Theoretical Study of the Friction Coefficient in the M-B Model

Round 1

Reviewer 1 Report

Review on “Study of the friction coefficient in the M-B model”

by Cao et al.

Manuscrip​t ID Coatings 1915366

 

 

A- General Comments

The paper in hand concerns a study of the friction coefficient in the M-B model where the distribution function and probability distribution density of microconvex body truncation area are derived by using mathematical and statistical means. Moreover, a new model of critical truncation area and friction coefficient in fractal surface contact process is proposed.

 

The topic of the paper is interesting, within the scope of the journal, and worthy of investigation. The originality of the work is acceptable and the study performed is adequate. However, the manuscript deserves a major revision and authors are invited to carefully take into account the comments and questions below before the manuscript can be recommended for publication in Coatings.

 

 

B- Detailed Comments and questions

 

Title

The title should be more explicit. How the study was performed should be explicit: for example, numerical, theoretical, or experimental.

 

Abstract

1- More explicit results are to be added at the end of the abstract.

2- What is the rationale behind deriving the distribution function and probability distribution density of microconvex body truncation area using mathematical and statistical means? This should be clarified somewhere maybe in the introduction.

3- It is not clear whether the originality resides in the modeling proposed itself or the results obtained with this modeling. Please clarify

 

Keywords

Keywords are ok.

 

1- Introduction

1- References relevant to Coatings should be added, if possible.

2- The originality of the work should be highlighted further at the end of the introduction (taking into consideration points 2 and 3 of the reviewer regarding the abstract).

 

2- Methods

1- References to most of the equations presented should be provided;

2- The quality of Figure 1 should be enhanced;

3- The main assumptions and/or original basis of the modeling proposed should be clarified.

 

3- Results

1- The title should read “Results and discussion”;

2- More physical analysis are to be added to this section;

3- The quality of all figures should be enhanced;

4- The selection of the values of parameters in Table 1 should be argued;

5- I am not showing results that demonstrates your statement in the abstract “the accuracy of this model is verified by comparing and analyzing the proposed model with the simulation results”. Please clarify.

 

4- Discussion

1- The title should read “Conclusions”;

2- The main outputs of the manuscript in terms of applications should be highlighted.

 

5- References

References relevant to Coatings should be added, if possible.

 

Author Response

Point 1：The title should be more explicit. How the study was performed should be explicit: for example, numerical, theoretical, or experimental.

Response 1: Already edited.

Point 2：More explicit results are to be added at the end of the abstract.

Response 2: Already edited.

Point 3：What is the rationale behind deriving the distribution function and probability distribution density of microconvex body truncation area using mathematical and statistical means? This should be clarified somewhere maybe in the introduction.

Response 3: There are two starting points: (1) Equation 1 gives the relationship between the specific asperity truncated area and its number. Only on this basis can a series of subsequent discussions be carried out; (2) As for the assumption that the truncated area of asperities is continuous, this makes the original discrete model of the truncated area distribution of asperities into a continuous model , allowing us to describe the truncated area distribution of asperities using the probability distribution functions and probability distribution densities describing continuous variables.

Point 4：It is not clear whether the originality resides in the modeling proposed itself or the results obtained with this modeling. Please clarify.

Response 4: The originality of this paper lies in the set of assumptions put forward and the model proposed accordingly.

Point 5：References relevant to Coatings should be added, if possible.

Response 5: Already edited.

Point 6：The originality of the work should be highlighted further at the end of the introduction (taking into consideration points 2 and 3 of the reviewer regarding the abstract).

Response 6: Already edited.

Point 7：References to most of the equations presented should be provided.

Response 7: The references for each formula are:

Equation 1, Reference 2;

Equation 5, Reference 8;

Equations 6, 7, reference 9;

Equations 8, 9, 11, 22, References, 10;

Equations 10, 13, reference 12;

Equation 14, reference 13;

Equation 19, reference 14;

Other formulas are based on the above formulas and the derivation of the assumptions in this paper.

Point 8：The quality of Figure 1 should be enhanced;

Response 8: Already edited.

Point 9：The main assumptions and/or original basis of the modeling proposed should be clarified.

Response 9: Already edited.

Point 10：The title should read “Results and discussion”.

Response 10: Already edited.

Point 11：More physical analysis are to be added to this section.

Response 11: Already edited.

Point 12：The quality of all figures should be enhanced.

Response 12: The data in Table 2 has been revised to make it consistent with the number of significant digits, and the "Changing rate of friction coefficient" has been added to facilitate a more intuitive comparison and analysis of the data.

Point 13：The selection of the values of parameters in Table 1 should be argued.

Response 13: There is no special consideration for the parameter selection in Table 1, just because No. 45 steel is more commonly used in the engineering field, so it is taken as an example.

Point 14：I am not showing results that demonstrates your statement in the abstract “the accuracy of this model is verified by comparing and analyzing the proposed model with the simulation results”. Please clarify.

Response 14: Added discussion about this section at the end of the "Results and discussion" section.

Point 15：The title should read “Conclusions”.

Response 15: Already edited.

Point 16：The main outputs of the manuscript in terms of applications should be highlighted.

Response 16: Already edited.

Point 17：References relevant to Coatings should be added, if possible.

Response 17: Already edited.

 

 

Author Response File: Author Response.docx

Reviewer 2 Report

The author conducted a numerical study on the friction coefficient in M-B model, based on the basic model of fractal theory, the distribution function and probability distribution density of micro-convex body truncation area. A new model of critical truncation area and friction coefficient in fractal surface contact process are proposed.

After reviewing the paper, I have the following observations and comments:

- Some data, notations, and presentations in the equations are not rigorous/clear enough to correctly understand the contents and what they are representing such as Eqs.1-2. There is an explanation of S_i at line 68, but it does not appear in Eqs.1 and 2. Hence, they must be explained more clearly in right order. Fractal dimension (D) must be explained.

-        M-B model must be explained clearly. What are M and B ?

-        In Figure 1, axis labels must be given with appropriate dimensions.

-   There are several physical quantities and parameters in the paper, but units were not provided throughout the paper. All the parameters must be given with their units in the text, Figures and tables.

-        An acceptable validation and error analysis for the numerical works must be performed. Comparisons with others (rather than the simulation or numerical studies) experimental works must be performed.

-        Literature survey can be improved.

With the view of the above observations, I concluded that this paper must be revised according to the comments given above for further consideration.

Author Response

Point 1：Some data, notations, and presentations in the equations are not rigorous/clear enough to correctly understand the contents and what they are representing such as Eqs.1-2. There is an explanation of S_i at line 68, but it does not appear in Eqs.1 and 2. Hence, they must be explained more clearly in right order. Fractal dimension (D) must be explained.

Response 1: Already edited.

Point 2： M-B model must be explained clearly. What are M and B ?

Response 2: It was proposed by Majumdar and Bhushan, so its abbreviated as“M-B model“.

Point 3： In Figure 1, axis labels must be given with appropriate dimensions.

Response 3: Figure 1 is a schematic diagram used to illustrate the stress-strain law of metals, which is only a qualitative display, and because the specific parameters of different metals are different, specific data cannot be directly marked. In the revised manuscript we have reworked Figure 1 and added units to the axis labels.

Point 4：There are several physical quantities and parameters in the paper, but units were not provided throughout the paper. All the parameters must be given with their units in the text, Figures and tables.

Response 4: Already edited.

Point 5：An acceptable validation and error analysis for the numerical works must be performed. Comparisons with others (rather than the simulation or numerical studies) experimental works must be performed.

Response 5: Due to limited conditions, it is temporarily difficult to carry out real physical experiments for this paper. The model proposed in this paper is mainly used to predict the change trend of friction coefficient, so the focus of the analysis is on the difference between the shape of the graph calculated based on this model and the graph of the simulation result.

Point 6： Literature survey can be improved

Response 6: Already edited.

 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Thank you for taking into consideration my comments. The manuscript is now ready for publication.

Reviewer 2 Report

After reviewing the revised form of the paper, I have the following observation. The revised form of the paper  well have been improved. The subject is explained clearly, discussed and compared properly with enough credit given to the contributions of the authors in this field.   Meaningful discussion and conclusions were made with the supporting data. All the comments from the reviewer were clearly responded by the authors, and necessary revisions were performed accordingly. With the view of the above observations, I concluded that the present form of the paper can be acceptable for the publication in the journal.