A mixed lubrication model for cold rolling was developed by separating, according to common concepts, the domain of calculation into two zones: the inlet zone and the zone of plastic strip bulk deformation. The analysis of the inlet zone mainly focuses on film formation from different lubricants based on the evolution of layers consisting of neat oil on the metallic surfaces. In the zone of plastic strip bulk deformation, contributions of boundary and hydrodynamic friction are modeled incorporating longitudinal and transversal roughness components. Lubricant pressure, which is influenced by the geometry of these roughness structures, is governed by hydrodynamic mechanisms. Additionally, lubricant temperature in the roll bite is predicted by an integrated thermodynamics sub-model. While coupling between the inlet and plastic deformation zones is performed iteratively, the highly non-linear and coupled equations for the latter zone are solved simultaneously by applying a variant of the well-known damped Newton-Raphson method.

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