An Analytical Solution for the Eddy Current Coil Located over a Conductive Disc with Two Layers of Different Radii

Abstract

In this work, an analytical model was derived for an air-core probe placed above a disc whose upper layer has a larger diameter than the lower layer. The proposed solution can be utilised in eddy current testing of screws, rivets, valves, and other elements with similar geometry, and made of electrically conductive materials. The final formulas for the change in the probe impedance were obtained using the truncated region eigenfunction expansion (TREE) method and expressed in closed form. The calculations were performed in Matlab for two disc configurations made of bronze, brass, and graphite. The results of the calculations of the impedance components were compared with the results of the measurements. Very good agreement was obtained within the entire frequency range. In no case did the errors in determining changes in resistance or reactance exceed 2 %.