## 4 Comparison of Simulation and Experiment Results  
The simulations and experimental analyses primarily focused on the external forces in the X and Z directions. The external force in the X direction was identified as the tangential force, while the external force in the Z direction was referred to as the nominal force. As Figure 11 shows, in both the curved-edge and straight-edge experimental parts the average values were obtained by analyzing the data from positions P7 to P8 and from positions P9 to P14 on the door panel, respectively, as depicted in Figure 8a. For simulation results, stable external force regions were identified to exclude the rapid fluctuations observed in the initial rapid increase and end rapid decrease curves depicted in Figure 4, ensuring the calculation of reliable average values. The average values of the obtained tangential external forces during pre-hemming at 45\({}^{\circ}\) and final hemming were 225 N and 239 N (straight-edge section) and 257 N and 262 N (curved-edge section), respectively. The corresponding average values of the obtained normal external forces were 1280 N and 1704 N (straight-edge section) and 1345 N and 1610 N (curved-edge section), respectively. The experimental results confirmed the simulation findings, with the measured average values of external tangential forces being 565 N and 574 N (curved-edge section) and 176 N and 223 N (straight-edge section) for pre-hemming 45\({}^{\circ}\) and final hemming, respectively. Similarly, the measured average values of external normal forces were 1705 N and 1764 N (curved-edge section) and 1468 N and 1705 N (straight-edge section) for pre-hemming at 45\({}^{\circ}\) and final hemming, respectively. Compared to the corresponding simulated values, the experimental measurements consistently showed higher normal forces in both the straight- and curved-edge sections. Tangential force values were also higher in the straight-edge section. Additionally, the normal external forces consistently exceeded the tangential forces. In the curved-edge section, both simulation and experimental results indicated that the roller hemming process leads to a pile-up phenomenon, where material accumulates along the edges due to the transverse slip of the door panel material. This accumulation affected the final shape and quality of the panel. As shown in Figure 11, the tangential force on the curved-edge was greater than that on the straight-edge, likely due to the more complex stress state in the curved area caused by material fiber accumulation during deformation. The large discrepancy between the experimental and the numerical results, particularly in the curved-edge section, may also stem from differences in boundary conditions and friction coefficients between the simulation and experiments, as well as the unaccounted influence of the robotic arm's rigidity during the hemming process. Figure 10: Experimental results involved measurements of the external forces in the x, y, and z directions, as shown in Figure 5b during the pre-hemming at 45\({}^{\circ}\) and final-hemming stages of roller hemming conducted in both curved-edge and straight-edge sections. The outer end of the panel to the inside of the reference line was defined as \"creepage\", with negative values indicating movement inwards. It was desirable that the values of both growing and creepage are as small as possible. The comparison between the experimental and the simulation results revealed creepage or growth; the initial flanging at the 90\({}^{\circ}\) position of the panel before bending deformation was defined as the reference line.