Theory of Magnetostatic Force Inspection Method for Monitoring the Oscillation Marks of Continuous Casting

Abstract

We report an investigation of magnetostatic force of a permanent magnet passing by casting slab in order to monitor oscillation marks on its surface. This problem represents a highly simplified yet enlightening version called magnetostatic force inspection method (MFIM). Our investigation is a combination of analytic theory, numerical simulation and experimental validation [1]. The method allows a prediction of the relationship between profile of the oscillation marks and the change in magnetostatic force. We test our predictions by performing a series of experiments and numerical simulation to overcome difficulty inherent to the analytic theory. We conclude that MFIM has ability of capturing the characteristics of oscillation marks although a refinement of responding theory is necessary to reduce the discrepancy to the predictions. The present results can serve as a prototype for research on magnetostatic inspection. This paper formulates the MFIM through computing the reaction force of the ferromagnetic material. The magnetic field of the small cubic permanent magnet is modeled by an exponential function together with Gauss distribution possibility density function and this approach makes magnetostatic force by various ferromagnetic oscillation marks solved analytically. Cases of regular profile, triangular, rectangular and circular mimicking marks, provide the key scaling laws of the method and illustrate relation between magnetostatic force and the geometric properties of oscillation marks. It provides a theoretical framework for the prediction of the sensitivity of MFIM in laboratory experiments and implementation in industrial practice.