Shear stress modification of the Bland-Ford cold rolling force model

Rolling force is a critical parameter in the control of the cold tandem rolling process, significantly impacting both thickness control accuracy and flatness control accuracy. The Bland-Ford model is currently the most widely used rolling force model in cold continuous rolling. However, this model uses the principal stress yield criterion and neglects the influence of shear stress, leading to increased calculation errors as the strip thickness decreases. This study proposes using the Mises yield criterion, which considers shear stress, to modify and reconstruct the Bland-Ford normal pressure model and rolling force model. The comparison of the normal pressure values before and after modification shows that the classic Bland-Ford normal pressure model, due to its neglect of shear stress, results in overestimated normal pressure values, with the maximum deviation occurring at the neutral angle. As the rolling thickness decreases and the reduction and friction coefficient increase, the calculation deviation also increases. Based on measured data from a 1340 mm four-stand cold rolling mill, the rolling forces of the final stand for different specifications and steel grades were calculated. The results indicate that the modified Bland-Ford rolling force model yields results almost identical to the classic Bland-Ford model for thick specifications (exit thickness >1 mm). However, for thin specifications (exit thickness ≤1 mm), the overall calculation accuracy can be improved by up to 1.87 %.