Upper Bound Analysis of Asymmetric Sheet Rolling Process

In this paper, asymmetric rolling process of metal sheets is investigated by method of upper bound. In analyses, the contact arches of the rolls are replaced by their chords. The material under deformation is divided into upper and lower regions separated by a line parallel to the midline of the sheet at exit. The intersection points of the chords with the mentioned line, boundary of the upper and lower regions, are selected as the origins of the cylindrical coordinate systems. Each region is divided into three deformation zones and based on the proposed velocity field presented, shear, friction, internal deformation and the total power terms are calculated. The total power is optimized with respect to the positions of the origins of the cylindrical coordinates systems and the positions of the neutral points. The results of the analysis including the required torque, rolling force and the curvature of the sheet at the exit, are compared with the analytical and experimental results of other researchers, as well as numerical simulation results obtained from Deform software. Finally, the effects of the asymmetric factors of the process, on the required torque, the rolling force and the curvature of the deformed sheet have been investigated.