## 4 Reinforcement Springback Compensation Method  
### Theory of Steel Bar Bending Springback  
According to the bending mechanism of steel bars, it can be seen that the steel bar is formed by bending mechanism, which is a complicated elastic-plastic bending deformation. Therefore, after the reinforcement is bent, due to the existence of residual stress, the reinforcement will bounce back at a certain angle, and the angle after the springback is the actual bending angle of the reinforcement [32]. The relationship between bending and forming parameters is shown in Figure 15, where \(d\) is the diameter of steel bar. \(\beta\) is the inclination angle of the curved crankshaft and center line; \(R\) is the radius of rotation of the curved crankshaft; \(R_{1}\) is the radius of the support shaft; \(R_{2}\) is the radius of the bending crankshaft; \(\alpha\) is the rotation angle of the curved crankshaft, and also, the angles of reinforcement are \(\theta_{1}\) and \(\theta_{2}\); \(\theta\) indicates the bending angle of the steel bar, namely, \(\theta_{3}\) and \(\theta_{4}\).  
The bending angle of the winding steel bar is controlled by the bending angle of the curved crankshaft. The relationship between the bending angle of the steel bar \(\theta\) and the bending angle of the curved crankshaft \(\alpha\) is as follows:  
\[\theta=\pi-\alpha \tag{1}\]  
Figure 14: Steel bar bending springback angle value.  
Figure 15: Bending angle diagram.  
In order to improve the accuracy of the actual bending angle, the overbending method is used to compensate for the bending springback angle. Figure 16 shows the diagram for the bending springback angle, reinforced bending angle for \(\theta_{1}\), reinforced radius of curvature for \(\rho_{1}\), and steel angle for \(\theta_{3}\). The springback phenomenon occurs after the steel bar bends. The springback angle is \(\Delta\theta\), the actual angle of the steel bar becomes \(\theta_{2}\), the radius of curvature of the steel bar becomes \(\rho_{2}\), and the actual bending angle of the steel bar is \(\theta_{4}\).  
Reinforcement bending belongs to elastic-plastic bending deformation. According to the principle of \"neutral layer unchanged\" in reinforcement bending springback [33], it can be obtained as follows:  
\[\rho_{1}\theta_{1}=\rho_{2}\theta_{2} \tag{2}\]  
By combining Equation (1) with Equation (2), the formula for calculating the bending springback angle \(\Delta\theta\) of the steel bar is shown in Equation (4). However, in the actual application process, the steel bar needs to be straightened, hoop bent, cut, and other processing processes. After several elastic-plastic deformations, the steel bar will produce work hardening [34]. Work hardening will lead to a reduction in plasticity and toughness of steel bars. Therefore, in practical application, because the influence of work hardening on the springback angle is considered, the theoretical formula cannot obtain the exact value of the springback angle. Therefore, in the processing of steel bars, the method of springback angle compensation is often used to control the accuracy of the steel bar bending angle.  
\[\theta_{1}=\frac{\rho_{2}}{\rho_{1}}\theta_{2}=\frac{\rho_{2}}{\rho_{1}}(\pi- \theta_{4}) \tag{3}\]  
\[\Delta\theta=\theta_{4}-\theta_{3}=(\pi-\theta_{4})(\frac{\rho_{2}}{\rho_{1}} -1) \tag{4}\]