Quasi-Equilibrium Stress Zone with Residual Displacement Causing Permanent Slippage in Shrink-Fitted Sleeve Rolls
Round 1
Reviewer 1 Report
The paper must be revised paying special attention to the following points:
The first chapter of introduction should be more extensive, making emphasis on each of the papers referenced. You can not reference from 1 to 19 without explaining anything else.
It would be convenient to carry out a study of how the mesh size affects the results.
Explain how the behavior of the material has been introduced in the simulations. The way to define the elastoplastic behavior will have a direct influence on the results.
Identify the tolerances of the interference diameters in the assembly.
These tolerances will directly influence the results obtained and nothing is said in the paper.
Study the different combinations of the previous tolerances on the results.
Define the type of friction selected in the simulation.
Author Response
Point 1: The first chapter of introduction should be more extensive, making emphasis on each of the papers referenced. You can not reference from 1 to 19 without explaining anything else.
Response 1: The authors appreciate it for the reviewer’s useful comments. The following sentences with reference number have been changed as suggested.
In Introduction
“Also, the rolls require the high hardness surface to prevent spalling caused by the cyclic contact loading1)-3). Currently most of the rolls are classified into integrated type, but another type sleeve rolls are also developed by shrink fitting the sleeve to the shaft as shown in Fig.14), 5).”
“In the previous study 6)-23), the residual deflection was investigated experimentally for small rolls.”
“And the ratio of the trunk length to the trunk diameter is larger than the actual ratio in order to clarify the influence of the length9).”
Point 2: It would be convenient to carry out a study of how the mesh size affects the results.
Response 2: The authors appreciate it for the reviewer’s useful comments. The following sentence has been added.
In Section2.2
“The mesh effect of FEM on the results is less than a few percent.”
Point 3: Explain how the behavior of the material has been introduced in the simulations. The way to define the elastoplastic behavior will have a direct influence on the results.
Response 3: The authors appreciate it for the reviewer’s useful comments. The following sentence has been corrected as suggested.
In Section2.2
In reference 8, it was confirmed that the experiment was conducted within the elastic range. Therefore FEM simulation is performed as three-dimensional contact elastic analysis.
Point 4: Identify the tolerances of the interference diameters in the assembly.
Response 4: The authors appreciate it for the reviewer’s useful comments. The following sentence has been added.
In Section 2.2
‘Shrink fitting ratio δ/d can be applied in the FEM simulation by using the option “interference closure” in FEM software Marc. After the shaft and sleeve are assembled the tolerances δ can be applied by using this option.’
Point 5: These tolerances will directly influence the results obtained and nothing is said in the paper.
Response 5: The authors appreciate it for the reviewer’s useful comments. The following sentence has been added.
In Section 2.2
‘Reference 6 indicates that the effect of δ/d on the residual deflection becomes smaller if shrink fitting ratio δ/d is larger than a certain value. The value used in this study = 1.0 × 10 - 3 is within this range, and this value = 1.0 × 10 - 3 was used in the experiment.’
Point 6: Study the different combinations of the previous tolerances on the results.
Response 6: The authors appreciate it for the reviewer’s useful comments. As shown above, in this research, the shrink fitting ratio was determined because shrinkage fit ratio does not affect residual displacement.
Point 7: Define the type of friction selected in the simulation.
Response 7: The authors appreciate it for the reviewer’s useful comments. The following sentence has been added.
In Section 2.2
‘In contact analysis by the analysis software used in this research, it has been told that the Coulomb friction model can be widely used for most practical applications except for bulk forming as encountered in e.g. forging processes. Three types of Coulomb friction models are aviliable, that is, arctangent model, stick-slip model and bilinear model. However, it is known that the arctangent model is unsuitable for estimating the typical relative sliding velocity priori when the sliding velocity varies largely during the analysis. Also, the stick-slip model needs a large amount of data to be determined from repetitive calculation process. In this study, therefore, the bilinear model is applied since the friction force is simply determined from the displacement.’
Reviewer 2 Report
This is a very interesting work that fits well within the scope of this Journal. However, some aspects need to be addressed prior to publication of this article. Major revisions are due.
Extensive proof of English is due.
Line 23: the author should improve the introduction and should present the reference paper reported in the paper. They use only one sentence to introduce 19 papers.
Line 58: please change “100x9.8” with “980”.
Table 1: are the properties of material reported in table 1 of the shaft or the slave? Please clarify the caption.
Line 72: which is the y direction reported in the text? Please show the reference system in the figures.
Line 73: please clarify the sentence “Since the loading condition is less than the plasticity range, the FEM simulation is performed as three-dimensional contact elastic analysis”.
Line 76: how many nodes has the element? (Four or eight?)
Line 76: how many degrees of freedom has each node?
Line 76: please report the number of total nodes.
Line 76: the authors should give more information about boundary condition and the contact elements used in the FEM model.
Line 76: the author should give more information about material model; have thay used linear material model or non linear model?
Line 76: have the author considered the plasticity in the model?
Lines 109, 110 and 133: please change “30x9.8” with “294”.
Lines 144, 146, 147 and 180: change “15 x 9.8”, “30 x 9.8” and “60 x 9.8” with “147”, “294”, and “588” respectively.
Line 217: change“60 x 9.8” with “588”.
Line 219: change“30 x 9.8” with “294”.
Figure 9: increase the sizes of images reported in figure 9.
Caption of figure 9: change“60 x 9.8” with “588” and “30 x 9.8” with “294”.
Line 225: change “Lb” with “Lu”.
The authors should change “15 x 9.8”, “30 x 9.8” and “60 x 9.8” with “147”, “294”, and “588” respectively in all text of paper.
Author Response
Point 1: Line 23: the author should improve the introduction and should present the reference paper reported in the paper. They use only one sentence to introduce 19 papers.
Response 1: The authors appreciate it for the reviewer’s useful comments. The following sentences with reference number have been corrected as suggested.
In Introduction
“Also, the rolls require the high hardness surface to prevent spalling caused by the cyclic contact loading1)-3). Currently most of the rolls are classified into integrated type, but another type sleeve rolls are also developed by shrink fitting the sleeve to the shaft as shown in Fig.14), 5).”
“The rolling rolls also require the straightness of the roll axis center within 0.02mm error at the end of shaft. Therefore, if a permanent residual roll deflection occurs during the operation, the sleeve constructed rolls cannot be used anymore. In the previous study 6)-9), the residual deflection was investigated experimentally for small rolls.”
” Huge amount of efforts have been done to improve the properties of rolling rolls 10)-21) but shrinkage fitted structures22),23) can be applied more widely to solve those problems in the world by clarifying and preventing this permanent slippage phenomenon.”
In Section 5
“Few studies are available for this circumferential slippage in rolling roll, but a similar phenomenon is known as interface creep in ball bearing attracting attention24) - 26) although no analytical studies can be found."
Point 2: Line 58: please change “100x9.8” with “980”.
Response 2: The authors appreciate it for the reviewer’s useful comments. The following have been changed as suggested.
“100x9.8”→ “980”
Point 3: Table 1: are the properties of material reported in table 1 of the shaft or the slave? Please clarify the caption.
Response 3: The authors appreciate it for the reviewer’s useful comments. The following caption of Fig.1 have been changed as suggested.
“Table 1 Material properties of Cr-Mo steel”→ “Table 1 Material properties of Cr-Mo steel shaft and sleeve”
Point 4: Line 72: which is the y direction reported in the text? Please show the reference system in the figures.
Response 4: The authors appreciate it for the reviewer’s useful comments. Figure 1 has been changed as suggested.
Point 5: Line 73: please clarify the sentence “Since the loading condition is less than the plasticity range, the FEM simulation is performed as three-dimensional contact elastic analysis”.
Response 5: The authors appreciate it for the reviewer’s useful comments. From the reference 8, since it was confirmed that it is within the yield range under this research condition, it was set as elastic analysis. The following sentence has been changed by using this option.
In Section2.2
In reference 8, by confirming the applied load is within the elastic range, the residual deflection is discussed in the experiment. Therefore FEM simulation is performed as three-dimensional elastic contact analysis.
Point 6: Line 76: how many nodes has the element? (Four or eight?)
Response 6: The authors appreciate it for the reviewer’s useful comments. The following sentences have been added.
In Section2.2
“Figure 2 shows the analysis model. Hexahedral primary element having 8 nodes is used with the minimum dimension of 1.25 mm, and the number of total nodes is 117900 and the number of total elements is 78,600. The EFM mesh effect on the results is less than a few percent.”
Point 7: Line 76: please report the number of total nodes.
Response 7: The authors appreciate it for the reviewer’s useful comments. The following sentence has been added.
In Section2.2
“Figure 2 shows the analysis model. Hexahedral primary element having 8 nodes is used with the minimum dimension of 1.25 mm, and the number of total nodes is 117900 and the number of total elements is 78,600. The EFM mesh effect on the results is less than a few percent.”
Point 8: Line 76: the authors should give more information about boundary condition and the contact elements used in the FEM model.
Response 8: The authors appreciate it for the reviewer’s useful comments. The following sentences have been added.
In Section2.2
“Reference 6 indicated that the effect of δ/d on the residual deflection becomes smaller if shrink fitting ratio δ/d is larger than a certain value. The value used in this study δ/d = 1.0 × 10 - 3 is within this range, and this value δ/d = 1.0 × 10 - 3 was used in the experiment. Shrink fitting ratio δ/d can be provided in the FEM simulation by using the option “interference closure” in MSC Marc/Mentat 2012. After the shaft and sleeve are assembled the tolerances δ can be applied by using this option.”
Point 9: Line 76: the author should give more information about material model; have they used linear material model or non linear model?
Response 9: The authors appreciate it for the reviewer’s useful comments. The following sentences have been added.
In Section2.2
In reference 8, by confirming the applied load is within the elastic range, the residual deflection is discussed in the experiment. Therefore, an elastic contact analysis is performed in this study.
Point 10: Line 76: have the author considered the plasticity in the model?
Response 10: The authors appreciate it for the reviewer’s useful comments. The following sentence has been added.
In Section2.2
In reference 8, by confirming the applied load is within the elastic range, the residual deflection is discussed in the experiment. Therefore, an elastic contact analysis is performed in this study.
Point 11: Lines 109, 110 and 133: please change “30x9.8” with “294”.
Response 11: The authors appreciate it for the reviewer’s useful comments. The following expressions have been changed as suggested.
“30x9.8”→ “294”
Point 12: Lines 144, 146, 147 and 180: change “15 x 9.8”, “30 x 9.8” and “60 x 9.8” with “147”, “294”, and “588” respectively.
Response 12: The authors appreciate it for the reviewer’s useful comments. The following expressions have been changed as suggested.
“15 x 9.8”→ “147”
“30 x 9.8”→ “294”
“60 x 9.8”→ “588”
Point 13: Line 217: change“60 x 9.8” with “588”.
Response 13: The authors appreciate it for the reviewer’s useful comments. The following expressions have been changed as suggested.
“60 x 9.8”→ “588”
Point 14: Line 219: change“30 x 9.8” with “294”.
Response 14: The authors appreciate it for the reviewer’s useful comments. The following expressions have been changed as suggested.
“30x9.8”→ “294”
Point 15: Figure 9: increase the sizes of images reported in figure 9.
Response 15: The authors appreciate it for the reviewer’s useful comments. Figure 9 has been changed as suggested.
Point 16: Caption of figure 9: change“60 x 9.8” with “588” and “30 x 9.8” with “294”.
Response 16: The authors appreciate it for the reviewer’s useful comments. The following expressions have been changed as suggested.
“60 x 9.8”→ “588”
“30 x 9.8”→ “294”
Point 17: Line 225: change “Lb” with “Lu”.
Response 17: The authors appreciate it for the reviewer’s correcting the misprint. The following expressions have been changed as suggested.
“Lb”→ “Lu”
Point 18: The authors should change “15 x 9.8”, “30 x 9.8” and “60 x 9.8” with “147”, “294”, and “588” respectively in all text of paper.
Response 18: The authors appreciate it for the reviewer’s useful comments. The following expressions have been changed as suggested.
“15 x 9.8”→ “147”
“30 x 9.8”→ “294”
“60 x 9.8”→ “588”
In a similar way, All Figures (Figure 1-Figure 14) and all Tables (Table 1- Table 2) have been corrected as suggested.
Reviewer 3 Report
The paper investigates the effect of friction between the shaft and sleeve in a sleeved (composite) backup roll on the residual roll deformations.
This is a very interesting and timely paper. The rolling process, having had a very long history, remains an open subject, where many interesting mechanical phenomena are yet to be studied, such as slippage in sleeved backup rolls.
I definitely recommend the paper for publication, but the text requires additional proof reading. Some sentences are awkward, and some paragraphs need to be restructured. For instance, on Page 2: "The sleeve was assembled to the shaft by shrinkage fitting. Then, the residual deflection was studied experimentally by Shimoda et al. The ratio of the sleeve thickness to the shaft diameter is slightly larger than the actual ratio. And the ratio of the trunk length to the trunk diameter is larger than the actual ratio in order to clarify the influence of the length." Firstly, a reference should be added here. Secondly, it is not clear what the authors refer to when the describe the geometry: Do the refer to their model versus the mentioned experimental studies or something else?
Section 2.2: Was there any specific reason for using a concentrated load W instead of, say, uniformly distributed load, that would represent better the contact conditions?
Section 2.2: it is stated that a shrink fitting of 10^-3 is used in the FE simulations, it would be very beneficial to explain how the sleeve and shaft were fitted in the model.
Sections 4-5 are difficult to follow and requires a revision. Another example that either needs to be elaborated or rephrased: Page 9 "the smaller slippage region becomes smaller". The form the results are presented is somewhat unconventional, although interesting and valuable for understanding of the mechanical processes in the rolls, but the sections would benefit from a clearer account.
Author Response
Point 1: I definitely recommend the paper for publication, but the text requires additional proof reading. Some sentences are awkward, and some paragraphs need to be restructured. For instance, on Page 2: "The sleeve was assembled to the shaft by shrinkage fitting. Then, the residual deflection was studied experimentally by Shimoda et al. The ratio of the sleeve thickness to the shaft diameter is slightly larger than the actual ratio. And the ratio of the trunk length to the trunk diameter is larger than the actual ratio in order to clarify the influence of the length." Firstly, a reference should be added here. Secondly, it is not clear what the authors refer to when the describe the geometry: Do the refer to their model versus the mentioned experimental studies or something else?
Response 1: The authors appreciate it for the reviewer’s comment recommending our paper for publication. The following sentences have been corrected as suggested.
In Introduction
“Also, the rolls require the high hardness surface to prevent spalling caused by the cyclic contact loading1)-3). Currently most of the rolls are classified into integrated type, but another type sleeve rolls are also developed by shrink fitting the sleeve to the shaft as shown in Fig.14), 5).”
“The rolling rolls also require the straightness of the roll axis center within 0.02mm error at the end of shaft. Therefore, if a permanent residual roll deflection occurs during the operation, the sleeve constructed rolls cannot be used anymore. In the previous study 6)-9), the residual deflection was investigated experimentally for small rolls.”
” Huge amount of efforts have been done to improve the properties of rolling rolls 10)-21) but shrinkage fitted structures22),23) can be applied more widely to solve those problems in the world by clarifying and preventing this permanent slippage phenomenon.”
In Section 2.1
The following sentences have been corrected as suggested.
“In this experiment, the ratio of the sleeve thickness to the shaft diameter is slightly larger than the actual ratio in real rolls. Also, the ratio of the trunk length to the trunk diameter is larger than the actual ratio in order to clarify the influence of the length9).”
In Section 5
“Few studies are available for this circumferential slippage in rolling roll, but a similar phenomenon is known as interface creep in ball bearing attracting attention24) - 26) although no analytical studies can be found."
Point 2: Section 2.2: Was there any specific reason for using a concentrated load W instead of, say, uniformly distributed load, that would represent better the contact conditions?
Response 2: The authors appreciate it for the reviewer’s useful comments. The analysis conditions in this research are in accordance with the experimental conditions in reference 6. Concentrated loading is used in the experiment of reference 7. The following sentence has been changed.
In Section2.2
“As shown in Fig.1, the shrinkage fitted sleeve roll will be analyzed under the same conditions; for example, in this model the distributed load in actual rolling is replaced by the concentrated load in accordance with the experiment7).”
Point 3: Section 2.2: it is stated that a shrink fitting of 10^-3 is used in the FE simulations, it would be very beneficial to explain how the sleeve and shaft were fitted in the model.
Response 3: The authors appreciate it for the reviewer’s useful comments. The analysis software used in this research has an option called interference closure. This option can for instance be used to simulate the effect of a shrink fit without using thermal strains. The bodies are modelled as just touching each other and the overlap of the shrink fit is input as a positive interference closure. The following sentence has been added.
In Section 2.2
‘Shrink fitting ratio δ/d can be applied in the FEM simulation by using the option “interference closure” in FEM software Marc. After the shaft and sleeve are assembled the tolerances δ can be applied by using this option.’
Point 4: Sections 4-5 are difficult to follow and requires a revision. Another example that either needs to be elaborated or rephrased: Page 9 "the smaller slippage region becomes smaller". The form the results are presented is somewhat unconventional, although interesting and valuable for understanding of the mechanical processes in the rolls, but the sections would benefit from a clearer account.
Response 4: The authors appreciate it for the reviewer’s useful comments. The following sentences have been inserted or changed as suggested.
In Section5
The following sentences have been inserted as suggested.
“In section 4.2, it was shown that the residual deflection is caused by the relative slippage between the sleeve and the shaft. From the stress distributions along the shrink-fitted surface, the relative slippage condition was discussed in terms of the stress quasi-equilibrium region.”
“In this section, first, to confirm the residual displacement, the slippage region will be investigated. If the slippage region is confirmed, the residual displacement should be found in a similar way in section4.2. Therefore, by removing the loading the residual displacement will be discussed.”
In Section5
The following sentences have been changed as suggested.
“As shown in Fig. 13 (b), after removing the initial loads as P(0) →0, the slippage region becomes smaller. However, the quasi-equilibrium stress region where the slippage occurs still exists near the loaded position θ=0 and θ=π .”
Round 2
Reviewer 1 Report
The review has been carried out properly so that the paper can be considered acceptable for publication.
Author Response
Dear Reviewer 1
Thank you for your useful suggestions.
I would like to re-submitt our paper "Quasi-Equilibrium Stress Zone with Residual Displacement Causing Permanent Slippage in Shrink-Fitted Sleeve Rolls"
Yours sincerely,
Hiromasa Sakai
Reviewer 2 Report
Accepted in present form.
Author Response
Dear Reviewer 2
Thank you for your useful suggestions.
I would like to re-submitt our paper "Quasi-Equilibrium Stress Zone with Residual Displacement Causing Permanent Slippage in Shrink-Fitted Sleeve Rolls"
Yours sincerely,
Hiromasa Sakai
