Submit to this Journal Review for this Journal Propose a Special Issue

Article Menu

Share Help Cite Discuss in SciProfiles

Open AccessFeature PaperArticle

Peer-Review Record

Multivariate Quadratic Nonlinear Regression Model of the Ultimate Pull-Out Load of Electrohydraulic Expansion Joints Based on Response Surface Methodology

Coatings 2021, 11(6), 689; https://doi.org/10.3390/coatings11060689

by Da Cai, Chenyu Jin, Jie Liang, Guangyao Li and Junjia Cui^*

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Coatings 2021, 11(6), 689; https://doi.org/10.3390/coatings11060689

Submission received: 1 May 2021 / Revised: 4 June 2021 / Accepted: 5 June 2021 / Published: 9 June 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 manuscript is focused on the electrohydraulic expansion joining process. Three parameters were investigated, the discharge voltage, the wire length, and the wire diameter. The influence of the different parameters in the pull-out loads of the joints and the corresponding mathematical relationship were considered.

The paper is interesting and fits the aim and scope of the journal.

Minor problems:

Introduction

The introduction is very interesting. However, the English must be revised.

Materials and Methods

Why was the loading speed set to 2 mm/min?

The joining specimen dimensions should be justified. Why was used a length of the overlap area of 20 mm? And a rectangular groove with a depth of 1 mm? And a width of 6 mm?

Results and Discussion

The quality of the figures should be improved.

Why the interaction between discharge voltage and the wire diameter is significant and the interaction between wire length and wire diameter is not significant?

I recommend the paper to be accepted after revision.

Author Response

Honorable editors and reviewers:

On behalf of my co-authors, we thank you very much for giving us an opportunity to revise our manuscript. We appreciate editor and reviewers very much for their positive and constructive comments and suggestions on our manuscript entitled “Multivariate quadratic nonlinear regression model of the ultimate pull-out load of electrohydraulic expansion joints based on response surface methodology” (ID: coatings-1225822). We have studied reviewer’s comments carefully and have made revisions which were marked up using the “Track Changes” function 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.

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

Comments and Response:

Reviewer #1:

The paper is interesting and fits the aim and scope of the journal. I recommend the paper to be accepted after revision.

Minor problems:

Q1. Introduction

The introduction is very interesting. However, the English must be revised.

Response:

We appreciate your suggestion. We have rechecked and corrected the errors in the revised manuscript with the assistance of a colleague who is well-versed in English.

Please see line 34 on page 1. As follows:

“However, the potential for weight reduction using pipe joining parts and frame structures made from lightweight materials was limited by the conventional joining technology [7].”

Please see line 35 on page 1. As follows:

“The conventional joining technologies included: thermal welding, mechanical fastening and adhesive bonding.”

Please see line 40 on page 1. As follows:

“The joining by forming processes could overcome certain disadvantages.”

Please see line 46 on page 2. As follows:

“The joining by forming processes can be classified based on forming direction, forming energy and strain rate.”

Please see line 49 and line 50 on page 2. As follows:

“Based on the strain rate, the joining was divided into joining by quasi-static forming and joining by high-speed forming.”

Please see line 51 on page 2. As follows:

“The joining by quasi-static forming processes include joining by rolling, joining by hydroforming, mechanical crimping, hydraulic crimping and joining by impulse forming.”

Please see line 53 on page 2. As follows:

“Henriksen et al. used numerical simulation and experiment methods to study the joining of steel pipes and steel flanges [10].”

Please see line 58 on page 2. As follows:

“In the mechanical crimping process of steel pipe,”

Please see lines 62-65 on page 2. As follows:

“Friction coefficient and yield stress were the main factors affecting the quality of hydraulic crimping [14]. However, the low formability of lightweight high strength alloys at room temperature could cause cracking problems [15].”

Please see line 67 on page 2. As follows:

“Different from joining by quasi-static forming, joining by impulse forming is a high-speed joining technology that can improve formability [16].”

Please see lines 71-75 on page 2. As follows:

“During the electro-magnetic crimping joining process, the discharge energy and the groove characteristics would affect the strength of the joint. In response to this characteristic, Weddeling et al. established an analysis method for determining process parameters such as discharge energy based on groove geometry and workpiece characteristics in the joining process [4, 17].”

Please see lines 77-81 on page 2. As follows:

“The pipes could also be joined by electrohydraulic expansion joining [18]. Compared with joining by quasi-static forming processes, the electrohydraulic expansion joining improves the forming limit of the forming area and joining efficiency. Compared with joining by electromagnetic forming, a more uniform pressure distribution can be obtained during the presented process [19, 20].”

Please see line 84 on page 2. As follows:

“the diameter and length of the wire can also affect the forming result [21].”

Please see lines 86-87 on page 2. As follows:

“However, the influence of these parameters on the pull-out load of the joints and the corresponding mathematical relationships have not been reported.”

Please see lines 90-92 on page 2. As follows:

Please see lines 95-103 on pages 2-3. As follows:

“Firstly, the experiment was designed based on the central composite design (CCD) technology. Secondly, the experimental results were statistically analyzed to obtain the multivariate nonlinear regression model of the ultimate pull-out load of electrohydraulic expansion joints based on response surface methodology. Subsequently, the model was used to analyze the influence of each parameter on the pull-out load separately and interactively. The main factors that affect the pull-out load were found. Finally, the process parameters were optimized with the goal of the ultimate pull-out load. Experiments were carried out to verify the optimization results under the optimized settings.”

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

Q2. Materials and Methods

Why was the loading speed set to 2 mm/min? The joining specimen dimensions should be justified. Why was used a length of the overlap area of 20 mm? And a rectangular groove with a depth of 1 mm? And a width of 6 mm?

Response:

We thank you very much for pointing out this problem. It was indeed necessary to explain the selection of the parameters in detail. In general, the selection of the parameters was based on actual applications and preliminary research. In the revised manuscript, we have clearly justified the selection of parameters. The detailed description on the selection of the parameters and their levels is as follow.

(1) For the selection of the loading speed

The mechanical properties of the joints were evaluated through pull-out tests. The loading speed was set to 2 mm/min. 2mm/min is a typical quasi-static loading speed. It has been applied to the quasi-static pull-out test of plate connection joints and the quasi-static pull-out test of pipe connection joints respectively [1, 2]. Therefore, the loading speed was set to 2 mm/min.

(2) For the selection of the joining specimen dimensions

The flare-free joints have played a very important role in aerospace. As shown in Figure R1, the flare-free pipe and pipe fitting were joined by deforming the pipe into premanufactured grooves in the pipe fitting [3]. In a typical flare-free joint, the contact length between the pipe fitting and the original pipe is 20 mm. The groove in the pipe fitting is rectangular in shape with a depth of 1 mm. Therefore, the length of the overlap area was 20 mm. The depth of the rectangular groove was 1 mm. In the preliminary research [3], three widths, 4mm, 6mm and 8mm, were studied. In order to investigate the relationship between the deformation characteristics and the groove width, other process parameters (e.g. wire diameter and wire length) remain unchanged. It was found that increasing groove width led to increasing the deformation degree of the inner pipe. However, due to the narrow groove, the deformation of the inner pipe corresponding to the 4mm width groove was small. For the groove with a width of 8 mm, the increase in the discharge voltage did not increase the deformation of the inner pipe significantly. Therefore, the research object of the process test was determined to be the groove with a width of 6 mm.

Figure R1. The flare-free joint [3].

Please see lines 145-146 on page 4. As follows:

“The loading speed was set to 2 mm/min [22, 23].”

Jiang, H.; Liao, Y.X.; Gao, S.; Li, G.Y.; Cui, J.J. Comparative study on joining quality of electromagnetic driven self-piecing riveting, adhesive and hybrid joints for Al/steel structure. Thin-Walled Struct. 2021,164:107903.
Cui, J.J.; Li, Y.; Liu, Q.X.X.; Zhang, X.; Xu, Z.D.; Li, G.Y. Joining of tubular carbon fiber-reinforced plastic/aluminum by magnetic pulse welding. J. Mater. Process. Technol, 2019,264 :273-282.
Cai, D.; Liang, J.; Ou, H.; Li, G.Y.; Cui, J.J. Mechanical properties and joining mechanism of electrohydraulic expansion joints for 6063 aluminum alloy/304 stainless steel thin-walled pipes. Thin-Walled Struct. 2021,161:107427.

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

Q3. Results and Discussion

The quality of the figures should be improved. Why the interaction between discharge voltage and the wire diameter is significant and the interaction between wire length and wire diameter is not significant?

Response:

We appreciate your suggestion. We have modified the picture resolution to make the picture clearer. At the same time, we have added some explanations in Figures 3, 4 and 10 to make the content conveyed by the figures more substantial. The analysis of variance method was applied to evaluate the significance of the mathematical model. The influence of process parameters and their interactions on the mechanical properties of the joints was investigated. Considering the 95% reliability, the model term with a probability value (p-Value, the smallest significance level that may make the null hypothesis H0 negative) lower than 0.05 was considered significant. Significant model terms probably have a real effect on the response [1]. Therefore, the interaction between discharge voltage and the wire diameter was significant (p-Value < 0.05) and the interaction between wire length and wire diameter was not significant (p-Value > 0.05). The possible reason is as follows. During the joining process, the energy stored in the capacitor was instantly released on the wire between the electrodes. Under the action of Joule heat, the wire underwent a sharp phase change. It experienced solid state, liquid state, gas state and plasma state successively, and finally developed into a plasma channel. It was accompanied by physical phenomena such as light radiation and shock waves [2, 3]. The vaporization of the wire is crucial for the generation of the shock wave. And the initial stored energy is much higher than the complete vaporization energy of the exploding wire [4]. The study found that there was an area of wire diameter in which most of the initially stored energy can be deposited in the wire. The reason was that the average current density of the thick wire was too low, the initial stored energy was not effectively transferred to the wire. While the diameter of the wire was small, it exploded too fast, leaving a lot of energy on the pulse forming line [5, 6]. Therefore, the interaction between discharge voltage and the wire diameter was significant. According to the research of Suhara et al., as the length of the metal wire increased, the uniformity of the phase change of the metal wire decreased. Factors such as phase change and thermal stress would cause the phase explosion or breakdown in some areas of the wire to form plasma in advance [7]. Therefore, the interaction between wire length and wire diameter was not significant.

Please see Figure 3 on page 5. As follows:

Figure 3. Electrohydraulic expansion joints in the CCD.

Please see Figure 4 on page 6. As follows:

Figure 4. Pull-out tests and clamping method.

Please see Figure 10 on page 12. As follows:

Figure 10. Predicted and experimental values based on optimized parameters.

Please see lines 313-324 on pages 10-11. As follows:

“During the joining process, the energy stored in the capacitor was instantly released on the wire between the electrodes. Under the action of Joule heat, the wire underwent a sharp phase change. It experienced solid state, liquid state, gas state and plasma state successively, and finally developed into a plasma channel. It was accompanied by physical phenomena such as light radiation and shock waves [28, 29]. The vaporization of the wire was crucial for the generation of the shock wave. And the initial stored energy should be higher than the complete vaporization energy of the wire [30]. The study found that there was an area of wire diameter in which most of the initially stored energy can be deposited in the wire. The reason was that the average current density of the thick wire was too low, the initial stored energy was not effectively transferred to the wire. While the diameter of the wire was small, it exploded too fast, leaving a lot of energy on the pulse forming line [31, 32].”

Please see lines 343-346 on page 11. As follows:

“The possible reason was analyzed as follows. As the length of the metal wire increased, the uniformity of the phase change of the metal wire decreased. Factors such as phase change and thermal stress would cause the phase explosion or breakdown in some areas of the wire to form plasma in advance [33].”

Zohoor, M.; Mousavi, S.M. Evaluation and optimization of effective parameters in electrohydraulic forming process. J. Braz. Soc. Mech. Sci. Eng. 2018, 40(11).
Yao, W.B.; Zhou, H.B.; Han, R.Y.; Zhang, Y.M.; Zhao, Z.; Xu, Q.F.; Qiu, A.C. An empirical approach for parameters estimation of underwater electrical wire explosion. Phys. Plasmas. 2019,26(9):093502.
Virozub, A.; Gurovich, V.T.; Yanuka, D.; Antonov, O.; Krasik, Y.E. Addressing optimal underwater electrical explosion of a wire. Phys. Plasmas. 2016,23(9):092708.
Li, L.X.; Qian, D.; Zou, X.B.; Wang, X.X. Effect of deposition energy on underwater electrical wire explosion. IEEE Trans. Plasma Sci. 2018,46(10):3444-3449.
Grinenko, A.; Krasik, Y.E.; Efimov, S.; Fedotov, A.; Gurovich, V.T.; Oreshkin, V.I. Nanosecond time scale, high power electrical wire explosion in water. Phys. Plasmas. 2006,13(4):042701.
Zhou, Q.; Zhang, Q.G.; Zhang, J.; Zhao, J.P.; Pang, L.; Ren, B.Z. Effect of circuit parameters and wire properties on exploding a copper wire in water. IEEE Trans. Plasma Sci. 2011,39(7):1606-1612.
Suhara, T.; Fukuda, S. Experimental determination of optimum condition for wire explosion in water and PMMA. Proc. SPIE. 1979,189:321-326.

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

Other revisions:

(1) References revisions

In the revised manuscript, we have added new references. The serial numbers of all references were accordingly readjusted.

Author Response File: Author Response.pdf

Reviewer 2 Report

Manuscript Number:

Title: Multivariate quadratic nonlinear regression model of the ultimate pull-out load of electrohydraulic expansion joints based on response surface methodology

Authors:Da Cai, Chenyu Jin, Jie Liang, Guangyao Li, Junjia Cui

ID: coatings-1225822

In the manuscript, according to the experimental results, the multivariate quadratic nonlinear regression model between process parameters (discharge voltage, wire length and wire diameter) and the ultimate pull-out load of the joints was established. The paper represents research related to a practical application. The scientific novelty is reduced, the more the authors' determination to make a complete study of the problem can be appreciated. However, the paper is correctly structured and well written and presents the authors' ability to operate with numerical methods in solving such problems. As results I can recommend the acceptance of this paper after corrections.

The abstract needs to be improved because it provides too much information which is then repeated in the paper. So, the abstract must contain, in summary, what was done in the paper, without discussions or details from the work.
Authors should improve the Introduction parts and the references needs to present the background of the research. At the end of this section must be statuated more clear the original contribution of the authors.
Some editing "glitches" need to be corrected.
Punctuations are used randomly. Insert comma, semicolon or full stop every time when is necessary. After each mathematical relation a such sign must exist.
The section Conclusions will be point out the original results of the paper and can be extended to highlight the contributions.
The paper must be improved in order to explain more clear the contribution of the author and the existing state of art.
A revision of English must be made.
I think the authors need to emphasize more clearly the contribution of the manuscript from a scientific point of view.

If the author take these into consideration, I recommend the acceptance of this paper.

Author Response

Honorable editors and reviewers:

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

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

Comments and Response:

Reviewer #2:

Q1. The abstract needs to be improved because it provides too much information which is then repeated in the paper. So, the abstract must contain, in summary, what was done in the paper, without discussions or details from the work.

Response:

We thank you very much for this excellent comment. We have modified the abstract according your suggestions. The work carried out in this paper has been summarized and introduced in the revised abstract. What’s more, a large amount of discussion or details of the work could not be seen in the revised abstract now. The revised abstract mainly contains a summary of the work that has been carried out and the main conclusions.

Please see the abstract on page 1. As follows:

“Electrohydraulic expansion joining has great potential for joining the light weight and high strength thin-walled pipes due to its high strain rate. Based on the central composite design (CCD) of response surface methodology, multiple experiments were performed. The multivariate quadratic nonlinear regression model between process parameters (discharge voltage, wire length and wire diameter) and the ultimate pull-out load of the joints was established. The results revealed that discharge voltage, wire length and wire diameter all had a significant effect on the ultimate pull-out load. The discharge voltage had the most significant effect. The interaction between the discharge voltage and the wire diameter had a significant effect on the ultimate pull-out load. The optimal parameter combination (discharge voltage = 6 kV, wire length = 10 mm, wire diameter = 0.833 mm) was obtained and verified through the experiments. This study would provide guidance for the choice of the process parameters in real applications.”

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

Q2. Authors should improve the Introduction parts and the references needs to present the background of the research. At the end of this section must be statuated more clear the original contribution of the authors.

Response:

We thank you very much for this excellent comment. We have modified the Introduction parts according your suggestions. We have rechecked and corrected the errors. We have introduced the research background by adjusting the description of the references. The pipe joining parts and frame structures made from lightweight materials have gained more and more attention in the field of lightweight vehicles. The joining by forming processes has been widely used in the pipe joining process by virtue of its own advantages. Based on the strain rate, the joining by forming processes was divided into joining by quasi-static forming and joining by high-speed forming. Electromagnetic forming and electrohydraulic forming are typical high-speed forming. Compared with joining by quasi-static forming processes, the electrohydraulic expansion joining improves the forming limit of the forming area and joining efficiency. Compared with joining by electromagnetic forming, a more uniform pressure distribution can be obtained during the presented process. Therefore, the electrohydraulic expansion joining has great application potential. During the electrohydraulic expansion joining process, the discharge energy and the wire characteristics (diameter and length) have a great in-fluence on the quality of the joints. However, the influence of these parameters on the pull-out load of the joints and the corresponding mathematical relationships have not been reported. In this paper, the experimental design method and mathematical statistical analysis method were applied to investigate the influence of discharge energy, wire length and wire diameter on the pull-out load of electrohydraulic expansion joints. Aluminum alloy pipes and stainless steel pipes were selected as test materials. Firstly, the experiment was designed based on the central composite design (CCD) technology. Secondly, the experimental results were statistically analyzed to obtain the multivariate nonlinear regression model of the ultimate pull-out load of electrohydraulic expansion joints based on response surface methodology. Subsequently, the model was used to analyze the influence of each parameter on the pull-out load separately and interactively. The main factors that affect the pull-out load were found. Finally, the process parameters were optimized with the goal of the ultimate pull-out load. Experiments were carried out to verify the optimization results under the optimized settings.

Please see line 34 on page 1. As follows:

“However, the potential for weight reduction using pipe joining parts and frame structures made from lightweight materials was limited by the conventional joining technology [7].”

Please see line 35 on page 1. As follows:

“The conventional joining technologies included: thermal welding, mechanical fastening and adhesive bonding.”

Please see line 40 on page 1. As follows:

“The joining by forming processes could overcome certain disadvantages.”

Please see line 46 on page 2. As follows:

“The joining by forming processes can be classified based on forming direction, forming energy and strain rate.”

Please see line 49 and line 50 on page 2. As follows:

“Based on the strain rate, the joining was divided into joining by quasi-static forming and joining by high-speed forming.”

Please see line 51 on page 2. As follows:

“The joining by quasi-static forming processes include joining by rolling, joining by hydroforming, mechanical crimping, hydraulic crimping and joining by impulse forming.”

Please see line 53 on page 2. As follows:

“Henriksen et al. used numerical simulation and experiment methods to study the joining of steel pipes and steel flanges [10].”

Please see line 58 on page 2. As follows:

“In the mechanical crimping process of steel pipe,”

Please see lines 62-65 on page 2. As follows:

Please see line 67 on page 2. As follows:

“Different from joining by quasi-static forming, joining by impulse forming is a high-speed joining technology that can improve formability [16].”

Please see lines 71-75 on page 2. As follows:

Please see lines 77-81 on page 2. As follows:

Please see line 84 on page 2. As follows:

“the diameter and length of the wire can also affect the forming result [21].”

Please see lines 86-87 on page 2. As follows:

“However, the influence of these parameters on the pull-out load of the joints and the corresponding mathematical relationships have not been reported.”

Please see lines 90-92 on page 2. As follows:

Please see lines 95-103 on pages 2-3. As follows:

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

Q3. Some editing "glitches" need to be corrected.

Response:

We appreciate your suggestion. We have rechecked and corrected the errors in the revised manuscript.

Please see line 12 on page 1. As follows:

“Based on the central composite design (CCD) of response surface methodology,”

Please see line 106 on page 3. As follows:

“Figure 1a shows the joining equipment.”

Please see line 114 on page 3. As follows:

“Figure 1. Principal of electrohydraulic expansion joining: (a) joining equipment; (b) joining diagram and process.”

Please see line 121 on page 3. As follows:

“As shown in Figure 1b, an interlocking joint that could transmit loads was formed. The wire material was aluminum”

Please see line 128 on page 3. As follows:

“Figure 2 shows the geometric dimensions of the specimens.”

Please see line 133 on page 3. As follows:

“The total length of the joint was 200 mm.”

Please see line 134 on page 3. As follows:

“The length of the overlap area was 20 mm.”

Please see lines 135-136 on page 3. As follows:

“The depth of the rectangular groove was 1 mm, and the width was 6 mm.”

Please see line 173 on page 5. As follows:

“where, β0 is regression intercept.”

Please see lines 181-182 on page 5. As follows:

“The electrohydraulic expansion joints in the CCD are shown in Figure 3.”

Please see line 186 on page 6. As follows:

“Figure 3. Electrohydraulic expansion joints in the CCD.”

Please see line 187 on page 6. As follows:

“As shown in Figure 4,”

Please see line 196 on page 6. As follows:

“the wire length of the wire was 20 mm,”

Please see line 197 on page 6. As follows:

“According to the Equation (2):”

Please see line 199 on page 6. As follows:

“where, E is the discharge energy,”

Please see line 203 on page 6. As follows:

“The discharge energy of 3.264 kJ was released on a wire with a diameter of 1 mm and a length of 20 mm”

Please see line 204 on page 6. As follows:

“The ultimate pull-out load of the joint was small.”

Please see line 230 on page 7. As follows:

“The comparison between the actual and predicted values is shown in Figure 5.”

Please see line 241 on page 8. As follows:

“where, y is ultimate pull-out load,”

Please see line 251 on page 8. As follows:

“The single factor sub-regression model under specific conditions could be obtained by fixing the two factors in Equation (4) at the center level.”

Please see line 252 on page 8. As follows:

“As shown in Figure 6, firstly, by fixing the wire length at 15 mm and wire diameter at 0.8 mm,”

Please see line 261 on page 9. As follows:

“It can be seen from Figure 6 that the design variables A, B, and C had a significant effect on the ultimate pull-out load.”

Please see line 271 on page 9. As follows:

“When analyzing the interaction of two parameters the response,”

Please see line 277 on page 9. As follows:

“Figure 7. Three-dimensional surface map and contour map showing the interaction of discharge voltage and wire length: (a) three-dimensional surface map; (b) contour map.”

Please see lines 278-279 on page 10. As follows:

“When the wire diameter was fixed at 0.8 mm, the discharge voltage ranged from 4 kV to 6 kV, and the wire length ranged from 10 mm to 20 mm, Figure 7 shows the three-dimensional surface map and contour map of the interaction effect of the discharge voltage and wire length on the ultimate pull-out load.”

Please see line 282 on page 10. As follows:

“As illustrated in Figure 7a,”

Please see line 290 on page 10. As follows:

“As illustrated in Figure 7b,”

Please see line 298 on page 10. As follows:

“Figure 8. Three-dimensional surface map and contour map showing the interaction of discharge voltage and wire diameter: (a) three-dimensional surface map; (b) contour map.”

Please see line 300 on page 10. As follows:

“Figure 8 shows the three-dimensional surface map and contour map of the interaction effect of the discharge voltage and wire diameter on the ultimate pull-out load.”

Please see line 303 on page 10. As follows:

“As illustrated in Figure 8a,”

Please see line 308 on page 10. As follows:

“As illustrated in Figure 8b,”

Please see line 331 on page 11. As follows:

“Figure 9. Three-dimensional surface map and contour map showing the interaction of wire length and wire diameter: (a) three-dimensional surface map; (b) contour map.”

Please see line 333 on page 11. As follows:

“Figure 9 shows the three-dimensional surface map and contour map of the interaction effect of wire length and wire diameter on the ultimate pull-out load.”

Please see line 336 on page 11. As follows:

“As illustrated in Figure 9a,”

Please see line 338 on page 11. As follows:

“As illustrated in Figure 9b,”

Please see lines 351-352 on page 11. As follows:

“As shown in Figure 10, when the discharge voltage was 6 kV,”

Please see line 386 on page 13. As follows:

“1. Liang, Q.; Zhang, T.; Zhu, C.; Bi, Y. Effect of riveting angle and direction on fatigue performance of riveted lap joints. Coatings 2021,11:236.”

Please see line 390 on page 13. As follows:

“3. Zhu, C.C.; Sun, L.Q.; Gao, W.l.; Li, G.Y.; Cui, J.J. The effect of temperature on microstructure and mechanical properties of Al/Mg lap joints manufactured by magnetic pulse welding. J. Mater. Res. Technol-JMRT 2019,8(3):3270-3280.”

Please see line 398 on page 13. As follows:

“7. Marre, M.; Brosius, A.; Tekkaya, A.E. Joining by compression and expansion of (none-) reinforced profiles. Advanced Mate-rials Research: Flexible Manufacture of Lightweight Frame Structures - Phase II: Integration 2008,43:57-68.”

Please see line 404 on page 13. As follows:

“10. Henriksen, J.; Nordhagen, H.O.; Hoang, H.N. Hansen, M.R.; Thrane, F.C. Numerical and experimental verification of new method for connecting pipe to flange by cold forming. J. Mater. Process. Technol. 2015,220:215-223.”

Please see lines 406-409 on page 13. As follows:

“11. Marre, M.; Rautenberg, J.; Tekkaya, A.E.; Zabel, A.; Biermann, D.; Wojciechowski, J.; Przybylski, W. An experimental study on the groove design for joints produced by hydraulic expansion considering axial or torque load. Mater. Manuf. Process. 2012,27(5):545-555.”

Please see lines 412-414 on page 13. As follows:

“13. Cho, J.R.; Song, J.I. Swaging process of power steering hose, : Its finite element analysis considering the stress relaxation. J. Mater. Process. Technol. 2007,187-188:497-501.”

Please see lines 415-418 on page 13. As follows:

“14. Shirgaokar, M.; Ngaile, G.; Altan, T.; Yu, J.H.; Balconi, J.; Rentfrow, R.; Worrell, W. J. Hydraulic crimping: application to the assembly of tubular components. J. Mater. Process. Technol. 2004,146(1):44-51.”

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

Q4. Punctuations are used randomly. Insert comma, semicolon or full stop every time when is necessary. After each mathematical relation a such sign must exist.

Response:

We thank you very much for pointing out this problem. We have rechecked and corrected the errors in the revised manuscript.

Please see line 130 on page 3. As follows:

“The inner diameter of the outer pipe was 25 mm. And the outer diameter of the outer pipe was 30 mm.”

Please see line 133 on page 3. As follows:

“The total length of the joint was 200 mm. The length of the overlap area was 20 mm.”

Please see line 144 on page 4. As follows:

“The steel mandrels were inserted at both ends of the joints to ensure that the pipes would not deform in the radial direction during the clamping process. The deformation of the pipes in the radial direction would affect the test results.”

Please see lines 149-152 on page 4. As follows:

“CCD is a mathematical method suitable for multi-factor testing. It is well adapted to analysis of the relationship among variables. The method is divided into two subsets. One subset estimates the liner relationship and interaction between the variables. The other subset determines the relative importance of each variable relative to the estimated response.”

Please see line 166 on page 5. As follows:

“This method can be used to optimize the response based on the rages of variables. The optimal set of variables can be obtained [26].”

Please see line 173 on page 5. As follows:

“where, β₀ is regression intercept. β_i, β_ii, β_ij are the linear, quadratic, and linear interaction effects of the factors, respectively.”

Please see line 188 on page 6. As follows:

“As shown in Figure 4, pull-out tests were carried out to obtain the response parameters (ultimate pull-out load). The ultimate pull-out load was to evaluate the mechanical properties of the joints.”

Please see line 203 on page 6. As follows:

“The discharge energy of 3.264 kJ was released on a wire with a diameter of 1 mm and a length of 20 mm. The shock wave generated was not sufficient to cause the inner pipe to deform significantly at the groove.”

Please see line 219 on page 7. As follows:

“In the analysis of variance, the linear terms A, B and C had a significant influence on the response.”

Please see line 221 on page 7. As follows:

“In this study, A, B, C, AC and C2 were significant model terms,”

Please see line 261 on page 9. As follows:

“It can be seen from Figure 6 that the design variables A, B and C had a significant effect on the ultimate pull-out load.”

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

Q5. The section Conclusions will be point out the original results of the paper and can be extended to highlight the contributions.

Response:

We thank you very much for this excellent recommendation. We have modified the conclusions according your suggestions. Firstly, this research was based on the central composite design (CCD) technology to complete the experimental design. Secondly, the experimental results were statistically analyzed to obtain the multivariate nonlinear regression model of the ultimate pull-out load of electrohydraulic expansion joints based on response surface methodology. Subsequently, the analysis of the model was completed and the original results were obtained. Finally, the main original conclusions were drawn as follows: (1) The results of the multivariate quadratic nonlinear regression model of the ultimate pull-out load of electrohydraulic expansion joints were in good agreement with the experimental results, which indicated that the model could accurately predict the ultimate pull-out load. (2) The discharge voltage, wire length and wire diameter had a significant effect on the ultimate pull-out load. The discharge voltage had the most significant effect. The interaction between the discharge voltage and the wire diameter had a significant effect on the ultimate pull-out load. (3) The optimal parameter combination was obtained. when the discharge voltage was 6 kV, wire length was 10 mm and the wire diameter was 0.833 mm, the ultimate pull-out load reached its peak, which was 18.296 kN. Based on the original results of the paper, we have carried out a reasonable expansion. This research created an experimental database for the practical application and further promotion of electrohydraulic expansion joining process. It also provided guidance for the choice of the process parameters in real applications.

Please see Conclusions. As follows:

“(1) The results of the multivariate quadratic nonlinear regression model of the ultimate pull-out load of electrohydraulic expansion joints were in good agreement with the experimental results, which indicated that the model could accurately predict the ultimate pull-out load.

(2) The discharge voltage, wire length and wire diameter had a significant effect on the ultimate pull-out load. The discharge voltage had the most significant effect. The interaction between the discharge voltage and the wire diameter had a significant effect on the ultimate pull-out load.

(3) The optimal parameter combination was obtained. when the discharge voltage was 6 kV, wire length was 10 mm and the wire diameter was 0.833 mm, the ultimate pull-out load reached its peak, which was 18.296 kN. This research created an experimental database for the practical application and further promotion of electrohydraulic expansion joining process. It also provided guidance for the choice of the process parameters in real applications.”

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

Q6. The paper must be improved in order to explain more clear the contribution of the author and the existing state of art.

Response:

We thank you very much for this excellent suggestion. It was indeed necessary to improve the paper to explain more clear the contribution of the author and the existing state of art. In the revised manuscript, firstly, we have clearly introduced the advantages of the electrohydraulic expansion joining process comparing with some of the existing techniques for joining of pipes. The necessity of studying electrohydraulic expansion joining process has been pointed out. Secondly, we have emphasized the importance of the influence of the process parameters on the electrohydraulic expansion joining process. Finally, we have described the contribution of the authors. The detailed description is as follow.

(1) Compared with quasi-static joining processes (rolling joining, hydraulic joining)

With the continuous improvement of the requirements for lightweight, some light weight and high strength thin-walled pipes are gradually being used in the joining pipe parts of aircraft and engines in the aerospace industry [1-7]. Low formability of light high strength alloys during quasi-static forming at room temperature could cause considerable problems [8]. As a typical high-speed forming, electrohydraulic forming could improve formability [9]. The main reasons included high strain rate, high hydrostatic stress and high-speed impact between the sheet and the mold [10-12]. Rolling joining and hydraulic joining are two methods for obtaining reliable joints. Both rolling joining and hydraulic joining are quasi-static joining processes. Electrohydraulic expansion joining is the application of electrohydraulic forming in the high-speed joining process. Therefore, compared with quasi-static joining processes (rolling joining, hydraulic joining), the presented process improves the forming limit of the forming area.

(2) Compared with joining by electromagnetic forming

The pressure distribution in the electromagnetic forming process is non-uniform. In the electrohydraulic forming process, the secondary pressure waves reflecting by the walls make the pressure more evenly over the surface of the blank being formed [13, 14]. Therefore, compared with joining by electromagnetic forming, electrohydraulic expansion joining can provide more uniform pressure distribution.

(3) The importance of the influence of the process parameters

Previous studies have shown that the different discharge energy would affect the pull-out load and the failure mode of the electrohydraulic expansion joints [15]. In the electrohydraulic forming process, the diameter and length of the wire could also affect the forming result [16]. Therefore, the discharge energy and the wire characteristics (diameter and length) have a great influence on the electrohydraulic expansion joining process. However, the influence of these parameters on the pull-out load of the joints and the corresponding mathematical relationships have not been reported. It is necessary to study the influence of the process parameters on the pull-out load of the joints and establish the corresponding mathematical relationship.

(4) The contribution of the author

In this paper, the experimental design method and mathematical statistical analysis method were applied to investigate the influence of discharge energy, wire length and wire diameter on the pull-out load of electrohydraulic expansion joints. Aluminum alloy pipes and stainless steel pipes were selected as test materials. Firstly, the experiment was designed based on the central composite design (CCD) technology. Secondly, the experimental results were statistically analyzed to obtain the multivariate nonlinear regression model of the ultimate pull-out load of electrohydraulic expansion joints based on response surface methodology. Subsequently, the model was used to analyze the influence of each parameter on the pull-out load separately and interactively. The main factors that affect the pull-out load were found. Finally, the process parameters were optimized with the goal of the ultimate pull-out load. Experiments were carried out to verify the optimization results under the optimized settings.

Please see lines 77-81 on page 2. As follows:

Please see lines 86-87 on page 2. As follows:

“However, the influence of these parameters on the pull-out load of the joints and the corresponding mathematical relationships have not been reported.”

Please see lines 90-103 on pages 2-3. As follows:

“In this paper, the experimental design method and mathematical statistical analysis method were applied to investigate the influence of discharge energy, wire length and wire diameter on the pull-out load of electrohydraulic expansion joints. Aluminum alloy pipes and stainless steel pipes were selected as test materials. Firstly, the experiment was designed based on the central composite design (CCD) technology. Secondly, the experimental results were statistically analyzed to obtain the multivariate nonlinear regression model of the ultimate pull-out load of electrohydraulic expansion joints based on response surface methodology. Subsequently, the model was used to analyze the influence of each parameter on the pull-out load separately and interactively. The main factors that affect the pull-out load were found. Finally, the process parameters were optimized with the goal of the ultimate pull-out load. Experiments were carried out to verify the optimization results under the optimized settings.”

Liang, Q.; Zhang, T.; Zhu, C.; Bi, Y. Effect of riveting angle and direction on fatigue performance of riveted lap joints. Coatings 2021,11:236.
Jiang, H.; Cong, Y.J.; Zhang, J.S.; Wu, X.H.; Li, G.Y.; Cui, J.J. Fatigue response of electromagnetic riveted joints with different rivet dies subjected to pull-out loading, Int. J. Fatigue. 2019,129:105238.
Zhu, C.C.; Sun, L.Q.; Gao, W.l.; Li, G.Y.; Cui, J.J. The effect of temperature on microstructure and mechanical properties of Al/Mg lap joints manufactured by magnetic pulse welding. J. Mater. Res. Technol-JMRT 2019,8(3):3270-3280.
Weddeling, C.; Woodward, S.T.; Marre, M.; Nellesen, J.; Psyk, V.; Tekkaya, A.E.; Tillmann, W. Influence of groove characteristics on strength of form-fit joints. J. Mater. Process. Technol. 2011,211(5):925-935.
Duan, L.M.; Jiang, H.; Zhang, X.; Li, G.Y.; Cui, J.J. Experimental investigations of electromagnetic punching process in CFRP laminate. Mater. Manuf. Process. 2021,36:223-234.
Wang, S.L.; Zhou, B.B.; Zhang, X.; Sun, T.; Li, G.Y.; Cui, J.J. Mechanical properties and interfacial microstructures of magnetic pulse welding joints with aluminum to zinc-coated steel, Mater. Sci. Eng. A. 2020,788:139425.
Marre, M.; Brosius, A.; Tekkaya, A.E.; Joining by compression and expansion of (none-) reinforced profiles. Advanced Materials Research: Flexible Manufacture of Lightweight Frame Structures - Phase II: Integration 2008,43:57-68.
Li, G.Y.; Deng, H.K.; Mao, Y.F.; Zhang, X.; Cui, J.J. Study on AA5182 aluminum sheet formability using combined quasi-static-dynamic tensile processes. J. Mater. Process. Technol. 2018,255:373-386.
Psyk, V.; Risch, D.; Kinsey, B.L.; Tekkaya, A.E.; Kleiner, M. Electromagnetic forming-a review. J. Mater. Process. Technol. 2011,211:787-829.
Maris, C.; Hassannejadasl, A.; Green, D.E.; Cheng, J.; Golovashchenko, S.F.; Gillard, A.J.; Liang, Y.T. Comparison of quasi-static and electrohydraulic free forming limits for DP600 and AA5182 sheets. J. Mater. Process. Technol. 2016,235:206-219.
Golovashchenko, S.F.; Gillard, A.J.; Mamutov, A.V. Formability of dual phase steels in electrohydraulic forming. J. Mater. Process. Technol. 2013,213:1191-1212.
Rohatgi, A.; Soulami, A.; Stephens, E.V.; Davies, R.W.; Smith, M.T. An investigation of enhanced formability in AA5182-O Al during high-rate free-forming at room-temperature: quantification of deformation history. J. Mater. Process. Technol. 2014,214:722-732.
Golovashchenko, S.F.; Gillard, A.J.; Mamutov, A.V.; Bonnen, J.F.; Tang, Z.J. Electrohydraulic trimming of advanced and ultra high strength steels, J. Mater. Process. Technol. 2014,214:1027-1043.
Liu, X.; Gu, W.B.; Liu, J.Q.; Xu, J.L.; Hu, Y.H.; Hang, Y.M. Dynamic response of cylindrical explosion containment vessels subjected to internal blast loading, Int. J. Impact Eng. 2019,135:103389.
Cai, D.; Liang, J.; Ou, H.; Li, G.Y.; Cui, J.J. Mechanical properties and joining mechanism of electrohydraulic expansion joints for 6063 aluminum alloy/304 stainless steel thin-walled pipes. Thin-Walled Struct. 2021,161:107427.
Zohoor, M.; Mousavi, S.M. Evaluation and optimization of effective parameters in electrohydraulic forming process. J. Braz. Soc. Mech. Sci. Eng. 2018, 40(11).

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

Q7. A revision of English must be made.

Response:

We appreciate your suggestion. We have rechecked and corrected the errors in the revised manuscript with the assistance of a colleague who is well-versed in English.

Please see line 40 on page 1. As follows:

“The joining by forming processes could overcome certain disadvantages.”

Please see line 108 on page 3. As follows:

“The equipment mainly included magnetic pulse generator and joining device.”

Please see line 118 on page 3. As follows:

“The shock waves caused by the expansion of the plasma channel were transmitted to the inner pipe at high speeds”

Please see line 124 on page 3. As follows:

“Wire diameter was set to 0.6 mm, 0.8 mm, and 1 mm. The discharge voltages of 4 kV, 5 kV and 6 kV were selected.”

Please see lines 129-130 on page 3. As follows:

“The length of the inner pipe was the same as that of the outer pipe which was 110 mm.”

Please see lines 155-156 on page 4. As follows:

“The corresponding numbers of the three variables were A, B and C, respectively.”

Please see lines 163-165 on page 5. As follows:

“The response surface method is an efficient mathematical and statistical technique that can be used to analyze the effects of different independent variables on the response of the complex system. This method can be used to optimize the response based on the rages of variables. The optimal set of variables can be obtained [26]”

Please see lines 168-169 on page 5. As follows:

“The relationship between the response and variables in the surface model can be established. The mathematical function between the response and variables can be determined.”

Please see lines 173-175 on page 5. As follows:

“where, β₀ was is regression intercept. β_i, β_ii, β_ij are the linear, quadratic, and linear interaction effects of the factors, respectively. x_i, x_j are the selected factors in the electrohydraulic expansion joining process, y refers to the response that is the ultimate pull-out load.”

Please see line 187 on page 6. As follows:

“As shown in Figure 4, pull-out tests were carried out to obtain the response parameter (ultimate pull-out load).”

Please see line 194 on page 6. As follows:

“The ultimate pull-out loads obtained based on the CCD are shown in Table 3.”

Please see lines 199-200 on page 6. As follows:

“where, E is the discharge energy, C_g is the capacitance of the magnetic pulse generator with a value of 408 μF, U is discharge voltage.”

Please see line 214 on page 7. As follows:

“The results of the analysis of variance are shown in Table 4.”

Please see lines 229-231 on page 7. As follows:

“The predicted values of response variable are presented in Table 3. The comparison between the actual and predicted values is shown in Figure 5. The data points were distributed near a straight line, indicating that the response surface could accurately predict the experimental results.”

Please see lines 241-242 on page 8. As follows:

“where, y is ultimate pull-out load, A is discharge voltage, B is wire length and C is wire diameter.”

Please see line 245 on page 8. As follows:

“because the coefficients were scaled to accommodate the units of each factor.”

Please see line 249 on page 8. As follows:

“In order to study the effect of the single factor on the response, the regression model was processed by dimensionality reduction method [27].”

Please see line 254 on page 8. As follows:

“the sub-regression model of discharge voltage for ultimate pull-out load could be obtained.”

Please see line 257 on page 8. As follows:

“the sub-regression model of wire diameter for the ultimate pull-out load was obtained.”

Please see line 279 on page 10. As follows:

“Figure 7 shows the three-dimensional surface map and contour map of the inter-action effect of the discharge voltage and wire length on the ultimate pull-out load.”

Please see line 300 on page 10. As follows:

“Figure 8 shows the three-dimensional surface map and contour map of the interaction effect of the discharge voltage and wire diameter on the ultimate pull-out load.”

Please see line 333 on page 11. As follows:

“Figure 9 shows the three-dimensional surface map and contour map of the interaction effect of wire length and wire diameter on the ultimate pull-out load.”

Please see line 355 on page 11. As follows:

“The relative error between the experimental value and the predicted value was 1.5%. Therefore, the model could be used to predict the optimal process parameters.”

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

Q8. I think the authors need to emphasize more clearly the contribution of the manuscript from a scientific point of view.

Response:

We appreciate your suggestion. Thanks for pointing out these. In the revised manuscript, Firstly, we have modified the section Introduction to emphasize the importance of process parameters to the electrohydraulic expansion joining process. The necessity of research has been explained. At the same time, the original contribution of the authors has been explained more clearly at the end of the introduction. Secondly, we have added more discussion on the results to make the paper be more scientific. Finally, we have pointed out the original results of the paper and expanded it to highlight contributions in the section Conclusions.

Please see line 53 on page 2. As follows:

“Henriksen et al. used numerical simulation and experiment methods to study the joining of steel pipes and steel flanges [10].”

Please see line 58 on page 2. As follows:

“In the mechanical crimping process of steel pipe,”

Please see lines 62-65 on page 2. As follows:

Please see line 67 on page 2. As follows:

“Different from joining by quasi-static forming, joining by impulse forming is a high-speed joining technology that can improve formability [16].”

Please see lines 71-75 on page 2. As follows:

Please see lines 77-81 on page 2. As follows:

Please see lines 86-87 on page 2. As follows:

“However, the influence of these parameters on the pull-out load of the joints and the corresponding mathematical relationships have not been reported.”

Please see lines 90-92 on page 2. As follows:

Please see lines 95-103 on pages 2-3. As follows:

Please see lines 313-324 on pages 10-11. As follows:

Please see lines 343-346 on page 11. As follows:

Please see Conclusions. As follows:

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

Other revisions:

(1) References revisions

In the revised manuscript, we have added new references. The serial numbers of all references were accordingly readjusted.

Round 2

Reviewer 2 Report

No comments

Article Menu

Multivariate Quadratic Nonlinear Regression Model of the Ultimate Pull-Out Load of Electrohydraulic Expansion Joints Based on Response Surface Methodology

Further Information

Guidelines

MDPI Initiatives

Follow MDPI