Rolling Tires on the Flat Road: Thermo-Investigation with Changing Conditions through Numerical Simulation

Round 1

Reviewer 1 Report

The degree of novelty is too low, the results are already known.

Not all results are correct: The maximum tire temperature will not increase with increasing inflation pressure.

For more details, please refer to the comments in the script.

 

Comments for author File: Comments.pdf

Author Response

Comments and Suggestions for Authors:

Authors can solve all remark in the “applsci-2257075_Reviewer#1-Comments” file.

 

Thank you for your comments and recommendations. Some answers are included here. The authors have solved and changed other comments in the revised draft.

 

Question: Are you planning on releasing the final mesh/model together with the paper? This would be great for others who want to also conduct simulations with a tire.

Answer: Unfortunately, there is no specific model for tire meshing using ANSYS ICEM software, so there’s nothing to be released. However, I will always be willing to help anyone who wants to create a mesh for tires using this software.

Question: How is the boundary applied to the rim? Is the rim considered rigid to a reference point? Or is it coupled elastically with this reference point from 3a

Answer: The author used a boundary condition named remote force, which applies a force to the inner surface of the rim via a remote point (the center point in Fig. 3a). This type of boundary is similar to the bearing load in Abaqus. On the other hand, the rim is made of structural steel and is not rigid.

Question: Please describe which maneuvre is simulated (free rolling, acceleration/braking, ...) and how this is achieved (e.g. torque applied to rim or not).

Answer: It is a free-rolling tire with respect to the road. In this case, the velocity is applied to the road for rolling analysis, and the rim is fixed at the center point. The rim is considered to have a fixed position with respect to the center point in any direction and free rolling around the x-axis.

Question: The heat transfer is strongly dependend on the driving speed (relative air speed). Has this been taken into account?

The transfer coefficient to the air seems to be very small in comparison to the transfer coefficient between the tread and road. Has standing air been used for modelling?

Answer: The heat transfer coefficients are taken from another literature (Ref. no. 22), and they assume that the heat transfer coefficients are constant. The author used standing air for the simulations.

Question: Please state how the friction is created (different speeds for tire and road)?

Answer: This friction is created by applying a frictional contact between the two parts.

Question: using the same colors for the scale in all 3 pictures should be used for a comparison.

Answer: Unfortunately, as far as I am concerned, the ANSYS Mechanical software does not allow users to change the maximum and minimum values of the color bar.

Question: Do you have an explanation for this effect? The sidewall is essentially stressed by the vertical deformation and this should surely be almost independent of the coefficient of friction.

Answer: From Ref. no. 22, the authors stated that “the high temperature area moves from the sidewall to the shoulder then to the tread with the increase of Young’s modulus of body-ply”. Thus, the authors think that the stiffness of the body-ply is not hard enough to overcome this phenomenon. The reason why it appeared with a friction coefficient of 0.5, we think that it is because the high friction increases the load on the rubber part along with the increasing temperature.

Question: Are the ranges for the load and pressure comparable? The range in load (100 kg to 600 kg) seems to be much bigger to me than the range for pressure (27 psi to 35 psi). Thus, a comparison does not make much sense for me.

A comparison would only make sense for me if the ranges were reasonable comparable (e.g. loads for a range of different cars as well as different tire pressures for these cars).

Answer: the load investigated in the paper ranges from lightweight to averaged size sedan cars or lightweight trucks. Moreover, the tire pressure studied is generally for small and medium-size cars. This is the range studied by the author to adapt to our need for research.

Question: The result cannot be right. The temperature must decrease with increasing tire inflation pressure due to the lower deformation.

Answer: the temperature is indeed higher with a lower inflation pressure of the tire with high load and high velocity due to the friction of the tire and the road. It is also concluded in many literatures. However, there are still some cases where the tire pressure and temperature are proportional. In fact, the load of the investigation is average, and the inflated pressure is low due to the conditions of the chosen vehicles. It is also observed in some literatures that the temperature is not always decreased with raising pressure. The reviewer should take a look at this paper: “Smith et al. - Simulation of Thermal Signature of Tires and Tracks. Simulation of thermal signature of tires and tracks. Mississippi State Univ Mississippi State Center for Advanced Vehicular Systems, 2012”. It does not have a DOI, but as far as I am concerned, this paper can be searched on google scholar. These explanations are added to the revised draft.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper investigates the temperature and heat flow generated by a rolling tire, with a specific focus on the hysteresis effects caused by the rubber component deformation. By utilizing the finite element method, the study examines the temperature and heat flow distributions of a tire under different conditions, with a simplified model consisting of rubber, body-ply, wire, and rim components. The study analyzes the combined effects of inflation pressure and vehicle loads on the tire temperature, and the heat flow distributions are obtained through steady-state thermal analysis. However, the article lacks comprehensive analysis of the tire temperature variations under multiple conditions and their mutual influence. The authors are suggested to have substantial revisions to improve.

 1.      The abstract and conclusion suggest that load has a more significant effect on tire temperature than the inflation pressure and speed. However, the units of load, tire pressure and speed differ, which may not be an appropriate comparison.

2.      Corrections should be made to the font size of the label in Figure 1 as it is too small.

3.      There is a repetition of the word "homogeneous" in Line 108.

4.      Further details such as element type, number of elements and element connection should be provided in the description of the finite element model of the hollow slab bridge in Lines 114-117.

5.      The sentence "the rim is considered to have constant displacement in any direction other than free rolling" in Lines 132-133 requires clarification.

6.      The range of speed in Table 3 is from 20 to 80km/h, while in Figure 13 it is from 20 to 140km/h, not consistent.

7.      The sentence in Lines 258-260 is ambiguous. It should be stated that when velocity increased from 20 to 40km/h, the strain energy density increased.

8.      The term "heat flux" in Line 304 should be replaced with "temperature."

Author Response

Comments and Suggestions for Authors:

This paper investigates the temperature and heat flow generated by a rolling tire, with a specific focus on the hysteresis effects caused by the rubber component deformation. By utilizing the finite element method, the study examines the temperature and heat flow distributions of a tire under different conditions, with a simplified model consisting of rubber, body-ply, wire, and rim components. The study analyzes the combined effects of inflation pressure and vehicle loads on the tire temperature, and the heat flow distributions are obtained through steady-state thermal analysis. However, the article lacks comprehensive analysis of the tire temperature variations under multiple conditions and their mutual influence. The authors are suggested to have substantial revisions to improve.

 

1. The abstract and conclusion suggest that load has a more significant effect on tire temperature than the inflation pressure and speed. However, the units of load, tire pressure and speed differ, which may not be an appropriate comparison.

Answer: Thank you for your comment, the authors eliminated this conclusion in the revised draft.

2. Corrections should be made to the font size of the label in Figure 1 as it is too small.

Answer: Thank you for your remark, the size of Figure 1 is appropriately scaled.

3. There is a repetition of the word "homogeneous" in Line 108.

Answer: Thank you for your remark, the line is adequately changed.

4. Further details such as element type, number of elements and element connection should be provided in the description of the finite element model of the hollow slab bridge in Lines 114-117.

Answer: Thank you for your recommendation, those details are added to the revised draft.

5. The sentence "the rim is considered to have constant displacement in any direction other than free rolling" in Lines 132-133 requires clarification.

Answer: Thank you for your recommendation, the sentence is corrected.

6. The range of speed in Table 3 is from 20 to 80km/h, while in Figure 13 it is from 20 to 140km/h, not consistent.

Answer: Thank you for your remark, the range from the table is corrected.

7. The sentence in Lines 258-260 is ambiguous. It should be stated that when velocity increased from 20 to 40km/h, the strain energy density increased.

Answer: Thank you for your comment, the sentence is properly corrected.

8. The term "heat flux" in Line 304 should be replaced with "temperature."

Answer: Thank you for your remark, the term in the revised draft is corrected.

Author Response File: Author Response.pdf

Reviewer 3 Report

1.       Abstract needs to be revised. Rubber is the material used in tires not a part.

2.       Line 67. Usage of finite element method instead of finite element technique is advised.

3.       Rewrite line 96. It’s not rubber’s size.

4.       Which kind of rubber is used in manufacturing the tire. Have the authors done experimental investigation to acquire Mooney-Rivlin constants, if so, then justify it’s usage compared to other material models. If authors have taken MR constants from literature, then please acknowledge them.

5.       How hysteresis is calculated.

6.       Have authors calibrated the steady state rolling (SSR) prior to dynamic rolling?

7.       Authors are advised to discuss more about the thermo-mechanical model.

TThe quality of images is very poor which can be improved.

9The conclusion needs to be elaborated in terms of quantitative data.

1 Title needs to be changed.

Author Response

Comments and Suggestions for Authors:

1. Abstract needs to be revised. Rubber is the material used in tires not a part.

Answer: Thank you for your comment, the abstract is revised and corrected adequately.

2. Line 67. Usage of finite element method instead of finite element technique is advised.

Answer: Thank you for your recommendation, the line is corrected as recommended.

3. Rewrite line 96. It’s not rubber’s size.

Answer: Thank you for your remark, the sentence is corrected.

4. Which kind of rubber is used in manufacturing the tire. Have the authors done experimental investigation to acquire Mooney-Rivlin constants, if so, then justify it’s usage compared to other material models. If authors have taken MR constants from literature, then please acknowledge them.

Answer: Thank you for your comment, the authors have taken those constants from other literature, and the authors cited this information in the revised draft.

5. How hysteresis is calculated.

Answer: Thank you for your comment, the authors have taken the other literature hysteresis and cited this in the revised draft.

6. Have authors calibrated the steady state rolling (SSR) prior to dynamic rolling?

Answer: Thank you for your question, the authors have already compared these rolling models for the reference case and achieved that the results vary roughly 4%. This simplification is reasonable for the author for the simplicity of the model and the saving of computational cost. This information is added to the revised draft.

7. Authors are advised to discuss more about the thermo-mechanical model.

Answer: Thank you for your comment, the discussions are added to the revised draft.

8. The quality of images is very poor which can be improved.

Answer: Thank you for your recommendation. The image quality is improved.

9. The conclusion needs to be elaborated in terms of quantitative data.

Answer: Thank you for your recommendation, the conclusion has been changed.

10. Title needs to be changed.

Answer: Thank you for your comment, the title has been changed.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

After looking at the revised version, still some "wrong" results in this paper can be noticed (maximum temperature increases with inflation pressure). Of course it is possible, that the results in this paper are right despite the common knowledge about this phenomena, but in this case an an in-depth analysis and discussion with the literature available so far is necessary. In the revised version only one sentence addresses this issue and mentions only one source to back the claims from this paper. This single source is from a (probably) non-reviewed conference and discusses tires for military vehicles with a high load (up to 9 kN). So it is questionable if this results relate to the lightweight sedan tires in this paper. It should be at least demonstrated that the model presented in this paper shows the expected behavior for higher loads: An inverse relationship between pressure and highest temperature. Again, this should be discussed in more depth and not just in one sentence.

Please note that I have not reviewed the whole revised version as the first version has been intensively reviewed and the most controversial point has not been addressed reasonable. So, just addressing the severe point mentioned before does not lead to a fully positive review.

Author Response

Authors can solve all remark in the “applsci-2257075_Reviewer#1-Comments” file.

Please see the answers to Reviewer#1's comments in the attached file.

Author Response File: Author Response.docx

Reviewer 2 Report

The authors have addressed the comments. 

Author Response

Authors can solve all remark in the “applsci-2257075_Reviewer#2's_Answers” file.

Please see the answers to Reviewer#2's comments in the attached file.

Author Response File: Author Response.docx

Reviewer 3 Report

Authors are advised to discuss material modeling of rubber composites. I hope following articles will be of help:

https://doi.org/10.1016/bs.aams.2022.09.002

https://doi.org/10.1016/j.polymertesting.2020.106856

Author Response

Authors can solve all remark in the “applsci-2257075_Reviewer#3-Comments” file.

Please see the answers to Reviewer#3-Comments in the attached file.

Author Response File: Author Response.docx

Round 3

Reviewer 1 Report

see commented manuscript attached

Comments for author File: Comments.pdf

Author Response

COMMENTS OF REVIEWERS

(Version3)

REVIEWER#1:

Comments and Suggestions for Authors:

1. Where does this value come from? It should be stated how this factor is determined as it will have a big influence on the results.

Answer: Thank you for your comment, the hysteresis value comes from the experimental literature, as we cited in the table. They use experimental data to approximate this value for rubber above 25 ºC.

2. What about the steel belt? This is an important part of the tire, does this tire model not have a steel belt?.

Answer: Thank you for your question, the steel belt is not included here. Other parts are indicated to represent the real tires with all components. Moreover, calculating the simulation with all components will take much more time and resources.

3. 1 seems to be a very low friction coefficient between tire and road. Why has this been chosen? Later on you write that 0.1 is for an icy road. Why has this been chosen as the "default" friction coefficient?

Answer: Thank you for your question, the value of the friction coefficient is chosen by the experimental literature that the authors validated.

4. How where the parameters for this simulation determined? E.g. literature, experiments, information from manufacturer, ....

Answer: Thank you for your question, these values are obtained by experiments in the literature, which is provided by Kenda Rubber Industrial Corporation.

5. Please also give more information about this, e.g. which element type and mesh size. Are the reinforcements/rebars also modeled with 3 dimensional elements? In the literature these parts are often modeled with a formulation similar to beams (in Abaqus a so called "rebar layer" is used).?

Answer: Thank you for your question, this information is given in the mesh sensitivity analysis below. Moreover, the reinforcements are also modeled with 3D elements with structural steel properties to achieve real behavior in structural and heating responses.

6. But then the question arises, why you need to use the transient solution, since you are interested in the steady-state...

Answer: Thank you for your question, the steady-state analysis is just for representing the model and cutting in time for simulations with low errors. The transient effects still match the best of the actual tire behaviors.

7. Is the rim modeled elastic or rigid?

Answer: Thank you for your question, the rim is modeled as a rigid body in the setup in order to reduce calculation time, and the inflated tire is clamped at the rim area.

8. Constantly means immediatlely? So the tire is still standing and the road is moving with about 80 km/h?.

Answer: Thank you for your question, the tire is standing and free to roll along with the movement of the road and the road travels with the constant velocity that applies immediately.

9. Which integration method (explidit/implicit) is used?.

Answer: Thank you for your question, we use the default scheme of ANSYS Mechanical software which is the Backward Euler method or implicit Euler method.

10. How has this temperature been determined? Moreover, for transient simulations I expect the inner temperature to start at the outer temperature and heat up during the simulation and reach different values at the equilibrium. This will have a huge impact on your results, as the inner temperature will be wrong for most of the parameter combinations. Therefore the complete heatflow could be wrong (e.g. if the tire is not rolling it will still heat up from the inside!). It should be made clear, that this is a great simplification of the model and introduces a great error source.

Answer: Thank you for your question, the heat transfer coefficient in Table 2 is taken from experimental data from reference 14, and the sink temperatures are extracted from literature no. 22. Moreover, the rolling of the tire is ensured during the post-processing steps.

11. The heat transfer is strongly dependend on the driving speed (relative air speed). Has this been taken into account? Please state in the text, that the values are for standing air! The transfer coefficient to the air seems to be very small in comparison to the transfer coefficient between the tread and road. Has standing air been used for modelling?

Answer: Thank you for your question, the values of the heat transfer coefficient are taken from experimental data from ref. 14 and these values are appropriate for the conditions investigated in the paper. Moreover, the standing air is not used for the modeling of the inner space of the tire due to the complicated form of fluid-solid interaction by using ANSYS. Instead, the appropriate inflated pressure and heat transfer properties are applied to the inner surfaces of the tire and rim to represent the filled air.

12. Seems to be a little low for my experience. Please compare your results to values from literature to validate your thermal results.

Answer: Thank you for your recommendation, the problems described in other literature are quite different compared to this study. Some include geometry without rim and wire (ref. 22) or different conditions and tire types. Hence, the comparison can only be made with the loading analysis where the difference is negligible compared to ref. 30.

13. You wrote in the coverletter that a free rolling tire is simulated. Therefore not much friction energy should heat up the tire?

Answer: Thank you for your question, the main sources of tire heating come from the hysteresis response of the tire and friction energy. However, the friction coefficient is quite low in this study, so there is not much friction energy generated and the maximum temperature is not quite high in the study.

14. A frictional contact is not enough to create friction. You also need a speed difference between both parts, how is this achieved? This should not be described here but in the section where you describe the model.

Answer: Thank you for your question, the velocity difference between the tire and the road is achieved by a velocity applied to the road, and the tire is fixed in any directional displacement with scope to the fixed center of the tire. This information can be observed in Fig. 3.

15. This is the first time that it is mentioned, that this paper is focused on lightweight! It should be mentioned on the beginning (abstract/introduction). Moreover, it should clearly be defined what is meant by lightweight as the load range used in this paper (1000 N to 6000 N) is within a normal range for combustion engine cars and not specifically lightweight.

Answer: Thank you for your question, the “lightweight” term here is for the loading range from 1 kN to 3 kN with reference to ref. 31 since their range of study is up to 9 kN. The sentence is corrected.

16. Overall the spread of the strain energy density over all velocities is only roughly 0.5 %. So maybe this seems to be more like a numerical variation than real changes. Maybe it would be better to use a scaling similar to the 2 previous variations to demonstrate that the heat flux stays more or less constant (and note that the change is small in the text). I would propose mentioning more precise how small this change is! In my opinion this is probably just some numerical noise and no real oscillation is happening here...

Answer: Thank you for your recommendation, the mention is already added to the draft.

17. Does significant mean higher? This seems to be a result of your modelling choices. You set the temperature at the outside to 25 °C and on the inside to 38 °C --> the tire is then heated from the inside.

Answer: Thank you for your question, the word is corrected in the draft.

18. Why has no normal road (friction roughly 1.0) been researched?

Answer: Thank you for your question, the friction coefficient of 1.0 is not the purpose of this study.

19. Why are here no graphs for the average and highest temperature as before.

Answer: Thank you for your question, the friction coefficient is unlike other variables since it affects the distribution of the tire most. Thus, it is beneficial for the readers to observe the distribution difference between the three cases.

20. Why is this modeled as transient? A steady-state simulation of the rolling tire should be fine I guess? Maybe I don't understand exactly which state you are researching, this is not made clear in the model description.

Answer: Thank you for your question, the transient response of the model simulates better the behaviors of the real tire than the steady-state analysis. This is already known for a long time. Moreover, the modeling of the study is clarified.

 

Author Response File: Author Response.docx