Hydrodynamic Lubrication in Rolling of Thin Strips

The process of thin strip rolling is analyzed considering the hydrodynamic lubrication effect. Hydrodynamic lubrication prevails when a film of lubricant fully separates the rolls from the strip. The conditions which produce hydrodynamic effects are the subject of this study. A dimensionless parameter, the Sommerfeld Number, is defined as a function of lubricant viscosity, roll velocity, strip thickness, and yield strength of the material. The critical Sommerfeld Number for occurrence of hydrodynamic lubrication is determined. Increasing lubricant viscosity and roll velocity or decreasing flow stress and strip thickness produce a larger Sommerfeld Number with an increased tendency for hydrodynamic effects. The thickness of the lubricant film and the velocity of the emerging strip are both determined as functions of the Sommerfeld Number, reduction in strip thickness, and of roll diameter. Graphical and numerical examples are presented.