A Three-Dimensional Model of Magnetic Reluctance of Rectangular Iron Core

Abstract

A three-dimensional distribution of magnetic filed is considered to obtain an analytical model of the magnetic reluctance of rectangular iron-cores whose ends face to the working airgaps in a magnetic system. The reluctance model is compared with a simple model based on the two-dimensional distribution to check the validity of this simple model for the effects of the length of iron core. First, the magnetic field is solved under an assumption that the magnetic intensity is uniform and perpendicular to the end surfaces. To obtain an analytical solution, however, a natural condition is neglected that the magnetic intensity is uniform on the side surfaces parallel to the longitudinal direction. Also, the concept of generalized functions is applied to discuss the convergence of an infinite cosine-function series; hence the result obtained is an approximation. Next, the magnetic reluctance is obtained from the magnetomotive force along the iron-core surface divided by the magnetic flux. The reluctance is expressed with two parts : a term corresponding to two-dimensional model and a term with a function of the iron-core length. Approximate equations are presented to avoid poor convergence of double infinite series, and numerical examples are given to show the results.