## 3 Roller Hemming in an Experimental Case
### Experiment of Roller Hemming  
The experimental equipment used in this study includes an industrial robot (YASKAWA-ESI65D, YASKAWA Co., Ltd., Fukuoka, Japan), a load cell (PUSHTON PSD-S1, Walfront Co., Ltd., Shenzhen, China), a load cell amplifier (CALT DY510, CALT Co., Ltd., Shanghai, China), a data logger (HIOKI LR8431, HIOKI Co., Ltd., Nagano, Japan), a roller, and a platform, as shown in Figure 5. During the roller hemming process, the load cell was mounted on the robotic arm, as indicated in Figure 5c, and the robot's built-in sensors, as shown in Figure 5d, were also employed. The real-time data from the sensing signals were captured by the data logger, which converted the signals and output them to a computer. This setup allowed simultaneous monitoring of forces in three directions. The experiments were then conducted in accordance with the roller's path, as illustrated in Figure 8. The door panel, previously flanged to 90\({}^{\circ}\), initiated roller machining directly from position P1 to position P14 and subsequently the pre-hemming process at a 45\({}^{\circ}\) angle. Immediately after the final-hemming process, the roller returned to P1 and again moved back to P14, thereby completing the entire robot rolling hemming process. This process encompassed flanging to 90\({}^{\circ}\), pre-hemming at 45\({}^{\circ}\), and final hemming. The specific geometric parameters of the experimental setup are detailed in Figure 9. The inner and outer panel thicknesses (\(t_{1}\) and \(t_{2}\)) were both 1 mm; however, the tensile test specimens were made from JISG 3302 SGCC hot-dip galvanized steel with a thickness of 0.75 mm. The difference in thickness between the tensile test specimens and the door panels was not expected to have a significant impact on the resulting stress-strain behavior. The flanging radius, \(R\), was 1 mm; the flanging height, \(F\), was 7 mm; and the distance between the inner and outer panels, \(G\), was 2 mm. The roller diameter, \(\mathbf{\phi}\), was 100 mm, and the roller's speed was set to 100 mm/s. The external force data at positions P1 to P14 were obtained after the roller hemming experiment. Following the final-hemming stage, the creepge/growth values at the curved-edge positions S1, S2, and S3 (as shown in Figure 2a), as well as at the straight-edge positions P10, P12, and P14, were measured using a vernier caliper. As shown in Figure 10, the experimental results illustrated the external forces applied by the roller on both curved-edge (P7-P8) and straight-edge (P9-P14) parts. Through the application of Equations (6) and (7), as well as the data presented in Table 6, the voltage data collected from the load cell is converted into the corresponding external force exerted on the roller. The load measurement tool model presented the components of the external forces in the x, y, and z directions, where the voltage signals were acquired from the force sensor and subsequently transformed into corresponding external force values. In the experimental results of the straight-edge part, both the external tangential and normal forces during the pre-hemming stage were smaller than those during the final-hemming stage. However, during the pre-hemming stage, the data for the external tangential and normal forces exhibited some degree of noise, possibly due to the rigidity of the robot arm itself. In the curved-edge part, the external force exerted by the roller in the direction of travel caused the material fibers to pile up, resulting in significant noise during both the pre-hemming and final-hemming stages. Figure 8: Schematic of roller running path and roller hemming process: flanging at 90\({}^{\circ}\), pre-hemming 45\({}^{\circ}\), and final-hemming stages in a flat surface curved and straight-edge (from P1 to P14). (**a**) A full view of the experimental process of car door roller hemming. (**b**) Roller hemming experiments were conducted following three stages. Figure 9: Schematic of the straight-edge flat surface and curve-edge flat surface geometry.