The influence of elastic deformation on the roll and the sheet in a hydrodynamically lubricated cold rolling process

A model has been developed for simulating hydrodynamic lubrication in cold rolling. Both Roelands’ and Barus’ viscosity-pressure relations have been applied. Thermal effects regarding heat development caused by plastic deformation as well as work hardening have been included. Furthermore, elastic deformation of the surfaces has fully been incorporated in the model, i.e., elastic deformation of both the strip and the rolls. The governing equations have been solved numerically throughout the entire contact i.e. inlet, work and outlet zone using a very dense grid. Multigrid techniques have been used to solve the equations. It will be shown here that roll flattening has a significant effect on film thickness. However, elastic deformation of the strip material in the inlet region even has a more pronounced effect on film thickness and thus on several process conditions. Furthermore, it is shown that the choice of the viscosity-pressure parameter is limited. Higher values of this parameter cause excessive shear stresses on the strip surface.