Lubricant flow between rough surfaces during closed-die forming

Friction and lubrication at the tool–workpiece interface plays a central role in metal forming processes. The mechanical phenomena are driven by the contact pressure, the yield strength of the materials, the roughness of the surfaces and the behaviour of the lubricants. In previous papers, friction laws for the boundary and mixed lubrication regimes were discussed with the plastic wave theory initiated by Bay and Wanhein. This paper deals with the full film lubrication regime between two rough surfaces separated by a low viscous lubricant. In the particular case of an axisymmetric geometry, the roughness of the tool and of the workpiece are described by triangular and sinusoidal profiles separated by a film of lubricant, the thickness of which is smaller than the height of the surface asperities. The laminar flow of the lubricant is modelled with the equation of thin film viscous fluid from which the local contact pressure, the friction stress and the flow rate are deduced. The proposed solution allows to observe the influence of the lubricant thickness and the effects of different kind of roughness on the pressure distribution as well as on the interface shear stress. The well-known solution of the flow between two flat dies is used as a reference, and for very thin lubricant films, large increases of the magnitude of the fluid pressure are found for different roughness geometries.