Analytical and Finite Element Analysis of the Rolling Force for the Three-Roller Cylindrical Bending Process

In the roll bending process, the rolling force acting on the roller shafts is one of the most important parameters since, on the one hand, it determines the process settings including the pre-loading, and, on the other hand, its distribution and size may affect the integrity of both the bending system and the final product. In this study, the three-roller bending process was modeled using a two-dimensional plane-strain finite element method, and the rolling force was determined as a function of plate thickness, upper roller diameter, and yield strength for various API steel grades. Based on the numerical simulation results, a critical bending angle of 41° was identified and the rolling systems were divided into two categories, of less than or equal to, and greater than 41°, and an analytical model for predicting the maximum rolling force was developed for each category. To determine the optimal pre-tensioning force, two optimization formulations were proposed by minimizing the maximum equivalent stress and the absolute maximum displacement. The rolling forces predicted by the analytical models were found to be in good agreement with the numerical simulation results, with relative errors generally less than 10%. The predictive analytical models developed in this study capture well the complex deformation behavior that occurs during the roll bending process of steel plates, providing guidelines and predictions for industrial applications of this process.