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.