Dynamical Models of the Camber and the Lateral Position in Flat Rolling

Abstract

In flat rolling, the lateral position of the product in the rolling mill and the camber (curvature of the product centerline seen in top view) are key process variables. We explore how their evolution can be analytically modeled based on nonlinear geometric relations, material derivatives, balance equations, constitutive equations for the material flow in the roll gap, and a change of coordinates to obtain a time-free formulation. Based on example problems, we verify the developed novel model and further illustrate the mechanisms behind it. Finally, a literature review on models in this field reveals that there is not yet a consensus on the correct analytical model of the evolution of the camber in flat rolling. The literature review shows that most published models are special cases of the model developed in this paper.