Upper bound analysis of rolling force and dog-bone shape via sine function model in vertical rolling

The control of the slab width in actual production is realized by the widely use of vertical rolling (edge rolling). According to the incompressibility condition, the sine function dog-bone model is firstly proposed in this paper for steady state deformation in vertical rolling with flat rolls combined with the actual conditions. Based on the first variation principle of rigid-plastic material, the variable upper bound integration method is used to integrate plastic deformation, shear and friction power terms. The upper bound solutions of rolling force and dog-bone shape are solved numerically, and this process is carried out using Matlab Optimization Toolbox by minimizing the total power functional. Results show that the rolling force increases and the dog-bone shape size become larger while engineering strain, initial thickness, or roll radius increases. The results obtained from sine function model are compared with those of experimental data in reference and FEM simulation, and a good agreement is found. The comparison shows that it is possible to determine the required optimum rolling force and dog-bone shape by using sine function model. (C) 2015 Elsevier B.V. All rights reserved.