Modeling the surface condition of ferromagnetic metal by the swept-frequency eddy current method

Many ferromagnetic metals have, either by design or by happenstance, a very thin surface layer of reduced magnetic permeability. Such a layer might occur intrinsically or it might be induced by surface treatments such as case hardening, shot peening, or surface alloying. We studied the frequency-dependent impedance of a small air-cored coil of wire placed flat upon ferromagnetic metal plates. The impedance changes for nickel and iron could not be fitted to the half-space model for any values of conductivity and permeability. It is likely that the permeability varies continuously with depth in the near-surface region. Hence, it is possible that a multiple-layer model would yield a better representation of the data with a layer depth closer to that observed. In this paper, we illustrate that the multiple-layer model improves the agreement between the measured data and the approximate analytic solution. The results show that the permeability of pure nickel and pure iron decay exponentially from the base to surface.