Circumferential Localization of a Crack in Cylindrical Ferromagnetic Rods Based on the Fourier Coefficients of the Radial Directional Magnetic Flux Leakage

In this article, we present a novel magnetic flux leakage method to estimate the circumferential position of a crack in cylindrical ferromagnetic rods by modeling the crack as a magnetic dipole. The first-order Fourier coefficients of the radial component of the magnetic flux leakage are measured using two coils with widths proportional to
$|\cos \varphi |$
and
$|\sin \varphi |$
, where
$\varphi $
is the circumferential location of the rod surface. The circumferential and axial location of a crack is estimated using only two sensors, as demonstrated for an S45C cylindrical rod.