Localization of multiple cracks in a cylindrical ferromagnetic rod based on the Fourier coefficients of the radial leakage magnetic flux

This paper presents a novel method of magnetic flux leakage testing to estimate the circumferential positions of multiple cracks in a cylindrical ferromagnetic rod by measuring the circumferential multiple-order Fourier coefficients of the radial leakage magnetic flux (LMF). By modeling the cracks as magnetic dipoles, the positions and intensities were estimated by solving the algebraic equations involving the Fourier coefficients. Sensors were developed and used to directly measure the zeroth, first, and second-order Fourier cosine and sine coefficients of the radial LMF. The circumferential and axial positions of one or two hole-shaped cracks in an S45C cylindrical rod were estimated using the proposed method.