Thickness measurement of metallic plates with finite planar dimension using eddy current method

TLDR

The Dodd‑Deeds model has traditionally been used to predict inductance changes in air‑cored sensors assuming infinitely large conducting plates, a condition that holds only when the sample is several times larger than the sensor coil radius, but many practical samples do not meet this requirement. This study proposes a modified analytical solution that introduces a non‑zero initial integration point to extend the Dodd‑Deeds model to finite‑size metallic plates. Theoretical derivation of the new initial integration point is presented to adapt the Dodd‑Deeds model for finite plates. An inverse relationship between the initial integration point and sample radius is observed, and simulation and experimental results confirm the accuracy of the proposed method for measuring plate thickness.

Abstract

Until now, the Dodd-Deeds model has been used to evaluate the inductance change in an air-cored sensor in the presence of an infinitely large conducting plate. In practice, it can be applied to the sample relatively larger than the radius of the sensor coil (normally >3-5 times larger), which can be regarded as a plate sample with infinite planar size. However, in various practical applications, the size of the tested sample may not satisfy this condition. In this article, a modified analytical solution based on the Dodd-Deeds model is proposed, which has introduced a new initial integration point instead of 0 for the analytical inductance of the finite-size metallic plate. Theoretical derivation has been presented for the derivation of the initial integration point. Moreover, an inversely proportional relation can be observed between the initial integration point and the radius of the test sample. The simulation and experimental measurements for the thickness of several finite-size metallic samples have been carried out for the verification of the proposed method.