Eddy current loss in saturated solid magnetic plates, rods, and conductors

Included in this paper is a procedure which utilizes the digital computer to solve eddy current loss problems when the magnetization process extends into the nonlinear region of the magnetization curve. The values of permeability used in the equations are obtained from the actual magnetization curve, thus eliminating the approximations employed in most previous investigations. The nonlinear partial differential equations are replaced by finite difference equations and solved by numerical methods on an IBM 7070 digital computer. The investigation covers cases of both rectangular plates and cylindrical rods. For the cylindrical rods, cases involving piecewise homogeneous material as well as cases involving homogeneous material are considered. The material is said to be of a homogeneous nature, as the term is used here, when it satisfies the requirements that 1) resistivity be constant throughout the material; and 2) flux density and magnetic intensity be related by the same magnetization curve throughout the material. A cylindrical rod, composed of two concentric cylinders of different magnetic and electrical properties, is the piecewise homogeneous case covered in the present paper. Throughout the investigation, it is assumed that flux density and magnetic intensity are related by a single valued curve; hence, hysteresis effects are neglected.