Four-Point Bending of Basic Rails: Theory and Experimental Verification

Mathematical models of prediction provide theoretical support for basic rail automation. The three-point bending method for basic rails is characterized by its simplicity and flexibility, and, as such, it is widely used in bending processes. However, due to the significant curvature changes that occur after bending, it is not suitable for scenarios requiring large arc bending, and its range of achievable deflections is limited. This study focuses on four-point bending, dividing the bending process into three stages and using a power-law material hardening model to establish different bending moment expressions for each stage. We derived the relationships between curvature, elastic zone ratio, load, and deflection, ultimately creating a load–deflection model. Based on the simple springback law, we developed the final bending prediction model. Finite element simulations were conducted to simulate the bending process under various conditions, using top punch distances ranging from 200 mm to 400 mm and die distances ranging from 600 mm to 1000 mm. These simulations validated the advantages and accuracy of the four-point bending prediction model in large arc bending. Additionally, a four-point bending experimental setup was established under specified conditions. The experimental results were compared with the theoretical model calculations, showing errors within 0.2 mm and thus verifying the accuracy of the four-point bending prediction model. The mathematical model developed in this study provides theoretical support for the automation of basic rail bending.