Three-dimensional analysis of edge rolling based on dual-stream function velocity field theory

A three-dimensional mathematical model for edge rolling using sine function dog-bone shape and the dual-stream function (DSF) method is established to research the plastic deformation of the slab at the vertical roll gap. A kinematically admissible velocity field is derived through DSF based on sine function model and the slab total power functional is obtained according to the upper bound theorem. The upper bound solutions of dog-bone shape and rolling force are solved numerically via minimizing the total power function by using the Matlab Optimization Toolbox. Satisfactory results are given while compared with experimental data in reference and FEM simulation, with good convergence, in various rolling conditions such as engineering strain, initial thickness and roll radius.