## 3 Formability Classification and Prediction Models  
### Analysis Modeling  
In this study, learning data were generated through FEA to predict formability based on the positions and forces of drawbacks. They were generated through analysis because the amount of data that can be obtained through experiments is limited, and a large amount of data is required for AI learning. The automobile fender example provided by Dynaform 5.9.4 was utilized for the model used in the analysis, and its geometry is shown in Figure 4a. FEA was obtained with an NVIDIA DGX STATION (Future Automotive Intelligent Electronics Core Technology Center, Cheonan, Republic of Korea). The model is single-action, in which the punch and binder are placed in the lower die, and the die is placed in the upper die. In this instance, drawbacks were placed on the binder to act on the binder material. As shown in Figure 4b, drawbacks were divided based on the curves and straight lines of the product, and 12 drawbacks were applied. The die moved at a speed of 5000 mm/s and the binder held the material with a force of 200 kN, as specified in Table 1. Drawing quality special killed (DQSK) steel was used as the material, with a thickness of 0.7 mm. This is a high-quality steel suitable for sheet metal forming and is primarily used in the deep drawing process. It is effective in minimizing wrinkling and tearing that may occur during forming because it has a low carbon content and uniform microstructures. In particular, DQSK steel has been widely used in automotive parts, home appliances, and building materials and is suitable for forming complex parts, such as fenders. Table 1 shows the material properties of the material. It has yield and tensile strengths of 154.3 MPa and 520.4 MPa, respectively. The material has a high elongation of more than 30%, with an elastic modulus of 207 GPa. The flow stress formula applied in the analysis was Hollomon's Law, given by Equation (1), where \(\sigma\) is the flow stress, \(K\) is the strength coefficient, \(\varepsilon\) is the effective strain, and \(n\) is the work hardening exponent. \[\overline{\sigma}=K\cdot\overline{\varepsilon}^{n} \tag{1}\]  
Figure 4: (**a**) Fender analysis modeling and (**b**) drawbead locations. A line model was applied as the drawback model applied in this study, rather than a geometry-controlled model. The parameters for geometry were calculated using the drawback forces. The drawbacks were applied as a line because the computation cost and time required for analysis are significantly reduced, and physical effects can be maintained. Furthermore, as the major role of drawbacks is to adjust the speed and resistance at which the sheet metal enters the die, resistance and restraining force are more important than geometry, and they can be replaced with drawback forces for effective simulation. Therefore, for drawback forces, the uplift force is calculated based on the restraining force ratio using the Stoughton experimental formula [23], which is given by Equation (2), where \(F_{r}\) is the restraining force [N], \(F_{u}\) is the uplift force [N], \(T\) is the thickness of the sheet metal [mm], \(R\) is the drawback radius [mm], \(\mu\) is the friction coefficient [-], and \(f(\mu)\) is the yield strength of the material [MPa]. In the equation, \(f(\mu)\) is a function related to the friction coefficient, and resistance is considered based on the friction force generated from the drawback. In this study, 0.125 was used as the friction force that acted on the material, die, punch, and binder. Typically, drawback forces are determined based on empirical data. However, in this study, 5 to 90% of the restraining force was applied to predict wrinkles and cracks according to the drawbead forces. Figure 5a shows the geometry after the initial analysis that did not apply drawbacks, and Figure 5b shows the wrinkle and fracture occurrence results by FLD. When drawbacks were not applied, no crack occurred, while many wrinkles were generated.