Analytical Model and Numerical Calculation of Probe Impedance Due to Multilayered Conductive Structures in Eddy Current Testing

The cylindrical coil above arbitrary number of conductive plates is modeled and analytical closed-form solution to the impedance change of the coil is presented based on the Maxwell’s equations under the quasi-static. The presented expression is a very complicated double generalized integral, because it has a singularity at zero and an integral of Bessel function. To choose an appropriate numerical method, the limit for the integrand in the impedance change expression at zero is examined and the convergence over the interval from zero to plus infinity is also investigated. Then partition-based integrand precomputation method is used to calculate the integrand for higher efficiency and adaptive Simpson algorithm is employed to calculate the integral of Bessel function for better accuracy. Simulations and experiments are carried out for thickness measurement. Good agreement between the results demonstrates that the developed model and numerical calculation method are verified, which not only contributes to the development of an analytical solver for probe impedance, but also can be used to optimize the parameters of experimental setup in eddy current testing.