Eddy-Currents in Solid Cylindrical Cores Having Non-Uniform Permeability

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Abstract
A method of estimating magnetization losses due to eddy-currents in solid cylindrical cores of ferromagnetic material is given. The conception of complex permeability is introduced to show the effects which hysteresis has upon the degree of flux penetration. A formula is given for the effective permeability which should be used in the classical treatment in which nonlinearities have been ignored. An arbitrary case in which the permeability changes across the core section is considered and the solution is extended to a core which is homogeneous, but whose permeability changes with the degree of magnetization. In this way errors due to a nonlinear B-H curve are reduced and the complex permeability notation is shown to lead to a more reasonable Steinmetz relationship. The eddy-current anomaly is mentioned and it is noted that the theory developed is suited to a consideration of the anomaly as explained in terms of time-lag effects.

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