Comment on “The Relationship Between Friction and Film Thickness in EHD Point Contacts in the Presence of Longitudinal Roughness” by Guegan, Kadiric, Gabelli, & Spikes

Abstract

Guegan and coworkers have addressed the important problem of friction of elastohydrodynamic contacts in the mixed regime. Any attempt at understanding friction in the mixed regime must address the friction in the full-film regime. To analyze fiction for the full film, they used a common, but unsupported, assumption that the friction curve is a rheological flow curve. The inconsistency can be demonstrated by integration over the contact with the assumed Eyring equation employing the known pressure dependence of the viscosity and also by a full numerical simulation which yields the same sinh friction curve without using the Eyring assumption.

Appendix

In 1926, Bridgman [14] provided an accurate description of the pressure dependence of viscosity for pressures to 1.2 GPa. For low pressure, the viscosity increase was slower than exponential and for high pressure faster than exponential, with an inflection at intermediate pressure. Figure 2 demonstrates this response. Classical EHL has ignored this behavior and substituted fictional accounts of viscometer measurements in support of the sinh-law [12].

To justify purely exponential response, a fictional account of the work of Barus [15] has been employed in EHL. Barus was a geophysicist, interested in the viscosity of extruding solids at high pressure [16] and is best known in rheology for the first report of extrudate swell. He experimented on soft solids, not liquids, and his equation was linear in pressure [15], not exponential due to slip of the solid specimen against the containment wall. However, Barus has been invoked even recently [17] to justify an exponential pressure dependence of lubricant viscosity when explaining friction using the sinh-law. Exponential response is only correct near the inflection.

The pressure–viscosity relation most often used by classical EHL is that of Roelands [18]. However, Roelands did not use viscometers to measure viscosity to EHL pressure. He validated his empirical expression with data from many laboratories. This expression can, for high viscosity liquids, be quite accurate for the slower than exponential response. Roelands variously set the pressure limitation as 0.1–0.2 GPa (page 108 of [18]) and 0.3–0.5 GPa (page 105 of [18]). A comparison [19] of the data presented by Roelands with all of the data available from the referenced sources showed that considerable data which did not fit the equation had been discarded for pressures typical of EHL. Justification for the use of the Roelands expression to EHL pressure came from the use of the sinh-law to model EHL friction for yet another Shell turbine oil, T33, in 1985 [20]. This was not based upon a viscometer measurement, and actual viscometer measurements on T33 published three years previously [21] clearly showed that the Roelands expression was inaccurate at even low pressure.