Aluminum alloy thin-walled structures are widely used in the automotive industry due to their advantages related to light weight and crashworthiness. They can be produced at room temperature by the electrohydraulic forming process. In the present study, the influence of the related parameters on the forming quality of a 6063 aluminum alloy sinusoidal corrugation tube has been assessed. In particular, the orthogonal experimental design (OED) and central composite design (CCD) methods have been used. Through the range analysis and variance analysis of the experimental data, the influence degree of wire diameter (WD) and discharge energy (DE) on the forming quality was determined. Multiple regression analysis was performed using the response surface methodology. A prediction model for the attaching-die state coefficient was established accordingly. The following optimal arrangement of parameters was obtained (WD = 0.759 mm, DE = 2.926 kJ). The attaching-die state coefficient reached the peak value of 0.001. Better optimized wire diameter and discharge energy for a better attaching-die state could be screened by CCD compared with OED. The response surface method in CCD was more suitable for the design and optimization of the considered process parameters.

Thin-walled structures have been widely used in the automotive industry to absorb energy, due to their advantages in crashworthiness and lightweight [

Geometry and manufacturing defects are two factors that affect the performance of thin-walled tubes during energy absorption. To ensure the absorption performance, a sinusoidal corrugation tube was proposed. This geometry can achieve stabilized collapse mode and low peak crushing force [

The high-speed forming process can improve formability significantly compared with the quasi-static forming process [

The electrohydraulic forming process (wire-assisted) could be divided into two steps. The first step was the shock wave generation process. The second step was the high-speed forming process. Peak pressure, specific impulse, and positive pressure action time were used to characterize the shock wave characterization in the first step. However, the mechanism of shock wave generation and energy conversion in the electrohydraulic forming process was complex. There is no complete theory to describe it yet [

Most of the published studies have focused on the improvement of formability and the analysis of the electrohydraulic forming process in the second step. Golovashchenko et al. [

The simulation has been an important tool for analyzing the forming process. Mamutov et al. [

In this study, the electrohydraulic forming process was used to manufacture an aluminum alloy sinusoidal corrugation tube. Firstly, experiments were designed based on the orthogonal experiment design (OED) and central composite design (CCD) technology. Secondly, experiments were carried out. The influence of the wire diameter and the discharge energy on the attaching-die state was analyzed. Subsequently, the optimal arrangement of parameters was given to achieve the best attaching-die state. It was verified by experiments. Finally, the two experimental design methods were compared. The wall thickness distribution was analyzed.

The commercial material 6063 aluminum alloy was used. The thickness of the aluminum alloy tube was 1 mm. The outer diameter of the aluminum alloy tube was 50 mm. The length of the tube was 203.5 mm. The chemical composition is presented in ^{3}. The tensile strength was 216 MPa, and the Poisson’s ratio was 0.33.

Alloy | Si | Fe | Mg | Cu | Mn | Cr | Zn | Ti | Al |
---|---|---|---|---|---|---|---|---|---|

6063 | 0.2∼0.6 | 0.35 | 0.45∼0.9 | 0.1 | 0.1 | 0.1 | 0.1 | 0.1 | Bal. |

The tube was formed by the electrohydraulic forming process. The schematic and equipment of the electrohydraulic forming process are presented in

The profile of sinusoidal corrugation and forming process are depicted in

D/mm | A/mm | W/mm |
---|---|---|

53.2 | 1.6 | 20 |

After the electrohydraulic forming process, the following function was defined to evaluate the attaching-die state of the tube:_{i}_{0}

OED is one of the important statistical methods for studying multi-factor and multi-level experiments and analyzing factor design [_{9} (3^{2}) was selected. In this study, the orthogonal table contained two design variables (discharge energy and wire diameter). The three levels of variables were set as low, intermediate, and high. The OED is listed in

Samples | Wire diameter | Discharge energy | C |
---|---|---|---|

1 | 0.6 mm | 2.25 kJ | 0.00290259 |

2 | 0.6 mm | 2.50 kJ | 0.00289698 |

3 | 0.6 mm | 2.75 kJ | 0.00236309 |

4 | 0.8 mm | 2.25 kJ | 0.00489241 |

5 | 0.8 mm | 2.50 kJ | 0.00214569 |

6 | 0.8 mm | 2.75 kJ | 0.00212129 |

7 | 1.0 mm | 2.25 kJ | 0.00868135 |

8 | 1.0 mm | 2.50 kJ | 0.00827654 |

9 | 1.0 mm | 2.75 kJ | 0.00500894 |

CCD is a method suitable for multivariate analysis. This method could determine linear relationships and interactions between variables. The importance of variables relative to the response can also be determined. Information about variables and experimental errors could also be obtained by this method [

Samples | Coded value | Real value | C | ||
---|---|---|---|---|---|

A | B | Wire diameter | Discharge energy | ||

1 | −1 | −1 | 0.6 mm | 2.25 kJ | 0.00290259 |

2 | 0 | −1 | 0.8 mm | 2.25 kJ | 0.00489241 |

3 | 0 | 0 | 0.8 mm | 2.5 kJ | 0.00214569 |

4 | −1 | 0 | 0.6 mm | 2.50 kJ | 0.00289698 |

5 | 1 | 1 | 1.0 mm | 2.75 kJ | 0.00500894 |

6 | 1 | 0 | 1.0 mm | 2.50 kJ | 0.00827654 |

7 | 0 | 0 | 0.8 mm | 2.5 kJ | 0.00214569 |

8 | 0 | 0 | 0.8 mm | 2.5 kJ | 0.00214569 |

9 | 0 | 0 | 0.8 mm | 2.5 kJ | 0.00214569 |

10 | −1 | 1 | 0.6 mm | 2.75 kJ | 0.00236309 |

11 | 0 | 1 | 0.8 mm | 2.75 kJ | 0.00212129 |

12 | 0 | 0 | 0.8 mm | 2.5 kJ | 0.00214569 |

13 | 1 | −1 | 1.0 mm | 2.25 kJ | 0.00868135 |

Direct-vision comparison and indirect vision comparison were used to compare the measurement results of the same indicator directly or indirectly. The direct-vision comparison method is a comparison method that does not rely on any functional relationship. It was adopted to compare the attaching-die state coefficient of each sample in the OED.

The response surface method is a statistical method for solving multivariate problems [_{0}_{i}_{ii}_{ij}_{i}_{j}

The formed sinusoidal corrugation tubes are shown in

The comparison of the attaching-die state coefficient of the sinusoidal corrugation tube at three discharge energies is shown in

The range analysis was performed on the results of the orthogonal experiment. The effect of process variables on attaching-die state coefficient can be found. _{1}_{2}_{3}_{1}_{2}_{3}_{4}_{5}_{6}_{7}_{8}_{9}

The range of the attaching-die state coefficient caused by the different levels can be calculated using

Wire diameter | Discharge energy | |
---|---|---|

_{1} |
0.00816266 | 0.01647635 |

_{2} |
0.00915939 | 0.01331921 |

_{3} |
0.02196683 | 0.00949332 |

0.002720887 | 0.005492117 | |

0.00305313 | 0.004439737 | |

0.00460139 | 0.00316444 | |

0.00460139 | 0.002327677 | |

Primary and secondary order | Wire diameter > discharge energy |

ANOVA was performed. The results are listed in ^{2}) value was selected to describe the proportion of the variability in the data explained by the ANOVA model and its value of 0.901 suggested acceptable accuracy of the model.

Source | Sum of squares | df | Mean square | F value | Sig. |
---|---|---|---|---|---|

_{1} |
3.951 × 10^{−5} |
2 | 1.975 × 10^{−5} |
15.126 | 0.014 |

_{2} |
8.152 × 10^{−6} |
2 | 4.076 × 10^{−6} |
3.121 | 0.153 |

Error | 5.224 × 10^{−6} |
4 | 1.306 × 10^{−6} |
||

Cor total | 5.288 × 10^{−5} |
8 |

ANOVA results showed that for different wire diameters, the average value of the attaching-die state coefficient was significantly different. For different discharge energies, the average value of the attaching-die state coefficient was not significantly different. The results of ANOVA also showed that the influence of the wire diameter on the attaching-die state was greater than that of discharge energy.

The response parameters (attaching-die state coefficient) and the experimental design data obtained using the CCD are shown in _{1}_{2}^{2} = 0.9404 suggested that the experimental and predicted values were in good agreement based on the response surface method.

The results of the ANOVA are given in _{0}

Source | Sum of squares | df | Mean square | F value | Prob > F | |
---|---|---|---|---|---|---|

Model | 6.256 × 10^{−5} |
5 | 1.251 × 10^{−5} |
22.08 | 0.0004 | Significant |

_{1} |
1.626 × 10^{−6} |
1 | 1.626 × 10^{−6} |
2.87 | 0.1341 | |

_{2} |
1.035 × 10^{−7} |
1 | 1.035 × 10^{−7} |
0.18 | 0.6820 | |

_{1}x_{2} |
2.454 × 10^{−6} |
1 | 2.454 × 10^{−6} |
4.33 | 0.0760 | |

_{1}^{2} |
1.557 × 10^{−5} |
1 | 1.557 × 10^{−5} |
27.48 | 0.0012 | |

_{2}^{2} |
2.400 × 10^{−7} |
1 | 2.400 × 10^{−7} |
0.42 | 0.5360 | |

Residual | 3.967 × 10^{−6} |
7 | 5.667 × 10^{−7} |
|||

Lack of fit | 3.967 × 10^{−6} |
3 | 1.322 × 10^{−7} |
|||

Pure error | 0.000 | 4 | 0.000 | |||

Cor total | 6.653 × 10^{−5} |
12 |

In the ANOVA, the linear terms _{1}_{2}_{1}^{2}_{2}^{2}_{1}x_{2}

To analyze the influence of various parameters on the attaching-die state of the formed tube, it was necessary to study the main factors in these parameters and their interactions.

According to the intuitive observation of experimental data, the optimal process parameters in OED are shown in sample 6 in

The reason account for this difference was the different characteristics of the two test design methods. The traditional OED was a design method using a linear mathematical model, which can find the best combination of multiple factors. However, OED can only analyze discrete data, and had the characteristics of low accuracy and poor prediction. The CCD and the response surface method used a non-linear model to obtain high-precision regression equations and made reasonable predictions to find the optimal process conditions.

The attaching-die state coefficient reached a peak of 0.001 when the wire diameter was 0.76 mm and the discharge energy was 2.926 kJ in CCD, but the samples with same parameters arrangement did not appear in OED. Compared to the parameter combination of 0.8 mm and 2.75 kJ, the superheating conditions in the wires were increased due to the larger discharge energy released in the wire of smaller mass. The intensity of the shock wave increased. The attaching-die state coefficient of the sinusoidal corrugation tube was small.

The thinning rate is one of the important parameters to evaluate the forming quality of bellows. The thinning ratio _{t}_{0}_{b}

The results showed that the maximum thinning ratio of the sinusoidal corrugation tubes increased with the increase of discharge energy. As shown in

The electrohydraulic forming process of the 6063 aluminum alloy sinusoidal corrugation tube was studied. The experiments based on OED and CCD were carried out. The influence of process parameters on the attaching-die state was found. The optimal arrangement of parameters was given to achieve the best attaching-die state. The main conclusions could be drawn as follows:

(1) Better optimized wire diameter and discharge energy for a better attaching-die state can be screened by CCD compared with OED. The response surface method in CCD was more suitable for the design and optimization of process parameters in the electrohydraulic forming process of the novel 6063 aluminum alloy sinusoidal corrugation tube.

(2) The influence of the parameters on the attaching-die state coefficient of the sinusoidal corrugation tube was not a simple linear relationship. The results of the nonlinear regression model of the attaching-die state coefficient were in good agreement with the experimental results, indicating that the model can accurately predict the attaching-die state coefficient.

(3) When the wire diameter was 0.76 mm and the discharge energy was 2.926 kJ in CCD, the attaching-die state coefficient reached the peak value of 0.001. The outer surface of the formed tube was in good contact with the inner surface of the die.

None.

This project is supported by National Natural Science Foundation of China (Grant Nos. 51975202 (Junjia Cui received the grant) and 52175315 (Guangyao Li received the grant)).

The authors confirm contribution to the paper as follows: study conception and design: Da Cai, Hao Jiang, Guangyao Li, Junjia Cui; data collection: Da Cai, Yinlong Song; analysis and interpretation of results: Da Cai, Hao Jiang, Guangyao Li, Junjia Cui; draft manuscript preparation: Da Cai, Hao Jiang, Junjia Cui. All authors reviewed the results and approved the final version of the manuscript.

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

The authors declare that they have no conflicts of interest to report regarding the present study.