Abstract

In this paper, an analytical model for a metal rod with a coating layer is proposed to evaluate circumferential crack from the signals of the surface magnetic field. In the proposed model, magnetic vector equations for four regions of space were built, and series expressions of the magnetic field were proposed by the truncated region eigenfunction method. The calculation results can show the three-dimensional distribution of axial and radial magnetic induction intensities on the surface of a metal rod clearly. In addition, the analytical model is verified by using comsol finite element simulation, which also demonstrates that induced eddy currents on the inner surface of the metal rod with cracks appear to be propelled toward the inner layer of the metal rod and the presence of a circumferential crack directly causes a decrease in the induced eddy current on the inner surface of the rod. The results calculated from the analytical model indicated that the model is capable of providing an accurate variation in the magnetic field due to circumferential cracks at different depths. The analytical results showed that the radial magnetic induction intensity increases by 0.16 × 10−3 T, while the axial magnetic induction intensity decreases by 0.3 × 10−3 T as the crack depth increases from 0 to 3 mm.

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