On the crucial role of ellipticity on elastohydrodynamic film thickness and friction

Abstract

The study reported here deals with elastohydrodynamic point contacts and it is focused on the influence of contact ellipticity. In five velocity–load reference cases, ellipticity was varied from slender to wide configurations, including the circular contact. For each case, Hertzian pressure, Hertzian area, load, and entrainment velocity were kept constant while the ellipticity was varied by changing the curvature radii. In this context, the maximum central film thickness did not occur for the infinitely wide contact, but for a slender configuration close to the circular case. Moreover, the minimum film thickness reached its optimum for a wide but finite elliptical contact. For low ellipticity ratios, specific film thickness features were obtained. In particular, very high central/minimum film thickness ratios are found. The cause of these behaviors was found in the change of the convergent shape. When the ellipticity was varied, the Poiseuille flows parallel and transverse to the entrainment direction were significantly modified and these modifications were quantitatively analyzed for the different cases. The competition between the Couette and the Poiseuille flows was totally different between the narrow and the wide elliptical contact, and this change was responsible for the film thickness variations with ellipticity. Ellipticity also had an effect on friction as it influenced the maximum pressure which in turn impacts the fluid viscosity.

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

“…Note that Chittenden and his co-authors were the only ones to explore the case k < 1 (narrow or slender configuration), and that they included the Hamrock & Dowson results to establish their analytical models, thus valid for both slender and wide configurations. This is also the case in the paper by Wheeler et al [11] who explored k values ranging from 0.2 to 5 delimited by the bold black dotted lines in Figs. 4(a) and 4(b).…”

“…Two main phenomena intervene in such conditions. The hydrodynamics effects are dominated by the lateral Poiseuille flow rates along the directions transverse to the entrainment velocity [11]. In the meantime a relatively larger radius of curvature in the u e direction reduces the wedge effect and thus the film building ability.…”

“…Under these circumstances, hydrodynamic effects are largely dominated by Poiseuille flows in the entrainment speed direction, the contact approaches the infinitely wide case and the places where the minimum film thickness occurs deviate from the lateral lobes towards the contact exit area [11]. For instance, with k = 2.92 and W = 800 N (the medium load case) one reaches the equality between the classical minimum thicknesses found on the lobes and the film thickness at the center of the exit zone of the contact [11], where the minima would occur if k was increased further, as in the case of line contacts. Here, for k = 2.92 the average c m / h h ratio obtained from all models (analytical and numerical) is equal to 1.28 (+28%), against 2.5 (+150%) in the circular configuration.…”

“…[11] and will not be detailed further. It results from recent modeling developments performed at LaMCoS, after the works of Doki-Thonon in the case of spinning EHD contacts [12,13] and those of Habchi who has laid the foundations inherent to this multiphysics model [14,15].…”

“…Both constitutive equations were fitted to independent characterizations carried out with high pressure devices, see Ref. [11] for more details.…”