Sloping-Invariance for Nonferrous Metallic Slabs at Multiple Frequencies by Eddy Current Sensors

Eddy current sensors have been widely applied to various measurements, whereas it is still obscure if these measurement techniques are workable for sloping samples. We start from a modified Dodd and Deeds's analytical solution for finite-size samples and find that the pseudo-linearity exists in the magnitude-phase curve of the theoretical mutual inductance. The curves for different conductivities have no intersections. The experiments for verifying the pseudo-linearity are conducted at multiple frequencies from 20 kHz to 100 kHz. We subsequently involve the sloping samples in our simulations and experiments at 20 kHz. The pseudo-linearity preserves in both the simulated and experimental results. To characterize this pseudo-linearity, we resort to the method of least squares. The obtained intercepts for the same conductivity at different tilting angles are almost the same. Hence the intercept is independent of the tilting angle. The intercepts for different conductivities are clearly separated. Thus, the intercepts for non-sloping samples can be directly utilized as the criterion to classify sloping samples. We then test the classification process at multiple frequencies, which works properly at all the frequencies. Our classification rates are advanced compared to those in the literature. This sloping-invariance (that is the tilting-angle-independent intercept) might make the eddy current sensors find wider applications.