Gap Measurement of Double-Layer Metal Tube Based on Analytical Solution of Eddy Current Array Under Transmit-Receive Mode

Flexible eddy current array (ECA) has a variety of operation modes, which can adhere to the surface of complex structure conductors with minimal liftoff. It is one of the new electromagnetic nondestructive testing technologies for thickness measurement, defect detection, and material deterioration evaluation of curved industrial equipment. This article studies the eddy current induction problem of the sinusoidal excitation single coil element outside a metal double-layer tube with an air gap under arbitrary liftoff. The coefficient of the relatively tilted coil in a cylindrical coordinate system is derived using the plane wave expansion in cylindrical waves. Using the matrix partitioning approach, we simplified the solution of the multivariate linear characteristic equations corresponding to the double-layer tube and obtained the expression of the tube reflection coefficient. Finally, the impedance change expression of the relatively tilted transmit-receive (T/R) coils outside the double-layer tube system was derived through the reciprocity theorem. The theoretical calculations and experimental results are consistent within the experimental frequency range of 100 Hz–100 kHz. Based on this analytical expression, a fast measurement algorithm for the gap thickness of the double-layer tube was simultaneously established to evaluate the corrosion thinning of the inner wall of the outer tube. For outer tubes with different diameters and conductivity, the measurement error of gap thickness is around 5%.