بررسی فرایند نورد متقارن ورق های سه لایه با استفاده از تابع جریان و تئوری حد بالا

In this paper, a mathematical model for symmetrical multi-layer sheet rolling, in which the layers are unbounded before rolling, by using the upper bound method and stream function theorem is proposed. Using this model, we can investigate the plastic deformation behavior of sheets at the roll gap during rolling. Effect of various rolling conditions such as initial and final thickness and flow stress of sheets, friction factors, rolling velocity and etc. on the rolling power and force, the thickness reduction of each layer, the relative length of plastic region in each layer and etc. are discussed. The velocity field derived from the newly proposed stream function can automatically satisfy the volume constancy and velocity boundary conditions within the roll gap. The optimized velocity fields are obtained through the minimization of total power, which is expressed by the function of five pseudo-independent parameters, during the plastic deformation. The analytical predictions from the proposed model were compared with the analytical and experimental results of other investigators and a good agreement is shown. Present model is applicable for simulating and online control applications of the rolling process of multilayer sheets.