Impedance of coils over layered metals with continuously variable conductivity and permeability: Theory and experiment

Abstract

The frequency-dependent impedance of right-cylindrical air-core eddy-current probes over thick metal plates whose conductivity and permeability vary as a function of depth in the near-surface region have been studied both experimentally and theoretically. Measurements of probe impedance were made from 1 kHz to 1 MHz using an impedance analyzer. Precision-wound air-core coils were used for testing the theory, and commercial eddy-current probes were used to connect with industrial practice. The samples were of two types. First, to model a continuous profile, otherwise uniform plates of metal covered with many thin, discrete layers of other metals were considered. Second, as a practical example, case-hardened titanium plates, whose near-surface conductivity varies smoothly and continuously as a function of depth, were considered. Two theoretical results are presented for continuously varying profiles. First, an exact closed-form solution (within the quasistatic approximation) is reported for the impedance of a right-cylindrical air-core probe above a nonmagnetic metal whose near-surface conductivity difference varies as a hyperbolic tangent as a function of depth. Second, a new numerical technique is reported for determining the impedance of an air-core probe above a layered material whose conductivity and permeability vary arbitrarily. It is shown that the numerical technique converges and that for a hyperbolic tangent profile it agrees with the closed-form analytic solution and experiment. In general, it was found that continuous profiles can be experimentally (and theoretically) simulated by stacking many thin layers with differing conductivities, and that the probe’s impedance change is larger if the conductivity change is localized at the surface, and is smaller for more diffuse profiles.

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