Objective: this paper aims to investigate mechanisms that generate defect signatures in magnetic particles inspection of wheelset axles. Framed within magnetostatic theory, the paper emphasizes the application of machine-vision techniques for automated interpretation of inspection results. It presents a systematic analysis of how surface defects and magnetization conditions influence the spatial distribution of magnetic flux leakage (MFL) and establishes analytical relationships between defect geometry and magnetic response metrics. Methods: under the magnetostatic approximation, a three-dimensional parameterized physical model of the wheelset-axle inspection zone was developed based on Maxwell’s equations and the constitutive relations of ferromagnetic materials. The model accounts for the object’s geometry in accordance with relevant technical standards and represents defects as equivalent air gaps. Numerical simulations were performed in the MATLAB environment using the finite element method (FEM). To mitigate boundary condition effects, the computational domain was expanded to include the surrounding air. Characteristics of local magnetic-field disturbances were evaluated via magnetic induction maps and analysis of surface scanning profiles. Results: the findings have demonstrated quantitative relationships between the magnetic field disturbance characteristics and defect parameters, notably depth, width, and orientation of defects. The results indicate that a monotonic increase in the peak magnetic flux density with growing defect depth, while the position of the maximum remains stable. Variations in defect width primarily affect the spatial extent of the leakage-field region, whereas changes in defect orientation induce pronounced asymmetry and a redistribution of magnetic flux density. Practical significance: these observed regularities provide a physical basis for formalizing characteristics of magnetic particle indications (e.g. brightness and geometric parameters). The findings can serve as a theoretical foundation for the design of intelligent machine-vision systems and for the development of automated defect-recognition algorithms for rolling stock maintenance and inspection.
Shen' et al. (Thu,) studied this question.