Influence of the lubricant on the limiting friction regime

Laetitia Martinie¹, David Philippon¹, Philippe Vergne¹

¹Univ Lyon, INSA-Lyon, CNRS UMR5259, LaMCoS, F-69621, FRANCE

INTRODUCTION: Classical friction curves in highly loaded lubricated contacts provided by literature may exhibit a plateau regime at high slide to roll ratios, as shown on Figure 1 for the benzyl benzoate BB (blue curve). The plateau regime is correlated to the Limiting Shear Stress (LSS), standing for the maximum tangential stress that can be measured in a contact.

Figure 1 – Friction curves of benzyl benzoate and squalane at 40°C and the given hertzian pressures.

Several theories have been suggested in literature to explain the physical origin of this asymptotic regime¹. However, none has been experimentally proven because of the technical limitations in such severe contact conditions.

One of the main assumptions advanced in literature is the glass transition experienced by the lubricant subjected to the very high pressures in the contact (> 1 GPa). Previous study^2,3 has indeed highlighted the link between the physical state of the lubricant and its macroscopic response in the whole contact. For example, Figure 2 shows apparent viscosities derived from the initial slope of friction curves measured on benzyl benzoate, representative of the lubricant rheological response at very low SRR.

Figure 2 – Normalized apparent viscosities of the BB derived from the initial slope of friction curves versus the Hertzian pressure normalized by the glass transition pressure P_g (inspired from ³). P_m stands for the mean contact pressure. Circled triangles correspond to the friction tests presented on Figure 1.

Two regimes emerge: i) an exponential increase of the apparent viscosity for hertzian contact pressures lower than the glass

transition pressure and ii) a plateau value of the apparent viscosity for mean contact pressures higher than the glass transition pressure.

To contrast with this result, at the same pressure order of magnitude, the plateau regime cannot be experimentally captured for some lubricating fluid, as for the squalane on Figure 1.

This study aims at understanding and experimentally validating the mechanisms behind the onset of the friction plateau regime at high contact pressures.

METHODS:  Tribological measurements are performed in a contact lubricated with squalane on a ball on disc tribometer. Experiments are designed, as for the benzyl benzoate⁴, in order to minimize thermal effects. These experiments are then analyzed in light of the squalane rheological characterization⁵.

RESULTS:  Glass transition has been shown to be correctly predicted by the WLF Yasutomi model fitted on experimental data, for two fluids of different nature (the benzyl benzoate and a commercial turbine mineral oil supplied by Shell^2,3). Indeed, the temperature dependent glass transition pressure P_g(T), derived from both the rheological model based on the 10¹² Pa.s viscosity criterion and Brillouin spectroscopic measurements, led to the same orders of magnitude. Regarding the squalane rheological behavior, a WLF Yasutomi model previously provided in literature⁵ leads, for the same temperatures, to a P_g(T) always higher than 1.5 GPa. These predictions are correlated to friction curves to validate the strong link between the lubricant physical state and its macroscopic response.

DISCUSSION: To better understand the different rheological responses of these two fluids, their fragility ⁶ are studied versus both pressure and temperature and compared to strong and fragile reference fluids from literature. The benzyl benzoate shows a fragile behavior relatively to both parameters, whereas the squalane exhibits a strong behavior versus pressure. This lower pressure sensitivity could be appreciated in light of the fluid molecular architecture (see Figure 3).

Figure 3 – Elementary molecules of the lubricants chosen in this study a) benzyl benzoate (ester of benzyl alcohol and benzoic acid) and b) squalane.

Indeed, the glass transition is described by Ediger⁷ as “a kinetic event which depends upon […] the time scales for molecular rearrangements”. Increasing pressure –thus density- in a sample would reduce the molecular mobility and consequently increase these rearrangement time scales. However, molecule architectures displayed on Figure 3 could explain the lower pressure sensitivity of this process for a linear hydrocarbon than for an ester with two benzene rings.

REFERENCES:  1. Martinie, Tribol. Lett. (2015), 2. NDiaye, to be submitted, 3. NDiaye, PhD Thesis (2017), 4. NDiaye, Tribol. Lett. (2017), 5. Bair, Tribol. Trans. (2017), 6. Bair, Proc. IMechE. (2007) 7. Ediger, J. Phys. Chem. (1996)