Analytical modified model of the cold bond rolling of unbounded double-layers sheet considering hybrid friction

Abstract

An analytical modified model of the cold bonding rolling of unbounded double-layers sheet is formulated to obtain the stress field of the double-layers sheet at the roll gap via the direct derivation without using Runge–Kutta numerical method. Generally Coulomb friction at the interface of unbounded sheets and between rolls and double-layers sheet are assumed. However, when the frictional coefficient at the interface of unbounded sheets is high enough, the friction needs to be modified. Thus hybrid friction should be taken into account at the interface so as to obtain the realistic rolling characteristics. In this study, the neutral point between the rolls and the double-layers sheet, the rolling pressure distribution along the contact interface between the rolls and the double-layers sheet, the horizontal stress of the whole double-layers sheet, the horizontal stresses in the component layers, the realistic shear stress at the interface of double-layers sheet, the rolling force, and the rolling torque, etc., can be calculated easily and effectively. Besides, obtaining the bonding point at the interface and the thickness ratio of the clad sheet at the exit are of great important. Moreover, the bonding conditions of the cold bond rolling of the unbounded double-layers sheet can be found to provide useful knowledge in carrying out the bond rolling to prevent the failure. In summary the complete formulae of the rolling pressure distribution, the rolling force, the rolling torque can be derived by this analytical modified model. This analytical approach proposed is suitable for the on-line bond rolling.