Conductivity and inner radius measurement of conductive tubes through frequency-dependent eddy current response analysis

This paper presents a novel method for simultaneously determining the conductivity and inner radius of conductive tubes through frequency-dependent eddy current response analysis. Accurate characterisation of these parameters is essential for ensuring operational integrity of metallic tubes and pipes used across industrial sectors, yet existing methods struggle with parameter coupling effects and computational inefficiency. Building upon the classical Dodd and Deeds electromagnetic model, a simplified analytical expression by employing modified Bessel functions and asymptotic expansion of complex quantities is derived. This approach exploits two key relationships: the correlation between the real part of coil inductance variation at high frequencies and inner radius and the relationship between the peak frequency of the imaginary part and both conductivity and inner radius. This dual-parameter analysis enables effective decoupling of the previously intertwined parameters. Experimental validation using tubes of three different materials (aluminium, copper, and brass) with varying dimensions demonstrates measurement errors less than 2% for both conductivity and inner radius across diverse material compositions and geometries. The method overcomes limitations of iterative techniques, offering significant advantages in computational efficiency and measurement accuracy.