# Energy-Economizing Optimization of Magnesium Alloy Hot Stamping Process

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## Abstract

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## 1. Introduction

^{9}T, of which 10–15% come from automobiles [2]. An efficient way to improve the energy efficiency and driving range of vehicles is mass reduction. Some lightweight materials, such as magnesium alloys, aluminum alloys, and ultra-high-strength steels, have been rapidly increasing in quantity and have been applied to the automotive industry [3]. Vehicles can conserve significant amounts of energy by using these lightweight materials [4].

## 2. Framework and Method

## 3. Energy-Economizing Indices of Hot Stamping

#### 3.1. Process Energy Consumption Indices

_{heating}is the heating energy consumption and E

_{forming}is the forming energy consumption.

_{convection}, Q

_{radiation}, and Q

_{conduction}are the heat losses by convection, radiation, and conduction, respectively, and can be calculated by as follows:

_{h}= 1/Ah is the convection resistance, T is the temperature, ΔT is the temperature difference between hot and cold fluid object, k is the Boltzmann constant, F

_{r}is the radiation shape factor, λ is the thermal conductivity, and R

_{λ}= δ/Aλ is the thermal resistance, δ is the thickness, t is the time.

_{blank}is the heat absorbed by sheet metal.

_{loss}(T, i) is thermal efficiency loss caused by the different heating temperatures and methods and i denotes the three heating means, namely, radiation, induction, and conduction.

#### 3.2. Forming Quality Indices

_{2})) or the safety marginal curve (Φ(ε

_{2})), this region of the shaped part will likely fracture. A long distance from the safety marginal curve Φ(ε

_{2}) indicates a high rupture tendency. Therefore, the average distance between the main strain of all elements and the Φ(ε

_{2}) curve can be used to quantify the fracture. Similarly, when the main strain of an area element is below the wrinkle limit curve (ψ(ε

_{2})), this area of the formed part will show a wrinkling trend; the farther the point from the ψ(ε

_{2}) curve, the higher the trend of wrinkling. The fracture distance and wrinkling trend are mainly used to predict the product forming quality in the finite element (FE) simulation, but the FLC limit diagram cannot be directly used to quantify the product forming quality in the actual stamping production process.

_{0}is the thickness of the blank, t

_{min}is the minimum thickness of the sheet material, t

_{max}is the maximum thickness of the sheet material, Δ

_{thinning}is the thinning rate, and Δ

_{thickening}is the thickening rate.

## 4. Multiobjective Optimization for Hot Stamping Process

#### 4.1. Optimization Variables

#### 4.2. Sample Selection

#### 4.3. Optimization Model and Solution Approach

_{1}, y

_{2}, and y

_{3}are the response functions of the energy-economizing indices, namely, energy consumption, thinning, and thickening, respectively, and x

_{m}are the design variables, namely, blank holder force, stamping speed, and forming temperature.

_{i}, x

_{j}represents the design variable; n is the minimum number of samples; a

_{0}is the minor error; a

_{i}, a

_{ii}, and a

_{ij}are the polynomial coefficients; and y represents the response of the energy-economizing indices of the stamping process.

## 5. Hot Stamping Process Optimization of ZK60 Magnesium Alloy for Energy Saving

_{h}), and forming temperature (T), are considered in the simulation process. The range of each process parameter is set as follows: stamping speed 2–11 mm/s, blank holder force 3–9 kN, and forming temperature 175–250 °C (the range of forming temperature is determined on the basis of existing research results in Reference [24]).

#### 5.1. Material Properties Testing

#### 5.2. FE Modeling and Simulation for Hot Stamping

- (1)
- Figure 9 depicts the initial positions of the die and blank, and the sheet metal is above the die.
- (2)
- The blank holder is close to the sheet metal at a certain speed (it can be set to different speeds, but it maintains a constant speed throughout the stamping process), which is called “holding.”
- (3)
- When the blank holder is finished, the sheet metal is fixed, and the punch starts to act. The “stamping” process begins when the punch contacts the sheet metal.
- (4)
- In the last stage of the simulation, the concave convex die is in a closed state, followed by the quenching stage.

#### 5.3. Process Parameters Optimization

_{1}be the energy consumption of hot stamping, y

_{2}the thinning rate of the stamping parts, and y

_{3}the thickening rate of the stamping parts. The developed model can then be described as

_{1}is the blank holder force, x

_{2}is the stamping speed, and x

_{3}is the forming temperature.

_{1}, y

_{2}, and y

_{3}are the objective functions. The goal is to minimize the stamping energy consumption and thickness variations in hot stamping.

#### 5.4. Stamping Experiments Verification

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Definition diagram of cracking and wrinkling quantification criteria. Φ(ε

_{2}) is the safety marginal curve, ψ(ε

_{2}) is the wrinkle limit curve, and φ(ε

_{2}) is the FLC.

**Figure 8.**True stress-strain curves for ZK60 magnesium alloy deformed at different temperatures and strain rates: (

**a**) 175 °C; (

**b**) 200 °C; (

**c**) 225 °C; (

**d**) 250 °C.

**Figure 11.**Thickness variation distribution demonstrated by the numerical simulation under different compromise solutions: (

**a**) compromise solution 1, (

**b**) compromise solution 2.

**Figure 12.**Equipment and die structures for hot stamping process of tube-shaped parts: (

**a**) 100 T partitioned VBHF hydraulic machine, (

**b**) die structure, (

**c**) physical die.

**Figure 13.**Hot stamping parts of experimentally stamped ZK60 magnesium alloy: (

**a**) Obtained part at the parameters of compromise solutions 1; (

**b**) Obtained part at the parameters of compromise solutions 2.

**Figure 14.**Thickness variation along the symmetrical section of the experimentally obtained parts and simulation result.

Blank Diameter d_{p} (mm) | Sheet Metal Thickness t_{0} (mm) | Drawing Height h (mm) | Punch Radius r_{1} (mm) | Die Radius r_{2} (mm) | Clearance δ (mm) | Friction Coefficient μ |
---|---|---|---|---|---|---|

100.0 | 1.0 | 20.0 | 7.0 | 8.0 | 1.2 | 0.12 |

Element | Si | Fe | Cu | Mn | Al | Zn | Ni | Zr |
---|---|---|---|---|---|---|---|---|

Quality score w | 0.0014 | 0.003 | 0.0011 | 0.008 | 0.0014 | 5.5 | 0.00048 | 0.53 |

Run | F_{h} (kN) | v (mm/s) | T (°C) | Energy Consumption (J) | Thinning (%) | Thickening (%) |
---|---|---|---|---|---|---|

1 | 2.1 | 4.7 | 250 | 46,212.27 | 5.09 | 8.1 |

2 | 2.5 | 3.5 | 225 | 32,165.84 | 4.3 | 8 |

3 | 2.8 | 5.1 | 200 | 28,919.08 | 4.32 | 7.3 |

4 | 3.1 | 8.3 | 250 | 48,726.87 | 5.96 | 7.6 |

5 | 3.5 | 4.3 | 225 | 33,066.23 | 9.62 | 6.8 |

6 | 3.8 | 6.3 | 250 | 47,463.92 | 5.78 | 7 |

7 | 4.2 | 9.5 | 225 | 37,347.17 | 9.64 | 7.8 |

8 | 4.5 | 5.9 | 200 | 29,853.32 | 7.71 | 6.8 |

9 | 4.8 | 7.5 | 200 | 31,439.71 | 5.08 | 7.4 |

10 | 5.2 | 9.9 | 225 | 37,667.46 | 7.75 | 8 |

11 | 5.5 | 7.1 | 225 | 35,622.90 | 7.01 | 7.1 |

12 | 5.8 | 5.5 | 250 | 46,978.99 | 16.12 | 6 |

13 | 6.2 | 9.1 | 200 | 32,932.06 | 6.12 | 7.7 |

14 | 6.5 | 8.7 | 200 | 32,596.56 | 6.04 | 7.5 |

15 | 6.9 | 3.1 | 250 | 44,981.23 | 6.74 | 6.2 |

16 | 7.2 | 6.7 | 200 | 30,775.07 | 5.84 | 7 |

17 | 7.5 | 7.9 | 250 | 48,664.86 | 8.59 | 6.4 |

18 | 7.9 | 3.9 | 225 | 32,835.24 | 11.86 | 5.7 |

Compromise Solutions | Process Parameters | Indices | ||||
---|---|---|---|---|---|---|

F_{h} (kN) | v (mm/s) | T (°C) | Energy Consumption (J) | Thinning (%) | Thickening (%) | |

Solution 1 | 8.0 | 3.0 | 225 | 31,785.57 | 6.2 | 5.7 |

Solution 2 | 4.7 | 3.3 | 200 | 26,190.36 | 4.8 | 5.9 |

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**MDPI and ACS Style**

Gao, M.; Wang, Q.; Li, L.; Ma, Z.
Energy-Economizing Optimization of Magnesium Alloy Hot Stamping Process. *Processes* **2020**, *8*, 186.
https://doi.org/10.3390/pr8020186

**AMA Style**

Gao M, Wang Q, Li L, Ma Z.
Energy-Economizing Optimization of Magnesium Alloy Hot Stamping Process. *Processes*. 2020; 8(2):186.
https://doi.org/10.3390/pr8020186

**Chicago/Turabian Style**

Gao, Mengdi, Qingyang Wang, Lei Li, and Zhilin Ma.
2020. "Energy-Economizing Optimization of Magnesium Alloy Hot Stamping Process" *Processes* 8, no. 2: 186.
https://doi.org/10.3390/pr8020186