Research on Multi-Directional Spalling Evolution Analysis Method for Angular Ball Bearing
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsDear Authors,
I have completed the review of your manuscript titled "Research on Multi-directional Spalling Evolution Analysis Method for Angular Ball Bearing". I appreciate the valuable contribution of your study.
Attached to this email, you will find a PDF document containing my comments and suggestions for major revisions to enhance the clarity and coherence of your manuscript. I believe addressing these points will further strengthen the overall quality of your work.
Best regards,
Comments for author File: 
Comments.pdf
I have carefully reviewed the English language in your manuscript and found it to be generally satisfactory.
Author Response
Author's Response to Reviewer
Dear Reviewer,
First and foremost, we would like to express our sincere gratitude for your valuable feedback on our manuscript. We truly appreciate the time and effort you have dedicated to reviewing our work and providing insightful suggestions.
Below are our responses to the questions and suggestions you raised:
- The Introduction contains numerous instances of unnecessary hyphens in various words, such as "bear-ing" (line 23), "ori-gins" (line 25), "Ow-ing" (line25), "sce-narios" (line 27), and "race-way" (line 30) and so on. Ensuring consistent and correct hyphenation would enhance readability.
Answer:
The spelling issues have been corrected as follows:
- Line 13: "pro-posed" to "proposed"
- Line 23: "bear-ings" to "bearings"
- Line 25: "race-way" to "raceway"
- Line 43: "in-ception" to "inception"
- Line 43: "ap-proaches" to "approaches"
- Line 46: "method-ologies" to "methodologies"
- Line 46: "anoma-lous" to "anomalous"
- Line 47: "en-gaged" to "engaged"
- Line 51: "mainte-nance" to "maintenance"
- Line 53: "charac-teristics" to "characteristics"
- Line 60: "model-ing" to "modeling"
- Line 68: "influ-ence" to "influence"
- Line 68: "spall-ing" to "spalling"
- Line 71: "mod-eling" to "modeling"
- Line 78: "bear-ing" to "bearing"
- Line 79: "micro-scopic" to "microscopic"
These corrections address the edition problems and ensure that the language is consistent and clear throughout the manuscript. Thank you for pointing out these issues
- The absence of an image depicting the analyzed bearing at the outset of the article hinders readers' ability to visualize the FEA models discussed later on. Including such an image would aid comprehension and engagement.
Answer: Image 9 has been added. Through the real bearing image to facilitate the reader's understanding.
- In lines 149-150, the presence of an initial crack in Figure 7 is mentioned, but the precise location of this crack within the figure is not specified. Providing clear annotation or indication of the crack's position would improve the clarity of the analysis.
Answer: The description associated with Figure 7 has been supplemented with information about the accepted crack model. The figure has been updated, and details about the crack have been added on Line 166:
" Figure 10 shows the mises stress simulation of an initial spalling crack with an initial an-gle of 90° and a length of 0.01mm at the edge of the spalling region after a propagation with a deflection angle of 55.92°. At this time, the initial crack depth is 0.02mm."
This addition provides a more detailed understanding of the initial crack model used in the simulation.
- Reference to Figure 18 in line 253 is likely intended to refer to Figure 12.
Correcting this inconsistency would ensure accuracy in referencing and avoid
confusion for readers.
Answer: The reference to Figure 18 has been changed to a reference to Figure 15.
- The article lacks details regarding the software used for conducting analyses and the specifics of meshing. Given that all analyses were software-based, providing this information is crucial for reproducibility and comprehensiveness. Extending the software used and describing the meshing process in much more detail would improve the rigour and completeness of the study.
Answer:
The description of cell type and size of grid division is added in the simulation modeling related description. Description is added to line 140:
"In the model, CPS4R cells are used for meshing, and the cell length is refined to 0.002mm at the contact point."
Then the description related to the simulation software calculations has been supplemented by the description of the stress-intensity factor calculation methods. The description is added to Line175:
" In finite element simulation software, the contour integral method (CIM) is frequently utilized to calculate the SIF at the crack front. This method is a prevalent numerical tech-nique specifically designed for determining the SIF, making it particularly well-suited for addressing crack problems in finite element analysis. The CIM involves the integration of the stress field along a contour that encircles the crack, thereby allowing the computation of the SIF. This technique is versatile and can be applied to a wide range of crack types and loading conditions."
These addition provides a more detailed understanding of the method for calculating stress intensity factors on crack tips in simulation software.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsThis is a paper on the numerical simulation of the evolution of spalling due to surface contact. The authors performed finite element analysis in the calculation of stress intensity and used the Paris law to estimate the spalling crack. The following is a list of comments.
1. The introduction is disorganized. It is unclear what the authors tried to address.
2. The authors stated that EHL would be used in the analysis. However, there is no information on the EHL analysis.
3. The method used in the work is well known, and contact deformation has been widely reported in literature.
4. There is no new information added to literature.
Comments on the Quality of English LanguageThe introduction is disorganized.
Author Response
Author's Response to Reviewer
Dear Reviewer,
We extend our heartfelt gratitude for your invaluable feedback on our manuscript. We deeply appreciate the time and effort you have devoted to reviewing our work and offering insightful suggestions.
Below are our responses to the questions and suggestions you raised:
- The introduction is disorganized. It is unclear what the authors tried to address.
Answer: To improve clarity and organization, the introduction has been revised to include a detailed explanation of the spalling fault evolution on the bearing raceway surface, as illustrated in Figure 1. Additionally, more comprehensive descriptions of the spalling fault evolution mechanism studied in this paper have been incorporated. Several spelling errors in the introduction have also been corrected to enhance readability and coherence.
- The authors stated that EHL would be used in the analysis. However, there is no information on the EHL analysis.
Answer: The description related to the EHL model in the introduction has been removed. Instead, references are provided when discussing the calculation results shown in Figure 8. This ensures that the focus remains on the relevant analysis presented in the study.
- The method used in the work is well known, and contact deformation has been widely reported in literature.
Answer: Thank you for your feedback. While it is accurate that the methods employed in our study are well-established and that contact deformation is a widely recognized phenomenon, the novelty and relevance of our research stem from its specific application to the evolutionary accelerated testing of bearing spalling faults. This approach is critical in industrial contexts where bearing lifetimes are intentionally shortened through pre-processing to induce spalling defects. Such methodologies require a deep understanding of the deformation mechanisms near spalling regions to accurately assess and optimize the acceleration factors used in these tests.
Our study contributes to this field by providing detailed insights into the expansion mechanisms of spalling, which have not been exhaustively explored in the context of accelerated life testing. By focusing on this aspect, we offer valuable data that can enhance the reliability and effectiveness of accelerated testing protocols. This, in turn, can lead to more accurate prediction models for bearing failure, ultimately contributing to better maintenance schedules and reduced downtime in industrial applications.
Furthermore, our research serves as a foundational study that can guide future investigations aiming to refine acceleration factors and improve the predictive capabilities of existing models. This is crucial for advancing the state of knowledge in bearing spalling and for developing more sophisticated and precise testing methods in the field.
In summary, although the basic methodologies are familiar, the application and the detailed examination of spalling expansion mechanisms provide significant value to both academic research and practical applications in bearing lifespan analysis. Thank you again for your constructive comment, which highlights an important aspect of our research's relevance and application.
- There is no new information added to literature.
Answer: Thank you for your observation regarding the contribution of our research to the existing body of literature. We acknowledge the importance of presenting novel insights, and we would like to clarify how our work extends beyond merely corroborating well-established models.
In our study, we utilize finite element simulation and a two-dimensional crack propagation model to analyze the spalling crack propagation mechanism. While these methodologies are indeed established within the field, the distinctiveness of our research lies in the specific application and refinement of these techniques to model the evolution of bearing spalling faults under various stress conditions and operational environments.
By integrating these models, our work offers a comprehensive understanding of the spalling behavior in high-reliability and long-life bearings, which is crucial for the design and testing of such components. This approach not only validates existing theories under new or more extreme conditions but also enhances the predictive capabilities of spalling progression, thus providing valuable insights into fatigue testing improvements.
Moreover, our research addresses a significant gap by quantifying the impact of different variables on the spalling process, which has not been extensively explored in the current literature. This contributes to a more robust framework for developing advanced fatigue tests that can lead to significant enhancements in bearing lifespan and reliability.
To further underline the novelty of our findings, we have revised our manuscript to emphasize these unique contributions more clearly. We appreciate your feedback, as it has provided us with an opportunity to better articulate the value and innovation of our research within the context of existing knowledge.
Author Response File: Author Response.docx
Reviewer 3 Report
Comments and Suggestions for AuthorsPresented problem is practically and scientifically interesting. I propose to publish the manuscript but after several corrections:
- new, original elements of investigations should be underlined,
- some edition problems, like parame-ters should be changed,
- the examined model (Figs 3,4) should be presented more clear,
- the accepted method, numerical program, technique of the analysis should be described wider,
- the notations in Fig.10 KI, KII should be improved,
- the description connected with Fig. 7, where the initial crack is presented should be supplemented with the information about the accepted crack model.
Author Response
Author's Response to Reviewer
Dear Reviewer,
We would like to express our heartfelt gratitude for your invaluable feedback on our manuscript. We deeply appreciate the time and effort you have devoted to reviewing our work and providing such insightful suggestions.
Below, we have addressed the questions and suggestions you raised:
- New, original elements of investigations should be underlined.
Answer: Figure 1 has been added to the introduction to enhance the reader's understanding of the spalling fault evolution process described in this paper. This visual aid underlines the new and original elements of our investigation, providing a clearer context for the study and highlighting the novel aspects of our research approach.
- Some edition problems, like ‘parame-ters’ should be changed
Answer: The spelling issues have been corrected as follows:
- Line 13: "pro-posed" to "proposed"
- Line 23: "bear-ings" to "bearings"
- Line 25: "race-way" to "raceway"
- Line 43: "in-ception" to "inception"
- Line 43: "ap-proaches" to "approaches"
- Line 46: "method-ologies" to "methodologies"
- Line 46: "anoma-lous" to "anomalous"
- Line 47: "en-gaged" to "engaged"
- Line 51: "mainte-nance" to "maintenance"
- Line 53: "charac-teristics" to "characteristics"
- Line 60: "model-ing" to "modeling"
- Line 68: "influ-ence" to "influence"
- Line 68: "spall-ing" to "spalling"
- Line 71: "mod-eling" to "modeling"
- Line 78: "bear-ing" to "bearing"
- Line 79: "micro-scopic" to "microscopic"
- The examined model (Figs 3,4) should be presented more clear
Answer: Figure 5 is added to illustrate the size parameters of the model and the corresponding constraints.
- The accepted method, numerical program, technique of the analysis should be described wider.
Answer: To provide a more comprehensive description of the accepted method, numerical program, and technique of the analysis:
- Line 115 has been expanded to include a description of the spalling fault evolution model based on existing three-dimensional cases, and it explains the feasibility of using a two-dimensional model in this study.
- References [25] and [26] have been added to support the formula calculations, enhancing the reliability of the analysis.
- Line 176 now includes an introduction to the specific methods used for calculating stress intensity factors, demonstrating that these methods are commonly employed in software analysis.
These additions aim to offer a wider and clearer understanding of the methodologies and techniques utilized in the study, ensuring that the analysis is well-documented and credible.
- The notations in Fig.10 KI, KII should be improved.
Answer: The notations in Figure 10 have been improved. The labels and units for KI and KII have been replaced and updated in Figure 13.
- The description connected with Fig. 7, where the initial crack is presented should be supplemented with the information about the accepted crack model.
Answer: The description associated with Figure 7 has been supplemented with information about the accepted crack model. The figure has been updated, and details about the crack have been added on Line 166:
" Figure 10 shows the mises stress simulation of an initial spalling crack with an initial an-gle of 90° and a length of 0.01mm at the edge of the spalling region after a propagation with a deflection angle of 55.92°. At this time, the initial crack depth is 0.02mm."
This addition provides a more detailed understanding of the initial crack model used in the simulation.
Author Response File: Author Response.docx
Reviewer 4 Report
Comments and Suggestions for AuthorsThe paper studies a model for spalling failure evolution in a bearing. A relevant field of study, which also could be applied to other applications. It is giving a good introduction to the topic and presents ways to approach, study and analyze the type of problem.
It could be good to add a picture already in the introduction to illustrate the type of fault in the problem. That would make it easier to understand the type of spalling fault that you study.
You could add referneces to Paris formula. It is a common model, but it is not included in most basic texts books. So it could be good to add references for further reading for students and scholars that are new in the topic.
Comments on the Quality of English LanguageThe language is in general good and easy to understand. Some minor improvments could be done in the abstract to make sure that the language is correct. Otherwise: the main thing to correct is the hyphens that are appearing randomly in the text (in some words) on the first page. Example: bear-ing, ori-gins, etc etc, en-gaged. But i am sure you see it and easily will fix it.
Author Response
Author's Response to Reviewer
Dear Reviewer,
We extend our heartfelt gratitude for your meticulous review and valuable feedback on our manuscript. Your insightful suggestions and the time you invested in evaluating our work are deeply appreciated.
Below, we address the questions and suggestions you raised:
- It could be good to add a picture already in the introduction to illustrate the type of fault in the problem. That would make it easier to understand the type of spalling fault that you study.
Answer: Figure 1 has been added to the introduction to illustrate the type of spalling fault under study, enhancing the reader's understanding of the problem.
- You could add referneces to Paris formula. It is a common model, but it is not included in most basic texts books. So it could be good to add references for further reading for students and scholars that are new in the topic.
Answer: References to Paris' formula have been added to Line 191.
- The language is in general good and easy to understand. Some minor improvments could be done in the abstract to make sure that the language is correct. Otherwise: the main thing to correct is the hyphens that are appearing randomly in the text (in some words) on the first page. Example: bear-ing, ori-gins, etc etc, en-gaged. But i am sure you see it and easily will fix it.
Answer: The language in the abstract has been refined to ensure correctness. Additionally, the random hyphens appearing in the text on the first page have been corrected as follows:
- Line 13: "pro-posed" to "proposed"
- Line 23: "bear-ings" to "bearings"
- Line 25: "race-way" to "raceway"
- Line 43: "in-ception" to "inception"
- Line 43: "ap-proaches" to "approaches"
- Line 46: "method-ologies" to "methodologies"
- Line 46: "anoma-lous" to "anomalous"
- Line 47: "en-gaged" to "engaged"
- Line 51: "mainte-nance" to "maintenance"
- Line 53: "charac-teristics" to "characteristics"
- Line 60: "model-ing" to "modeling"
- Line 68: "influ-ence" to "influence"
- Line 68: "spall-ing" to "spalling"
- Line 71: "mod-eling" to "modeling"
- Line 78: "bear-ing" to "bearing"
- Line 79: "micro-scopic" to "microscopic"
These corrections have been made to enhance the readability and accuracy of the manuscript.
Author Response File: Author Response.docx
Reviewer 5 Report
Comments and Suggestions for AuthorsThe article proposes a numerical approach for analysing crack propagation in bearings in the presence of spalling. Specifically, a two-dimensional model has been proposed to examine rectangular spalling (from a two-dimensional perspective). The topic is interesting, although it has been addressed in other articles before. I think the model should be better described. I believe that, before being published, it needs a major review.
1. The introduction, despite being detailed, show many typos: for example, ow-ing, ap-proaches and so on (there are at least 17 words misspelled in this way)
2. I think it is better to use a white background in the Finite Element figures. Also the legend background should be edited.
3. The FE model should be more detailed: it is not clear if you used a plain stress or strain 2D element, what are the dimensions of the model? The roller is not modelled as elastic, why? How is the model constrained? How were the loads applied? If the crack is modelled, which properties were applied?
4. Page 6: please, amend the capital letters after the equations.
5. The authors estimate the crack propagation rate: which Paris’ law coefficients were applied?
6. I don't think I understood how the SIF was calculated from the FE model: did you use any technique implemented in the software or did you extrapolate some results from the simulations and, then, calculated the SIF?
7. Figure 10: please, amend the unit of measure of SIF.
8. Page 9, simulations for positions L and R: “Q is changed to half of its original value”, is the model symmetric? I'm missing the reason why you applied a halved load.
9. Please, report the reference to Eq. 4.
10. Your model is planar; consequently, no mode III can be detected. Do you think it is reasonable? There are several papers where mode III propagation in bearings crack is investigated.
Comments on the Quality of English LanguageThe introduction, despite being detailed, show many typos: for example, ow-ing, ap-proaches and so on (there are at least 17 words misspelled in this way)
Author Response
Author's Response to Reviewer
Dear Reviewer,
We sincerely appreciate your thoughtful and detailed feedback on our manuscript. Your comments and suggestions have been invaluable, and we are grateful for the time and effort you invested in reviewing our work.
Please find below our responses to the questions and suggestions you raised:
- The introduction, despite being detailed, show many typos: for example, ow-ing, ap-proaches and so on (there are at least 17 words misspelled in this way)
Answer: We have corrected the spelling errors throughout the introduction as follows:
- Line 13: "pro-posed" to "proposed"
- Line 23: "bear-ings" to "bearings"
- Line 25: "race-way" to "raceway"
- Line 43: "in-ception" to "inception"
- Line 43: "ap-proaches" to "approaches"
- Line 46: "method-ologies" to "methodologies"
- Line 46: "anoma-lous" to "anomalous"
- Line 47: "en-gaged" to "engaged"
- Line 51: "mainte-nance" to "maintenance"
- Line 53: "charac-teristics" to "characteristics"
- Line 60: "model-ing" to "modeling"
- Line 68: "influ-ence" to "influence"
- Line 68: "spall-ing" to "spalling"
- Line 71: "mod-eling" to "modeling"
- Line 78: "bear-ing" to "bearing"
- Line 79: "micro-scopic" to "microscopic"
- I think it is better to use a white background in the Finite Element figures. Also the legend background should be edited.
Answer: The background color of the figures in the Finite Element simulations has been adjusted as suggested:
- Figures 3, 4, 6, and 10 now feature a white background.
We appreciate your recommendation to enhance the clarity and readability of these figures. This change has indeed made the diagrams more accessible and visually appealing. Thank you for your attentive and constructive feedback.
- The FE model should be more detailed: it is not clear if you used a plain stress or strain 2D element, what are the dimensions of the model? The roller is not modelled as elastic, why? How is the model constrained? How were the loads applied? If the crack is modelled, which properties were applied?
Answer: The details and parameters of the Finite Element (FE) model have been enhanced as suggested:
- The description of the model setup, including the type of elements used (plain stress or strain 2D elements), the dimensions of the model, and other specifics, has been added to Line 126.
- Additional details on the constraints and load applications, the elastic properties of the roller, and the properties applied to the modeled crack are now included and depicted in Figure 5.
These updates aim to clarify the modeling approach and provide a comprehensive understanding of the simulation conditions. We are grateful for your observations, which have significantly improved the transparency and thoroughness of our presentation. Thank you for your guidance.
- Page 6: please, amend the capital letters after the equations.
Answer: The case of the letters following the equations has been corrected as suggested:
Line 193, 202, 203, 214: "Where" has been changed to "where."
- The authors estimate the crack propagation rate: which Paris’ law coefficients were applied?
Answer: The parameter values for Paris’ law, which are used to estimate the crack propagation rate, have been added to Line 224 of the manuscript.
- I don't think I understood how the SIF was calculated from the FE model: did you use any technique implemented in the software or did you extrapolate some results from the simulations and, then, calculated the SIF?
Answer: The methodology for calculating the SIF at the crack tip using finite element software has been detailed in Line 176 of the manuscript.
- Figure 10: please, amend the unit of measure of SIF.
Answer: The units of measurement for the SIF in Figure 13 have been corrected as suggested.
- Page 9, simulations for positions L and R: “Q is changed to half of its original value”, is the model symmetric? I'm missing the reason why you applied a halved load.
Answer: The explanation regarding the application of a halved load during simulations for positions L and R has been clarified in Line 264 of the manuscript:
"When the roller rolls through the center of the spalling region, the forces are symmetrical in the L and R directions."
This addition provides context for why the load was adjusted to half of its original value, explaining the symmetrical nature of the model under these specific conditions. We appreciate your query, as it highlighted a need for clearer exposition in our description. Thank you for helping us improve the completeness of our manuscript.
- Please, report the reference to Eq. 4.
Answer: References [25] and [26] have been added to Line 208, to provide the necessary citations for Equation 4.
- Your model is planar; consequently, no mode III can be detected. Do you think it is reasonable? There are several papers where mode III propagation in bearings crack is investigated.
Answer: A description of the feasibility of 2D model modeling is added to Line 115:
“In reference [20], a three-dimensional crack propagation model is established. In this model, the center of the spalling region coincides with the maximum stress point of the bearing outer ring. The results show that the crack torsion angle caused by mode III crack is basically within the range of 10 degrees. Therefore, it is feasible to establish a two-dimensional crack propagation model without considering mode III crack to analyze the evolution process of spalling fault of angular contact ball bearings.”
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsDear Authors,
I appreciate the care and attention you have given to addressing each point.
I have no further comments. Thank you for your valuable contributions to the study.
Best regards,
Reviewer 3 Report
Comments and Suggestions for AuthorsThe manuscript has been improved. Problem is valuable and interesting so I propose publishing.
Reviewer 5 Report
Comments and Suggestions for AuthorsThe paper can be accepted in present form.
