## 4 Results and Discussion
### SPIF Experimental Validation  
To order to understand the forming accuracy and surface quality of the truncated pyramids component under different forming angles, the optimal process parameters from the simulation were selected to conduct SPIF experiments with different forming angles (51 \({}^{\circ}\), 54 \({}^{\circ}\) and 57 \({}^{\circ}\)) at a forming temperature of 200 \({}^{\circ}\)C, a feed rate of 1000 mm/min and a forming tool rotation speed of 400 rpm. As shown in Figure 7, the morphology of the outer and inner surfaces of the truncated pyramid component at different forming angles is shown. It can be seen that the forming angle has a significant impact on the surface. The surface becomes smoother with the increasing forming angle. At the forming angle of 51\({}^{\circ}\), obvious microcracks (indicated by the red dashed line) can be found at the corner of the outer surface. Microcracks are also found at the corner with a forming angle of 54\({}^{\circ}\). With the increasing forming angle, not only the microcracks on the outer surface are improved, but also the wave ridges produced by the forming tool on the inner surface are gradually reduced [12]. Besides, more microcracks and wrinkles are observed on the outer surface compared to the inner surface. These localized microcracks and wrinkles on the outer surface lead to the cracking of the component upon further deformation. This is consistent with [PERSON] [18] and [PERSON] [29]. Figure 6: Maximum thinning rate and standard deviation of wall thickness of truncated pyramids component under different forming angles. Measurement of the contour and wall thickness of the truncated pyramid component under different forming angles are shown in Figure 8. SPIF belongs to die-less forming, and the geometric contour does not fit with the design contour within a depth of 5 mm, showing a slight bending. However, it can be observed that the geometric contour of the region in the X direction has a smaller deviation compared to the design contour in the Y direction. The reason is that the billet formed in the X direction has a shorter side, and the relatively longer side has a shorter forming length to obtain effective support from the molds on both sides. The deeper the forming depth, the smaller the difference. The larger the forming angle, the better the profile curve of the experimentally formed component fit well with the designed geometry. The longer edge of the sheet are less stable as the short edge during SPIF processing, this results in a higher thickness deviation in the Y direction compared to the X direction (Figure 8d). When the forming depth reaches around 20 mm, the contact area between the forming tool and the thin sheet increases significantly, and the heat generated causes the thin sheet to soften quickly. This not only results in the rapid wear of the thin sheet surface, but also causes bending in this area. This  
Figure 7: Surface morphology of truncated pyramids component under different forming angles. (a,b) 51\({}^{\circ}\), (c,d) 54\({}^{\circ}\) and (e,f) 57\({}^{\circ}\). is also the reason why this area has the thinnest thickness. It is worth noting that the closer the center position is, the thicker the sheet becomes, even exceeding the initial thickness of the sheet. In the central area, the maximum thickness of the plate is 3.6 mm, 3.5 mm and 3.2 mm, respectively. This is because the formed component is in a pyramid shape, and as the depth gradually increases during the SPIF process, the area of the forming area of the forming tool gradually decreases. When reaching the bottom layer, the formed area is the smallest. Therefore, when the forming tool runs along the spiral trajectory, it causes the sheet to accumulate towards the middle under wear conditions. In summary, as the forming angle increases, the forming performance is better, and the surface quality and contour accuracy are better. Combining simulation and modeling can provide a better understanding of the impact of forming angles on forming accuracy and surface quality.