## 2 Materials and Methods
### FE Simulation Model and Testing of Open-Die Forging Process  
Geometric models of the punch, die, and billet tube are meticulously constructed to meet the precise shape and size requirements of the product, as depicted in Figure 2a. As shown in Figure 2b, the geometric models of the workpiece, punch, and die are developed using Catia software and formatted as *.STL files to be integrated into the simulation environment. To initiate the initial experimental study, assess the research model's suitability, and analyze and identify potential instability and form folding defects in the workpiece after stamping, the geometrical parameters of the workpiece and forming tool are set during both simulation and experiment. Specifically, the upsetting ratios are \(H0/D0=0.6\) and \(S0/D0=0.35\), while the tilt angle of the punch is set to \(\alpha=15^{\circ}\) degrees. The numerical simulation software employed in this study is DEFORM-3D. To compute stress distribution, strain, displacement, and material flow velocities using the finite element method, a mesh of the workpiece and die is required. In our approach, the workpiece was discretized into 75,000 elements, the punch into 10,000 elements, and the mold into 20,000 elements. For the simulation setup, the initial temperature of the workpiece was set at 1100 \({}^{\circ}\)C, while the upper and lower die temperatures were maintained at 25 \({}^{\circ}\)C. The lower die was immobilized, and the upper die was set to move at a velocity of 100 mm/s. The interaction between the workpiece and die followed the Tresca contact condition with a friction coefficient of 0.4. Additional material conditions were configured in accordance with the values outlined in Table 2. Notably, this study introduced variable strain rate and temperature conditions that are contingent on stress and variation, as detailed by Equation (1). The simulation procedures (Figure 2c) were executed using DEFORM-3D software, and the simulation model is visually depicted in Figure 2b. To ensure congruence with the experimental setup, the mold used in the simulation is designed to match the shape and size of the actual experimental mold. The test equipment is tailored to match real production conditions. The equipment clusters are modularized and easily interconnected to form a complete system. The schematic diagram illustrating the main modules and components of the experimental system is displayed in Figure 3. The integration of these main modules allows for efficient control of the shaping process, facilitating convenient adjustments during experimentation. The experimental diagram is straightforward, enabling swift parameter adjustments. Data measurement and storage are \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(A\) & \(m_{1}\) & \(m_{2}\) & \(m_{3}\) & \(m_{4}\) & \(m_{5}\) & \(m_{6}\) & \(m_{7}\) & \(m_{8}\) \\ \hline
14,087.5 & \(-0.003\) & \(0.2814\) & \(0.0297\) & \(-0.0177\) & \(-0.0003\) & \(-0.0415\) & \(0.0001\) & \(-0.311\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Values of parameters used for determining yield stress values of C45 steel in Equation (1) [61]. automated and conducted concurrently with the forming process, yielding rapid results displayed on the screen. Figure 3: Diagram depicting experimental equipment and process. Figure 2: Geometric model of the mold and billet tubes (**a**), the numerical simulation model (**b**), and the simulation algorithm (**c**) for advancing flange-forming technology in open-die forging through numerical simulation. With the modules calculated, designed, and selected, the next step is to assemble these modules sequentially. Initially, the complete set of molds is assembled, positioned, and clamped on the slide and table of the FCP-160-ton crankshaft press. Subsequently, the sensor is placed beneath the intermediate die and clamped to the lower die assembly. Through cables and wires, the sensor is connected to other modules in the mold and measuring device system.