A robust model for rolling of thin strip and foil

A new analysis for cold rolling of thin strip and foil is developed. This model follows the approach of Fleck et al. [8], but relaxes their assumption of a central flat neutral zone. Instead of following their inverse method to obtain the pressure distribution in this neutral zone, an explicit equation for the contact pressure variation is obtained from the sticking condition in this region. This significantly simplifies the solution method, leading to a much more robust algorithm. Moreover the method treats the cases either where the roll retains its circular arc or where there is very significant roll deformation in the same way, greatly simplifying the method of obtaining solutions. This will facilitate the incorporation of other effects such as the friction models currently being developed. Results are in line with the theory of Fleck et al. [8]. The effect of entry and exit tensions on the non-dimensional load and forward slip is investigated. It is found that the effect of equal entry and exit tensions is equivalent to reducing the yield stress of the strip by this tension stress.