An analytical approach to asymmetrical cold- and hot-rolling of clad sheet using the slab method

An analytical model for the general asymmetrical cold- and hot-rolling of clad sheet bonded before rolling was derived to investigate the stress field of the clad sheet at the roll gap, using the slab method. This model assumes the friction between the rolls and the clad sheet to be constant shear friction (i.e. tau = mk). With the frictional factor, m, equal to unity, corresponding to the so-called sticking friction, this model can simulate hot clad-sheet rolling. The model can also simulate cold clad-sheet rolling when m is less than unity. The neutral points between the upper and lower rolls and the clad sheet, the rolling pressure distribution along the contact interface between the roll and the clad sheet, the horizontal stresses in the component layers of the clad sheet, the shear stress at the interface of the clad sheet, the rolling force, etc., can be easily and rapidly calculated using this model. The above-mentioned characteristics of clad-sheet rolling, affected by various rolling conditions such as the thickness ratio and shear yield stress ratio of the raw clad sheet, roll speed ratio, frictional factor ratio, roll radius ratio, reduction, etc., were analysed systematically; by this approach, the complete forms for the rolling pressure distribution, shear stress at the interface, rolling force and rolling torque could be obtained. Moreover, the CPU time needed using this analytical model is about 1/20-1/25 of that using the Runge-Kutta numerical method under the same rolling conditions.