A Novel Three-Dimensional Fractal Model for the Normal Contact Stiffness of Mechanical Interface Based on Axisymmetric Cosinusoidal Asperity

Round 1

Reviewer 1 Report

The authors present a more accurate modelling method for calculating contact parameters, which takes into account the inherent roughness effects of the contacting surfaces.  This is based on determination of the fractal dimension of the surface, assuming the asperities which form the contact are axisymmetric cosinusoidal in form, and that they deform elastoplastically.  The model is demonstrated to match experimental results well.  The effect of fractal dimension is then explored computationally.

The English is clear, the literature review section is thorough, the explanations are good and written in a simple and transparent style.

I've picked up a few small criticisms that I think would be easy to address.

1. In the abstract (line 20-21) "The rationality of the simulation results..."  I don't think "rationality" is quite the right word?  I think you are trying to say that the fact that the results are so convincing is in part a consequence of the choice of asperity shape.  I cannot think of a better replacement word in this context, but I would perhaps suggest you change the whole sentence to convey your intended meaning more clearly.

2. In the Introduction section, the first 4 paragraphs are a literature review.  the final paragraph (page 2, line 97) is a statement of the authors' actions to take the research forward.  I would suggest adding subsections, for example: 1.1 Context (this is a paragraph that you haven't yet written.  Please say why having a good model for contact is important.  1.2 Literature Review (your first 4 paragraphs). 1.3 New approach (your final paragraph). 

3. Diagrams and figures would benefit from some improvements, so that font types and sizes are legible and consistent.

4. The mathematical typesetting is rather poor, which makes it hard to read and see easily what the main terms are.  For example, in Equation (1) there are brackets within brackets, both with the same style, which can be confusing.  And the brackets are not the same height as the fraction term they enclose.  Equation (3) is horribly cramped, and should be spread over multiple lines.  Th summation indices and exponents are hard to read.  The exponent of 1/2 is shown as a full fraction and would be better as a small fraction.  Bracket heights are problematic.  Sqaure brackets should enclose curly brackets, not the other way around.  I am being very fussy, but the more clearly the mathematics is set out, the more likely readers are to interact with it.

5. In the first sentence of section 3 (page 4, line 160) you should say that this is an assumption.  It is self-evidently true for high numbers of asperities, but this is an averaging effect from random distributions.  It is a reasonable assumption, but that should be acknowledged.

Other than those criticisms (which are entirely minor), this is a very interesting paper, and I have been pleased to have had the opportunity to review it.

Author Response

We thank the reviewers for his careful read and thoughtful comments on the previous manuscript. We have carefully taken his comments into consideration in preparing our revision, which has resulted in a paper that is clearer, more compelling, and broader. Please see the attachment for the detailed modification.

Author Response File: Author Response.pdf

Reviewer 2 Report

I can recommend the publication of this manuscript after a minor revision.

1. Write keywords in alphabetical order.

2. Line 41: Minor mistake: “..... Zhang and Sayles [11,12] proved..”. Wrong references [11,12]. No “Sayles”.

3. Line 50: Minor mistake: “...Tian [16]....” it should be written as “Tian et al. [16]...”

4. Line 53: Minor mistake: “...Zhang [17] derived....” it should be written as “......Zhang et al. [17] derived...”

5. Line 56: Minor mistake: “...Wang [18] takes....” it should be written as “.....Wang et al. [18] takes...”

6. Line 75: Minor mistake: “...Pan [22] considered......” it should be written as “.....Pan et al. [22] considered.. ”

7. Line 77: Minor mistake: “...Jiang [23] combined..........” it should be written as “.....Jiang et al. [23] combined.... ”

8. Lines 81, 93: Minor mistake: “..An [27] had 81 proved.............” it should be written as “.....An et al. [27] had proved..... ”

9. Line 90: Minor mistake: “..Saha [30] established...” it should be written as “.....Saha et al. [30] established...... ”

10. Line 122 and so on: insert references for all mathematical formulas. Specify all the parameters involved in all equations.

11. Line 189, Minor mistake: “.By definition, The normal contact load..”

12. Insert more information about the statistics.

13. Give more details about the advantages and disadvantages, as well as the limits of the proposed method.

14. Improve the quality (resolution) of figs. 5 and 6.

15. Lines 510-511, 525-526, the wrong title of Journal: ... Journal of Tribology-transactions of The Asme - J TRIBOL-TRANS ASME...

16. Line 553, Specify pages.

17. Insert Data Availability Statement, Conflict of interest.

 

Author Response

We thank the reviewers for his careful read and thoughtful comments on the previous manuscript. We have carefully taken his comments into consideration in preparing our revision, which has resulted in a paper that is clearer, more compelling, and broader. Please see the attachment for the detailed modification.

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper presented a novel three-dimensional fractal model for the normal contact stiffness of mechanical interface based on axisymmetric cosinusoidal asperity. The results reported is reasonable and useful for the researchers in contact mechanics. Before it can be accepted, the authors have to clarify the following comments.

1. The geometric parameters such as the curvature radius of the asperity R in Eq. (13) are calculated using the traditional definitions. Obviously, R is independent on any fractal parameters such as D. Is this way right?

2. What the difference between this submission and the reference [27]?

3. The literature reviews in Line 81-83 and 93-96 seem to be the same.

4. The authors should check the style for citing authors' name of references. For example, in Line 75, Pan [22] should be replaced by Pan et. al. [22].

Author Response

We thank the reviewers for his careful read and thoughtful comments on the previous manuscript. We have carefully taken his comments into consideration in preparing our revision, which has resulted in a paper that is clearer, more compelling, and broader. Please see the attachment for the detailed modification.

Author Response File: Author Response.pdf