Lubrication of Rolling Surfaces by a Ree-Eyring Fluid

Recent measurements of thicknesses of lubricant films between cylinders rolling at moderate speeds have agreed reasonably well with the predictions of Grubin's formula, but at high speeds and with high viscosity lubricants significant disagreements have been observed. Therefore, the elastohydrodynamic theory underlying that formula is reconstructed so to be based, not on a Newtonian model for the lubricant, but on the Ree-Eyring model which permits shear stress to develop at a lessening rate as shear rate increase. A formula comparable to Grubin's is derived, and it is shown that the changes in the formula are in the direction needed to explain the observed discrepancies between experimental data and the former theory. Exhaustive examination or use of this new formula is hampered by lack of data on the Rev-Eyring parameters, so further experimental work is recommended.