Engineering topics
Nagel, James R.
Publications and source records attributed to Nagel, James R..
Finite-Difference Simulation of Eddy Currents in Nonmagnetic Sheets via Electric Vector Potential
The magnetic excitation of eddy currents in thin metal sheets is a mathematically challenging problem with many practical applications. Since the eddy current density is a solenoidal field on a 2-D plane, we may express it as the curl of a separate vector field with only one scalar component. This new field is governed by a unique form of the vector-Poisson equation that is readily solved numerically through standard finite-difference techniques. For the special case of a weakly induced eddy current, the self-inductance terms can be neglected to produce a sparse system matrix that is easily inverted. For a strongly induced eddy current, self-inductance must be included at the cost of a more complex and dense system matrix. The method is validated against the CST EM Studio software suite by producing nearly identical results in only a tiny fraction of the computational time.
Eddy current separation for recovery of non-ferrous metallic particles: A comprehensive review
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Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field
In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space—an infinite slab in one dimension, a longitudinal cylinder in two dimensions, a transverse cylinder in two dimensions, and a sphere in three dimensions. Numerical simulations are also performed in parallel with analytic computations, all of which verify the accuracy of the derived expressions.