Numerical modelling of lubricated foil rolling

A model of lubricated cold strip rolling (1, 2) is extended to the thin foil regime. The model considers the evolution of asperity geometry and lubricant pressure through the bite, treating the strip using a conventional slab model. The elastic deflections of the rolls are coupled into the problem using an elastic finite element model. Friction between the roll and the asperities on the strip is modelled using the Coulomb and Tresca friction factor approaches. The shear stress in the Coulomb friction model is limited to the shear yield stress of the strip. A novel modification to these standard friction laws is used to mimic slipping friction in the reduction regions and sticking friction in a central neutral zone. The model is able to reproduce the sticking and slipping zones predicted by Fleck et al. (3). The variation of rolling load, lubricant film thickness and asperity contact area with rolling speed is examined, for conditions typical of rolling aluminium foil from a thickness of 50 to 25 μm. T he contact area and hence friction rises as the speed drops, leading to a large increase in rolling load. This increase is considerably more marked using Coulomb friction as compared with the friction factor approach. Forward slip increases markedly as the speed falls and a significant sticking region develops.

Rolling of thin strip and foil: Application of a tribological model for "mixed" lubrication

A mechanical model of cold rolling of foil is coupled with a sophisticated tribological model. The tribological model treats the "mixed" lubrication regime of practical interest, in which there is "real" contact between the roll and strip as well as pressurized oil between the surfaces. The variation of oil film thickness and contact ratio in the bite is found by considering flattening of asperities on the foil and the build-up of hydrodynamic pressure through the bite. The boundary friction coefficient for the contact areas is taken from strip drawing tests under similar tribological conditions. Theoretical results confirm that roll load and forward slip decrease with increasing rolling speed due to the decrease in contact ratio and friction. The predictions of the model are verified using mill trials under industrial conditions. For both thin strip and foil, the load predicted by the model has reasonable agreement with the measurements. For rolling of foil, forward slip is overestimated. This is greatly improved if a variation of friction through the bite is considered.