Analysis of cold and hot plate rolling using dual stream functions

Three dimensional deformation of the plate rolling process is modeled using an upper bound method. A kinematically admissible velocity field including spread is derived by means of dual stream function (DSF). The rigid plastic boundary at the inlet zone is assumed as quadratic and spread function is also assumed in quadratic form. The upper bound equation was solved numerically and optimization is carried out via Matlab 6.0 optimization toolbox. The rolling force and shape changes in three principal directions are determined for different deformations, friction factors and temperatures. The experiments are carried out with AA5454-O aluminum alloy at different %deformations and temperatures to show the validity of the analysis. The results obtained from the analysis are compared with experimental results and a good agreement is found. The conducted theoretical and experimental analysis showed that it is possible to determine the required optimum rolling force and final shape by using the DSF. The results could well be an important feedback for metal flow and workpiece manipulation, and so can be used in metal rolling plants having or aiming automation in large scale continuous manufacturing routes.