Investigation of roll bite behavior with various cold rolling conditions using semi-analytic solutions of von karman’s rolling equation

Abstract

This article proposes a semi-analytical solution of von Karman’s rolling equation on the elastic foundation. The
roll indentation is considered as the spring compression of the elastic foundation of the work roll. A non-circular
contact arc is obtained naturally as a part of the solution of the governing equation. Two elastic zones and four
plastic zones are included. Hooke’s law is applied in elastic zones, von Mises’ yield criterion is used in plastic
yielding and unyielding zones, and material stress-strain curves are employed in plastic loading and unloading
zones. The solution of each zone was derived separately and a computer program was designed accordingly. The
computing time is very short and the required core memory is very small. The results show that the compressive
stress curves form a “friction hill” while the shape of the normal stress curve depends on the rolling parameters.
A typical cold rolling case is selected as the basic study case. The results of this proposed model and the popular
Bland-and-Ford model are shown to make comparison between these two models. Key rolling parameters included
in the comparison results are the entry gage, the exit gage, the entry tension, the exit tension, the work roll
diameter, the yield stress, and the friction coefficient. Rolling feasibility derived from this proposed model is not
only on the existence of the convergent solution but also on whether or not the solution can follow the properties of
the rolled material.