The Environmental and Economic Importance of Mixed and Boundary Friction^†

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

The manuscript can be accepted for publication.

Author Response

Thanks for the review.

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

It can be accepted now.

Author Response

Thanks for the review.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this manuscript, the authors discussed the environmental and economic importance of mixed and boundary lubrication inside combustion engines. The authors pointed out that the existed approaches to estimate mixed/boundary friction underestimated the mixed/boundary friction losses. Based on the experimental data, the authors established a new model to estimate the proportion of mixed/boundary lubrication. Although this article offers an interesting perspective on the issue, it is not ready for publication due to the following concerns.

1. The most data included in this manuscript come from one published paper of the authors (reference [6]).

2. The authors established a new model to estimate mixed/boundary friction based on some experimental data, which are quite limited. The applicability of the model isn’t well validated due to the diverse range of practical situations.

3. To reduce carbon emission, it is important to improve the tribological performance among interaction surfaces, regardless of whether it involves hydrodynamic or boundary/mixed lubrication. Therefore, the significance of estimating mixed/boundary friction losses is not particularly prominent.

Author Response

In this manuscript, the authors discussed the environmental and economic importance of mixed and boundary lubrication inside combustion engines. The authors pointed out that the existed approaches to estimate mixed/boundary friction underestimated the mixed/boundary friction losses. Based on the experimental data, the authors established a new model to estimate the proportion of mixed/boundary lubrication. Although this article offers an interesting perspective on the issue, it is not ready for publication due to the following concerns.

1. The most data included in this manuscript come from one published paper of the authors (reference [6]).

Reply: The reviewer points out that engine friction data discussed in the paper mainly comes from one recent reference (reference [36] in the resubmitted manuscript). Although that is true, there are many other published engine friction publications, the main ones of which have been added to the references in the resubmitted manuscript (references [28]- [35]), and there is a general consensus amongst all these papers of the typical distribution of friction losses amongst the main engine components, and so the authors consider that the use of data from reference [36] will not unduly affect the estimates reported.

2. The authors established a new model to estimate mixed/boundary friction based on some experimental data, which are quite limited. The applicability of the model isn’t well validated due to the diverse range of practical situations.

Reply: It is not clear to us why the reviewer thinks the new model for mixed/boundary lubrication discussed in the paper, based on experimental measurements, is not well validated. Many researchers currently use the Greenwood-Tripp model, as discussed in the paper, which is not based on any experimental data, and as discussed in the paper, appears to significantly underestimate the amount of mixed/boundary friction in a lubricated contact. Surely a model that is based on experimental data is an improvement on this.

3. To reduce carbon emission, it is important to improve the tribological performance among interaction surfaces, regardless of whether it involves hydrodynamic or boundary/mixed lubrication. Therefore, the significance of estimating mixed/boundary friction losses is not particularly prominent.

Reply: The reviewer rightly points out that it is the total friction and wear losses that result in the high financial and environmental impact of lubricants (and tribology in general). However, we disagree that there is no interest from tribologists in understanding how much of these losses are due to fluid film lubrication and how much to mixed/boundary friction. For example, in a particular contact, if it is found that the majority of friction comes from mixed/boundary lubrication, then the approach to reducing friction (increasing viscosity, using friction modifier additives, changing materials etc.) would be completely opposite to that of a contact whose friction is dominated by fluid-film lubrication (in this case, the main approach to reducing friction would be to reduce fluid viscosity).

Reviewer 2 Report

Comments and Suggestions for Authors

Comments for author File: Comments.pdf

Author Response

The abstract mentions a model that estimates the proportion of mixed/boundary lubrication, denoted as X, as a function of the λ value. However, the precise equation for this relationship is not provided. The text mentions a "reverse S-curve" but does not present the specific mathematical expression for X as a function of λ.

Reply: The expression for the reverse S-curve behaviour of X versus λ is explicitly given as equation (18) in the revised manuscript.

2. No need of citation in abstract…… friction losses [2-5].

Reply: Citation in manuscript mentioned by reviewer has been removed.

3. Mention some brief results in last sentences of the abstract.

Reply: Results for the financial impact and associated CO₂ emissions are now included in the abstract.

4. The statement in the text mentions that "it is generally assumed, in tribology, that moving rough surfaces are fully separated when the 𝜆 ratio is greater than about 3." This assumption might oversimplify the complex nature of surface interactions. The separation of surfaces in tribology is influenced by various factors, and a rigid cutoff at 𝜆 = 3 may not universally capture the conditions for full separation.

Reply: The author makes a good point, that although a value of l of 3 is often mentioned in textbooks as a “cut-off” after which full film lubrication occurs, it is apparent from the various published mixed/boundary friction models that asperity contact still occurs when l > 3. For example, in the simple Greenwood and Williamson example model with an exponential probability distribution function, X = exp(-l), the value of X when l = 4 is roughly 0.0183. A sentence has been added, together with a reference [5], that says that some researchers have seen the impact of rough surfaces for l > 5.

5. The expression for the overall friction coefficient (𝑓) presented in the text is simplified to 𝑓 = 𝑓𝐴𝑋 + 𝑓𝐹(1− 𝑋). While this expression has been reported previously, it simplifies the complex interplay between rough surfaces and fluid film in mixed/boundary lubrication. The actual relationship might be more intricate and dependent on various parameters.

Reply: The reviewer is right to point out that equation (6) (in the revised manuscript) is a simplistic approach to calculating the overall friction coefficient. A sentence has been added to make this clear

6. Section 2 discusses the assumption of elastic deformation in surface contact models and justifies it based on the "running-in" process of components. However, the text does not explicitly address the potential limitations or conditions under which the assumption might break down. It's important to acknowledge the range of conditions and materials for which this assumption holds true and when it might not be applicable.
7. The text provides equations and graphical representation of different models predicting the proportion of mixed/boundary lubrication (X) versus the 𝜆 ratio. However, it does not thoroughly discuss the limitations or applicability of each model in different scenarios. A more critical examination of the strengths and weaknesses of each model and potential factors influencing their accuracy would enhance the scientific rigor.
8. The text mentions the interesting feature of a single "master curve" that fits the experimental data well. It acknowledges some scatter in the data but states that a single curve passing through the data is still useful as a guide. It would be beneficial to provide information on the statistical methods used for curve fitting and a brief discussion on the implications of the scatter for the reliability of the model.

Reply 6-8: Section 2 has been substantially rewritten. The graph containing the “master curve” has been removed as a different version of the graph is available in reference [25], and the reader is referred to that and other references for experimental details. The main point of this section is to highlight that, in calculating mixed/boundary friction, one of the sources of uncertainty is the precise mixed/boundary model used, as different models predict different values of X for the same value of l. Some additional comments have also been added about the assumption of elastic deformation of asperities. Our view is that during “running-in”, components will either “run-in” in the normal way, or they will fail. If they “run-in” in the normal way, at the end of “running-in”, there will usually be a lower surface roughness, hardening of the surface, and potentially a change in form of the contact. However, a recent reference has been added [18] which casts some doubt on this assumption, although that work was based on indentation experiments, rather than on the normal sliding friction that occurs in engines.

9. Section 3 discusses the impact of mixed/boundary friction on vehicle fuel consumption, stating that it is less than expected due to most occurrences happening at low speeds. While this explanation is reasonable, it might be useful to include a concise summary of the quantitative impact of mixed/boundary friction on fuel consumption and any relevant empirical data or references supporting this claim.

Reply: A quantitative standard power balance model has now been used, in Section 3, to calculate actual fuel consumption losses (in grams) during the driving cycle. This approach enables the precise calculation of the fuel used to overcome engine friction, and how much fuel is required to overcome mixed/boundary friction.

10. The text relies on assumptions about fuel consumption and its distribution between different components. It would be helpful to acknowledge these assumptions explicitly and discuss their potential impact on the accuracy of the estimates. For example, the assumption that the fuel consumption due to mixed/boundary friction is the same for diesel-fueled passenger cars might warrant further consideration and clarification.

Reply: The comments in the original manuscript about diesel passenger cars have been removed from the revised manuscript.

11. Given the complexity of the system being analyzed, it could be beneficial to perform a sensitivity analysis on key parameters or assumptions. This would help in understanding how variations in these factors might affect the overall estimates.

Reply: The estimated fuel consumption figures from the power balance model are in good agreement with “back of the envelope” calculations. In essence, the “back of the envelope” calculations assume that a certain amount of fuel is needed to overcome engine friction in the NEDC driving cycle (typically 20-25%) and that an engine has a certain “average” amount of mixed/boundary friction (typically 20-30%, mainly from the valve train). Thus, this simple approach would suggest the amount of fuel needed to overcome mixed/boundary friction in a fully warmed up passenger car engine is in the range 4% to 7.5%. This argument has been included in the revised manuscript and hopefully addresses the reviewer’s comments.

12. The text refers to data from references [6], [11], [26], and [27]. Providing additional information about the reliability and credibility of these data sources would strengthen the overall scientific integrity of the analysis.

Reply: Section 3 has been substantially rewritten, with two new figures added, and the paragraph referring to data from references [6], [11], [26], [27] has now been removed. In addition, a new Section 4 has been added for heavy-duty trucks. It is interesting to note that it is estimated that only 1% of fuel is needed to overcome mixed/boundary friction in heavy-duty trucks, compared to 5% for passenger cars. However, because of the much greater fuel consumption of heavy-duty trucks, the financial impact and CO₂ emissions from heavy-duty trucks is substantially greater than that from passenger cars.

13. The text provides estimates like "approximately 10%" and "around 100 billion liters," which might benefit from more precise quantification. Rounding figures can introduce uncertainties, and it's crucial to convey the precision of the measurements accurately.

Reply: It is difficult to be exact about the precise financial and environmental impact because different engines have different amounts of mixed/boundary friction, and the way in which vehicles are driven (their driving cycle, and the local weather conditions) have a massive impact on the amount of mixed/boundary friction. In addition, factors such as the price of fuel differ substantially in different countries, and even the CO₂ emissions from 1 litre of fuel will differ depending on the biofuel content. The figures reported are estimated, “ball-park”, figures.

14. The phrase "superlubricity" is mentioned as a speculative approach. It's essential to provide a clear definition or reference to its scientific meaning, as different researchers might interpret it differently. Clarity in terminology is crucial for effective communication.

Reply: The paragraph on superlubricity, and the associated references, have been removed from the revised manuscript.

15. While the work discusses findings and estimates derived from recent experimental data by the Imperial College Tribology Group, it fails to provide the necessary specifics about the study. This includes details on the experimental setup, methodology, and potential limitations of the research.

Reply: Section 2, which describes the various mixed/boundary friction models, does describe a model (equation (18)) that uses experimental data from Imperial College. This section has been substantially rewritten, and in the revised manuscript the reader is referred to the original reference [20] for the details that the reviewer requires.