Implicit Elastoplastic Finite Element Analysis of a Wheel Bearing Shaft Clinching Process Using the Multi-Body Function
Round 1
Reviewer 1 Report
The paper presents interesting engineering issues, however, to be considered for future publication it should be improved with the following comments:
1. In the introduction, it would be appropriate to state clearly what the novelty of the present paper is in relation to other thematically similar research papers.
2. It would be useful to expand the introduction to include work on advanced analysis closely associated with FEM, such as: (DOI) 10.1016/j.compstruct.2020.112388.
3. Equations 22-32 should be presented in compensated form, i.e., it is pointless to show so many similar forms of equations with minor changes, which does not add anything significant to the work, but only generates additional unnecessary equation notation.
4. Figure 2 should show in enlarged form the relevant details shown in it.
5. In Figure 8, the vertical axis is shown in Tons. Rather, it should be in N or kN.
6. Conclusions are quite laconically presented and either should be significantly expanded based on a better presentation of the quantitative and qualitative evaluation of the results, or there should be a comprehensive discussion section before hand.
Author Response
Reviewer 1.
The paper presents interesting engineering issues, however, to be considered for future publication it should be improved with the following comments:
1. In the introduction, it would be appropriate to state clearly what the novelty of the present paper is in relation to other thematically similar research papers.
ANS. The followings are the improvements for emphasizing the novelty of this study:
It is noteworthy that most researchers have imposed velocity-prescribed boundary conditions because the corresponding constrained dies are amenable to numerical analysis.
Here, a rotary forging process with a force-prescribed roller for fabricating DPTR WBU was analyzed by the implicit elastoplastic FEM with a multi-body treatment scheme. The finite element analysis was conducted with an emphasis on accurate predictions of the tight fitting of the bearing races with the hollow shaft before rotary forming and cavity formation around the armpit of the bent shaft during rotary forming, as well as the effects of this cavity formation on the residual stresses in the bearing inner races.
2. It would be useful to expand the introduction to include work on advanced analysis closely associated with FEM, such as: (DOI) 10.1016/j.compstruct.2020.112388.
ANS. The following sentence and the references are added:
A clinching process of assembling the WBUs thus belongs to the complicated mechanical or structural engineering problems [9-12].
3. Equations 22-32 should be presented in compensated form, i.e., it is pointless to show so many similar forms of equations with minor changes, which does not add anything significant to the work, but only generates additional unnecessary equation notation.
ANS. Chapter 2 was deleted because the related contents can be found from the Ref. [37].
4. Figure 2 should show in enlarged form the relevant details shown in it.
ANS. Figure 2 was enlarged
5. In Figure 8, the vertical axis is shown in Tons. Rather, it should be in N or kN.
ANS. The unit of y-axis was changed from ton to kN.
6. Conclusions are quite laconically presented and either should be significantly expanded based on a better presentation of the quantitative and qualitative evaluation of the results, or there should be a comprehensive discussion section before hand.
ANS. We improved the Conclusion together with the Chapter 3 for more detailed discussion. All the sentences in red were improved.
Thanks the reviewer for valuable comments and recommendations.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Section 2 present a lot of equations, such as many of them concerns generalities well known in FEM. There is nothing about large deformations problems in the paper, for example, the objectivity of the constitutive behavior, since large deformations and large rotations arise in such simulations.
There is a lot of space dedicated to FEM kinematics, but nothing about one very crucial point: the constitutive behavior of materials. The only information is the Ramberg-Osgood flow law in Table 1. Such flow law is a very basic one and might not reflect very well the behavior of the material during plastic deformation.
There seems to be a problem in bibliography since in the downloaded manuscript reference list stops at ref 38, while text cite for example ref [48,49] in the caption of Figure 1 line 154. Authors have to check links of ref and bibliography one by one to be sure.
Line 246, authors mention the Coulomb friction coefficient but how it has been identified.
Line 259, authors mention a penalty contact condition. What type of contact conditions did they use, is it the same for all contacting regions ?
Line 266, authors mention two temperatures for the inner races, what is the temperature of the shaft ? There is no expansion coefficient on the shaft, while you have one for the races, so how the gap value can be ensured during computation ? Authors have to clarify this point since the initial conditions before deforming process are not clear.
There is no information concerning the roller, is it a rigid surface that is used ? If true, how can you ensure a correct BC and CC between the roller and the shaft ? If not, what are the deformations of this part ? Also, line 290, it is not clear in the text, for the reader to be sure of what type of BC is used for the roller, is it finally a prescribed load or displacement. If it is a load, why, in fig 8 such a large gap between applied load and reaction forces ? This might come from problems in FEM formulation, or the way this predicted load is computed.
There is no information concerning the FEM software used for the simulations, nothing about the time needed for computations, the type of computer,...
Author Response
Reviewer 2
This paper present a FEM analysis of a forging problem for automotive industry. The global approach used in this paper is an engineering application.
1. Section 2 present a lot of equations, such as many of them concerns generalities well known in FEM. There is nothing about large deformations problems in the paper, for example, the objectivity of the constitutive behavior, since large deformations and large rotations arise in such simulations. There is a lot of space dedicated to FEM kinematics, but nothing about one very crucial point: the constitutive behavior of materials. The only information is the Ramberg-Osgood flow law in Table 1. Such flow law is a very basic one and might not reflect very well the behavior of the material during plastic deformation. There seems to be a problem in bibliography since in the downloaded manuscript reference list stops at ref 38, while text cite for example ref [48,49] in the caption of Figure 1 line 154. Authors have to check links of ref and bibliography one by one to be sure.
ANS. Chapter 2 was deleted because the related contents can be found from the Ref. [37]. The mistake of cited references was cleared.
2. Line 246, authors mention the Coulomb friction coefficient but how it has been identified.
ANS. The frictional condition in the rotary forging is very complicated. It is one of serious research topics. We thus assumed the frictional condition, based on the experiences in the friction. Thus, we improved the sentence as follows and added the related references:
The tribological conditions at the interface between materials were established, based on the experiences [33, 34], by reference to the Coulomb friction law with a frictional coefficient of 0.1
3. Line 259, authors mention a penalty contact condition. What type of contact conditions did they use, is it the same for all contacting regions?
ANS. We applied a direct contact condition (non-penalty scheme) to the material-forging roller in which a node penetrating into the opposite body is considered as the contact node. The other interfaces were treated by the same penalty scheme with identical penalty constants.
4. Line 266, authors mention two temperatures for the inner races, what is the temperature of the shaft? There is no expansion coefficient on the shaft, while you have one for the races, so how the gap value can be ensured during computation? Authors have to clarify this point since the initial conditions before deforming process are not clear.
ANS. We found that the expression may cause some confusion. We thus improved the related sentences as follows:
Note that the inner races were tightly press-fitted (in a mechanical sense) before assembly. The gap before the press-fitting was 0.01 mm, which was reflected by the shrink-fitting of the upper and lower inner races by the equivalent thermal loads of -35.5°C and -32.7°C, respectively. Thus, these thermal loads were applied to the respective inner races during shrink-fitting simulation before assembly simulation.
5. There is no information concerning the roller, is it a rigid surface that is used? If true, how can you ensure a correct BC and CC between the roller and the shaft? If not, what are the deformations of this part? Also, line 290, it is not clear in the text, for the reader to be sure of what type of BC is used for the roller, is it finally a prescribed load or displacement. If it is a load, why, in fig 8 such a large gap between applied load and reaction forces? This might come from problems in FEM formulation, or the way this predicted load is computed.
ANS. Lines 243-244 in the original manuscript stated the mathematical idealization of the dies and tools. We applied the same direct contact check scheme to the material-forging roller interface. The penetration was allowed within the input limit of 0.01 mm. The penetrated distance was reduced step by step by pushing the node up to the actual contact surface. The tool velocity was approximately obtained to meet the required force at the stroke or time, following the force-velocity convergence scheme [Joun et al., 2001, Finite element simulation of the cold forging process having a floating die, J. Mater. Process. Technol., 112, pp.121-126]. During the solution iteration, all the nodes on the contact condition is treated as the essential boundary. The final solution was obtained when the force in the force loop becomes acceptable. That’s why there is some error between the input and predicted forming loads, which is a matter of convergence and computational efficiency
6. Figure 4, the forming loading curve is increasing continuously. What about the end of the process, do you release the load? So that when you talk about "after homogenizing", what does it means?
ANS. At the final time or stroke, we assumed that the forging roller moves up on sudden. It is believed that this assumption is acceptable.
7. There is no information concerning the FEM software used for the simulations, nothing about the time needed for computations, the type of computer,...
ANS. For the details of the FEM software and computational time taken to obtain the whole solution in Fig. 7, we moved, improved, or added the related contents or sentences as follows:
<Software>
A general-purpose implicit rigid- or elastic-thermoviscoplastic FE package AFDEX (Altair APA) [35, 36, 37] was used, based on the tetrahedral MINI-element scheme [33] with automatic adaptive meshing or remeshing [32]. The multi-body scheme [31] was employed to deal with the bearing inner races, which gives an accurate prediction of the stress and spring back of the material during homogenizing stage.
Thanks the reviewer for valuable comments and recommendations.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The authors have considered most of my remarks in their revised manuscript.
