Kinematic and Dynamic Conditions in Metal Rolling of Porous Materials

Abstract

Mathematical modeling of plastic deformations in rolling consists in a consequent combination of the general energetic relationship in plasticity and the variation inequality expressed the principle of minimum of entire deformation energy. A real deformation state in a plastic zone beneath rolls and corresponding kinematic and dynamics conditions on the contact surface are considered as a limited one for the consequent approximate deformation states and are found out by the method of approximated approach. Any realization of this method on personal computers requires a rational construction of a kinematic-possible velocity field in the spatial domain on plastic flow. Using the ordinary propositions and a new assumptions the authors have constructed a simple kinematic-possible velocity field in the plastic zone beneath rolls. On the base of the consequent approach in which the general energetic relationship and the variation inequality are interrelated the authors have been able to find out the geometric, kinematic and dynamics characteristics of plastic deformation’s states in metal rolling.