# Springback Prediction of Free Bending Based on Experimental Method
## 3 Experimental Verification
### Springback Experiment  
According to the experimental \(U\)-\(R\) relationship, the corresponding bending angle can be obtained, and the single bending experiment was carried out according to the theoretical bending angle and springback bending angle. A Q235 carbon steel tube with a diameter of 32 mm and a wall thickness of 2 mm was used as the tube blank. Because the forming process is influenced by the value of U, the processing process was divided into five stages: first straight section, first transition section, arc section, second transition section, and second straight section. Because the springback phenomenon does not occur in the straight section, only the springback phenomena of the first transition section, the bending section and the second transition section were considered. First, single bends were processed to observe the stress and strain phenomena of the cross-section of the bending section. The experiment showed that the actual arc length was shorter than the theoretical arc length. In the process of tube bending formation, the conventional distribution of the wall thickness \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**U (mm)**} & **2.2** & **2.35** & **2.5** & **2.55** & **2.7** & **3.25** & **3.5** & **5** \\ \hline
1 & 1771.2 & 1427.5 & 1207.6 & 1115.11 & 1015.3 & 762.93 & 635.61 & 373.3 \\
2 & 1734.9 & 1427.5 & 1207.6 & 1090.7 & 1012.9 & 770.56 & 627.63 & 373.54 \\
3 & 1747.1 & 1419.3 & 1210.3 & 1120.1 & 989.7 & 773.13 & 629.21 & 373.33 \\
4 & 1878.5 & 1403.4 & 1199.6 & 1172.1 & 1005.5 & 768 & 627.63 & 376.66 \\
5 & 1797.4 & 1419.3 & 1200.3 & 1188.2 & 1000.3 & 765.46 & 626.06 & 373.86 \\
6 & 1734.9 & 1435.7 & 1203 & 1140.5 & 1021.3 & 760.42 & 637.23 & 373.3 \\
7 & 1734.9 & 1357.6 & 1198.5 & 1139.3 & 997.3 & 765.46 & 627.23 & 371.65 \\
8 & 1771.9 & 1460.9 & 1196.7 & 1141.1 & 1110.1 & 760.42 & 630.8 & 375.54 \\
9 & 1771.9 & 1411.3 & 1201.7 & 1137.3 & 1005.4 & 762.93 & 632.39 & 372.75 \\
10 & 1759.4 & 1411.3 & 1201.7 & 1155.1 & 1002.3 & 760.42 & 622.94 & 373.86 \\ Average & 1770.21 & 1417.38 & 1202.7 & 1139.55 & 1015.81 & 764.973 & 629.673 & 373.776 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Table of Al6061 \(U\)-\(R\) Relationship Experimental Data. Figure 4: \(U\)-\(R\) curve: (**a**) Q235 \(U\)-\(R\) curve; and (**b**) Al6061 \(U\)-\(R\) curve. took the neutral layer as the boundary, and the outer wall of the tube was thinned while the inner wall was thickened. In the free-bending process, under the action of the axial thrust force and the bending moment of the bending die, the strain neutral layer of the tube deviated like the outer side of an arc, and in this process, the inner side led to the thinning of the outer arc wall of the tube and the accumulation of the inner arc wall. As shown in Figure 5, it can be clearly seen that the inner side of the arc is thickened, and the outer side of the arc is thinned. This is due to the fact that the neutral layer deviates to the outside of the arc during free bending [26]. Excessive accumulation in the inner side leads to the reduction of extrusion of the arc segment, which is also the reason why the experimental arc segment is smaller than the theoretical arc segment in the actual measurement process. Through measurements, it can be seen that the actual arc length is shorter than the theoretical arc length, so the compensation experiment was considered for the transition section and arc section. First, a single bend experiment with a single bend angle of 45\({}^{\circ}\) was carried out. The tube was processed according to the theoretical value, and the formed tube is shown in Figure 6a. After the original tube is formed without any treatment, the actual included angle is 76\({}^{\circ}\), and the springback angle \(\alpha\) can be calculated by Equation (9):  
\[\alpha=\theta_{1}-\theta_{0} \tag{9}\]  
It can be seen that the initial springback angle without treatment is 31\({}^{\circ}\), and the error is large. Next, the compensation experiment is carried out for each segment. 1.