The spatial oscillation of velocity fields in the roll bite of strip cold rolling by the upper bound approach

¹ ArcelorMittal R&D, BP 30320, 57283 Maizières, France
e-mail: ngo.quang-tien@arcelormittal.com
² Université paris Est, UR Navier, École des Ponts ParisTech, 6 et 8 avenue Blaise-Pascal, 77455 Marne-la-Vallée Cedex, France

Received: 26 August 2011
Accepted: 18 January 2012

Abstract

Following the Upper Bound Method (UBM), the velocity field in a rolling process is the one that minimises the power function [W. Prager, P.G. Hodge, Theory of Perfectly Plasticity Solids, Wiley, New York, 1951]. Generally, a family of velocity fields with few parameters is studied and the velocity field which minimises the power function is the best approximation of the real one. The lower the power, the better the approximation is. This paper presents a new family of velocity fields for the UBM approach of a rolling process in plane-strain conditions (2D). That family is based on the addition by an “oscillating perturbation” to a classic velocity field whose longitudinal component is constant in the strip thickness. We show that the best field of that family gives a better approximation than the classic one. This study proves there is an oscillating part in the velocity field during the rolling process. A careful observation of the fields obtained by a finite-element method, Lam3-Tec3 (1), shows that the oscillation phenomenon is in fact really present. And the oscillations predicted by the analytical model (UBM) match the FEM results very well.