An investigation of contact problem between strip and work roll with a smooth straight surface during cold rolling

Abstract Under the assumption of elastic roller, and the neglect of heat transfer problem, this paper explores the distribution of elastic deformation of the work roll with initially smooth straight surface in the rolling area during the rolling process, and analyzes the effect of this deformation distribution on the strip shape after rolling. Based on the large deformation—large strain theory, the update Lagrangian formulation (ULF) and the incremental principle were used to develop 3D elastic-plastic analytical model of aluminum strip rolling. The flow stress was considered the function of strain and strain rate to infer the governing equation containing the effect of strain rate. Besides, in this article, we propose an iteration procedure to calculate the contact force between strip and work roll, and the contact deformation of the work roll. In the treatment of the contact problem, the work roll was regarded as a rigid body at the beginning of each step. The incremental displacement and contact force of strip nodes were first calculated, and then entered into the first iteration loop. The contact forces of strip nodes were allocated to the work roll to calculate work-roll elastic deformation. The elastic deformation of work-roll nodes would be compensated to the incremental displacement of the strip nodes (the work-roll deformation increment was added on the incremental displacement of strip node). Then the new contact nodal forces were derived from the finite element program of strip. The above procedures were repeated to incorporate the new contact nodal forces into the first iteration loop to obtain the new strip node incremental displacement. An error range was also designated as the comparison standard to compare the displacement increments of the strip from two iterations to determine whether the iteration was completed. This paper considers the initial shape of work roll is straight and smooth. The elastic deformation distribution on the work roll surface in the rolling area is analyzed to serve as the basis for work-roll radius compensation. Finally, deformation of strip shape is also discussed.