Distributed Current Source Method for Modeling Magnetic and Eddy-Current Fields Induced in Nonferrous Metallic Objects

This paper presents a new modeling method to determine the harmonic eddy current (EC) field induced in a nonferrous metal and its corresponding magnetic flux density (MFD) by an EC-based sensing system for geometrical measurements, which accounts for the boundary effects of the object. Modeled using a distributed current source (DCS) method in state-space representation, the EC field is formulated as a two-step constrained least-square problem to solve for its real and imaginary parts. Two practical techniques to improve the efficiency and accuracy of the EC solutions are illustrated. The first refines the DCS distribution based on the skin-depth effects, and the second takes advantages of commercial mesh-generation software to facilitate the modeling of EC induced in complex-shaped objects. The DCS-based EC models are verified numerically by comparing computed results with two-dimensional (2-D) analytical axisymmetric solutions and commercial finite-element analysis, and evaluated experimentally with an EC sensor that measures the MFD generated by the induced EC in different materials and geometrical configurations.