Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Measuring Co-Axial Hole Size of Finite-Size Metallic Disk Based on a Dual-Constraint Integration Feature Using Multi-Frequency Eddy Current Testing

Version 1 : Received: 23 September 2020 / Approved: 25 September 2020 / Online: 25 September 2020 (10:12:55 CEST)

How to cite: Huang, R.; Lu, M.; He, X.; Peyton, A.; Yin, W. Measuring Co-Axial Hole Size of Finite-Size Metallic Disk Based on a Dual-Constraint Integration Feature Using Multi-Frequency Eddy Current Testing. Preprints 2020, 2020090601 (doi: 10.20944/preprints202009.0601.v1). Huang, R.; Lu, M.; He, X.; Peyton, A.; Yin, W. Measuring Co-Axial Hole Size of Finite-Size Metallic Disk Based on a Dual-Constraint Integration Feature Using Multi-Frequency Eddy Current Testing. Preprints 2020, 2020090601 (doi: 10.20944/preprints202009.0601.v1).

## Abstract

This paper presents a new approach of eddy current methods for determining the size of the co-axial hole in the metallic circular disk. In recent decades, for the air-cored sensor probe, the impedance change due to the presence of an infinite metal plate can be calculated by the Dodd-Deeds model. However, in practical measurements, the sample cannot match with the condition required - ‘infinite’, thus the Dodd-Deeds model could not be applied to the disk with finite size and certainly not a co-axial hole in the center. In this paper, a dual-constraint analytical method is proposed. That is, the upper and lower limits of the integration are substituted with specific values instead of the original 0 and . Besides, it is found that, once the outer radius of the disk is fixed (i.e. the lower limit of integration is fixed), the upper limit reduces linearly as the size of the coaxial hole increases. Both the FEM simulation and experiments have been carried out to validate this method. The radius of the hole can be estimated based on the dual-constraint integration feature.

## Subject Areas

Hole size measurement; finite-size metallic disk; eddy current testing; non-destructive testing

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