A two-dimensional friction model has been developed for cold metal rolling in the “mixed” lubrication regime. Roughness is modelled using superimposed short and long wavelength asperities with a lay orientated along the rolling direction. The hydrodynamic pressure in the lubricant is solved using Reynolds’ equation, coupled with the crushing process of the two-wavelength roughness. This allows for the solution of film thickness and contact area ratio and hence friction coefficient through the roll-bite. The model extends the authors’ earlier model  by allowing for a variation in hydrodynamic pressure across the width of the contact. Predictions for both the surface roughness and the friction coefficient are in reasonable agreement with published measurements.
A Friction Model for Cold Strip Rolling With Two-Wavelength Surface Roughness in the “Mixed” Lubrication Regime
Contributed by the Tribology Division for publication in the ASME JOURNAL OF TRIBOLOGY. Manuscript received by the Tribology Division December 11, 2001; revised manuscript received September 24, 2002. Associate Editor: C. H. Venner.
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Le , H. R., and Sutcliffe, M. P. F. (June 19, 2003). "A Friction Model for Cold Strip Rolling With Two-Wavelength Surface Roughness in the “Mixed” Lubrication Regime ." ASME. J. Tribol. July 2003; 125(3): 670–677. https://doi.org/10.1115/1.1538191
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