A multi-scale model for friction in cold rolling of aluminium alloy

A simple and robust friction model is proposed for cold metal rolling in the mixed lubrication regime, based on physical phenomena across two length scales. At the primary roughness scale, the evolution of asperity contact area is associated with the asperity flattening process and hydrodynamic entrainment between the roll and strip surfaces. The friction coefficient on the asperity contacts is related to a theoretical oil film thickness and secondary-scale roll surface roughness. The boundary friction coefficient at the "true" asperity contacts is associated with tribo-chemical reactions between fresh metal, metal oxide, boundary additives, the tool and any transfer layer on the tool. The asperity friction model is verified by strip drawing simulations under thin film lubrication conditions with a polished tool, taking the fitting parameter of the boundary lubrication friction factor on the true contact areas equal to 0.1. Predicted values of average friction coefficient, using a boundary friction factor in the range 0.07-0.1, are in good agreement with measurements from laboratory and industrial rolling mill trials.