A comprehensive mathematical model for an accurate calculation of the oil film thickness of strip cold rolling

Abstract

The surface quality of cold rolled strip is related to a greater extent on the rolling oil film thickness, and there are many factors that affect the oil film thickness. Considering the various factors comprehensively, an integrated mathematical model is established, such as roughness of rolls and strips, elastohydrodynamic lubrication, friction heat and plastic deformation heat in the rolling zone, viscosity varying with temperature and pressure, etc. A series of equations are developed, such as the Reynolds equation of partial membrane hydrodynamic lubrication based on average flow theory, equation of oil film thickness on rough elastic surface, the thermal interface equations between strip, oil film and roller surface, surface asperity contact pressure equation, lubricant viscosity and density equations, motion equation of the oil film, etc. This model is solved by finite difference method to get the film pressure, oil film thickness, and temperature distribution in the rolling zone. The average rolling pressure, the roll, and strip temperature calculated by the model are very close to the field test results. Comparing the minimum film thickness calculated by the model with the regression formula of other literature test, the error is less than 10%. The minimum oil film thickness is analyzed. It increases with the decrease of the rolling force and is approximately proportional to the rolling speed and lubricant viscosity.