A multi-field analysis of hydrodynamic lubrication in high speed rolling of metal strips

Abstract

This paper presents a multi-field analysis of full hydrodynamic lubrication in high speed cold rolling of metal strips. A robust method was developed to solve the fluid field (the lubricant flow at the roll-strip interface) and solid field (the elastoplastic deformation of a metal strip) in a simple step. The elastoplastic deformation of the strip was solved by a dynamic explicit finite element method while the hydrodynamic pressure was calculated by the Reynolds equation. A cavitation boundary was introduced to determine the hydrodynamic pressure when the lubricant film breaks down. In addition, the coupled interaction between the lubricant flow and the elastoplastic deformation of the strip, which was caused by the hydrodynamic pressure and lubricant shear stress at the solid-liquid interface, were successfully treated by an additional penalty term. Both the pressure-driven term and lubricant shearing term were used to calculate the lubricant shear stress. The introduced penalty method enables a stable numerical calculation of Reynolds equation at a high hydrodynamic pressure. The method has overcome the traditional difficulties in solving the interface contact pressure within separated zones and has led to new understanding of the effects of rolling speed and pressure coefficient of the lubricant on the hydrodynamic pressure and lubricant film thickness.