Three-dimensional analysis of shape rolling using a generalized upper bound approach

A generalized analytical method has been proposed to study external shape and calculate pressure and torque for the process of rolling shaped sections. The proposed method is based on the upper bound analysis. To determine kinematically admissible velocity fields, flow lines have been mathematically formulated using the parameterization of curves. Based on the calculated velocity fields, an upper bound has been found on rolling power. The calculated power has been minimized with respect to unknown variables to yield the value closest to the actual power required. The proposed general method has been applied to certain rolling passes including square-to-oval and round-to-oval. Velocity fields and power relations have been obtained for each process. Computer analysis has been carried out for all the mentioned passes using dimensions and conditions from experiments conducted by other workers. External shape, average roll torque and average rolling pressure results from the analysis have been compared with analytical solutions, numerical analyses and experimental data presented by other workers. It was concluded that the present method gave very good results and was quicker and easier to use.