Thickness and conductivity determination of thin coatings on ferromagnetic substrates in the case of cylindrical symmetry

An eddy current method allowing the determination of parameters of a thin nonmagnetic conductive coating on a ferromagnetic conductive substrate is reported. At a single operating frequency, two independent quantities can be determined: a permeability-to-conductivity ratio of the substrate and a thickness-conductivity product of the coating. Thus, thickness or conductivity of the coating can be determined independent of variations of the substrate magnetic and electrical parameters. A simple theoretical formula for the normalized electrical impedance of the test coil is obtained using asymptotic expansions of Bessel functions. The method was applied to the evaluation of electrogalvanized wires in the frequency range 100 kHz-1 MHz. A set of low carbon steel wires with diameter around 2.2 mm, coated with zinc layers having thicknesses in the range 2.7-64.6 mu m, was investigated using two long coils. Experimental data of the electrical impedance were compared to those predicted. Agreement between theory and experiment is excellent for coatings thicker than 12 mu m. Despite discrepancies between theory and experiment for very thin layers arising from various imperfections of the coating and interfaces, the method was applied successfully in the thickness range below 12 mu m. To do this, two parameters: an apparent conductivity of the coating and a thickness offset, were introduced. The mathematical inversion of the experimental data with the two-variable Newton-Raphson method and the asymptotic formula is extremely fast. The technique developed has an extremely low sensitivity to variations of the ferromagnetic substrate conductivity and magnetic permeability. A magnetizing field of 0-23 000 A/m, producing large variations in the substrate magnetic permeability, does not significantly influence results of the coating thickness determination. The agreement between measured thickness and that obtained by a chemical method is excellent, typically within 0.5 mu m. An uncertainty of the thickness or conductivity determination better than 1% is obtained. (C) 1997 American Institute of Physics