IMPEDANCE OF COILS OVER LAYERED METALS WITH CONTINUOUSLY VARIABLE CONDUCTIVITY AND PERMEABILITY - THEORY AND EXPERIMENT

The frequency-dependent impedance of right-cylindrical ar-core eddy-cu rrent probes over thick metal plates whose conductivity and permeabili ty vary as a function of depth in the near-surface region have been st udied both experimentally and theoretically. Measurements of probe imp edance were made from 1 kHz to 1 MHz using an impedance analyzer. Prec ision-wound air-core coils were used for testing the theory, and comme rcial eddy-current probes were used to connect with industrial practic e. 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 varie s smoothly and continuously as a function of depth, were considered. T wo theoretical results are presented for continuously varying profiles . First, an exact closed-form solution (within the quasistatic approxi mation) is reported for the impedance of a right-cylindrical air-core probe above a nonmagnetic metal whose near-surface conductivity differ ence varies as a hyperbolic tangent as a function of depth. Second, a new numerical technique is reported for determining the impedance of a n air-core probe above a layered material whose conductivity and perme ability vary arbitrarily. It is shown that the numerical technique con verges and that for a hyperbolic tangent profile it agrees with the cl osed-form analytic solution and experiment. In general, it was found t hat continuous profiles can be experimentally (and theoretically) simu lated 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 .