force, etc. are derived and transient phenomena are also considered. As a numerical example, the distribution of current and flux density in time and space in the interior of a solid iron plate is determined for different boundary conditions, and the eddy current losses are calculated. Due to the variable permeability, a discretization error appears in the form of a peculiar high-frequency ripple with sharp peaks. This represents a considerable obstacle if relaxation methods are attempted.