Analytical model of a T-core coil above a multi-layer conductor with hidden hole using the TREE method for nondestructive evaluation

Abstract

Purpose In eddy current nondestructive testing, a probe with a ferrite core such as an E-core coil is usually used to detect and locate defects such as cracks and corrosion in conductive material. However, the E-core coil has some disadvantages, such as large volume and difficulty in the process of winding the coils. This paper aims to present a novel T-core probe and its analytical model used for evaluating hidden holes in a multi- layer conductor. Design/methodology/approach By using a cylindrical coordinate system, the solution domain is truncated in the radial direction. The magnetic vector potential of each region excited by a filamentary coil is derived, and the expansion coefficients of the solutions are obtained by matching the boundary and interface conditions between the regions. By using the truncated region eigenfunction expansion method, the final expression in closed form for the impedance of the multi-turn coil is worked out, and the impedance calculation is performed in Mathematica. For frequencies ranging from 100 Hz to 100 kHz, both the impedance changes of the T-core coil above the multi-layer conductor without a hidden hole and in the absence of the layered conductor were calculated, and the influence of a hidden hole in the multi-layer conducting structure on the impedance change was investigated. Findings The correctness of the analytical model of the T-core coil was verified by the finite element method and experiments. The proposed T-core coil has higher sensitivity than an air-core coil, and similar sensitivity and smaller size than an E-core coil. Originality/value A new T-core coil probe and its accurate theoretical model for defect evaluation of conductor were presented; probe and analytical model can be used in probe design, detection process simulation or can be directly used in defect evaluation of multi-layer conductor.