## 8 Results Analysis
### Optimization Result Analysis  
Using the optimized process parameters obtained from the particle swarm optimization (PSO), the mold taper angle, friction coefficient, and drawing speed were set to 14.77\({}^{\circ}\), 0.0384, and 1.0687 m/s, respectively. After recalculating, the maximum drawing force was found to be 60.4 kN, the maximum temperature was 102.8 \({}^{\circ}\)C, and the average wall thickness and wall thickness uniformity were 2.161 mm and 0.01%, respectively. Compared with the wall thickness uniformity obtained by the current process, it is reduced by 28%, as shown in Table 13. It can be seen that the optimized parameter combination can improve the uniformity of wall thickness.  
According to research by [PERSON] [10], the influence of wall thickness non-uniformity on drawing force, axial displacement of the core head, and equivalent stress were analyzed. With the increase in wall thickness non-uniformity, the drawing force decreases by 6%, the fluctuation amplitude increases 16 times, the momentum of the core head increases and gradually weakens, and the yield strength and tensile strength of the copper pipe decrease, which can easily lead to tensile cracking and distortion. According to research by [PERSON] [42], increasing the wall thickness accuracy of the tube body by \(\pm\)5% can increase the steel pipe yield by 2.6%, and the statistical results show that the yield can increase by 2.2-5.1%.  
After optimization, the temperature field distribution during the joint drawing process is shown in Figure 21a and the wall thickness distribution is shown in Figure 21b. As the tube blank enters the taper section of the outer die, it begins to contact the mold, and due to friction, the temperature of the tube blank starts to rise. When the tube blank enters the sizing section, deformation begins, the wall thickness gradually decreases, and the temperature continues to rise.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter Combination** & **Average Wall Thickness/mm** & **Wall Thickness Uniformity** & **Optimization Percentage** \\ \hline Before optimization & 2.162 & 0.014\% \\ Post optimization & 2.161 & 0.01\% \\ \hline \hline \end{tabular}
\end{table}
Table 13: Comparison of optimization results.  
Figure 21: Distribution cloud. (**a**) Temperature distribution results; (**b**) thickness distribution results.  
As shown in Figure 22a, the drawing force of the tube first increases and then decreases over time; specifically, the drawing force increases as the tube passes through the taper section of the outer die and decreases once the tube enters the sizing section. The maximum drawing force reaches 60.4 kN, which is significantly lower than the maximum drawing force of 77.3 kN observed in the sampling simulation experiment. Throughout the deformation zone, the drawing force on the tube remains relatively stable, with no significant fluctuations or sudden increases.  
The temperature field curve shown in Figure 22b indicates that the temperature rapidly rises as the tube enters the taper section of the drawing die. The highest temperature of 102.8 \({}^{\circ}\)C occurs after the tube blank completely exits the sizing section. These results demonstrate that the optimized process is stable and effective. Therefore, it is feasible to increase the drawing speed from the current 0.6 m/s to 1.0687 m/s, which not only improves the wall thickness uniformity and dimensional accuracy of the tube but also greatly enhances production efficiency.