Geometrical Optimization of the EHL Roller Face/Rib Contact for Energy Efficiency in Tapered Roller Bearings
Round 1
Reviewer 1 Report
Comments and questions:
It is quite necessary to reduce the energy consumption of taper roller bearings by optimal design of contacts. The main purpose of this paper is to evaluate the tribological properties of the face roller/rib contacts with different geometry parings. And the predictions with the machine learning approach were verified by EHL simulations.
- The authors consider the shear-thinning effect by introducing the Ree-Eyring model, but the thermal-thinning effect induced by the sliding component might also impact the tribological behaviors.
- In practice, the running conditions are usually unstable, the speed and load imposed on the contacts may instantaneously vary, causing changes in sliding-rolling ratios and hence the frictional losses.
Author Response
Response to reviewers
Dear editors, dear reviewers,
we would like to thank you for your feedback and the opportunity to resubmit a revised version of our manuscript entitled "Geometrical optimization of the EHL roller face/rib contact for energy efficiency in tapered roller bearings".
We would also like to take this opportunity to express our thanks to the learned reviewers for the positive feedback and helpful comments. Based on the instructions provided by the reviewers, we uploaded the file of the revised manuscript with changes highlighted in yellow. Furthermore, we have responded specifically to each suggestion below.
It is our belief that the manuscript has substantially improved after making the suggested edits. We hope the revised version will be received favorably and are looking forward to hearing from you in the near future.
Sincerely yours
Sven Wirsching and Max Marian
Point-by-point responses
Reviewer #1:
It is quite necessary to reduce the energy consumption of taper roller bearings by optimal design of contacts. The main purpose of this paper is to evaluate the tribological properties of the face roller/rib contacts with different geometry parings. And the predictions with the machine learning approach were verified by EHL simulations.
Response:
The authors would like to thank the reviewer for his/her positive feedback as well as the helpful comments. We have addressed the raised points below. Changes in the manuscript are highlighted in yellow.
Comment #1:
The authors consider the shear-thinning effect by introducing the Ree-Eyring model, but the thermal-thinning effect induced by the sliding component might also impact the tribological behaviors.
Response:
We absolutely agree that thermal-thinning effects might also impact the tribological behavior of the roller end face/rib spinning EHL contact. Taking them into account, however, also increases computational costs and may cause instabilities for certain factor combinations, which is why they were neglected considering the large number of calculations performed within the DoE. Yet, we assume that the consideration aforementioned points would rather lead to quantitative differences and that the qualitative assertions remain valid. We have added such statements in section 4.2, where we discussed the applicability and limitations of our manuscript.
Comment #2:
In practice, the running conditions are usually unstable, the speed and load imposed on the contacts may instantaneously vary, causing changes in sliding-rolling ratios and hence the frictional losses.
Response:
Within the scope of this contribution, only a pure axial load case was investigated. Given that applied normal load and the rotational speed of the bearing are constant, the stable conditions for the roller end face/rib EHL contact are valid. However, we absolutely agree with the learned reviewer that the operating conditions may vary in practice and that and that radial loads lead to the formation of a load zone and thus to variable forces and speeds for each individual roller end face/rib EHL contact during one revolution of the bearing. Again, we have added some statements in section 4.2, where we discussed the applicability and limitations of our manuscript.
Thanks again for the detailed evaluation of our study and valuable comments. We are convinced that the manuscript has gained in quality and hope our revised version will be received favorably.
Reviewer #2:
This work presents a geometrical optimization of the EHL roller face / rib contact in tapered roller bearings. The proposed methodology combines Machine Learning (ML), Optimization Techniques and EHL Simulations. The authors are commended for undertaking such a project, which shows once more the potential of using advanced technologies like ML, in the analysis of tribological systems. Overall, the manuscript is very well-written, and the proposed results are novel and interesting. The manuscript can be accepted for publication in Lubricants. Below are a few suggestions for improvement:
Response:
The authors are particularly grateful for the positive feedback as well as the detailed and specific comments. We have addressed mentioned points below (changes in the manuscript are highlighted in yellow) and believe that the manuscript was substantially improved after suggested edits.
Comment #1:
Literature review: It is true that the literature on such contacts with spinning (as roller face / rib) is rather scarce, but there are in my opinion a few works that were omitted by the authors. Particularly, Philippe Vergne and his team at INSA de Lyon (in collaboration with SKF R&D) published some experimental (on a test bench called TRIBOGYR) and numerical work on EHL contacts with spinning (typical of roller face / rib contacts) in the last decade. Such works should be mentioned in the literature review here for their relevance.
Response:
Thank you for making us aware of this. So far, our literature review mainly accounted for investigations with a specific focus on the roller end face/rib EHL contact. We now have expanded this a bit to cover more general aspects of spinning EHL contacts and also included works from the group mentioned.
Comment #2:
Page 4, lines 118-122: The Dowson & Higginson, Roelands and Ree-Eyring relations should be provided, out of completeness, and in order for the reader to fully understand / identify the parameters of Table 1. In addition, the authors are advised to add a statement that a better rheological characterization of the lubricant would be due if a quantitative evaluation of lubrication performance (particularly friction) was sought. Given that the current analysis is rather qualitative, it is acceptable that the authors employ rather simplistic rheological models, which parameters are often chosen in a non-rigorous way (e.g. Eyring stress), to force agreement with experiments.
Response:
We have included the corresponding equations for the models. We also appreciate the additional comments and have included a respective statement on the rheological characterization in section 4.2 (applicability and limitations).
Comment #3:
Table 2: The units of the pressure-viscosity coefficient and the pressure limiting shear stress are missing.
Response:
Thank you for pointing this out. We have completed the units.
Comment #4:
Equation (12) provides the distance between the two rigid bodies to the projection plane for the case of a sphere. How about the expressions for torus and cone? These should also be provided out of completeness.
Response:
We have added the respective equations.
Comment #5:
Page 6, line 182: “initial viscosity and density” should be “ambient viscosity and density”.
Response:
We have changed this as suggested.
Comment #6:
Page 6, lines 183-184: This sentence is not clear. Isn’t the normalization of x done with respect to a’ and that of y done with respect to b’, as per equation (14)? If so, I also don’t understand why the calculation domain is rectangular (Page 6, lines 205-206)? It should be a square. All this requires some clarification.
Response:
In our case, the contact was normalized to the Hertzian contact width of an ideal point-contact, where a' is equal to b'. We see that this can be confusing and therefore have now clarified this by replacing b' with a' for the y-direction as well. This also determines the calculation domain as presented in the paper.
Comment #7:
Equation (17): I believe du/dx should be du/dz, no? Also, the function F should be provided.
Response:
The equation was correct. The function F(τ) was now provided in Eq. 10.
Comment #8:
Equations (18) and (19): What’s T? Is it the non-dimensional equivalent of t? Please clarify.
Response:
T corresponds to the temperature. However, this boundary condition is not necessary here, since the calculation is isothermal. We have adjusted the equations.
Comment #9:
Page 8, line 255: “exemplary results” should be “sample results”. The word “exemplary” means “ideal”, and it is inappropriately used here. The same applies to lines 260 and 269.
Response:
We have changed this as suggested.
Comment #10:
Sections 3.2, 3.3 and 3.4: The authors use throughout these sections the terminology “lubricant gab”. I believe they mean “lubricant gap”. If so, this should be corrected.
Response:
We are sorry for these mistakes and have corrected the text, tables and figures accordingly.
Comment #11:
Page 12, lines 316-316: The authors are referring to Figure 5 here, but I believe the reference should be to Figure 6. If so, please rectify.
Response:
Thank you for making us aware of this mistake. This has been corrected.
Thanks again for the detailed evaluation of our study and valuable comments. We honestly believe that the manuscript has gained in quality and hope our revised version will be received favorably.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
This work presents a geometrical optimization of the EHL roller face / rib contact in tapered roller bearings. The proposed methodology combines Machine Learning (ML), Optimization Techniques and EHL Simulations. The authors are commended for undertaking such a project, which shows once more the potential of using advanced technologies like ML, in the analysis of tribological systems. Overall, the manuscript is very well-written, and the proposed results are novel and interesting. The manuscript can be accepted for publication in Lubricants. Below are a few suggestions for improvement:
- Literature review: It is true that the literature on such contacts with spinning (as roller face / rib) is rather scarce, but there are in my opinion a few works that were omitted by the authors. Particularly, Philippe Vergne and his team at INSA de Lyon (in collaboration with SKF R&D) published some experimental (on a test bench called TRIBOGYR) and numerical work on EHL contacts with spinning (typical of roller face / rib contacts) in the last decade. Such works should be mentioned in the literature review here for their relevance.
- Page 4, lines 118-122: The Dowson & Higginson, Roelands and Ree-Eyring relations should be provided, out of completeness, and in order for the reader to fully understand / identify the parameters of Table 1. In addition, the authors are advised to add a statement that a better rheological characterization of the lubricant would be due if a quantitative evaluation of lubrication performance (particularly friction) was sought. Given that the current analysis is rather qualitative, it is acceptable that the authors employ rather simplistic rheological models, which parameters are often chosen in a non-rigorous way (e.g. Eyring stress), to force agreement with experiments.
- Table 2: The units of the pressure-viscosity coefficient and the pressure limiting shear stress are missing.
- Equation (12) provides the distance between the two rigid bodies to the projection plane for the case of a sphere. How about the expressions for torus and cone? These should also be provided out of completeness.
- Page 6, line 182: “initial viscosity and density” should be “ambient viscosity and density”.
- Page 6, lines 183-184: This sentence is not clear. Isn’t the normalization of x done with respect to a’ and that of y done with respect to b’, as per equation (14)? If so, I also don’t understand why the calculation domain is rectangular (Page 6, lines 205-206)? It should be a square. All this requires some clarification.
- Equation (17): I believe du/dx should be du/dz, no? Also, the function F should be provided.
- Equations (18) and (19): What’s T? Is it the non-dimensional equivalent of t? Please clarify.
- Page 8, line 255: “exemplary results” should be “sample results”. The word “exemplary” means “ideal”, and it is inappropriately used here. The same applies to lines 260 and 269.
- Sections 3.2, 3.3 and 3.4: The authors use throughout these sections the terminology “lubricant gab”. I believe they mean “lubricant gap”. If so, this should be corrected.
- Page 12, lines 316-316: The authors are referring to Figure 5 here, but I believe the reference should be to Figure 6. If so, please rectify.
Author Response
Response to reviewers
Dear editors, dear reviewers,
we would like to thank you for your feedback and the opportunity to resubmit a revised version of our manuscript entitled "Geometrical optimization of the EHL roller face/rib contact for energy efficiency in tapered roller bearings".
We would also like to take this opportunity to express our thanks to the learned reviewers for the positive feedback and helpful comments. Based on the instructions provided by the reviewers, we uploaded the file of the revised manuscript with changes highlighted in yellow. Furthermore, we have responded specifically to each suggestion below.
It is our belief that the manuscript has substantially improved after making the suggested edits. We hope the revised version will be received favorably and are looking forward to hearing from you in the near future.
Sincerely yours
Sven Wirsching and Max Marian
Point-by-point responses
Reviewer #1:
It is quite necessary to reduce the energy consumption of taper roller bearings by optimal design of contacts. The main purpose of this paper is to evaluate the tribological properties of the face roller/rib contacts with different geometry parings. And the predictions with the machine learning approach were verified by EHL simulations.
Response:
The authors would like to thank the reviewer for his/her positive feedback as well as the helpful comments. We have addressed the raised points below. Changes in the manuscript are highlighted in yellow.
Comment #1:
The authors consider the shear-thinning effect by introducing the Ree-Eyring model, but the thermal-thinning effect induced by the sliding component might also impact the tribological behaviors.
Response:
We absolutely agree that thermal-thinning effects might also impact the tribological behavior of the roller end face/rib spinning EHL contact. Taking them into account, however, also increases computational costs and may cause instabilities for certain factor combinations, which is why they were neglected considering the large number of calculations performed within the DoE. Yet, we assume that the consideration aforementioned points would rather lead to quantitative differences and that the qualitative assertions remain valid. We have added such statements in section 4.2, where we discussed the applicability and limitations of our manuscript.
Comment #2:
In practice, the running conditions are usually unstable, the speed and load imposed on the contacts may instantaneously vary, causing changes in sliding-rolling ratios and hence the frictional losses.
Response:
Within the scope of this contribution, only a pure axial load case was investigated. Given that applied normal load and the rotational speed of the bearing are constant, the stable conditions for the roller end face/rib EHL contact are valid. However, we absolutely agree with the learned reviewer that the operating conditions may vary in practice and that and that radial loads lead to the formation of a load zone and thus to variable forces and speeds for each individual roller end face/rib EHL contact during one revolution of the bearing. Again, we have added some statements in section 4.2, where we discussed the applicability and limitations of our manuscript.
Thanks again for the detailed evaluation of our study and valuable comments. We are convinced that the manuscript has gained in quality and hope our revised version will be received favorably.
Reviewer #2:
This work presents a geometrical optimization of the EHL roller face / rib contact in tapered roller bearings. The proposed methodology combines Machine Learning (ML), Optimization Techniques and EHL Simulations. The authors are commended for undertaking such a project, which shows once more the potential of using advanced technologies like ML, in the analysis of tribological systems. Overall, the manuscript is very well-written, and the proposed results are novel and interesting. The manuscript can be accepted for publication in Lubricants. Below are a few suggestions for improvement:
Response:
The authors are particularly grateful for the positive feedback as well as the detailed and specific comments. We have addressed mentioned points below (changes in the manuscript are highlighted in yellow) and believe that the manuscript was substantially improved after suggested edits.
Comment #1:
Literature review: It is true that the literature on such contacts with spinning (as roller face / rib) is rather scarce, but there are in my opinion a few works that were omitted by the authors. Particularly, Philippe Vergne and his team at INSA de Lyon (in collaboration with SKF R&D) published some experimental (on a test bench called TRIBOGYR) and numerical work on EHL contacts with spinning (typical of roller face / rib contacts) in the last decade. Such works should be mentioned in the literature review here for their relevance.
Response:
Thank you for making us aware of this. So far, our literature review mainly accounted for investigations with a specific focus on the roller end face/rib EHL contact. We now have expanded this a bit to cover more general aspects of spinning EHL contacts and also included works from the group mentioned.
Comment #2:
Page 4, lines 118-122: The Dowson & Higginson, Roelands and Ree-Eyring relations should be provided, out of completeness, and in order for the reader to fully understand / identify the parameters of Table 1. In addition, the authors are advised to add a statement that a better rheological characterization of the lubricant would be due if a quantitative evaluation of lubrication performance (particularly friction) was sought. Given that the current analysis is rather qualitative, it is acceptable that the authors employ rather simplistic rheological models, which parameters are often chosen in a non-rigorous way (e.g. Eyring stress), to force agreement with experiments.
Response:
We have included the corresponding equations for the models. We also appreciate the additional comments and have included a respective statement on the rheological characterization in section 4.2 (applicability and limitations).
Comment #3:
Table 2: The units of the pressure-viscosity coefficient and the pressure limiting shear stress are missing.
Response:
Thank you for pointing this out. We have completed the units.
Comment #4:
Equation (12) provides the distance between the two rigid bodies to the projection plane for the case of a sphere. How about the expressions for torus and cone? These should also be provided out of completeness.
Response:
We have added the respective equations.
Comment #5:
Page 6, line 182: “initial viscosity and density” should be “ambient viscosity and density”.
Response:
We have changed this as suggested.
Comment #6:
Page 6, lines 183-184: This sentence is not clear. Isn’t the normalization of x done with respect to a’ and that of y done with respect to b’, as per equation (14)? If so, I also don’t understand why the calculation domain is rectangular (Page 6, lines 205-206)? It should be a square. All this requires some clarification.
Response:
In our case, the contact was normalized to the Hertzian contact width of an ideal point-contact, where a' is equal to b'. We see that this can be confusing and therefore have now clarified this by replacing b' with a' for the y-direction as well. This also determines the calculation domain as presented in the paper.
Comment #7:
Equation (17): I believe du/dx should be du/dz, no? Also, the function F should be provided.
Response:
The equation was correct. The function F(τ) was now provided in Eq. 10.
Comment #8:
Equations (18) and (19): What’s T? Is it the non-dimensional equivalent of t? Please clarify.
Response:
T corresponds to the temperature. However, this boundary condition is not necessary here, since the calculation is isothermal. We have adjusted the equations.
Comment #9:
Page 8, line 255: “exemplary results” should be “sample results”. The word “exemplary” means “ideal”, and it is inappropriately used here. The same applies to lines 260 and 269.
Response:
We have changed this as suggested.
Comment #10:
Sections 3.2, 3.3 and 3.4: The authors use throughout these sections the terminology “lubricant gab”. I believe they mean “lubricant gap”. If so, this should be corrected.
Response:
We are sorry for these mistakes and have corrected the text, tables and figures accordingly.
Comment #11:
Page 12, lines 316-316: The authors are referring to Figure 5 here, but I believe the reference should be to Figure 6. If so, please rectify.
Response:
Thank you for making us aware of this mistake. This has been corrected.
Thanks again for the detailed evaluation of our study and valuable comments. We honestly believe that the manuscript has gained in quality and hope our revised version will be received favorably.
Author Response File: Author Response.pdf
