A Fast Three-Dimensional Model for Strip Rolling

Abstract

Rolling Models have come a long way from the first empirical relations about forward slip and bite conditions to their current state, which allows local quantities to be calculated in two and three dimensions. In this paper, state-of-the-art of analytical modelling of the rolling process is shown with a fully three-dimensional rolling model for hot and cold strip rolling with stress distributions in the longitudinal, vertical and lateral directions. For this purpose, von Karman’s strip approach is extended to account for the stress gradient in lateral direction, as was already shown in different papers. The stress gradient in the vertical (through-thickness) direction is introduced by a modern implementation of Orowan’s inhomogeneous deformation theory. The local stress distributions are compared to results from Finite-Element Calculations obtained with modern FEM codes. It will be shown, under which circumstances expensive FEM calculations can be replaced by simpler models like the one proposed here, which are more time and cost-effective without a significant loss in result precision. The rolling model is extended with a Finite Element Beam Model for work and backup roll deformation, as well as local work roll flattening and thermal crown for hot rolling. The Effects of those features on stress distribution and exit strip profile are shown for hot and cold rolling.