Dynamic Tangential Contact Stiffness and Damping Model of the Solid–Liquid Interface
Round 1
Reviewer 1 Report
The paper presents a very complex mathematical approach for dynamical solid-liquid interface under mixed lubrication. The results are verified with existing experimental results.
There are some minor revisions that I have to ask for
1.Subscripts for S in ??P?, Eq. 18
2.Line 199 – Pns is described in § 3.4 and not § 3.2. From Eq. 12, P should be a pressure or a normal load per unit of area and not a “solid normal contact load”. It is correct that P1 = Pns from Eq 48, which results from a Sum (∑ ) of “solid normal contact load” for each real contact area of the joint, not by integration of Pns on a surface.
3.In Eq. 19 – It is Ff instead of F
4.There are three Eqs. 22 (lines 242-250)
5.Eq 27 is missing
6.Line 426 and 544 – GPa instead of Gpa
7.What is the value of ms – Eq. 18, line 213, the coefficient of contact friction between two rough surfaces, that you used in your calculation?
8.Is it ms from Eq. 18 or m (Eq. 19) involved in Eqs 27-42?
9.Line 429 – mmSuperscript2/s
10.Line 455 – Measurement unit for normal load is missing
11.Line 549 – Check the measurement units the viscosity (kinematic or dynamic)? is 40mm?, the cSt? is 82.4mm?, the cSt? is 13.6mm2/s?, the viscosity index is 170?
Author Response
Dear reviewer,
Sincerely appreciate for your precious time and valuable comments. The comments are highly insightful and very helpful for revising and improving our paper, as well as the important guiding significance to our research. All of our authors should apologize for those mistakes and unclear formulations in our paper. Your comments have been studied carefully and replied point by point with supplement and explanation, which have been hoped to meet with your approval in great honor. Revised portion are underlined in red in the revised paper ("machines-1862754 revision. docx"). The main corrections are given below.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The current work explores the dynamic tangential stiffness and damping characteristics of lubricated conjunctions under mixed-lubrication conditions. The proposed analytical/numerical approach is validated against experiments. Overall, the manuscript is well-written, the work is novel, and the results are interesting. The manuscript may be accepted for publication pending minor revisions, as detailed below:
1- Page 2, lines 91-92: The authors state that there are few works on tangential stiffness and damping characteristics of lubricated contacts, but there are at least a couple of recent works that are worth mentioning in that regard by Changjiang Zhou et al. in Tribology International (vol. 109, pp.319-327) and Applied Mathematical Modelling (vol. 61, pp. 634-649).
2- Equation (9): There’s a missing parameter in the first term of this equation. I believe “(i,j) P(i,j)” should be “A(i,j) P(i,j)”.
3- Page 5, line 187: I believe “AP(i,j)” should be “Delta_P(i,j)”.
4- Equation (18): I believe “F_f” should be “F”, simply.
5- Page 6, line 224: I believe “k_r” and “c_r” should be “k_Tau” and “c_Tau”.
6- Page 7, line 243: I believe “Delta_F’_Taud” should be “F’_Taud” and “Delta_F’_Tauv” should be “F’_Tauv”.
7- Page 7: Equation numbering requires correction here. There are 3 equations that are numbered (22).
8- Equation (22): I believe “Delta x’” should be “Delta x’_i”.
9- Equations (24)-(26): What is “delta_e”? It is not defined anywhere. Also, on line 297, the authors define “k” as the critical yield stress coefficient, but “k” is not used anywhere in equations (24)-(26).
1- Page 11, line 339: “py” should be “p_y”.
1- Page 13, line 392: “An” should be “A_n”.
1- Equation (50): The curly bracket of the last integral term should be closed (right bracket is missing).
1- Page 15, line 423-424: What’s the consolidation-consolidation interface? Is it a software? Please provide more details and an adequate reference for readers who are not familiar with this interface.
1- Page 15, line 427-428: The unit for the radius of curvature R is missing. I believe it’s “m”.
1- Page 15, line 439: The unit for X0 is missing, or is it dimensionless?
1- Page 15, lines 431-433: The definitions of the different dimensionless parameters should be provided.
1- Page 16, line 455 and page 17, line 473: The unit for the normal load is missing.
1- Figure 7: What is the value of X_0 for these results, it is not specified in the text.
1- Figures 8 and 9: What is the normal load for these results, it is not specified in the text.
2- Section 5: A brief description of the experimental apparatus and techniques is needed here. Referring the reader to references [13] and [44] is not sufficient, especially that in reference [13] the apparatus was developed to measure normal stiffness and damping, whereas in the current work it is used to measure tangential stiffness and damping. The authors need to (at least) briefly explain how this was done.
2- Page 19, line 549: There’s something wrong here with units. Viscosity is given in mm! Please verify and correct.
2- Section 5: Though the stiffness experimental results seem reasonable and match relatively well with theoretical results, damping results seem to be more scattered, with a less successful agreement with experiments. Can the authors provide some explanations in this regard? Is repeatability an issue in these experiments? Are the shown results averaged ones (obtained from several attempts), or are they obtained from a single attempt? Please elaborate.
Author Response
Dear reviewer,
Sincerely appreciate for your precious time and valuable comments. The comments are highly insightful and very helpful for revising and improving our paper, as well as the important guiding significance to our research.Your comments have been studied carefully and replied point by point with supplement and explanation, which have been hoped to meet with your approval in great honor. Revised portion are underlined in red in the revised paper ("machines-1862754 revision. docx"). The main corrections are given below.
Author Response File: Author Response.pdf
