In metalworking, rolling is a metal-forming process in which slab is passed through one or more pairs of the rolling dies to reduce the thickness and to make the thickness uniform. Modeling of rolling die contact with the slab primarily needs to describe the Tribology of contact phenomena. The central concern of numerical modeling is used in this work to indicate a set of equations, derived from the contact principle, that transfer the physical event into the mathematical equations. Continuum rolling contact phenomena is considered to explain how a contact region is formed between rolling die and slab and how the tangential force is distributed over the contact area with coefficient of friction. At the end, elasticity stress behavior of rolling die contact with the slab for a number of cyclic loads is modeled. The model includes new proposed constitutive equations for discontinuity of the velocity–pressure distribution in rolling contact from the entry side to exit side of the neutral point. To verify the model, finite element simulation and experimental data from the literature are considered. The results show good agreement with finite element simulation and experimental data.
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