Simple Models for Mixed and Boundary Friction

ABSTRACT

Recent research by Taylor and Sherrington [1] has led to an accessible method for calculating friction in mixed and boundary contact regimes. The approach involves a re-interpretation of the Stribeck curve. There are two steps. In the first the Lambda Ratio is plotted on the x-axis. In the second a normalised version of mixed/boundary friction values, representing the proportion of boundary friction to mixed friction (X), is plotted on the y-axis. Placing measured data on these axes results in friction data falling on, or close to, a “universal curve” permitting a reverse Signoid fit curve to be established. The approach works well for lubricants for non-addivated lubricants and simple modifications can be made to account for friction modifiers and anti-wear additives in formulated oils [2]. 

More recently this research has been extended and alternative equations, which do not contain fitting parameters, but stiil provide good fits to experimental data have been determined. The main purpose of this newer work is to develop equations to predict mixed/boundary friction for surfaces which have differring surface roughness height distributions, particularly to assist modelling of the effect of changes in surface topography on friction during running-in. [3].

While the above approaches offer a new and simple approaches to calculating mixed and boundary friction, it should be noted that other researchers have also proposed simple equations relating X to l [4, 5, 6]. However, these equations have not been widely adopted.

This presentation will present a summary of the research into simple methods to predict mixed and boundary friction coefficients conducted by both these authors and other researchers, and explain why wider adoption of such models would be of benefit.

REFERENCES

[1] Taylor, R. I. and Sherrington, I. “A Simplified Approach to the Prediction of Mixed and Boundary Friction”, Trib Int 2022;175;107836 https://doi.org/10.1016/j.triboint.2022.107836 

[2] Taylor, R. I. Sherrington, I. “Prediction of Friction Coefficients in Mixed Lubrication Regime for Lubricants Containing Anti-Wear and Friction Modifier Additives”. Tribology On-Line. 18 (4) (2023) pp 185 – 195. DOI https://doi.org/10.2474/trol.18.185 

[3] R. I. Taylor and I. Sherrington, “Modelling Mixed/Boundary Friction using the Lambda ratio and Overlap Coefficients for Realistic Rough Surface Height Distributions”. https://doi.org/10.1080/10402004.2025.2574843 

[4] A.V. Olver and H.A. Spikes, “Prediction of Traction in Elastohydrodynamic Lubrication”, Proc IMechE Part J, 212, 321-332, 1998 https://doi.org/10.1243%2F1350650981542137 

[5] Castro, J., and Seabra, J. “Coefficient of Friction in Mixed Film Lubrication: Gears versus Twin-Discs”, Proc. IMechE. Pt. J: Journal of Engineering Tribology, 221, pp 399–411, 2007 https://doi.org/10.1243%2F13506501JET257 

[6] Zhu, D., and Hu, Y. A computer program package for the prediction of EHL and mixed lubrication characteristics, friction, subsurface stresses and flash temperatures, based on measured 3-D surface roughness. Trib. Trans. 44(3)(2001), pp.383-390 https://doi.org/10.1080/10402000108982471