Prediction and mechanism analysis of the force and shape parameters using cubic function model in vertical rolling

Vertical rolling has been widely applied to control slab widths in hot plate rolling plants. In this research, due to the high ratio of width/thickness of the slab in vertical rolling, a symmetric cubic function model is established to depict the three-dimensional dog bone shape of the slab. The three-dimensional kinematically admissible velocity and strain rate fields are innovatively established based on the dual-stream function (DSF) method and the boundary conditions. According to the first variational principle of rigid-plastic, the numerical results of the force and shape parameters are obtained. To decrease the computation load and time, the Geometrical Approximation (GA) yield criterion, the Pavlov projection principle, and the mean value theorem are utilized to calculate the plastic deformation, shear, and friction power terms separately, and the analytical results of the slab shape and rolling force are received later. To certify the effectiveness of the submitted model, the computed slab shapes are compared with the results of other models and the rolling forces are compared with the measurements in a plate plant. Good agreement is found. Furthermore, the effects of key rolling process parameters, such as width reduction, thickness, and vertical roll radius, on the slab shape and stress state are illustrated. The variation mechanisms of the force and shape parameters are used to process parameters setting and adjusting.