**1. Introduction**

Rapid economic development has recently accelerated increases in the consumption of energy, especially in industrial sectors, which is causing a series of environmental problems, such as greenhouse gas (GHG) emissions [1]. The GHG emissions in China reach 1.03 <sup>×</sup> 10<sup>9</sup> 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].

Hot stamping was developed to manufacture the structural components of automobiles by using lightweight materials to achieve decreased weight, improved safety, and enhanced crashworthiness [5]. Hot stamping can improve the formability of these lightweight materials, which overcomes the limits of traditional cold stamping [6]; it is particularly suitable for manufacturing complex parts [7]. Moreover, the high forming precision and reduced springback of hot stamping have led to its wide application in the automotive and aircraft industries.

However, the high-temperature forming conditions of blanks in the hot stamping process consume additional energy. Heating the sheet material to a certain temperature improves the energy consumption of hot stamping compared with that of cold stamping [8]. The energy consumption and environmental effects of the hot stamping industry warrant attention. Process energy consumption models of hot stamping have been developed to qualify its energy consumption [9]. The associated carbon footprint is identified to analyze its environmental effects [10]. All the results show that oven curing accounts for a large amount of the products' energy consumption and environmental impact. Therefore, one efficient pathway towards energy-economizing hot stamping is promoting the energy efficiency in the blank heating process. The thermal transfer and loss principle is basic for energy efficiency improvement in oven curing. To study the thermal aspects of the hot stamping process, based on the identification of the heat transfer coefficient in hot stamping [11], Abdulhay et al. proposed the heat-transfer modeling of all heat-transfer modes occurring during the hot stamping phases [12].

A suitable stamping temperature is very important in optimizing the energy efficiency of hot stamping. The product forming quality and energy consumption are determined by process parameters. Many researchers have focused on the optimization of these parameters to solve the product forming quality problem of hot stamping. Xiao et al. found that decreasing forming temperature and increasing forming speed can improve the formability of AA7075 through a hot uniaxial tensile test [13]. More than one object should be considered in multiobjective optimization methods, such as the weighted sum method [14], the global criterion-based method [15], and genetic algorithms [16], which are widely applied in the hot stamping to solve the conflict between different evaluation indices of forming quality. Kitayama et al. used sequential approximate optimization with radial basis function network to optimize the parameter of blank holder force trajectory, with the aim of reducing the products' springback [17]. Zhou et al. focused on numerical simulations, together with the combination of response surface methodology (RSM) and nondominated sorting genetic algorithm II (NSGA-II) to optimize aluminum alloy hot stamping [18]. In order to reduce the influence of the stochastic property of process parameters on forming quality, Xiao et al. integrated multiobjective stochastic approaches, such as RSM, NSGA-II, and Monte Carlo simulations (MCSs), to obtain the optimal process parameters of aluminum hot stamping [19].

The above analysis reveals that the energy consumption and environmental soundness of the hot stamping process are of serious concern. But research on how to reduce the energy consumption of the hot stamping process is still insufficient. Process optimization is an excellent way to solve this problem. But the process parameters have been optimized using numerous methods and multiobjective optimization methods to enhance only the product forming quality. Energy consumption should not be neglected in the parameters optimization of the hot stamping process. In particular, hot stamping optimization with consideration for energy saving is worth studying due to its relevance to energy-efficient manufacturing. However, there is still a lack of effective methods regarding both the optimization of energy consumption and in terms of improving the forming quality at present. In this study, a novel parameter optimization method for the hot stamping process is proposed with the multiobjective improvement of forming quality and process energy consumption.

#### **2. Framework and Method**

Different process parameters determine the amount of energy consumption and product forming quality of hot stamping. Product forming defects, such as wrinkles, cracks, or high energy consumption, will appear when sheet materials are processed under inappropriate process parameters. This can be avoided by adjusting and selecting appropriate process parameters in hot stamping. Process optimization is an efficient way to reduce the energy consumption and avoid forming defects in the hot stamping process.

A descriptive flowchart depicting the major steps of the proposed methodology is shown in Figure 1, which provides an outline for this study. A hot stamping process contains heating and forming processes; energy and material are supplied for the process with different processing parameters. In order to achieve an environmentally-friendly manufacturing process, energy reduction is essential. Process energy consumption and forming quality are considered in the process optimization method of hot stamping, which are taken as the energy-economizing indices. These indices of hot stamping are regarded as the optimization objectives. The forming quality and energy consumption under different process parameters are qualified by the developed models or simulation and experiments. The range and constraints of the optimized process parameters should be initially determined in accordance with the forming performance and requirements. Then, sample points should be selected in the design space for experiments, and the corresponding simulations or experiments be conducted to obtain the corresponding evaluation index values of each sample point. Our model was developed to study the relationship between the process parameters and each index, which was solved using a multiobjective genetic algorithm (NSGA-II) and offers feasible optimized solutions. The comparison between the numerically-predicted technical parameters of the stamps and the real experimental results demonstrate the applicability of the method. The multiobjective optimization method can improve the energy efficiency of hot stamping while maintaining the required quality of the stamps. The proposed energy-economizing can provide a reference for industrial manufacturing and production, especially for vehicle production.

**Figure 1.** Methodological framework.

#### **3. Energy-Economizing Indices of Hot Stamping**

#### *3.1. Process Energy Consumption Indices*

The hot stamping process begins by heating a sheet material to a given range of temperatures to improve formability. Therefore, the energy consumption of hot stamping is associated with the energy used for heating and that used for forming. The total energy consumption of hot stamping, *E*, can be calculated as

$$E = E\_{\text{breating}} + E\_{\text{forming}} \tag{1}$$

where *E*heating is the heating energy consumption and *E*forming is the forming energy consumption.

After being heated in a furnace, the sheet material is delivered to a piece of forming equipment and immediately formed in a closed tool. Thus, the heat is transferred to the environment and tools in those processes; this transfer is described as heat loss, Δ*Q*. The heat loss includes convection and radiation losses with ambient air during the transfer to the forming equipment, and the losses by heterogeneous approaches of convection, radiation, and conduction in the forming process [12]. Therefore, the heat loss (Δ*Q*) can be calculated as

$$
\Delta Q = Q\_{\text{convection}} + Q\_{\text{radiation}} + Q\_{\text{conduction}} \tag{2}
$$

where *Q*convection, *Q*radiation, and *Q*conduction are the heat losses by convection, radiation, and conduction, respectively, and can be calculated by as follows:

$$Q\_{\text{convection}} = Q(\mathbb{R}\_{\hbar}, \Delta T, \Delta t) = A h \Delta T \Delta t,\tag{3}$$

$$Q\_{\text{radiation}} = kF\_\text{r}A \Big( (T + \Delta T)^4 - T^4 \Big) \Delta t,\tag{4}$$

$$Q\_{\text{conduction}} = Q(\mathcal{R}\_{\lambda}, \Delta T, \Delta t) = A\lambda \frac{\Delta T}{t\_0} \Delta t\_\prime \tag{5}$$

where *A* is the heat transfer area, *h* is the convection coefficient, *Rh* = 1/*Ah* is the convection resistance, *T* is the temperature, Δ*T* is the temperature difference between hot and cold fluid object, *k* is the Boltzmann constant, *F*<sup>r</sup> is the radiation shape factor, λ is the thermal conductivity, and *R*<sup>λ</sup> = δ/*A*λ is the thermal resistance, δ is the thickness, *t* is the time.

The total heat, *Q*, can be calculated by Equation (6), which combines the heat in the blank and the heat loss.

$$Q = Q\_{\text{blank}} + \Delta Q\_{\prime} \tag{6}$$

where *Q*blank is the heat absorbed by sheet metal.

The energy consumption used for heating can be calculated as

$$E\_{\text{heating}} = \frac{Q}{1 - \eta\_{\text{loss}}(T, i)},\tag{7}$$

where ηloss(*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.

The forming stage in hot stamping is similar to that in cold stamping, as shown in Figure 2. The heated sheet material is placed on a die with a blank holder to avoid wrinkle defects. The forming press controls the punch to draw the blank into the die and to form it into the desired shape with the elastic–plastic deformation of the sheet metal and the contact friction between the sheet material and dies [20]. Therefore, the energy consumption of the forming stage in the hot stamping process can be quantified from two perspectives. The direct ways are measuring and estimating the energy consumption of the forming equipment [21], which can be described as

$$E\_{\text{forming}} = \int\_{t\_{\text{start}}}^{t\_{\text{end}}} F(t)v(t)dt / \eta(t),\tag{8}$$

where *F* is the output force of the actuator of the forming equipment, which varies with the working conditions; *v* is the punch speed, and η is the energy efficiency in the stamping process.

**Figure 2.** Forming process of hot stamping.

The second method involves consideration of the deformation process of the sheet material, and then analysis and modeling of the process energy consumption with the related parameters. The energy consumption of the sheet metal forming process may be divided into that required for plastic deformation, bending, and frictional energies [8]. These analytical quantification methods of calculating the process energy consumption are detailed in Reference [22].

#### *3.2. Forming Quality Indices*

The thinning and thickening of critical elements are used to indicate whether fractures have occurred in the blank forming process. Springback cannot be regarded as a forming quality index because the springback of hot stamping is considerably less than that of cold stamping. A sheet metal will crack if its thickness is less than a certain critical value. The rupture distance refers to the vertical distance between the strain point of dangerous elements and the forming limit curve (FLC), as shown in Figure 3. When the main strain of a region element of the formed part is above the FLC (ϕ(ε2)) or the safety marginal curve (Φ(ε2)), this region of the shaped part will likely fracture. A long distance from the safety marginal curve Φ(ε2) indicates a high rupture tendency. Therefore, the average distance between the main strain of all elements and the Φ(ε2) curve can be used to quantify the fracture. Similarly, when the main strain of an area element is below the wrinkle limit curve (ψ(ε2)), this area of the formed part will show a wrinkling trend; the farther the point from the ψ(ε2) 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.

**Figure 3.** Definition diagram of cracking and wrinkling quantification criteria. Φ(ε2) is the safety marginal curve, ψ(ε2) is the wrinkle limit curve, and ϕ(ε2) is the FLC.

Therefore, in the actual production and the experiment, thinning and thickening can be used to represent the possibility of fracture and wrinkling, respectively. These indices are calculated using Equations (9) and (10). An excessively large thinning rate of a sheet metal in a certain area means that the fracture trend is too large, whereas a disproportionately high thickening rate indicates a possible wrinkling phenomenon.

$$
\Delta\_{\text{thrinning}} = (t\_0 - t\_{\text{min}}) / t\_0 \times 100\% \tag{9}
$$

$$
\Delta\_{\text{thickness}} = (t\_{\text{max}} - t\_0) / t\_0 \times 100\% \tag{10}
$$

where *t*<sup>0</sup> 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, Δthinning is the thinning rate, and Δthickening is the thickening rate.

#### **4. Multiobjective Optimization for Hot Stamping Process**

#### *4.1. Optimization Variables*

The considered process parameters are regarded as optimization variables in the hot stamping optimization process. Many process parameters affect the energy consumption and forming quality of stamping parts, such as stamping speed, blank holder force, friction conditions, tool gap, and draw-bead geometry parameters. The influence of the draw-bead is usually not considered because the draw-bead is typically used only in stamping extremely complex-shaped parts. In addition, the shape parameters of the draw-bead are complex, and have independent design criteria for some simple stamping processes. The clearance between the punch and die substantially affects the springback of the forming parts, which usually accounts for 110–120% of the sheet metal thickness. The die gap is usually ignored as a design variable because of the small springback in the hot stamping process. No quantitative analysis exists for the effect of friction on product forming quality because the friction conditions in an actual stamping workshop are determined by the lubricating oil, die material, and coating. Therefore, in hot stamping optimization, three process parameters, namely, stamping speed, blank holder force, and forming temperature, should be considered. A certain range of process parameters should be experimentally analyzed to obtain the optimal process parameters.

After the optimization variables are determined, a certain sample point is selected in the design space for experiment. The surrogate model between each process parameter and its corresponding index value is established on the basis of RSM, and the process parameters are optimized on the basis of the multiobjective genetic algorithm.

#### *4.2. Sample Selection*

The Latin hypercube design (LHD) is an efficient sampling method; it is advantageous in sampling efficiency and running time due to its reduced number of iterations. This method is especially suitable for computer simulation experiments. A good feature of this method is that sample points are selected from the entire design space. Therefore, the optimal process parameters can be determined systematically and accurately with less experiments by using this method. LHD evenly divides the design space of each variable into several layers, and these layers obtain some special points through random combination to determine the design matrix. Each level of each parameter is sampled only once.

#### *4.3. Optimization Model and Solution Approach*

The energy-economizing optimization aims to obtain a set of process parameters that will produce stamping parts with good forming quality (no cracks, wrinkling, or noticeable thickening and thinning) and low energy consumption. The objective function and constraints of the optimization process can be given as

$$F = \min(y\_1, y\_2, y\_3)$$

$$\text{s.t.} \begin{cases} h\_i(\mathbf{x}) = 0 \ (i = 1, 2 \cdots n) \\ \mathbf{g}\_j(\mathbf{x}) \ge 0 \ (j = 1, 2 \cdots n) \\ \mathbf{x}\_m^{\min} < \mathbf{x}\_m < \mathbf{x}\_m^{\max} \ (m = 1, 2 \cdots n) \end{cases} \tag{11}$$

where *y*1, *y*2, and *y*<sup>3</sup> are the response functions of the energy-economizing indices, namely, energy consumption, thinning, and thickening, respectively, and x*<sup>m</sup>* are the design variables, namely, blank holder force, stamping speed, and forming temperature.

Determining the mapping function through theoretical derivation is difficult due to the complex relationship between process parameters and target quantity. RSM is an effective method of building substitute models. The RSM polynomial regression model adopts a quadratic regression equation. On the basis of experimental data, the coefficient of the regression equation is obtained through the least squares method to construct the functional relationship between the optimization variable and target quantity. The commonly used second-order polynomial response surface model can be represented by

$$y = a\_0 + \sum\_{i=1}^{n} a\_i \mathbf{x}\_i + \sum\_{i=1}^{n} a\_{ii} \mathbf{x}\_i^2 + \sum\_{i=2}^{n} \sum\_{j=1}^{i-1} a\_{ij} \mathbf{x}\_i \mathbf{x}\_j. \tag{12}$$

where *xi*, *xj* represents the design variable; *n* is the minimum number of samples; *a*<sup>0</sup> is the minor error; *ai*, *aii*, and *aij* are the polynomial coefficients; and *y* represents the response of the energy-economizing indices of the stamping process.

NSGA-II is a multiobjective genetic algorithm that ensures good convergence and robustness by introducing a fast nondominated sorting algorithm, elite strategy, and congestion degree comparison operator, and other strategies [23]. The multiobjective optimization problem of hot stamping can be solved by programming NSGA-II.

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

On the basis of the proposed energy-economizing optimization method of hot stamping, the tube-shaped part, whose common profile is shown in Figure 4, is selected as a case to investigate the proposed method. Table 1 presents the tool size and relevant parameters of the sheet metal. The stamping material is ZK60 magnesium alloy, which is a lightweight material with strong deformation capability and good heat treatment strengthening effect. Three variable process parameters, namely, stamping speed (*v*), blank holder force (*F*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]).

**Figure 4.** Stamping of tube-shaped part.


**Table 1.** Parameters for drawing processes of tube-shaped parts.

On the basis of the aforementioned experimental design method, the LHD sampling method is used to sample the point in the range of each process parameter, and the least number of sample points required by the response surface model is determined through the least squares method. The number of samples *n* can be determined in terms of the equation *n* = (*m* + 1)(*m* + 2)/2 of the number of considered process parameters *m*. Given that the number of process parameters *m* is 3, the number of samples *n* is at least 10. Eighteen design sample points are selected to improve the accuracy of the response surface model, and Figure 5 illustrates their value distribution.

**Figure 5.** Sample distribution of LHD in the range of each process parameter.

#### *5.1. Material Properties Testing*

Accurate mechanical property parameters and an equivalent stress model are vital for analyzing the hot deformation of magnesium alloy. The goal is to identify the mechanical properties of ZK60 magnesium alloy under different temperatures, which are used for the theoretical calculation of energy consumption and simulation. Table 2 shows the chemical composition of ZK60 magnesium alloy. A series of hot unidirectional tensile experiments is performed on an MTS810 system material testing machine (Figure 6) at different temperatures. The testing samples are designed on the basis of the GB/T4338-2006 high-temperature tensile testing method of metallic materials, and the thickness of the samples is 2 mm, as shown in Figure 7.

**Table 2.** ZK60 magnesium alloy chemical composition (%).


**Figure 6.** MTS810 material experimental system.

**Figure 7.** ZK60 magnesium alloy tensile sample.

The hot unidirectional tensile experiments are performed under invariable temperatures of 175 ◦C, 200 ◦C, 225 ◦C, and 250 ◦C. The samples are kept in an environmental cabinet for 15 min after being clamped at different temperatures. The samples are then stretched with different speeds to obtain the stress-strain curve of ZK60. Three groups of experiments are conducted under the same parameters, and the average values are regarded as the experimental results under the corresponding conditions. Figure 8 exhibits the obtained true stress–strain curve of ZK60 magnesium alloy.

A flow stress mathematical model of ZK60 magnesium alloy is established on the basis of the Fields–Backofen equation in consideration of the softening factor proposed by Zhang et al. [25]. In accordance with the experimental stress–strain curves of ZK60 magnesium alloy under various temperatures, the corresponding flow stress mathematical model is developed as

$$
\sigma = 746\varepsilon^{0.1101} \varepsilon^{0.0262} \exp\left(-0.00665T - 0.94781\varepsilon\right),
\tag{13}
$$

where σ is the stress of the investigated ZK60 magnesium alloy, ε is the strain of the ZK60 magnesium alloy, and . ε is the strain rate of ZK60 magnesium alloy.

**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.

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

The FE simulation model is established in accordance with the actual hot stamping process, as shown in Figure 9. The punch is placed above the sheet metal, the die is at the bottom, and the sheet metal lies above the die and below the blank holder. In the simulation process, the mold is regarded as a rigid body without elastic deformation; thus, it cannot be meshed. A Belytschko–Tsay shell element with five Gaussian thickness dimension integration points is used to divide the sheet metal mesh, and the thickness of the sheet metal is set as 1 mm. The initial unit number of the sheet metal is 3925, and the grid refinement level is set as 2. The kinematic relations of the tools and blank are as follows:


In accordance with the friction condition between the blank and tools in the actual stamping process, the friction coefficient is set as 0.12 in the simulation. The blank is heated via in-mold heating. This heating method is advantageous in that the variation of temperature is relatively small; therefore, the temperature distribution of the sheet is uniform and has good formability. However, the energy consumption used for heating will be considerably higher than that for furnace heating. The simulations are performed on the basis of the design points in Figure 5, and the corresponding

energy consumption is calculated through a previous energy consumption theoretical model. Table 3 shows the results.

**Figure 9.** Numerical simulation model of the tube-shaped part.


