Can full film occur when Lambda = 0.6?

surface roughness image

The holy grail of tribologists studying lubricated systems is often to predict the contact lifespan. For this purpose, you can compute the minimum film thickness h_m separating the two bodies… but only if you make the assumption that the body surfaces are perfectly flat! This is obviously never the case outside of a laboratory. With all due care, you can use this thickness value obtained under coarse assumptions and compare it to the mean roughness height sum of the bodies \sigma. A contact with \Lambda = h_m/\sigma > 3 tends to have an almost unlimited lifespan (elastohydrodynamic lubrication regime). For the second category of contacts (\Lambda = h_m/\sigma < 1), the theory predicts a harsher contact behaviour and a limited lifespan (boundary lubrication regime). The method described here is the state of the art and is better described in another Tribonet wiki article.

However, researchers and engineers often reported that this method tends to be too critical. Many contacts falling in the second category show a very smooth behaviour, low wear and a very long lifespan! While it is always better to predict failure too critically than not enough critically, this method is not satisfactory nowadays. Indeed, a film thickness which is more thick than enough means that the lubricant viscosity could be reduced. As viscosity reduction often translates into friction and power losses reductions, it is mandatory to improve the model discriminating a long lifespan contact from a short lifespan contact.

Hansen et al. [1] tackled this question in their work. Through carefully designed experiments, ran on a WAM test rig (Figure 2), they studied the way the surfaces adapt to the supposedly boundary lubrication conditions and whether or not this potentially damaging lubrication regime occurred in the contact.

Figure 2: description of the WAM device and the ECR tension measurement used in this study (from [1])

A reference case was defined with a maximum pressure in the contact of 1.69 GPa (200 N load) and a limited sliding (slide-to-roll ratio SRR = 0.1). Two other cases similar to the reference case can be reported here: in the first one a larger maximum pressure was applied (2.44 GPa and 600 N load), and in the second one a larger sliding was applied (SRR = 1.0). The experiment operating conditions clearly indicated a boundary lubrication regime as (approximately) \Lambda = 0.5 for all cases. As a result, a rather large friction coefficient, solid to solid contact and a noticeable wear are expected.


Will these contacts show boundary lubrication behaviour? To put it very briefly, yes… and then no! Indeed, during the first revolutions of the ball-on-disc machine the friction coefficient of the different contacts was the highest and decreased rapidly. More importantly, solid to solid contacts clearly occurred: the electric contact resistance (ECR) curve was under 50%, indicating that the two solids permanently had contact asperities linking them through direct contact. These are the signs of boundary lubrication.

However, after a few thousands of revolutions (known as running-in), the friction coefficient was lower and the ECR plateaued at almost 100% indicating that solid to solid contact was almost not occurring anymore. This means that the contact showed signs of elastohydrodynamic lubrication!

The classical lubrication theory explains that the boundary lubrication regime occurring at the beginning probably severely affected the roughness topography as solid to solid contact occurred: it is likely that it acted as a grinding process. Therefore, a much smaller roughness is expected which would lead to a much larger \Lambda. A ratio \Lambda > 3 would indicate the transition toward elastohydrodynamic lubrication.

But after the first investigations (see Figure 1), a \Lambda = 0.6 was measured! So the predicted lubrication regime is still the potentially damaging boundary lubrication. However, the observed lubrication regime is clearly elastohydrodynamic.

Figure 3: Zoom on the surface track (area III in Figure 1) (from [1])

So, what happened?! Well, this is precisely where Hansen and his colleagues made an interesting work: they were able to precisely measure surface topography at the same place before and after the experiment (see Figure 1 and Figure 3). They noticed that the roughness height was affected, but that the slope of the roughness bumps was also importantly modified by the running-in. This slope strongly influences in return the lubrication of the bump itself, allowing for a local elastohydrodynamic lubrication to occur and full film to take place! This is known as the micro-elastohydrodynamic regime.

Thanks to their experiment design, they were able to distinguish the effect of sliding and the effect of load on the roughness height and slope evolutions. To summarize the contributions from this paper, Hansen et al. clearly demonstrated that the classical \Lambda parameter is not sufficient to describe the lubrication condition: the roughness shape is at least as much responsible for elastohydrodynamic regime as the roughness height. Besides, the hydrodynamic pressure locally generated by the bump can be estimated based on an analytical formula proposed in the paper. This can serve as a basis to estimate whether the pressure is sufficient to shape the roughness through plastic deformation and let the transition between boundary lubrication and elastohydrodynamic lubrication regimes to occur.


Feel free to read more about this open access article [1] and its author.


[1] Hansen, J., Björling, M. & Larsson, R. Lubricant film formation in rough surface non-conformal conjunctions subjected to GPa pressures and high slide-to-roll ratios. Sci Rep 10, 22250 (2020).

After a PhD thesis with SKF at the INSA de Lyon - LaMCoS dedicated to the lubrication of large size roller bearings, Jean-David joined SIMTEC ( to continue helping industries to develop their processes and products.

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