On Mechanical and Motion Behavior of the Normal Impact Interface between a Rigid Sphere and Elastic Half-Space
Huailong Shi
Round 1
Reviewer 1 Report
This paper addresses an interesting problem, which is the description of the collision problem in wheel-rail interaction process. Generally, this paper is well written. Before publication, the following editorial comments can be considered.
1. Line 93, a space should be inserted after “)”.
2. Line 251-257, the row spacing is too large.
3. Line 162 and 187, the fourth-level subheadings are used, please confirm if it is appropriated.
4. In “4. Concluding remarks”, third-level subheadings are used. It is suggested to change the heading of this part to “Discussion and Conclusion”, or consider adding an independent part of the discussion, before the final conclusion.
5. It is suggested to provide more calculation results and more comparative analysis to better present the proposed methods.
Author Response
Reviewer 1#: This paper addresses an interesting problem, which is the description of the collision problem in wheel-rail interaction process. Generally, this paper is well written. Before publication, the following editorial comments can be considered.
1. Line 93, a space should be inserted after “)”.
Response: Thanks for your careful check, and this has been revised.
2. Line 251-257, the row spacing is too large.
Response: Thanks for your careful check, and this has been revised.
3. Line 162 and 187, the fourth-level subheadings are used, please confirm if it is appropriated.
Response: Thanks for your advice, and this has been adjusted.
4. In “4. Concluding remarks”, third-level subheadings are used. It is suggested to change the heading of this part to “Discussion and Conclusion”, or consider adding an independent part of the discussion, before the final conclusion.
Response: Thanks for your advise. The heading has been changed to ‘Discussions and conclusions’.
5. It is suggested to provide more calculation results and more comparative analysis to better present the proposed methods.
Response: Thanks for your advise. The numerical simulations were not conducted in this paper due to the fact that the simulation tools are based on the traditional static-equilibrium-based Hertz contact theory, which is significantly different from the basic theories adopted in this paper (kinematics and particle dynamics theory). Note that some of the obtained results can be reduced to that of Hertz contact theory. The equal deformation depth in the contact and non-contact regions, and the proportional relationship between the stress or strain in the contact area and the center point of the collision at any moment are consistent with the Hertz contact theory, which preliminarily verifies the reliability of current study. More detailed calculation results and more comparative analysis will be presented in our future work.
Reviewer 2 Report
The paper needs more citation for literature review, stating the basic equations for Hertz and the basic equations for the collisions and the kinematic forces. But I believe that the significant of the research is not clearly stated, so what is the importance of this research and how that will benefit other researchers.
The paper has 120 equations, all should be cited in the text with better explanation for the abbreviations and illustrate more about the movement between all these equations.
The text in general needs to be rewritten.
Author Response
Reviewer 2#: The paper needs more citation for literature review, stating the basic equations for Hertz and the basic equations for the collisions and the kinematic forces. But I believe that the significant of the research is not clearly stated, so what is the importance of this research and how that will benefit other researchers.
Response: Thanks for your advice. Almost all the formulas based on the classical Hertz contact theory as well as the collision forces can be found in Refs. [1-3]. This paper presents exact solutions for the mechanical behavior of the interface during the normal collision between a rigid sphere and an elastic half-space based on kinematics and particle dynamics theory, which is significantly different from the static-equilibrium-based traditional contact theory. Accounting for your suggestion, the importance/significance of current study has been highlighted in the last paragraph of introduction.
The paper has 120 equations, all should be cited in the text with better explanation for the abbreviations and illustrate more about the movement between all these equations.
Response: Thanks for your advice, and this has been corrected now.
The text in general needs to be rewritten.
Response: Thanks for your advice. We have carefully proofread the manuscript to minimize typographical and grammatical errors, and some of the awkward and wordy language has been fine-tuned for better expressions.
Reviewer 3 Report
Too many assumptions are made during the formulation derivation of contact. There is an absence of case studies through numerical simulations, for instance, finite element analysis or rigid-flexible coupling system dynamics.
Author Response
Reviewer 3#: Too many assumptions are made during the formulation derivation of contact. There is an absence of case studies through numerical simulations, for instance, finite element analysis or rigid-flexible coupling system dynamics.
Response: Thanks for your comments. Some assumptions are adopted first, and then its rationality and uniqueness have been proven according to the physical and mathematical logic. The numerical simulations were not conducted in this paper due to the fact that the simulation tools are based on the traditional static-equilibrium-based Hertz contact theory, which is significantly different from the basic theories adopted in this paper (kinematics and particle dynamics theory). Note that some of the obtained results can be reduced to that of Hertz contact theory. The equal deformation depth in the contact and non-contact regions, and the proportional relationship between the stress or strain in the contact area and the center point of the collision at any moment are consistent with the Hertz contact theory, which verifies the reliability of current study.
Reviewer 4 Report
This paper presents exact solutions for the mechanical behavior of the interface during the normal collision between a rigid sphere and an elastic half-space based on kinematics and particle dynamics theory, which is interesting and within the scope of this journal. It is recommended to accept for publication after revising the language error carefully.
Author Response
Reviewer 4#: This paper presents exact solutions for the mechanical behavior of the interface during the normal collision between a rigid sphere and an elastic half-space based on kinematics and particle dynamics theory, which is interesting and within the scope of this journal. It is recommended to accept for publication after revising the language error carefully.
Response: Thanks for your positive comments. We have carefully proofread the manuscript to minimize typographical and grammatical errors, and some of the awkward and wordy language has been fine-tuned for better expressions.
Round 2
Reviewer 3 Report
The authors have responded to the comments and it can be suitable for potential publication.
Regarding the Hertz contact theory, it is found that there are more publications besides those cited in the reference list. It is suggested to tell the difference.
[1] Double-parameter Hopf bifurcation analysis of a high-speed rail vehicle with an alternative wheel/rail contact approximation. Vehicle System Dynamics, 2022, DOI: 10.1080/00423114.2022.2050770
[2] Improved lateral-dynamics-intended railway vehicle model involving nonlinear wheel/rail interaction and carbody flexibility[J]. Acta Mechanica Sinica, 2021, 37(6): 1000–1015.
