Fatigue Reliability Design Method for Large Aviation Planetary System Considering the Flexibility of the Ring Gear

Round 1

Reviewer 1 Report

The present paper fundamentally deals with the optimization of the ring gear rim thickness for large planetary geared transmissions for aviation. The overall structure and presentation is acceptable however some major improvements must be made.

Since the paper deals with structural analysis the details on the computation of the load, deformations and stresses must be explained in further detail and the employed models and methods must be described or at least cited in the paper. In paragraph 2.1 the authors cite the employed software "RotationMaster" however the reviewer was not able to find any relevant sources of this model. Furthermore, several approaches are available in literature and must be compared and cited for comparison. Without this improvement the rest of the paper cannot be scored since all the model description is confusing even for an expert reader and the results are strongly dependent on this point.

Author Response

Dear reviewer, we are grateful to reviewer for your effort reviewing our paper and your positive feedback. We have carefully addressed all the reviewer’s concerns. Please see below our replies. We hope you are satisfied with our answers and the new data we provided. Changes highlighted in yellow have been made accordingly, in the revised manuscript and in there vised supplementary information.

 

Point 1: Since the paper deals with structural analysis the details on the computation of the load, deformations and stresses must be explained in further detail and the employed models and methods must be described or at least cited in the paper.

 

Response 1: With special thanks to the reviewers for your valuable comments. Due to space limitation, the text does lack a precise representation of the modeling and analysis mechanism of the simulation model, including the description of the specific methods and details of the load, deformation and stress calculations. The relevant content has now been added to the manuscript in its entirety.

 

 

Point 2: In paragraph 2.1 the authors cite the employed software "RotationMaster" however the reviewer was not able to find any relevant sources of this model. Furthermore, several approaches are available in literature and must be compared and cited for comparison.

 

Response 2: With special thanks to the reviewers for your valuable comments. The "RotationMaster" here actually refers to the "RomaxDesigner" analysis software. And the real name of the software is not directly mentioned in the article because our unit has a confidential cooperation project with Romax company at this time. This software is used in this paper to implement the input of system-level model results to submodels, it has certain technical advantages in program setting. In addition, the introductory section of the article has been carefully sorted out logically and the content has been trimmed. It makes the research significance of the whole text more prominent and the contrast of research methods more distinct.

Author Response File: Author Response.docx

Reviewer 2 Report

Please see attached document for minor and major comments/recommendations.

Comments for author File: Comments.pdf

Author Response

Dear reviewer,I'm sorry to answer your question in this way,this is because I cannot submit two documents at the same time on the system of this page.I have submitted a revised manuscript and I will contact the editor to send you an electronic file of my response letter(Author to respond reviewer).This will make it easier for you to view my answers to the comments and suggestions you have asked.

we are grateful to reviewer for your effort reviewing our paper and your positive feedback. We have carefully addressed all the reviewer’s concerns. Please see below our replies. We hope you are satisfied with our answers and the new data we provided. Changes highlighted in yellow have been made accordingly, in the revised manuscript and in there vised supplementary information.

Minor Comments:

 

ve been made accordingly, in the revised manuscript and in there vised supplementary information.

Point 1:

Line 13: the phrase “probabilistic fatigue strength” is used only in the abstract. Consider changing it to “fatigue strength distribution” as it is used in the body of the article.

Line 83: add space after “[16].”

Line 102: Delete the full stop and one space before “[21]”.

Line 142: Either change the word “commonly” to “common” or add the word “used” after“commonly”.

 

Response 1: With special thanks to the reviewers for your valuable comments. The English language and writing style of our articles were revised as appropriate, and corrected the errors in the article according to your instructions.

 

 

Point 2:

Lines 175 to 177: This sentence might need a reference.

 

Response 2: With special thanks to the reviewers for your valuable comments. This sentence really need a reference, and we have marked in the article.

 

 

Point 3: Lines 182 to 187: This sentence is extremely long and need to be broken down.

 

Response 3: With special thanks to the reviewers for your valuable comments. We have modified this long sentence. In the revised manuscript, the corresponding changes are marked in yellow.

 

 

Point 4: Line 207: The phrase “ordinary computer” is vague. Give a better explanation to the minimum possible specification of the computer that can perform the task.

 

Response 4: With special thanks to the reviewers for your valuable comments. The term "ordinary computer" refers to an ordinary home version of a computer, not a large workstation. In the revised manuscript, the corresponding changes are marked in yellow.

Point 5: Lines 215 to 219: This sentence is extremely long and need to be broken down. Use of bullet points might help to list the benefits of using the “semi-analytic FE technology”.

 

Response 5: With special thanks to the reviewers for your valuable comments. We have modified this long sentence. In the revised manuscript, the corresponding changes are marked in yellow.

 

 

Point 6: Line 225: You may consider changing the word “axis” to “shaft”.

 

Response 6: With special thanks to the reviewers for your valuable comments. We have changed the word “axis” to “shaft”. And we have checked the entire documentation to ensure that the term is uniform.

 

 

Point 7: Lines 281 and 287: be consistent in stating the phrase “sub-model”. In those lines the dash between the words is missing. Please check the entire document for this inconsistency.

 

Response 7: With special thanks to the reviewers for your valuable comments. We have modified the phrase “sub-model”. And we have checked the entire documentation to ensure that the term is uniform.

 

 

Point 8:

Line 416: Change the word “model” to “equation”.

Line 559: Add the word “be” after “will”.

Line 586: Change the word “indicating” to “indicates”

Line 595: The phrase “As the same time” seems to be isolated from the next sentence with a full stop. Change the full stop to comma and change the upper case “C” of “Considering” to “c”.

Line 629: delete the “-“ in the middle of the word “levels”.

 

Response 8: With special thanks to the reviewers for your valuable comments. We corrected the errors in the article according to your instructions.

 

 

Major Comments:

 

Point 9: The consideration of more exhaustive list of the sources of uncertainty in planetary gear system is recommended. For example, uncertainty in system assembly that could influence center distance and brings about misalignment is one consideration. The variability in gear backlash could be another one, etc.

 

Response 9: With special thanks to the reviewers for your valuable comments. The uncertainty of material strength is mainly considered in the reliability analysis of this paper. Because of the limited analytical capability of the simulation model, the uncertainties associated with the dimensions of the structure cannot be taken into account at this time. Hopefully, it will be improved in the next study.

 

 

Point 10: Lines 230-231: The authors are recommended to justify the use of RIGID bearing races in modeling the bearings in the system.

 

Response 10: With special thanks to the reviewers for your valuable comments. The support stiffness and engagement stiffness in the simulation model have been re-explained specifically in the paper.

 

 

Point 11: Table 1: State what material is used to build the planetary gear train. The Elastic modulus won’t be enough to describe the material property.

 

Response 11: With special thanks to the reviewers for your valuable comments. About materials of planetary gear train, we have made additional remarks in Table 1 in the article.

 

 

Point 12: Lines 305 to 309: How is the reduction in computation cost justified?

 

Response 12: With special thanks to the reviewers for your valuable comments. The article splits the calculation of tooth root stresses in large aerospace planetary mechanism systems into two parts: the system-level and the secondary sub-model. The system-level analysis is based on finite element semi-analytical methods with high computational efficiency. In the secondary sub-model calculation session, it is not necessary to consider the complete load-bearing unit body of all gears in the system, but only the geometric characteristics and stress states of the gear teeth where meshing occurs. In general, the semi-analytical finite element method is used for the relatively complex computational part of this large system. The complex geometric relationships of the gear teeth  are also taken into account(based on the secondary sub-model).

 

 

Point 13: Figure 2(d): I recommend to remove the stress values on the nodes.

 

Response 13: With special thanks to the reviewers for your valuable comments. We corrected the Figure 2(d) to your suggestions. And now Figure 2(d) becomes Figure 5(d).

 

 

Point 14: The correlation between the experimental fatigue test and the theoretical analysis in this research is not well established. You may consider adding few sentences or a paragraph on how the experimental results are used in the analytical work. It is stated in the abstract that the fatigue test is used to establish a probabilistic fatigue strength and need to be explained at the end of Chapter 3 how the results will be implemented in the computational work.

 

Response 14: With special thanks to the reviewers for your valuable comments. The stress level of the gears under actual service conditions is much lower than the stress level used in the test. Therefore, the P-S-N curve in Fig. 7(b) can be extrapolated to the low stress direction. Then the gear strength conditions applicable to the actual service conditions can be obtained. Additional explanation has been provided in the text.

 

 

Point 15: Lines 374 and 375: How are the test stress levels and the number of test points selected? Justification/explanation is recommended.

 

Response 15: With special thanks to the reviewers for your valuable comments. Grouping method is adopted in the gear test, and four stress levels are respectively 649 MPa, 618 MPa, 586 MPa, and 555 MPa. With the reduction of stress, fatigue life of gear become more and more dispersed. Therefore, as the stress de- creases, the number of test points is increased. The highest stress level has 17 test points, and the next levels respectively have 22 and 29 points. When the level drops to 555 MPa, the dispersion of test data becomes significantly large, so 38 test points are used at this level.

 

 

Point 16: Equation (2): You need to define what “z” is right after this equation.

 

Response 16: With special thanks to the reviewers for your valuable comments. We have explained in detail this parameter in the article.

 

 

Point 17: Figure 5: The figure is supposed to display “Sensitivity dimensions of system performance indexes” but only a model of a ring is displayed. You may need to change either the title or the figure.

 

Response 17: With special thanks to the reviewers for your valuable comments. The degrees of freedom and related parameter settings of the ring gear model are specified in the model introduction section. This specifies the concept and quantitative representation of the dimensionless ring gear rim thickness. The concept and quantitative representation of the dimensionless of the ring gear rim thickness is indicated here. Effect of Internal Gear Flexibility on the Quasi-Static Behavior of a Planetary Gear Set.

 

 

Point 18: Line 537 to 538: Sentence is not complete. You may need to connect the two successive sentences.

 

Response 18: With special thanks to the reviewers for your valuable comments. We have modified Equations according to your suggestions.

 

 

Point 19: Lines 547, 551, 555 to 557 and Equations (16) and (170: I recommend the notation of the fitting polynomials to be Y1(x) and Y2(x)than Y(1) and Y(2).

 

Response 19: With special thanks to the reviewers for your valuable comments. We have modified Equations according to your suggestions.

Point 20: Figure 6: Consider giving a reference to the Figure as this is a flow chart of well-known previously established algorithm.

Response 20: With special thanks to the reviewers for your valuable comments. A reference is indeed needed here, and we have marked in the article.

 

 

Point 21: Lines 568 to 570: How are the six parameters selected? Justify/Explain.

 

Response 21: With special thanks to the reviewers for your valuable comments. Regarding the setting of the parameters related to the genetic algorithm, they are generally set within the corresponding ranges. For the selection of parameters in this paper, we have referred to the literature (Liang X, Liu Y, Huang M. Improved NSGA2 Algorithm to Solve Multi-Objective Flexible Job Shop Scheduling Problem[C]//2020 IEEE 8th International Conference on Computer Science and Network Technology (ICCSNT). IEEE, 2020: 22-25). And also completed the selection of parameters with the help of the multi-objective optimization toolbox of genetic algorithm in MATLAB software.

Author Response File: Author Response.docx

Reviewer 3 Report

A thorough, well conducted analysis of thin-rimmed gear issues, combined with a dedicated mathematical approach.

The subject area is well covered and analysed. The article could use an overall check of the English language and writing style.

Unnecessary text in line 656 "Please add:"

Author Response

Dear reviewer, we are grateful to reviewer for your effort reviewing our paper and your positive feedback. We have carefully addressed all the reviewer’s concerns. Please see below our replies. We hope you are satisfied with our answers we provided.

The English language and writing style of our articles were revised as appropriate. And the unnecessary text in line 656 has been deleted.

 

Author Response File: Author Response.docx