Analysis of Plane Strain Cold Rolling Using a Flow Function and the Weighted Residuals Method

Summary

The upper bound approach used in cold rolling is based on a flow function built from the prescribed streamlines in the deforming zone. Differentiating the flow function, the velocity and strain rate fields are obtained. The roll torque is calculated from the upper bound theorem. The stress field in the deformation region is evaluated by combining the results derived from the stream function with the plasticity equations and the boundary conditions by the weighted residuals method. The roll separating load and the roll pressure distribution are then obtained. The results are presented for aluminium and steel for several geometrical and friction conditions. The method has proved to be capable of describing plane strain rolling. The results agree with experimental data and indicate a large advantage over the finite element method in computing time and computer resources.