The determination of the pressure—viscosity coefficient of a lubricant through an accurate film thickness formula and accurate film thickness measurements

Abstract

The pressure-viscosity coefficient is an indispensable property in the elastohydrodynamic (EHD) lubrication of hard contacts, but often not known. A guess will easily lead to enormous errors in the film thickness. This article describes a method to deduct this coefficient by adapting the value of the pressure-viscosity coefficient until the differences between accurate film thickness approximation values and accurate film thickness measurements over a wide range of values are at a minimum. Eleven film thickness approximation formulas are compared in describing the film thickness of a test fluid with known value of the pressure-viscosity coefficient. The measurement method is based on spacer layer interferometry. It is concluded that for circular contacts the newer more versatile expressions are not better than some older approximations, which are limited to a smaller region of conditions, and that the older fits are as least as appropriate to find the pressure-viscosity coefficient of fluids, in spite of the limited data where they have been based on.

On the relevance of analytical film thickness EHD equations for isothermal point contacts: Qualitative or quantitative predictions?

“…Concerning central film thickness, van Leeuwen [1,2] concluded that for both moderately-loaded and highly-loaded EHD contacts, Chittenden et al [8] formula was the more accurate and that its validity transcended the area where it was originally designed for. As for minimum film thickness, the use of Chevalier ratios [6] combined with the Nijenbanning et al [5] formula has shown, from experimental confrontation, to be the more consistent over very wide ranges of the (M, L) parameters [3].…”

“…The widely-used expressions mentioned below were selected on the basis of (i) van Leeuwen studies [1,2] and (ii) a previous experimental work [3] in which the capabilities of some of them were quantitatively compared with measurements performed over wide ranges of operating conditions and for numerous lubricants of different nature:…”

“…To the best of the authors' knowledge, very few-if not any-papers have dealt with these concerns. Except maybe those of van Leeuwen [1,2] of whom it was not the primary objective: his aim was to derive the most accurate values of viscositypressure coefficients from, on one side, central film thickness measurements performed in circular contacts and, on the other side, a wide collection of EHD film thickness equations. Though indirectly, he showed that certain expressions were more relevant than others through their ability to provide correct values of viscosity-pressure coefficients.…”

History, Origins and Prediction of Elastohydrodynamic Friction

“…So long as inlet shear thinning does not occur, the composite piezoviscous response over the inlet region can be measured using high pressure rheometry [3] or estimated directly from measurements of EHD film thickness [4] [5] and applied in regression-based film thickness equations [6]. For polymer solutions and some very high molecular weight base fluids, where inlet shear thinning does occur, its effect can also be taken into account [7] [8].…”

Theoretical and Experimental Study of the Friction Behavior of Halogen-Free Ionic Liquids in Elastohydrodynamic Regime

“…If we assume that at ambient pressure (p = 0), the slopes of the Barus and Roelands equation are equal, then the Barus parameter can be obtained from the Roelands one using [27]:…”