Cold rolling mill process: a numerical procedure for industrial applications

This paper proposes a model which is useful for forecasting the reduction of strip thickness in high-speed strip rolling with an emulsion lubricant that is able to maintain hydrodynamic lubrication. The approach of the model is different when compared to those of other authors who assume to know: the original and the final thickness of the strip, the length of the three zones, the film shape or the film thickness at the edges, the pressure at the end of the work zone or the pressure gradients equal to zero in the work zone; and who in addition integrate the outlet zone backwards from the exit. However, in this work, even though the model is analyzed as a combination between classical equations of slab analysis and equations of lubrication the pressure gradient null in the work zone is not considered but the well-known bi-dimensional expression of Reynolds, in its full equation, is applied. In this way the shape of the lubricant film, not known a priori, could be evaluated by using the integration procedure with adequate boundary conditions at the edges of the three zones. Furthermore, the problem is formulated as a free boundary one, and a numerical procedure, applied to an industrial plant, is presented with some results. The model includes lubricant flow and lubricant viscosity depending on pressure.