An Efficient Multi-Scale Modeling Method that Reveals Coupled Effects Between Surface Roughness and Roll-Stack Deformation in Cold Sheet Rolling

Abstract In thin-gauge cold rolling of metal sheet, the surface roughness of work rolls (WRs) is known to affect the rolled sheet surface morphology, the required rolling load, and the roll wear. While modeling of rough surfaces using statistical asperity theory has been widely applied to problems involving semi-infinite solids, the application of asperity distributions and their elastic-plastic behavior has not been considered in roll-stack models for cold sheet rolling. In this work, a simplified-mixed finite element method (SM-FEM) is combined with statistical elastic-plastic asperity theory to study contact interference and coupling effects between a rough work roll (WR) surface and the roll-stack mechanics in cold sheet rolling. By mixing equivalent rough surface contact foundations, Hertz foundations, and Timoshenko beam stiffness, an approach is created to efficiently model interactions between the micro-scale asperities and the macro-scale roll-stack deformation. Nonlinearities from elastic-plastic material behavior of the asperities and the sheet, as well as changing contact conditions along the roll length, are also accommodated. Performance of the multi-scale SM-FEM approach is made by comparison with a continuum finite element virtual material model. 3D studies for a 4-high mill reveal new multi-scale coupling behaviors, including nonuniform roughness transfer, and perturbations to the sheet thickness “crown” and contact force profiles. The described multi-scale SM-FEM approach is general and applies to rough surface contact problems involving plates and shear-deformable beams having multiple contact interfaces and arbitrary surface profiles.