Rigorous Solution of Eddy Current Losses in Rectangular Bar for Single Plane Domain Wall Model

Abstract

Williams, Shockley, and Kittel, and other authors have presented a simple domain model in which magnetization takes place by the movement of a single plane domain wall. The net flux is zero when the domain wall is in the middle of the cross section and the material is magnetized fully when the wall moves to the surface. Maxwell's equations for the case of a rectangular bar are rigorously solved for any position of the wall and expressions are derived for the current stream function in both regions I and II. The stream function was calculated using an IBM 705 computer and is shown for various positions of the wall and for several ratios of the sides of the rectangle. The power loss for sinusoidal applied induction is calculated. The results show that the loss in the material increases as the distance traversed by the wall, i.e., the dimension of the rectangle at right angles to the domain wall increases. This solution with some modification also applies to thin laminations; where the domain model, proposed by several authors, consists of domains of equal width alternately magnetized in opposite directions to give the unmagnetized state. The domain walls are perpendicular to the plane of the sheet and magnetization in the sheet plane takes place by lateral movement of these domain walls. For any given thickness of the laminations, a domain wall spacing can be determined to correlate the power loss with experimental values.