Rough Surface Contact Modelling—A Review

Round 1

Reviewer 1 Report

This is overall a fairly thorough review of rough surface contact, although it focuses mostly on elastic and statistical models. I do think it provides a good contribution to the field and should be published. Perhaps the title should reflect these focal points somehow?

One thing that did bother me, was that it was stated many times throughout the paper (and abstract) that friction is proportional to load and this is due to contact area being a linear function of load. However, it seems like it would be better say ‘approximately’ in most situations. Friction hardly ever really follows a linear relationship. In addition, most of the rough surface contact models do not predict a perfectly linear relation between contact area and load. The hardness model (Ar=F/H) and some other simplified models are closest to this.  It seems like it would be good to make this clear throughout the paper that the relationships are not truly linear.

Page 2, Line 58, It would probably be best to say that hardness is proportional to yield strength. Even then, it is more accurate to say it is a function of it as it will change with other properties (hardening, elasticity) and the contact geometry.

Page 3, line 125. The paper does report some more recent rough surface contact material, but overall I feel it is not as broad as it could be. Again, I think it should be stated that this work leaves out many papers on related topics such as asperity shoulder-shoulder contact, sliding, tangential load, asperity shapes, property variation, and some work on variation of asperity distributations, among other things. I do understand that not every paper and topic can be discussed, because there are many.

Page 5: There has been some extremely interesting work done aiming at measuring roughness over a wider range of scales than ever before. I think it would be worth mentioning:

Gujrati, A., et al., Combining TEM, AFM, and Profilometry for Quantitative Topography Characterization Across All Scales. ACS Applied Materials & Interfaces, 2018. 10(34): p. 29169-29178. https://0-doi-org.brum.beds.ac.uk/10.1021/acsami.8b09899

Page 6: In regards to the spectral moments and fractals, this recent paper should probably be recognized as it provides some closed form solutions:

Green, I., 2020. Exact Spectral Moments and Differentiability of the Weierstrass-Mandelbrot Fractal Function. Journal of Tribology, 142(4), p.041501. https://0-doi-org.brum.beds.ac.uk/10.1115/1.4045452

Page 8 and 9. An exact solution of the Greenwood and Williamson model with a full Gaussian distribution was published in 2011 here (see Eq. 9):

Jackson, R.L. and Green, I., 2011. On the modeling of elastic contact between rough surfaces. Tribology Transactions, 54(2), pp.300-314. https://0-doi-org.brum.beds.ac.uk/10.1080/10402004.2010.542277

The above fits directly into the paper and should definitely be mentioned.

Page 10, Line 443. I believe the BGT model is nearly linear.

Page 10, Line 455, It has been debated if the Persson model is actually an exact solution for complete contact. See

Xu, Y., Jackson, R.L. and Marghitu, D.B., 2014. Statistical model of nearly complete elastic rough surface contact. International Journal of Solids and Structures, 51(5), pp.1075-1088. https://0-doi-org.brum.beds.ac.uk/10.1080/10402004.2010.542277

Page 16, Line 663, There are many elastic-plastic models of asperities and rough surface contact that are not mentioned in this work. Perhaps that should be mentioned. There are some listed in this reference:

Ghaednia, Hamid, et al. "A review of elastic–plastic contact mechanics." Applied Mechanics Reviews 69.6 (2017). https://0-doi-org.brum.beds.ac.uk/10.1115/1.4038187

Actually, these review papers here also have some good information, but a little older now:

Bhushan, Bharat. "Contact mechanics of rough surfaces in tribology: multiple asperity contact." Tribology letters 4, no. 1 (1998): 1-35.

Bhushan, B., 1996. Contact mechanics of rough surfaces in tribology: single asperity contact. Appl. Mech. Rev. May 1996, 49(5): 275-298 (24 pages) https://0-doi-org.brum.beds.ac.uk/10.1115/1.3101928

Page 15, Table 2. I like this comparison of the film thickness and rough surface contact modeling predictions. I wonder if a more direct comparison could also be included that shows how they differ based on the ratio of real contact area to nominal as function of lambda?

Author Response

Many thanks to the reviewer for their useful comments. I have tried to address their concerns below: 

1. Amontons' law does state that friction is proportional to load. In many rough surface contact models, a check is often done that the model predicts such a proportionality. It is true, as the reviewer states, that for some models this proportionality is only approximate (for example the early elastic models of Archard) or in other models (such as Greenwood & Williamson) the proportionality is exact (for the case where an exponential distribution of peak heights is assumed) but only over the range where the asperities deform elastically. The manuscript will be updated to include the word approximately where appropriate.
2. Page 2, line 58 - the sentence will be update to make it clearer what the relationship is between hardness and yield strength
3. Page 3, line 125 - a sentence will be added to point the reader to other work which was not included in the review
4. Page 5 - the authors thank the reviewers for their suggestion of a recent reference that measures roughness over a wider range of scales which will be included in the references
5. Page 6 - the suggested reference on spectral moments and fractals will also be included 
6. Page 8 and 9 - the authors thank the reviewer for the reference by Jackson et al that reports an exact solution of the Greenwood and Williamson model with a full Gaussian distribution and we will include that reference in the final manuscript
7. Page 10 - the reviewer's comments on the BGT and Persson model will be considered and the manuscript will be updated to reflect those comments and to include the suggested references
8. Page 16 - many thanks to the authors for the additional references on elastic-plastic asperity models - we will include these in the references
9. Page 15 - Table 2 - this table shows how X varies with lambda. Although X is generally considered to be the load supported by the asperities divided by the total load, work by the authors that is under consideration for publication in another journal has found that in fact X can equally well be  considered to equal the ratio of real contact area (relative to the real contact area when lambda = 0). Some comments will be added to the text to make this clearer. 

Reviewer 2 Report

This review presents an interesting case study of rough surface contact modeling. The general organization and language accuracy and writing are very good. The following points are minor issues:

• Please write the full name of the abbreviation such as nN to MN.
• The review focused on the presentation of previous models of load carried by the asperities only. The study lacks predictions for previous studies of rough surface contact modeling.
• in this review, the reader could benefit from some explanation of the tribo-layer formation mechanisms under dry friction and lubrication.
• The review presented the impact of traditional lubricant additives (ZDDP, ....) without the new trend of nano-additives in lube oils (nanolubricants)
• The review articles are an analysis of the topic. Please provide analysis in terms of what is the current status of the field, what are the challenges of rough surface contact modeling in tribological applications.
• In the conclusion, what would be the research work gaps (scientific problems) for the topic in order for its future extension?

Author Response

Many thanks to the reviewer for the useful comments. The response to those comments is below: 

1. The manuscript will be updated to include the full name of the abbreviations nN to MN
2. The manuscript will be updated to include a brief description of tribo-layer formation mechanisms
3. The reviewer comments that nano-additives in lubricants are not considered. The author is not aware of any commercially available lubricants that contain such additives - these are still very much at the research stage. Inclusion of these additives in a review such as this would be worthwhile when they are more widely used in commercial lubricants.
4. Some discussion of research gaps was included in the manuscript. In particular, although there are elasto-plastic models being used, the process of wear particles breaking off and then taking part in the sliding process does not appear to have been investigated theoretically and in addition, the changing material properties (both substrates and tribo-laters) are not usually accounted for. The authors will make clearer what they consider to be gaps that could be the basis for further research.

Reviewer 3 Report

The paper is an excellent and valuable review. The following suggestions are made to improve the manuscript further: 

1) the first sentence should refer to boundary friction rather than simply friction. 

2) In section 6 the roughness which is discussed to determine when the surface first contact is the ex-situ surface roughness. To fully account for the the transition between full film, mixed and boundary friction in EHL conjunctions amplitude reduction needs to be considered. A good description [a &b ].

[a] Zhang, Y., Biboulet, N., Venner, C.H. and Lubrecht, A.A., 2020. Prediction of the Stribeck curve under full-film Elastohydrodynamic Lubrication. Tribology international, 149, p.105569.

[b]Venner, C.H., Couhier, F., Lubrecht, A.A. and Greenwood, J.A., 1997. Amplitude reduction of waviness in transient EHL line contacts. In Tribology Series (Vol. 32, pp. 103-112). Elsevier.

3) The following statement  "Understanding how friction 551
modifiers influence the shape of the friction versus  curve is still an currently active area of research."  is very interesting and potentially valuable to the readers. However it seems to be unsupported with regard to the literature cited and should be discussed further. 

Author Response

Many thanks to the reviewer for their very useful comments. We have provided a response to the various points below: 

1. The manuscript will be updated so the first sentence refers to boundary friction rather than simply friction.
2. Many thanks to the reviewer for pointing out that roughness amplitudes are reduced in elastohydrodynamic contacts. The reviewer is correct in that the roughnesses used in the paper are those measured when the surface is outside of the contact. A paragraph will be added to mention this effect and to refer to the suggested references provided by the reviewer. 
3. The comment about friction modifiers specifically referred to the recent data reported by the Imperial College group (Dawczyk et al). In that paper, it was demonstrated that both unadditivated lubricants (base oils) and oils that contained ZDDP anti-wear additives could fit on a "universal" curve of X versus lambda. This relied on using the correct surface roughness of the (thick) tribo-layer to calculate lambda. However, for friction modifiers, the films formed are not thick enough to change the lambda value, so any changes to the shape of the friction versus lambda ratio curve will mean such fluids do not fit on the "universal" curve of Daczyk et al. It is likely that in addition to the lambda ratio, the low surface stress of the friction modifiers will need to accounted for to better understand the shape of their friction curves. A couple of sentences will be added to make this clearer to the reader.

Round 2

Reviewer 2 Report

The authors have addressed all the changes that all reviewers have suggested and I think that the manuscript is suitable for publication.