On the Existence of Self-Excited Vibration in Thin Spur Gears: A Theoretical Model for the Estimation of Damping by the Energy Method
Round 1
Reviewer 1 Report
Dear Authors,
I have some comments to your article:
1. In the last part of the Introduction, there is a lack of information on how an article about content is organized.
2. Figure 3. - no dot at the end of the figure caption.
3. Please harmonize the lower indices in the equations. Indexes in symbols in text and equations should be written in the same way. Especially the lower indexes.
4. Line 234 - should be written without a unit of KW (equation 24).
5. The first item of literature is an example. The text is its citation. Please, change it. (1. Author 1, A.B.; Author 2, C.D. Title of the article. Abbreviated Journal Name Year, Volume, page range, DOI.)
6. The cited literature items are quite old. You can expand the References list by a few newer more items.
Author Response
Author Response File: 
Author Response.docx
Reviewer 2 Report
The authors address an interesting problem of self-excited vibration in gears. They state (line 60) that "few papers" have dealt with this problem, yet decline to cite any of them - even though their own work (Journal of Aerospace Power 31(1):241-248) appears to be of relevance.
The analysis appears generally sound, but the presentation displays some carelessness. For example (line 157), α(k) can simply be expressed as kεπ; equations (14) and (16) are stated for all values of k, yet equations (13) and (15) give different expressions for k=1.
The results are based on analytical calculation of WF (equations 10-16) and finite element calculation of WD (equations 20-21). There is no validation against alternative methods and no convergence study, so although the results seem sensible there is no guarantee of their correctness or accuracy. This is my most serious concern with the paper.
The English has minor errors throughout. The notation is not in alphabetical order and the references are all misnumbered due to the appearance of a dummy reference 1.
Author Response
1. The authors address an interesting problem of self-excited vibration in gears. They state (line 60) that "few papers" have dealt with this problem, yet decline to cite any of them - even though their own work (Journal of Aerospace Power 31(1):241-248) appears to be of relevance..
According to the reviewer's comment, the relevant literature was cited.
2. The analysis appears generally sound, but the presentation displays some carelessness. For example (line 157), α(k) can simply be expressed as kεπ; equations (14) and (16) are stated for all values of k, yet equations (13) and (15) give different expressions for k=1.
The error formula was corrected. The contradiction in Equations 13 (15) and 14 (16) is because the formula is incorrectly expressed and has been corrected in the paper.
3. The results are based on analytical calculation of WF (equations 10-16) and finite element calculation of WD (equations 20-21). There is no validation against alternative methods and no convergence study, so although the results seem sensible there is no guarantee of their correctness or accuracy. This is my most serious concern with the paper.
This paper proposed a theoretical model for the phenomena of self-excited vibration in thin spur gears occurring in engineering applications, and gave an explanation for the phenomenon. Since there is not much relevant research, no suitable comparison method has been found. However, the analysis of the convergence of the algorithm was added in the paper.
4. The English has minor errors throughout. The notation is not in alphabetical order and the references are all misnumbered due to the appearance of a dummy reference 1.
According to the reviewer's comment, some grammatical mistakes and format problems have been corrected. Notation was rearranged alphabetically and the reference number was re-adjusted.
Author Response File: Author Response.docx
Reviewer 3 Report
The paper titled “On the Existence of Self-excited Vibration in Thin Spur Gears: A Theoretical Model for the Estimation of Damping by the Energy Method” concerns very interesting topic of self-induced vibrations in mechanical systems. In particular, the authors examine the influence of axial forces on the stability of a thin spur gear. The theoretical analysis has been supported by a numerical investigation by using a finite element model of a gear wheel proving that the travelling wave on the driving and driven wheel, in absence of proper damping, the system encounters instability.
In my opinion, the paper is very well written and organized. The authors provided a good explanation of the theoretical analysis and particular attention has been granted to the results. Check line 344.
Author Response
The paper titled “On the Existence of Self-excited Vibration in Thin Spur Gears: A Theoretical Model for the Estimation of Damping by the Energy Method” concerns very interesting topic of self-induced vibrations in mechanical systems. In particular, the authors examine the influence of axial forces on the stability of a thin spur gear. The theoretical analysis has been supported by a numerical investigation by using a finite element model of a gear wheel proving that the travelling wave on the driving and driven wheel, in absence of proper damping, the system encounters instability.
In my opinion, the paper is very well written and organized. The authors provided a good explanation of the theoretical analysis and particular attention has been granted to the results. Check line 344.
Thank you for your evaluation and review of this article. The reference cited error in line 344 has been corrected.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Dear Authors,
Thank you very much for introducing changes that have improved the quality of the article.
I have no more comments.
Author Response
Thank you very much for introducing changes that have improved the quality of the article.
I have no more comments.
Thank you for your evaluation and review of this article.
Reviewer 2 Report
The authors have addressed some of the issues raised at the previous review. They have improved the presentation and corrected errors in the English, though introducing a few new ones. I recommend that the text be checked by a native English speaker before publication.
A useful convergence study has been added, but it is a pity that the authors were not able to validate the work against competing methods.
Author Response
The authors have addressed some of the issues raised at the previous review. They have improved the presentation and corrected errors in the English, though introducing a few new ones. I recommend that the text be checked by a native English speaker before publication.
A useful convergence study has been added, but it is a pity that the authors were not able to validate the work against competing methods.
This paper was checked and revised by a native English speaker.
The paper is not compared to other methods. If a suitable comparison method is found, we will submit it to the journal as a supplement.
Author Response File: Author Response.docx
