A Unified Velocity Field for the Analysis of Flat Rolling Process

The subject of this paper is analysis of the flat rolling process by upper bound method. In this analysis the arc of contact has been replaced by a chord and the inlet and outlet shear boundaries of the deformation zone have been assumed as arbitrarily exponential curves. A unified kinematically admissible velocity field has been proposed that permits the possible formation of internal defects. By minimizing the required total power with respect to the neutral point position and the shape of the inlet and outlet shear boundaries, the rolling torque has been determined. The velocity components obtained from the upper bound method have been compared with the FE simulation. The analytical results have been showed a good agreement between the upper bound data and the FE results. A criterion has been presented to predict the occurrence of the split ends and central bursts defects during flat rolling process. Comparison of analytically developed approach for rolling torque and internal defects with published theoretical and experimental data have been showed a good agreement. Finally, the effects of process parameters on the safe and unsafe zones sizes have been investigated. It is shown that with increasing of the friction factor, the safe zone size is decreased.