A Novel Nonlinear Magnetic Equivalent Circuit Model for Magnetic Flux Leakage System

To ensure efficient inspection using the magnetic flux leakage (MFL) method, generating a flux density near the saturation level within the tested material is essential. This requirement brings high flux density conditions in the system’s pole regions. Hence, leakage flux within the slot is excessively triggered, leading to distortion of the defect signal. In this context, the system dimensions stand out as one of the most significant factors affecting the mentioned flux distributions. Therefore, various alternative solutions with different system dimensions arise in the design process of the MFL system. This study proposes a magnetic equivalent circuit (MEC) model to achieve optimal system design. The proposed MEC model is designed considering the nonlinear behavior of the material, leakage flux, and fringing effects. Verification results demonstrate that the MEC model consistently tracks the finite element analysis (FEA) results in calculating the flux densities. Furthermore, the relative errors in the flux density calculations of the tested material are at a maximum level of 10.2% and an average of 5.2% compared to the FEA. These findings indicate that the proposed MEC model can be effectively utilized in rapid prototyping and optimization procedures of MFL system design by providing fast solutions with reasonable accuracy.