Roll deformation and stress distribution under thermo-mechanical loading in cold rolling

Tool deformation in metal forming is an important phenomenon that is critical not only for controlling the shape and size of final product but also for minimizing its cost. Under the assumption of an elastic roller and including the heat transfer effects, in this paper we determine the distribution of elastic deformation of the roller when it comes in contact with the strip in cold rolling. Using a coupled approach, the heat transfer phenomenon between roll and strip has been modeled analytically to predict roll temperature distribution by simulating non-uniform heat flux at the interface. This temperature distribution along with the mechanical load results in roll deformation with large localized stresses. Roll deformation has been modeled by using a thermo-elastic finite element method. Thermal and deformation models have been coupled and an iterative procedure has been developed to calculate optimum roll diameter. Finally, the deformed roll radius is utilized for calculating the exit strip thickness. It is found that the calculated thickness under thermo-mechanical load agrees very well with the experimental value reported in the published literature. The developed combined analytical–numerical model can easily be implemented on a personal computer and takes less memory and computational time, which is a marked advantage over pure numerical schemes.