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Numerical Simulation and Parameter Analysis of Electromagnetic Riveting Process for Ti-6Al-4V Titanium Rivet

Coatings 2021, 11(8), 878; https://doi.org/10.3390/coatings11080878

by Yangfan Qin

, Yuxuan Liao, Guangyao Li, Junjia Cui

and Hao Jiang^*

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Reviewer 3: Anonymous

Coatings 2021, 11(8), 878; https://doi.org/10.3390/coatings11080878

Submission received: 18 June 2021 / Revised: 8 July 2021 / Accepted: 20 July 2021 / Published: 22 July 2021

(This article belongs to the Special Issue Advanced Joining Technologies of Alloys and Composites in the Automotive, Aeronautic and Astronautic Fields)

Round 1

Reviewer 1 Report

The current study investigates the electromagnetic riveting process of TC4 titanium sheets. For this, the authors conducted the axisymmetric electromagnetic-structural coupling simulations.

The authors provide some findings of their work such as stating that that the punch displacement was highly affected by the structural parameters of riveting setup. This is commonly known relation.

Abstract: "EMF" has not been defined.

The whole manuscript: Many abbreviations have not been defined the first time they appear in the main text.

It is not known what parameter the contours in Figure 8 relate to.

The input parameters used in the neural network model have not been specified.

The details of training process of neural network model have not been completely discussed.

Proper preparation of input data to the network and the selection of many network parameters (i.e. activation function) determine the quality of calculations. I found no details in this aspect.

The structure of the manuscript does not match Instructions for Authors. Some sections contain mixed Methods and Results. They should be clearly separated as individual sections / subsections. For details please, see Instructions for Authors.

Figures 9 shows the typical network structure (line 216). The structure of the network used in the research should be included here.

English grammar must be checked in the whole manuscript.

Author Response

Honorable reviewer:

On behalf of my co-authors, we thank you very much for giving us an opportunity to revise our manuscript. We appreciate you very much for your positive and constructive comments and suggestions on our manuscript entitled “Numerical Simulation And Parameter Analysis of Electromagnetic Riveting Process for Ti-6Al-4V Titanium Rivet” (ID: coatings-1284759), We have studied your comments carefully and have made revisions which marked in red in the paper. We have tried our best to revise our manuscript according to the comments. Attached please find the revised version, which we would like to submit for your kind consideration. Looking forward to hearing from you.

Our responses to reviews’ comments and suggestions present as follows.

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Comments and Response:

Reviewer #1

The current study investigates the electromagnetic riveting process of TC4 titanium sheets. For this, the authors conducted the axisymmetric electromagnetic-structural coupling simulations.

Q1: The authors provide some findings of their work such as stating that that the punch displacement was highly affected by the structural parameters of riveting setup. This is commonly known relation.

Response: We appreciate the reviewer’s kindly comment. As an important component of electromagnetic riveting process, the significance of structural parameters of riveting setup on the punch displacement was commonly known relation. However, the parameter study of the driver plate and the amplifier in riveting setup has not been reported yet. Besides, the detail parameter effects of the structural parameters within driver plate and amplifier were unclear. Thus, this paper systematically studied the influences of structural parameters of driver plate and amplifier.

Q2: Abstract: "EMF" has not been defined.

Response: We thank you very much for this advice. The meaning of EMF has been added in the revised paper.

Please see line 43-45. As follows:

The EMR device was mainly consisted of two parts: discharge equipment (electromagnetic force (EMF) setup) and riveting setup [9].

Q3: The whole manuscript: Many abbreviations have not been defined the first time they appear in the main text.

Response: Thank you for giving us these kindly suggestions. Your suggestions are very helpful for our paper. Through your suggestions, we have made a lot of improvements to this paper. Besides, the nomenclature part has been added in the revised paper.

Please see line 31-32. As follows:

Due to the increasing demand for lightweight materials such as aluminum alloy, titanium alloy, carbon fiber reinforced polymer (CFRP) in automotive fields, the traditional joining technologies meet huge challenge in achieving excellent connection quality within qualified fatigue performance and service life.

Please see line 45-47. As follows:

The EMF setup provided the riveting energy based on the resistor-inductor-capacitor (RLC) attenuating oscillating circuit, which was composed of capacitor banks, resistor, inductor, and coils [10].

Please see line 86-87. As follows:

Cui et al. [24] studied the effect of the rivet die on the formation mechanism of the ad-iabatic shear bands (ASBs) in the rivet driven head and obtained the optimal riveting die.

Please see line 122-123. As follows:

Fig. 3(a) shows the finite element model (FEM) used for the analysis of the 2D ax-isymmetric EMR model using loose-coupled method.

Please see line 196-199. As follows:

As shown in Fig. 6 (b), the punch speed was shot by high-speed camera with digital image correlation (DIC) 3D full-field strain analysis system to compared the actual and the numerical punch speed.

Please see Nomenclature part with units part on page 19. As follows:

Nomenclature part with units

Symbol	Unit	Meaning
EMR	-	Electromagnetic Riveting Process
EMF	-	Electromagnetic Force
RBF	-	Radial Basis Function
CFRP	-	Carbon Fiber Reinforced Polymer
RLC	-	Resistor-Inductor-Capacitor
ASBs	-	The Adiabatic Shear Bands
FEM	-	Finite Element Model
MURX	-	Magnetic Permeability
RSVX	Ω·m	Resistivity
E	Pa	Elastic Modulus
υ	-	Poisson Ratio
ρ	kg/m³	Density
DIC	-	Digital Image Correlation
R_in	mm	Inner Diameter of Driver Plate
R_out	mm	Outer Diameter of Driver Plate
H_D	mm	Height of Driver Plate
H_P	mm	Height of Platform
H_T	mm	Height of Transition Zone
A	°	Angle
W_T	mm	Width of Transition Zone

Q4: It is not known what parameter the contours in Figure 8 relate to.

Response: Thanks very much for pointing out these errors. In the revised manuscript, we have added the information of the parameters in the contour of Fig. 12.

Please see Figure 12 in page 12. As follows:

Figure 12. Rivet deformation comparison between the numerical simulation and metallographic microstructure in two simulation approaches: (a) Loose coupling method; (b) Sequential coupling method; (c) Radial displacement comparison between two methods.

Q5: The input parameters used in the neural network model have not been specified.

Response: We appreciate the reviewer’s suggestions. Thanks for your suggestions and pointing out our errors. In the revised manuscript, we have added the input parameters and the output parameter in the topology diagram of RBF.

Please see Figure 14 in page 14. As follows:

Figure 14. Topology diagram of RBF.

Q6: The details of training process of neural network model have not been completely discussed.

Response: Thanks very much for pointing out these errors. In the revised manuscript, we have added the details of training process of RBF network model in the revised manuscript.

Please see line 322-324. As follows:

Within the 349 valid sampling points, 325 points were used as the training data to construct the RBF regression model and the rest 24 points were used as the test data. The root mean square error of the RBF approximation model was 6.11%.

Q7: Proper preparation of input data to the network and the selection of many network parameters (i.e. activation function) determine the quality of calculations. I found no details in this aspect.

Response: Thank you for kindly giving these good comments. In the revised manuscript, we have added information of preparation of input data and the network parameters.

Please see line 316-322. As follows:

The network architecture of RBF prediction model is shown in Fig. 14. For the EMR process, this network predicted the punch displacement and impact velocity for the given structural parameters of driver plate and amplifier. The elliptical basis function with the Mahalanobis distance was adopted in this paper due to the ability to rank the input variables in the order of influence on the output variable. The Gaussian function was used in this work as the processing function.

Q8: The structure of the manuscript does not match Instructions for Authors. Some sections contain mixed Methods and Results. They should be clearly separated as individual sections / subsections. For details please, see Instructions for Authors.

Response: Thank you for giving us these kindly suggestions. Your suggestions are very helpful for our paper. Through your suggestions, we have made a lot of improvements to this paper. In order to make the logic clearer, we divided the mixed Methods and Results.

Please see line 272-294 in section 3.1. As follows:

Under the condition that five current waves were considered, Fig. 11 show the changes of impact velocity of punch in two simulation approaches. Unlike the EMF response, the impact velocity of sequential coupled model differed at 300 μs with the loose coupled model. Since the EMF was calculated based on the origin position of driver plate, the punch velocity calculated by loose coupled method was larger than the sequential simulation model. Consequently, the deformation of rivet was overestimated than experiment in loose coupling numerical model, as shown in Fig. 12.

Figure 11. The impact velocity of punch in loose and sequential coupled model.

In order to verify the accuracy of the rivet deformation, the riveted specimen was cut along the axis of the rivet shaft. Fig. 12(a) and (b) show the comparisons between the numerical simulation result and metallographic microstructure result inside the rivet using two algorithms. It was obviously seen that the rivet head had the same drum characteristics and the same zoned deformed structure in both sides. In addition, the severe deformation occurred in the center position of the rivet head both in the metallographic result and simulation result. As shown in Fig. 12 (c), the comparison of radial displacement in rivet shaft between two methods was quantitatively analyzed through the relative difference. From the bottom side to the top side of the rivet shaft, the relative difference of the radial displacement significant increased and reached the maximum value of 13.43%.

Q9: Figures 9 shows the typical network structure (line 216). The structure of the network used in the research should be included here.

Response: We appreciate the reviewer’s suggestions. In the revised manuscript, we modified the network structure based on the research content and added the detail information in Figure 14.

Please see Figure 14 in page 14. As follows:

Figure 14. Topology diagram of RBF.

Q10: English grammar must be checked in the whole manuscript.

Response: Thank you for giving us these kindly comments and suggestions on the language. The English language errors have been carefully checked and corrected in the revised manuscript. The details of the modification are presented as follows.

Please see line 50-52. As follows:

After multiple transmission, reflection, and superposition, the plastic deformation on the rivet shaft caused by the impact forces led to the riveted connection on target sheets, eventually.

Please see line 53-64. As follows:

According to the principle above, EMR has advantages in joining dissimilar mate-rials with stable forming process and uniform deformation. Thus, many researches paid attention to the mechanical properties and failure behaviors of electromagnetic riveted joints [6, 11]. For instance, Jiang et al. [9] investigated the mechanical behav-iors (static tensile and fatigue properties) of Al-CFRP electromagnetically riveted lap joints. The results showed that the rivet squeezing effect under static shear loading caused the bending of the Al sheet and the damage of the CFRP sheet. Moreover, Jiang et al. [12] put further efforts on mechanical properties of Al/CFRP EMR joints and found that the locking modes and discharge energy had obvious effects on connection performance. In addition, Jiang et al. [13] achieved Al/steel self-piecing rivet-ed-adhesive hybrid joints by electromagnetic riveting process and the mechanical tests showed better reliability than the separated connection methods.

Please see line 86-87. As follows:

Cui et al. [24] studied the structural effect of the rivet die on the formation mechanism of the adiabatic shear bands (ASBs) and obtained the optimal riveting die.

Please see line 265-267. As follows:

This indicated that the displacement of the workpiece had a unignorable influence on the electromagnetic force.

Please see line 287-289. As follows:

As shown in Fig. 12 (c), the comparison of radial displacement in rivet shaft between two methods was quantitatively analyzed through the relative difference.

Reviewer 2 Report

The article concerns an interesting issue of modeling and analysis of Electromagnetic Riveting Process.

The work is written correctly, without major errors and faults, but I would introduce the following changes:

- I recommend to change the designation of TC4 to the more commonly used Ti-6Al-4V,
- page 2 line 68 - FE model - when first time used should be full name Finite Element (FE) model ...,
- Any discussion about prior research should be explained using the past tense - so please change for example Page 3 line 105 and please do the revision of the article grammar,
- the meaning of i, t, n, T0 in Fig. 2b should be explained in the text or even better in the title of the drawing - I did not find them in the text,
- I have not found any information about how many elements the model used, and Fig. 3a shows that the mesh was very dense - how did this affect the calculation time?
- the symbols used in Table 1,2,3 require additional explanation of their meaning as comments under the table? (yes, most of them are explained in the text, but in my opinion they should be placed under the table so that the reader does not have to look for it),
- Figs. 12 and 13 are not fully legible, maybe it would be good to enlarge them (e.g. Fig. 19)?

Please also note the description of the calculation model - it lacks clarity in some places. How was the material data used in the simulation determined?

The summary states that the article compares the sequential coupling simulation method, the loose coupling simulation method and the experiments results, but the Conclusions did not mention a word about this comparison.

For such an extensive scope of research and analysis, this part (Conclusions) is written very sparingly.
Bearing in mind the volume of the conducted research, I recommend extending the discussion of the results obtained.

I am also surprised that the riveting issues are described in Coatings, the main topic of which is coatings and surface engineering, where does this choice come from?

Author Response

Honorable reviewer:

Our responses to reviews’ comments and suggestions present as follows.

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Comments and Response:

Reviewer #2

The article concerns an interesting issue of modeling and analysis of Electromagnetic Riveting Process.

Q1: The work is written correctly, without major errors and faults, but I would introduce the following changes:

-I recommend to change the designation of TC4 to the more commonly used Ti-6Al-4V,

Response: We appreciate the reviewer’s suggestions. Thanks for your suggestions and pointing out our errors. In the revised manuscript, we have corrected above-mentioned errors.

Please see line 2-3. As follows:

Numerical Simulation and Parameter Analysis of Electromagnetic Riveting Process for Ti-6Al-4V Titanium Rivet

Please see line 9-13. As follows:

In this work, the axisymmetric sequential and loose electromagnetic-structural coupling simulation models were conducted to perform the electromagnetic riveting process of Ti-6Al-4V titanium rivet, and the parameter analysis of riveting setup was performed based on the sequential coupled simulation results.

Please see line 97-99. As follows:

Please see line 172-173. As follows:

The AA5052 aluminum alloy sheet of 2 mm and the AA6082 aluminum alloy sheet of 4 mm were jointed with Φ5 × 12 mm Ti-6Al-4V titanium rivets by the EMR experiments.

Please see line 186-188. As follows:

Particularly, the Cowper-Symonds parameters of Ti-6Al-4V titanium rivet used in this study were cited from Chen’s experimental procedure [28].

Please see Table 3. As follows:

Material	MURX	RSVX (Ω·m)	E (Pa)	υ	ρ(kg/m³)	Yield stress (Pa)	Tangent modulus (Pa)	m	p
AA5052	1	2.7×10⁻⁸	25.1×10⁹	0.33	2800	100.8×10⁶	379×10⁶	0.25	6500
AA6082	1	2.7×10⁻⁸	66×10⁹	0.33	2800	240×10⁶	261 ×10⁶	0.25	6500
Ti-6Al-4V	1	42×10⁻⁸	88×10⁹	0.34	4500	1009×10⁶	4527 ×10⁶	0.2617	247640
Steel	1	46×10⁻⁸	210×10⁹	0.28	7850	-	-	-	-
Cu	1	1.72×10⁻⁸	-	-	-	-	-	-	-
Air/Far field	1	-	-	-	-	-	-	-	-

Please see line 193-195. As follows:

In order to verify the accuracy of the above finite element model and the feasibil-ity of the EMR process, the AA5052 aluminum alloy sheet of 2 mm and the AA6082 aluminum alloy sheet of 4 mm were jointed with Φ5x12 mm Ti-6Al-4V titanium rivets.

-page 2 line 68 - FE model - when first time used should be full name Finite Element (FE) model ...,

Please see line 31-32. As follows:

Please see line 45-47. As follows:

The EMF setup provided the riveting energy based on the resistor-inductor-capacitor (RLC) attenuating oscillating circuit, which was composed of capacitor banks, resistor, inductor, and coils [10].

Please see line 86-87. As follows:

Cui et al. [24] studied the effect of the rivet die on the formation mechanism of the ad-iabatic shear bands (ASBs) in the rivet driven head and obtained the optimal riveting die.

Please see line 122-123. As follows:

Fig. 3(a) shows the finite element model (FEM) used for the analysis of the 2D ax-isymmetric EMR model using loose-coupled method.

Please see line 196-199. As follows:

As shown in Fig. 6 (b), the punch speed was shot by high-speed camera with digital image correlation (DIC) 3D full-field strain analysis system to compared the actual and the numerical punch speed.

Please see Nomenclature part with units part on page 19. As follows:

Nomenclature part with units

Symbol	Unit	Meaning
EMR	-	Electromagnetic Riveting Process
EMF	-	Electromagnetic Force
RBF	-	Radial Basis Function
CFRP	-	Carbon Fiber Reinforced Polymer
RLC	-	Resistor-Inductor-Capacitor
ASBs	-	The Adiabatic Shear Bands
FEM	-	Finite Element Model
MURX	-	Magnetic Permeability
RSVX	Ω·m	Resistivity
E	Pa	Elastic Modulus
υ	-	Poisson Ratio
ρ	kg/m³	Density
DIC	-	Digital Image Correlation
R_in	mm	Inner Diameter of Driver Plate
R_out	mm	Outer Diameter of Driver Plate
H_D	mm	Height of Driver Plate
H_P	mm	Height of Platform
H_T	mm	Height of Transition Zone
A	°	Angle
W_T	mm	Width of Transition Zone

-Any discussion about prior research should be explained using the past tense - so please change for example Page 3 line 105 and please do the revision of the article grammar,

Please see line 111-112. As follows:

The flow chart of the loose-coupled and sequential-coupled simulation models for EMR were illustrated in Fig. 1.

Please see line 50-52. As follows:

After multiple transmission, reflection, and superposition, the plastic deformation on the rivet shaft caused by the impact forces led to the riveted connection on target sheets, eventually.

Please see line 53-64. As follows:

Please see line 86-87. As follows:

Cui et al. [24] studied the structural effect of the rivet die on the formation mechanism of the adiabatic shear bands (ASBs) and obtained the optimal riveting die.

Please see line 265-267. As follows:

This indicated that the displacement of the workpiece had a unignorable influence on the electromagnetic force.

Please see line 287-289. As follows:

As shown in Fig. 12 (c), the comparison of radial displacement in rivet shaft between two methods was quantitatively analyzed through the relative difference.

-the meaning of i, t, n, T0 in Fig. 2b should be explained in the text or even better in the title of the drawing - I did not find them in the text,

Response: We appreciate the reviewer’s kindly comment. Thank you for pointing out our errors. In the revised manuscript, we have modified the statement of the i, t, n, T₀with the same meaning.

Please see Figure 1 on page 3. As follows:

Figure 1. Flow chart of the EMR simulation model: (a) Loose-coupled method; (b) Sequential-coupled method.

-I have not found any information about how many elements the model used, and Fig. 3a shows that the mesh was very dense - how did this affect the calculation time?

Response: We appreciate the reviewer’s suggestions. In order to balance the calculation accuracy and calculation efficiency, we have conducted the mesh sensitivity study on the deformable bodies before the further analysis of electromagnetic and structural field results. The mesh sensitivity results are listed as follows. Upon the mesh sensitivity results, the mesh size of the rivet, riveted sheets, punch, and restrict die were set to 0.1mm. In the revised manuscript, we have added the discussion about mesh sensitivity in the developed FE model.

Mesh size	0.5mm	0.3mm	0.2mm	0.1mm	0.05mm	0.01mm
Displacement Response	Divergence	Element Distortion	3.366 mm	3.338 mm	3.3383 mm	Exceeding calculation resources
Calculation Time	-	-	50 min	70 min	350 min	-

Please see line 131-135. As follows:

In order to balance the calculation accuracy and calculation efficiency, we have con-ducted the mesh sensitivity study on the deformable bodies before the further analysis of electromagnetic and structural field results. Upon the mesh sensitivity results, the mesh size of the rivet, riveted sheets, punch, and restrict die were set to 0.1mm.

-the symbols used in Table 1,2,3 require additional explanation of their meaning as comments under the table? (yes, most of them are explained in the text, but in my opinion they should be placed under the table so that the reader does not have to look for it),

Response: Thank you for this kindly comment. In the revised manuscript, we added the explanation of the meaning of the symbols and deleted some unnecessary symbols.

Please see Table 1 on page 5. As follows:

Entity	Element type	DOFs
Driver plate	PLANE13	A_x, A_y,Volt
Coil	PLANE13	A_x, A_y,Volt
Air	PLANE13	A_x, A_y
Far field	INFIN110	A_x, A_y
Specially, A_x means the freedom in the x direction; A_y means the freedom in the y direction; Volt means the freedom in the voltage calculation.

Table 1. The elements used in modeling electromagnetic field.

Please see Table 2 on page 6. As follows:

Table 2. Discharge circuit parameters of the EMR system.

Inductance

(L) /H

Resistance

(R) /Ω

Attenuation coefficient

(β) /s⁻¹

Oscillatory frequency

(ω) /(rad⋅s⁻¹)

Capacitance

(C) /F

7.8×10⁻⁶

4.35×10⁻²

2.79×10³

1.77×10⁴

408×10⁻⁶

Please see Table 3 on page 7. As follows:

Table 3. Material properties used in simulating the electromagnetic and structural fields.

Material	Magnetic Permeability	Resistivity (Ω·m)	Elastic modulus (Pa)	Poisson ratio	Density (kg/m³)	Yield stress (Pa)	Tangent modulus (Pa)	m	p
AA5052	1	2.7×10⁻⁸	25.1×10⁹	0.33	2800	100.8×10⁶	379×10⁶	0.25	6500
AA6082	1	2.7×10⁻⁸	66×10⁹	0.33	2800	240×10⁶	261 ×10⁶	0.25	6500
Ti-6Al-4V	1	42×10⁻⁸	88×10⁹	0.34	4500	1009×10⁶	4527 ×10⁶	0.2617	247640
Steel	1	46×10⁻⁸	210×10⁹	0.28	7850	-	-	-	-
Cu	1	1.72×10⁻⁸	-	-	-	-	-	-	-
Air/Far field	1	-	-	-	-	-	-	-	-

-Figs. 12 and 13 are not fully legible, maybe it would be good to enlarge them (e.g. Fig. 19)?

Response: Thanks very much for pointing out these errors. In the revised manuscript, we have checked all the figures and enlarged the unclear ones.

Please see Figure 8 on page 10. As follows:

Figure 8. The temporal distribution of EMF on the driver plate in loose-coupled model: (a) t=10 μs; (b) t=80 μs; (c) t=260 μs; (d) t=440 μs; (e) t=620 μs; (f) t=800 μs.

Please see Figure 9 on page 11. As follows:

Figure 9. The temporal distribution of EMF on the driver plate in sequential-coupled model: (a) t=10 μs; (b) t=80 μs; (c) t=260 μs; (d) t=440 μs; (e) t=620 μs; (f) t=800 μs.

Q2: Please also note the description of the calculation model - it lacks clarity in some places. How was the material data used in the simulation determined?

Response: Thank you for kindly giving these good comments. In the revised manuscript, we have added the explanations for the use of material data in the simulation model.

Please see line185-188. As follows:

The detailed material properties using in the numerical model obtained from the fitted results are exhibited in Table 3. Besides, the Cowper-Symonds parameters of Ti-6Al-4V titanium rivet used in this study were cited from Chen’s experimental procedure [28].

Q3: The summary states that the article compares the sequential coupling simulation method, the loose coupling simulation method and the experiments results, but the Conclusions did not mention a word about this comparison.

Response: Thank you for giving us these kindly comments. In the revised manuscript, we modified the conclusion part and added the comparison results between sequential and loose coupling numerical model.

Please see conclusion on page 18. As follows:

In this paper, the numerical simulations and structural parameter analysis were conducted to analyze the EMR process. From the simulation results above, the main conclusions are as follows:

By considering the effect of workpiece deformation in the EMR process, the se-quential coupling method had a high simulation accuracy in the punch speed and rivet deformation. The maximum relative difference of electromagnetic force on driver plate and radial displacement in rivet shaft was 34.86% and 13.43%, re-spectively.
The RBF approximation analysis results based on the sequential numerical model showed that the outer diameter and the height of the driver plate had a signifi-cant first-order effect on the response of displacement. Meanwhile the platform height, transition zone height, angle, and transition zone width of amplifier pre-sented a strong interaction effect.
The optimal structural parameters of driver plate and amplifier were obtained based on the parameter optimization model. It was found that the optimal design could effectively improve the velocity of the punch from 6.13 m/s to 8.12 m/s with a 32.46% increasement. Besides, the displacement of punch increasing from 3.38 mm to 3.81 mm would lead to 80.55% increasement in the maximum radial dis-placement of rivet shaft. This indicated the deformation of rivet was efficiently improved by using the optimal rivet model.

Q4: For such an extensive scope of research and analysis, this part (Conclusions) is written very sparingly.

Q5: Bearing in mind the volume of the conducted research, I recommend extending the discussion of the results obtained.

Response: We appreciate the reviewer’s suggestions. In the revised manuscript, we made a significant modification of the discussion of the results obtained to improved the novelty of this paper.

Please see line 264-271, As follows:

With the time increasing, the relative difference of electromagnetic force gradually rose and reached the maximum value of 34.86%. This indicated that the displacement of the workpiece had a unignorable influence on the electromagnetic force. The differences in the EMF responses were directly mapped to the corresponding current density response.

Figure 10. Comparison of the magnetic-time force at special point (r=60 mm) between loose and sequential coupling algorithms.

Please see line 281-294, As follows:

Please see line 361-379, As follows:

Pareto effect plot was commonly adopted to compare the relative magnitude and statistical significance of the main effect, square effect, and the interaction effect. The Pareto effects of all significant parameters in driver plate and amplifier (beyond the reference line) were shown in Fig. 17. It could be obviously seen that the outer diameter (R_out) and the height of the driver plate (H_D) had a significant first-order effect on the response of displacement. This because the outer diameter of driver plate had an important effect on the EMF utilization, while the height significantly influenced the weight of the driver plate. Besides, the structural parameters of amplifier had a strong interaction effect on the displacement response. This second-order and third-order interaction effect illustrated the curvilinear contour in the Fig. 16. The most remarkable interaction effect between the transition zone height (H_T), angle (A), and transition zone width (W_T) revealed the design of transition zone could efficiently enhance the response of displacement. In addition, the platform height (H_P) showed a unignorable first-order effect, which was consistent with the result in Fig. 16(b) and Fig. 16(d). This was because the structure of driver plate had an important effect on the EMF utilization and further influenced the riveting process. Moreover, the structure of amplifier dominated the force transmission path and most of the weight of the equipment, which was a multi-level synthesis of shape parameters.

Figure 17. Pareto effect of the parameters in driver plate and amplifier.

Please see line 397-405 and Figure 20, As follows:

Fig. 20 demonstrate the comparison of equivalent strain in rivet and radial displacement in rivet shaft between baseline and optimal design. The strain distribution tendency and the position of the maximum strain value were similar before and after optimization. However, for the optimal design, the deformation was more concentrated in the rivet head, while the expansion of the rivet shaft was deeper, as shown in Fig. 20(b). The displacement of punch increased from 3.38 mm to 3.81 mm with the 13% increasement, while the maximum radial displacement of rivet shaft increased from 0.36 mm to 0.65mm with the 80.55% increasement.

Figure 20. The comparison of equivalent strain in rivet and radial displacement in rivet shaft between baseline and optimal design: (a) Equivalent strain in rivet; (b) Radial displacement in rivet shaft.

Q6: I am also surprised that the riveting issues are described in Coatings, the main topic of which is coatings and surface engineering, where does this choice come from?

Response: Thank you for kindly giving these good comments. In fact, this manuscript was submitted to the special issue “Advanced Joining Technologies of Alloys and Composites in the Automotive, Aeronautic and Astronautic Fields” in Coatings. The scope of the special issue concluded modeling and simulation of joining processes, which was the main topic of this paper. Thus, we make the choice to submit the manuscript to the journal.

Reviewer 3 Report

The current study investigates the riveting using electromagnetic process for a titanium rivet. For this, the authors develop a structural simulation models of the riveting process and analysed the parameters of the riveting setup. The authors found the punch displacement was influenced by the structural parameters of the riveting setup.
It is not clear in the abstract of what are these structural parameters, there is a lot of focus on the numerical models and their validity but not much about the riveting setup parameters.
Please consider reviewing the abstract and highlight the novelty, major findings and conclusions.
Although I must say that the images in Figure 1 are interesting, but please consider removing figure 1, it is more suitable for a literature review chapter in a thesis but not in a scientific paper. We know what EMR process is and how it works.
The authors spend a lot of efforts in the introduction talking about how the EMR process works and about the riveting process and its advantages but not much about past studies in the literature on similar or different materials and what they found.
In lines 92-94, this was not mentioned clearly in the abstract, please consider making the last paragraph in the introduction like what you mention in the abstract.
Before line 92 the authors are encouraged to answer the following question: What is the research gap did you find from the previous researchers in your field? Mention it properly. It will improve the strength of the article.
What are the limitations/advantages in each model?
Line 105-116 again the authors are giving us step by step details of how the model was setup, but this kind of description is more suited to a chapter in a thesis and not in a scientific paper. Please only give the major details which are sufficient to explain the nature of the numerical models used and how they were formed.
Why the mesh size in the two models shown in Figure 3 are different?
Did the authors conduct a mesh convergence study?
The authors should add a list of nomenclature for all the symbols and Greek letters used in this work at the end of the manuscript.
Table 2 why the authors use those specific parameters in their model? Why not a range of discharge parameters for the EMR system to test the validity of the FE model over a wider range.
Line 171 the authors use some parameters values from a previous study, was this study conducted on the same material? And also using the same device? Please discuss and explain.
Table 3 needs references if this data was not measured by the authors. (Add it on the table caption not in the text itself).
Please make sure to discuss mesh sensitivity in your developed FE model.
Does the contact mechanism between different parts in your model have any influence on the deformation in the rivet?
Please enlarge Figure 13 it is not easy to read the data and results from them. Or move them to an appendix and keep one of each for explanation and discussion.
Line 274 “at special point” what is special about it? Or do you mean at the same point?
Line 276 “The reason is that the displacement of driver plate was slight at….”What do the authors mean by slight?
Line 277 “the EMF response from the loose-coupled model was overestimated….” By how much, please be specific when you discuss such important issues in your models. Also why those differences existed, what are the reasons behind that?
So far I don’t see any scientific explanation of any of the observations made in the FE models, only describing the results obtained from them.
Section “3.2.2. RBF results” please write the full meaning of RBF
Figure 16 needs to be enlarged it is not clear and difficult to read the y axis data on the right side.
Line 330 “that there were two optimal ranged for…” this sentence does not read well, please check the word ranged or do you mean ranges?
Lines 335-337 why? Here the authors observed some phenomenon, but they did not attempt to explain them or compare them to similar studies from the open literature.
Line 364 “The displacement of punch increased from 3.38 mm to 3.81 mm” how significant is this difference in riveting applications, you could give an example saying how does the displacement of punch can influence the deformation of the rivet and its influence on the structural application where the rivet(s) are installed.
The results are merely described and is limited to comparing the numerical observation. The authors are encouraged to include more detail discussion and critically discuss the observations from this investigation with existing literature.

Author Response

Honorable reviewer:

Our responses to reviews’ comments and suggestions present as follows.

-------------------------------------------------------------------------------------------------------

Comments and Response:

Reviewer #3

The current study investigates the riveting using electromagnetic process for a titanium rivet. For this, the authors develop a structural simulation models of the riveting process and analysed the parameters of the riveting setup. The authors found the punch displacement was influenced by the structural parameters of the riveting setup.

Q1: It is not clear in the abstract of what are these structural parameters, there is a lot of focus on the numerical models and their validity but not much about the riveting setup parameters.

Response: Thank you for pointing out this problem. In the revised manuscript, the structural parameters of EMR setup, such as the outer diameter, the height of the driver plate and other aspects, were mentioned. Moreover, the effects of these parameters on punch displacement were presented with specific values.

Please see Abstract on page 1. As follows:

Abstract: Electromagnetic riveting process (EMR) is a high-speed impact connection technology with the advantages of fast loading speed, large impact force and stable rivet deformation. In this work, the axisymmetric sequential and loose electromagnetic-structural coupling simulation models were conducted to perform the electromagnetic riveting process of Ti-6Al-4V titanium rivet, and the parameter analysis of riveting setup was performed based on the sequential coupled simulation results. Besides, the single-objective optimization problem of punch displacement was conducted using Hooke-Jeeves algorithm. Based on the adaptive remeshing technology adopted in air meshes, the deformation calculated in the structural field was well transferred to the electromagnetic field in the sequential coupled model. Thus, the sequential coupling simulation results presented higher accuracy on the punch speed and rivet deformation than loose coupling numerical model. The maximum relative difference of electromagnetic force on driver plate and radial displacement in rivet shaft was 34.86% and 13.43%, respectively. The parameter analysis results showed that the outer diameter and the height of the driver plate had a significant first-order effect on the response of displacement, while the platform height, transition zone height, angle, and transition zone width of amplifier presented a strong interaction effect. Using the obtained results on the optimal structural parameters, the punch speed was effectively improved from 6.13 m/s to 8.12 m/s with a 32.46% increasement. Besides, the displacement of punch increasing from 3.38 mm to 3.81 mm would lead to 80.55% increasement in the maximum radial displacement of rivet shaft. This indicated the deformation of rivet was efficiently improved by using the optimal rivet model.

Q2: Please consider reviewing the abstract and highlight the novelty, major findings and conclusions.

Response: Thank you very much for your advices. In the revised manuscript, significant modifications have been made for the abstract. Major effects of those structural parameters were quantified. Furthermore, the optimized results were given through the comparison with the base line design.

Please see Abstract on page 1. As follows:

Q3: Although I must say that the images in Figure 1 are interesting, but please consider removing figure 1, it is more suitable for a literature review chapter in a thesis but not in a scientific paper. We know what EMR process is and how it works.

Response: Thank you very much for your advices. In the revised manuscript, figure 1 has been removed and only the main part of the principals of EMR was kept.

Please see Line 42-52. As follows:

In the EMR process, the mutually exclusive EMF was an instantaneous, homogeneous, and stable impact force worked on the rivet [1, 8]. The EMR device was mainly consisted of two parts: discharge equipment (electromagnetic force (EMF) setup) and riveting setup [9]. The EMF setup provided the riveting energy based on the resistor-inductor-capacitor (RLC) attenuating oscillating circuit, which was composed of capacitor banks, resistor, inductor, and coils [10]. In detail, the discharge equipment first released the high-frequency current through the coil and generated the motional current in the driver plate. Consequently, a high-intensity repulsive force was produced between the coil and the driver plate, and propagated in the form of waves inside the amplifier. After multiple transmission, reflection, and superposition, the plastic deformation on the rivet shaft caused by the impact forces led to the riveted connection on target sheets, eventually.

Q4: The authors spend a lot of efforts in the introduction talking about how the EMR process works and about the riveting process and its advantages but not much about past studies in the literature on similar or different materials and what they found.

Response: Thank you very much for pointing out this problem. In the revised manuscript, several modifications have been made on the Introduction section. The research findings from former studies mentioned in our paper were highlighted.

Please see line 53-64. As follows:

According to the principle above, EMR has advantages in joining dissimilar materials with stable forming process and uniform deformation. Thus, many researches paid attention to the mechanical properties and failure behaviors of electromagnetic riveted joints [6, 11]. For instance, Jiang et al. [9] investigated the mechanical behaviors (static tensile and fatigue properties) of Al-CFRP electromagnetically riveted lap joints. The results showed that the rivet squeezing effect under static shear loading caused the bending of the Al sheet and the damage of the CFRP sheet. Moreover, Jiang et al. [12] put further efforts on mechanical properties of Al/CFRP EMR joints and found that the locking modes and discharge energy had obvious effects on connection performance. In addition, Jiang et al. [13] achieved Al/steel self-piecing riveted-adhesive hybrid joints by electromagnetic riveting process and the mechanical tests showed better reliability than the separated connection methods.

Please see line 75-83. As follows:

Many researchers investigated the divergence between loose coupling and sequential coupling numerical simulation method of electromagnetic forming process. Bartels et al. [22] adopted two different simulation methods of electromagnetic metal forming process. The simulation results showed that the deviation between two methods gradually increased with time and leaded to the overestimation of the loose coupling numerical model. Yu et al. [23] found that the simulation accuracy of sequential coupling simulation for electromagnetic tube compression was highly improved by considering the effect of tube deformation on the electromagnetic geometry. However, the studies of differences between two algorithms in EMR process were limited.

Q5: In lines 92-94, this was not mentioned clearly in the abstract, please consider making the last paragraph in the introduction like what you mention in the abstract.

Response: Thank you very much for your good advice. In the revised manuscript, the last paragraph in the introduction was modified through your advice.

Please see line 97-108. As follows:

In this paper, the axisymmetric sequential and loose electromagnetic-structural coupling simulation models were conducted to perform the electromagnetic riveting process of Ti-6Al-4V titanium rivet, and the parameter analysis of riveting setup was performed based on the sequential coupled simulation results. Firstly, a loose coupled and a sequential coupled EMR simulation models were established in 2D axisymmetric form separately to simulated the EMR process of aluminum alloy sheets with titanium alloy rivet by using multi-physic software ANSYS. Then the obtained results of EMF, current density on driver plate, the rivet velocity of the punch, and the deformation form of rivet were compared to assess the divergence of different types of numerical models. Next, parameter analysis of riveting setup (driver plate and amplifier) was performed based on the sequential coupled simulation results. Finally, the sin-gle-objective optimization problem of punch displacement was conducted using Hooke-Jeeves algorithm.

Q6: Before line 92 the authors are encouraged to answer the following question: What is the research gap did you find from the previous researchers in your field? Mention it properly. It will improve the strength of the article.

Response: Thank you very much for your good advice. In the revised manuscript, some interesting research findings from former studies were highlighted and several research subjects were pointed out accordingly.

Please see line 75-83. As follows:

Please see line 91-96. As follows:

Note that abovementioned parameter studies were aimed at the subjects of coil and the rivet die. The other two major parts of EMR setup, namely the driver plate and the amplifier, have not been explored yet. Meanwhile, the driver plate undertook the whole EMF, and the amplifier reflected and superimposed the stress wave into rivet. Thus, it was of great significance to study the parameter effects of the structural pa-rameters within driver plate and amplifier.

Q7: What are the limitations/advantages in each model?

Response: Thank you for your kindly comment. Electromagnetic riveting process (EMR) is a complex electromagnetic-structural coupling process. Numerical simulation offers an opportunity to overcome the problem. Currently, two main strategies are developed to simulate the EMR: loose coupling method and sequential coupling method. The loose coupling method is simple, which treat the electromagnetic field and structural field as two independent problems, while the sequential coupling method can overcome the magnetic structure coupling problem successfully because the workpiece deformation on magnetic field analysis is considered [1]. Thus, the loose coupling method have higher simulation efficiency, while the sequential coupling method could obtain higher simulation accuracy.

[1] Cui XH, Mo JH, Li JJ, Huang L, Zhu Y, Li ZW, Zhong K. Effect of second current pulse and different algorithms on simulation accuracy for electromagnetic sheet forming. International Journal of Advanced Manufacturing Technology. 2013, 68(5-8): 1137-1146.

[2] Zhang X, Yu HP, Li CF. Multi-filed coupling numerical simulation and experimental investigation in electromagnetic riveting. International Journal of Advanced Manufacturing Technology. 2014, 73: 1751-1763.

Q8: Line 105-116 again the authors are giving us step by step details of how the model was setup, but this kind of description is more suited to a chapter in a thesis and not in a scientific paper. Please only give the major details which are sufficient to explain the nature of the numerical models used and how they were formed.

Response: We appreciate the reviewer’s suggestions. In the revised manuscript, we have simplified the details of how the model was setup and focused on the major details which are sufficient to explain the nature of two numerical models.

Please see line111-118 on page 3. As follows:

The flow chart of the loose-coupled and sequential-coupled simulation models for EMR were illustrated in Fig. 1. The electromagnetic filed analysis and structural field analysis were solved in ANSYS/EMAG and ANSYS, respectively. It could be easily seen that the loose coupling model treated the electromagnetic field and structural field as two independent issues, while the electromagnetic analysis and the structural analysis were iteratively performed in the sequential coupling model. The calculated defor-mation results were updated to the electromagnetic field based on the adaptive remeshing technology used in air meshes.

Q9: Why the mesh size in the two models shown in Figure 3 are different?

Response: Thank you for kindly giving this good comment. In the sequential coupling and loose coupling model, the mesh size, boundary condition, and material properties were kept constant to ensure the simulation accuracy. In Fig.3, the schematic figures had different layouts based on the principle of two models. Due to the different magnification of the detailed figure, the mesh size in the two models looked like different.

Q10: Did the authors conduct a mesh convergence study?

Response: We appreciate the reviewer’s suggestion. For the finite element analysis, the mesh convergence significantly influenced the simulation accuracy. In this paper, we have conducted the mesh convergence study before further analysis of electromagnetic field and structural field results. Upon the mesh convergence study and the mesh sensitivity study, the mesh size of rivet, riveted sheets, punch, and the restrict die were set to 0.1mm. The mesh convergence study results are listed as following table.

Mesh size	0.5mm	0.3mm	0.2mm	0.1mm	0.05mm	0.01mm
Mesh convergence	Divergence	Convergence	Convergence	Convergence	Convergence	Exceeding calculation resources

Q11: The authors should add a list of nomenclature for all the symbols and Greek letters used in this work at the end of the manuscript.

Response: We thank you very much for this advice. Your suggestions are very helpful for our paper. The nomenclature part has been added in the revised paper.

Please see Nomenclature part with units part on page 19. As follows:

Nomenclature part with units

Symbol	Unit	Meaning
EMR	-	Electromagnetic Riveting Process
EMF	-	Electromagnetic Force
RBF	-	Radial Basis Function
CFRP	-	Carbon Fiber Reinforced Polymer
RLC	-	Resistor-Inductor-Capacitor
ASBs	-	The Adiabatic Shear Bands
FEM	-	Finite Element Model
MURX	-	Magnetic Permeability
RSVX	Ω·m	Resistivity
E	Pa	Elastic Modulus
υ	-	Poisson Ratio
ρ	kg/m³	Density
DIC	-	Digital Image Correlation
R_in	mm	Inner Diameter of Driver Plate
R_out	mm	Outer Diameter of Driver Plate
H_D	mm	Height of Driver Plate
H_P	mm	Height of Platform
H_T	mm	Height of Transition Zone
A	°	Angle
W_T	mm	Width of Transition Zone

Q12: Table 2 why the authors use those specific parameters in their model? Why not a range of discharge parameters for the EMR system to test the validity of the FE model over a wider range.

Response: We thank you very much for this suggestion. In this paper, the specific energy value was chosen based on the optimal pre-trial-experiment results. The parameter in Table 2 were obtained fitting from the experimental data. The influence of the discharge energy on the riveting process was not explored in this study, which was widely studied in former references. Thus, the simulation model was verified in the specific energy condition by the riveting deformation and impact speed, which was in good agreement with the experimental results.

Q13: Line 171 the authors use some parameters values from a previous study, was this study conducted on the same material? And also using the same device? Please discuss and explain.

Response: Thank you for kindly giving these good comments. In the Cowper-Symonds constitutive model, the m and P are the specific parameters for aluminum alloy. As presented in some former research, the m and P were set as 0.25 and 6500 for the aluminum alloy they used, such as AA5052 aluminum alloy [1], 2A12 aluminum alloy [2], AA3003 aluminum alloy [3], and AA6082-T6 aluminum alloy [4]. The simulated results were in good agreement in their studies.

[1] Liu D H, Li C F, Yu H P. Numerical modeling and deformation analysis for electromagnetically assisted deep drawing of AA5052 sheet [J]. Trans. Nonferrous Mer. Soc. China. 2009, 19(5): 1294-1302.

[2] Zhang, X.; Zhang, M.Y.; Sun, L.Q.; Li, C.F. Numerical simulation and experimental investigations on TA1 titanium alloy rivet in electromagnetic riveting. Archives of Civil and Mechanical Engineering. 2018, 18(3), 887-901.

[3] Cui, X.H.; Mo, J.H.; Li, J.J.; Huang, L.; Zhu, Y.; Li, Z.W.; Zhong, K. Effect of second current pulse and different algorithms on simulation accuracy for electromagnetic sheet forming. International Journal of Advanced Manufacturing Technology, 2013, 68(5-8):1137-1146.

[4] Cui, J.J.; Qi, L.; Jiang, H.; Li, G.Y.; Zhang, X. Numerical and experimental investigations in electromagnetic riveting with dif-ferent rivet dies. International Journal of Material Forming. 2018, 11(6), 1-12.

Q14: Table 3 needs references if this data was not measured by the authors. (Add it on the table caption not in the text itself).

Response: Thank you for kindly giving this good suggestion. In the revised manuscript, the references of the data in Table 3 were added on the table caption.

Please see paragraph 3 on page 7. As follows:

Table 3. Material properties used in simulating the electromagnetic and structural fields [28].

Material	Magnetic Permeability	Resistivity (Ω·m)	Elastic modulus (Pa)	Poisson ratio	Density (kg/m³)	Yield stress (Pa)	Tangent modulus (Pa)	m	p
AA5052	1	2.7×10⁻⁸	25.1×10⁹	0.33	2800	100.8×10⁶	379×10⁶	0.25	6500
AA6082	1	2.7×10⁻⁸	66×10⁹	0.33	2800	240×10⁶	261 ×10⁶	0.25	6500
Ti-6Al-4V	1	42×10⁻⁸	88×10⁹	0.34	4500	1009×10⁶	4527 ×10⁶	0.2617	247640
Steel	1	46×10⁻⁸	210×10⁹	0.28	7850	-	-	-	-
Cu	1	1.72×10⁻⁸	-	-	-	-	-	-	-
Air/Far field	1	-	-	-	-	-	-	-	-

Q15: Please make sure to discuss mesh sensitivity in your developed FE model.

Mesh size	0.5mm	0.3mm	0.2mm	0.1mm	0.05mm	0.01mm
Displacement Response	Divergence	Element Distortion	3.366 mm	3.338 mm	3.3383 mm	Exceeding calculation resources
Calculation Time	-	-	50 min	70 min	350 min	-

Please see line 131-135. As follows:

Q16: Does the contact mechanism between different parts in your model have any influence on the deformation in the rivet?

Response: Thank you for giving us this good comment. In the structural field analysis, the contact mechanism between driver plate, amplifier, and punch was ignorable because of the higher stiffness and no initial gap. However, the contact mechanism between punch, rivet, riveted sheet, and restrict die had influence on the deformation of the rivet. Thus, we set the mesh size of those components the same value of 0.1 mm. Besides, the penalty contact function with the friction coefficient value of 0.2 was adopted to simulate the contact behavior. In the revised, we have added the detail contact information of the structural field analysis model.

Please see line 130-131. As follows:

During the structural field simulation, penalty contact function with the friction coefficient value of 0.2 was adopted to simulate the contact behavior.

Q17: Please enlarge Figure 13 it is not easy to read the data and results from them. Or move them to an appendix and keep one of each for explanation and discussion.

Response: Thanks very much for pointing out these errors. In the revised manuscript, we have checked all the figures and enlarged the unclear ones.

Please see figure 8 on page 10. As follows:

Figure 8. The temporal distribution of EMF on the driver plate in loose-coupled model: (a) t=10 μs; (b) t=80 μs; (c) t=260 μs; (d) t=440 μs; (e) t=620 μs; (f) t=800 μs.

Please see figure 9 on page 11. As follows:

Figure 9. The temporal distribution of EMF on the driver plate in sequential-coupled model: (a) t=10 μs; (b) t=80 μs; (c) t=260 μs; (d) t=440 μs; (e) t=620 μs; (f) t=800 μs.

Q18: Line 274 “at special point” what is special about it? Or do you mean at the same point?

Response: Thank you for pointing out this error. The “special point” was the same point as the measured point in Fig. 12. In the revised manuscript, we have modified the statement.

Please see line 259-260. As follows:

In order to evaluate the electromagnetic field response between two simulation algorithms, Fig. 12 shows the change of EMF at measured point with time.

Q19: Line 276 “The reason is that the displacement of driver plate was slight at….” What do the authors mean by slight?

Response: Thank you for pointing out this error. The slight displacement here means limited or small displacement. This is because the deformation of rivet was limited due to the deformation time of 20 μs.

Please see line 262-263. As follows:

The reason is that the displacement of driver plate was limited at this time (within 1e-3 mm).

Q20: Line 277 “the EMF response from the loose-coupled model was overestimated….” By how much, please be specific when you discuss such important issues in your models. Also why those differences existed, what are the reasons behind that?

Response: Thank you for pointing out this problem. In the revised manuscript, the relative difference of electromagnetic force was quantified with a maximum value of 34.86%. Furthermore, the reason that causing the difference was discussed as well.

Please see line 264-271. As follows:

Figure 10. Comparison of the magnetic-time force at special point (r=60 mm) between loose and sequential coupling algorithms.

Q21: So far I don’t see any scientific explanation of any of the observations made in the FE models, only describing the results obtained from them.

Response: Thank you for pointing out this problem. In the revised manuscript, the differences on electromagnetic forces and radial displacements between the established FE models were quantified. Therefore, the reasons that led to the simulated errors were given.

Please see line 264-271, As follows:

Figure 10. Comparison of the magnetic-time force at special point (r=60 mm) between loose and sequential coupling algorithms.

Please see line 281-294, As follows:

Please see line 361-379, As follows:

Figure 17. Pareto effect of the parameters in driver plate and amplifier.

Please see line 397-405 and Figure 20, As follows:

Q22: Section “3.2.2. RBF results” please write the full meaning of RBF

Response: Thank you for your suggestion. In the revised manuscript, we have added the full meaning of RBF.

Please see section 3.2.2 on page 13. As follows:

3.2.2. Radial Basis Function Model results

Q23: Figure 16 needs to be enlarged it is not clear and difficult to read the y axis data on the right side.

Response: Thanks very much for pointing out these errors. In the revised manuscript, we have checked all the figures and enlarged the unclear ones.

Please see Figure 15 on page 14. As follows:

Figure 15. Contour map of the driver plate geometry on punch displacement: (a)H_D and R_in (R_out =75 mm); (b) H_D and R_out (R_in =10 mm); (c) R_in and R_out (H_D =5.5 mm).

Please see Figure 16 on page 15. As follows:


(a)	(b)

(c)	(d)

(e)	(f)

Figure 16. Contour map of the amplifier geometry on punch displacement: (a) A and H_T (H_P =10 mm, W_T =30 mm); (b) A and H_P (H_T =20 mm, W_T =30 mm); (c) A and W_T (H_P =10 mm, H_T =20 mm); (d) H_T and H_P (W_T =30 mm, A =45 °); (e) H_T and W_T (H_P =1 0mm, A =45 °); (e) H_P and W_T (H_T =20 mm, A =45 °).

Q24: Line 330 “that there were two optimal ranged for…” this sentence does not read well, please check the word ranged or do you mean ranges?

Response: Thank you for pointing out this error. In this sentence, the word ranged should be changed to ranges, which means the angle had two optimal ranges for the displacement response. The first range was 0° to 20°, while the second range was 40° to 60°. In the revised manuscript, we have modified the sentences.

Please see line 350-351. As follows:

Fig. 16 (a) and Fig. 16 (c) demonstrated that there were two optimal ranges for the angle of transition zone with different matched H_T and W_T. The first range was 0° to 20°, while the second range was 40° to 60°.

Q25: Lines 335-337 why? Here the authors observed some phenomenon, but they did not attempt to explain them or compare them to similar studies from the open literature.

Response: Thank you for pointing out this error. In the revised manuscript, we added the Pareto effect analysis to explain the phenomenon observed in Fig. 15 and Fig. 16.

Please see paragraph 3 on page 3. As follows:

Figure 17. Pareto effect of the parameters in driver plate and amplifier.

Q26: Line 364 “The displacement of punch increased from 3.38 mm to 3.81 mm” how significant is this difference in riveting applications, you could give an example saying how does the displacement of punch can influence the deformation of the rivet and its influence on the structural application where the rivet(s) are installed.

Response: Thank you for your good questions. In the revised manuscript, the relative differences on punch displacements and radial displacements of rivet shaft were given. The results showed that 13% increasement in punch displacement would lead to 80.55% increasement in radial displacement of rivet shaft. Meanwhile, the comparison of the punch speed was also added in the revised manuscript.

Please see line 387-388. As follows:

It was found that the optimal design could effectively improve the velocity of the punch from 6.13 m/s to 8.12 m/s with a 32.46% increasement.

Please see line 397-405. As follows:

Please see Figure 20 on page 18. As follows:

Q27: The results are merely described and is limited to comparing the numerical observation. The authors are encouraged to include more detail discussion and critically discuss the observations from this investigation with existing literature.

Please see line 264-271, As follows:

Figure 10. Comparison of the magnetic-time force at special point (r=60 mm) between loose and sequential coupling algorithms.

Please see line 281-294, As follows:

Please see line 361-379, As follows:

Figure 17. Pareto effect of the parameters in driver plate and amplifier.

Please see line 397-405 and Figure 20, As follows:

Round 2

Reviewer 1 Report

The authors have addressed all my comments and suggestions. The quality of the article has been significantly improved. This manuscript can be accepted.

Reviewer 3 Report

The authors have provided all needed answer, paper can now be accepted.

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Numerical Simulation and Parameter Analysis of Electromagnetic Riveting Process for Ti-6Al-4V Titanium Rivet

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