The nature of the logarithmic traction gradient

Great significance has been attached to the logarithmic traction gradient in elastohydrodynamic lubrication. It has been used to justify the assumption of logarithmic constitutive behavior. We have calculated viscous traction curves from the viscous shear response that is observable by simulation or experiment out of contact. This response includes Newtonian, shear-thinning of the ordinary power-law type, and rate independent behavior. The calculated traction curves can be reasonably described by a sinh law using fictitious viscosity and Newtonian limit. These system model parameters behave as expected from cases where the same system model was applied to measured traction. We conclude that for point contact, the logarithmic gradient results from rate-independent (limiting stress) behavior combined with greater than exponential pressure-viscosity behavior. Shear-thinning has little effect on this gradient in point contact. On the other hand for line contact, shear-thinning of the ordinary type (Carreau) is essential for the appearance of a logarithmic gradient. (C) 2002 Elsevier Science Ltd. All rights reserved.