Study on minimum thickness for asymmetrical hot-and-cold PV rolling of sheet considering constant shear friction

The minimum thickness for the asymmetrical hot-and-cold PV rolling of sheet is proposed theoretically. With view to deriving the minimum thickness, the complete formula on general asymmetrical hot-and-cold rolling of sheet is derived by an analytical approach based on the slab method with constant shear friction. Two analytical models for the minimum thickness for hot-and-cold PV rolling are established, one considers the same friction factors of upper and lower rolls (i.e. me=0), the other considers the different friction factors of upper and lower rolls (i.e. me≠0). The relationships between ratio of roll radius to initial thickness and bite angle for two models are proposed. The comparisons of front tension and rolling force per unit width for two models are discussed. From an analytical approach, values of minimum thickness can be obtained.