Analytical Solution for a Flexible Coil on the Surface of Multilayer Metal Tube and Its Application in Coating Thickness Measurement

In the nuclear industry, the coating thickness measurement of Zircaloy cladding tubes plays a crucial role in ensuring the safe operation of nuclear reactors. Although the eddy current method is widely used for near-surface electromagnetic parameter detection of metallic plates, it is still difficult to detect the coating thicknesses of the multilayer metal tube. This article presents an analytical solution of the impedance for a flexible coil on the surface of the multilayer metal tube featuring a “metal substrate–metal coating-oxide coating” structure, and a dual-frequency eddy current method is proposed to measure the metal coating and oxide coating thicknesses. First, a multilayer metal tube detection model is established, and the boundary condition equations for magnetic flux density are formulated using the second-order magnetic vector potential (SOVP) method. An air layer is introduced at the “metal substrate–metal coating” interface to ensure the solvability of all undetermined coefficients, and the analytical solution of the impedance for a flexible coil on the surface of the tube is derived. Second, a dual-frequency eddy current method combined with the Levenberg-Marquardt (LM) algorithm is put forward for the inversion of coating thicknesses. The frequency selection approach is, furthermore, introduced by analyzing the sensitivity function corresponding to each coating thickness. Finally, the proposed method was employed to measure multilayer metal tubes with different chromium coating thicknesses (5– $15~\mu $ m) and oxide coating thicknesses (0– $22~\mu $ m). The results show that the absolute errors of chromium and oxide coating thickness are less than 3.36 and $2.72~\mu $ m, respectively.