Analytical Model of an I-core Coil for Nondestructive Evaluation of a Conducting Cylinder below an Infinite Plane Conductor

An analytical model for eddy current testing of an I-core coil located above a two-layer conductive material is presented. The upper layer is an infinite plane conductor, and the bottom layer is a conductive cylinder. The method of truncated region eigenfunction expansion (TREE) is used to solve this axisymmetric problem. First the magnetic vector potential of a filamentary coil coaxial with the I-core over the two-layer conductor is considered. Then the closed form expression for the impedance of the multi-turn coil with rectangular cross section is derived by using the principle of superposition from the filamentary coil field. For frequencies ranging from 0.1 kHz to 10 kHz, both the impedance changes of the I-core coil located above the infinite plane conductor without the conducting cylinder, and in the absence of the two-layer conductor are calculated using Mathematica, respectively. The influence of the conducting cylinder below the infinite plane conductor on the impedance change is analyzed. The analytical calculation results are verified by the finite element method and experiment, the results agree very well, which verifies the correctness of the analytical model.