An Improved Dipole Model of 3-D Magnetic Flux Leakage

In this paper, we present an improved analytical 3-D magnetic flux leakage (MFL) model of the field due to the occurrence of a surface-breaking defect in a ferromagnetic specimen. This model is based on our recent magnetic dipole model (MDM) of the MFL field, which was derived from the first principles of Maxwell's equations. The MDM assumes a ferromagnetic specimen with a small defect exposed to a uniform external magnetic field, which is strong enough to saturate the specimen locally and causes uniform magnetization around the defect. Under this assumption, the MFL field can be mathematically described as if it is caused by magnetic charges on the surface of the defect. The magnitude and the sign of these magnetic charges are given by the magnetization vector and the local unit vector normal to the surface of the defect. Our original MDM uses only one parameter to describe the normal vector, and can only be used to analyze simple defect shapes, such as cylinders and cuboids. Our improved model in this paper uses two parameters to describe the normal vector, and can be used to analyze a wider range of defects, such as cones, ellipsoids, and real defect shapes. We illustrate our improved model by comparing its solution to that of the original MDM and validating it with the finite-element method simulations for different defect shapes. Our analysis shows that the improved model gives a good approximation of the MFL fields for a much wider range of defect shapes than the original MDM does.