## 3 Optimization of Structural Parameters of Steel Bar Hoop Bending Machine
### Finite Element Simulation and Experimental Analysis
#### 3.1.2 Simulation of Steel Bar Bending  
In the experiment, an HRB400 high-strength steel bar was widely used in building construction, with an elastic modulus of \(E=2.06\times 10^{5}\) MPa, a Poisson's ratio of \(\
u=0.3\), and a bending speed of 6.28 rad/s. In order to visually express the influence of various factors on the steel bar, the size and distribution of steel bar stress at the bending angle of \(90^{\circ}\) were selected for analysis. (1) The influence of the size of the support shaft on the bending of the steel bar. According to Table 2, the parametric model was established and the simulation solution analysis was carried out. The diameter D\({}_{1}\) of the commonly used support shaft on-site is 10 mm-40 mm, and three different sets of support shaft diameters are used to simulate the steel bar bending process when the support shaft diameter is 20 mm, 30 mm, and 40 mm. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Name**} & **Density** & **Modulus of** & **Poisson’s** & **Yield** & **Tangent** \\  & **(Kg/m\({}^{3}\))** & **Elasticity (Pa)** & **Ratio** & **Strength (Pa)** & **Modulus (Pa)** \\ \hline Steel bar & 7850 & \(2.06\times 10^{11}\) & 0.3 & \(4\times 10^{8}\) & \(8\times 10^{8}\) \\ Support shaft & 7850 & \(2\times 10^{11}\) & 0.3 & — & — \\ Bent crankshaft & 7850 & \(2\times 10^{11}\) & 0.3 & — & — \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model material parameters. Figure 4: Finite element model of a steel bar bending mechanism. Figure 5 shows the longitudinal cross-sectional stress distribution of steel bars at 90\({}^{\circ}\) bending angle under different support shaft diameters. Steel bar bending springback is the effect of elastoplastic deformation, as shown in the figure; with the increase in the diameter of the support shaft, the stress-distribution surface after bending of the steel bar gradually increases, and the maximum stress value gradually decreases. Therefore, reducing the diameter of the support shaft can effectively reduce the residual stress of the reinforcement. Simulation results show that when the diameter of the support shaft is 20 mm, the stress value is the smallest. The influence of bending shaft size on steel bar bending. The  
Figure 5: Stress cloud diagrams of steel bars for different support shaft sizes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Steel Bar** & **Bending Shaft** & **Diameter of** & **Turning Radius** \\
**Diameter (mm)** & **Speed (rad/s)** & **Support Shaft** & **Bending Shaft** & **of the Bending** \\  & & **(mm)** & **(mm)** & **Axis (mm)** \\ \hline
10 & 6.28 & 20 & 40 & 80 \\
10 & 6.28 & 20 & 50 & 80 \\
10 & 6.28 & 20 & 60 & 80 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation experiment parameter table. Figure 6 shows the longitudinal-section stress-distribution cloud of a steel bar at a bending angle of 90\({}^{\circ}\) under different bending axis sizes. As shown in the figure, with the increase in the diameter of the bending shaft, the stress-distribution surface and the maximum stress value of the steel bar after bending change little, and the three sets of simulation results are basically the same. Therefore, changing the diameter of the bending axis cannot effectively reduce the residual stress of the steel bars. (3) The influence of the rotation radius of the bending axis on the bending of the steel bar. According to Table 4, the parametric model was established, and the simulation solution analysis was carried out. The rotation radius R of the commonly used bending shaft is 60 mm-100 mm, and three different sets of bending shaft rotation radii are used to simulate the steel bar bending process when the bending shaft rotation radius is 60 mm, 70 mm, and 80 mm.