## 3 Roller Hemming in an Experimental Case  
### Experiments of Load Cell Calibration  
The experimental process was carried out using a robotic system, specifically an industrial robotic arm, as illustrated in Figure 5a, which presents a 3D model of the industrial robot arm that had the same structure and functions as those of the actual experimental equipment. In this study, a tool attached to the tip of the robot rollers was employed to accomplish the robot roller hemming process. The robot used in the present study was operated along six axes of rotation; an additional device was attached to the conventional tool (load measurement system) to measure loads in three directions, and the roller rotation moved along the vertical direction z (red arrow) and tangent direction x (blue arrow). The sensor was installed at the end of the robot arm, as shown in Figure 5b, and the device structure is illustrated in Figure 5c, which illustrates a model of the tool used for measuring tangential direction external forces, while Figure 5d depicts a schematic diagram of the device for sensing normal direction external forces on the roller, positioned on the robot arm. The complete acquisition of external forces during the roller hemming process is displayed in Figure 5e, where the device captures real-time sensing signals, which are subsequently computer-converted from voltage to load data. Specifically, the electrical signal is obtained from the load cell (PUSHTON PSD-S1), then amplified by the load cell amplifier (CALT DY510), and finally output to the data logger (HIOKI LR8431). The data logger comes with built-in software that exports the data in CSV format for further analysis on a computer. In this study, three channels were used with a sampling rate of 100 times per second. Figure 6 illustrates a schematic diagram of load calibration, where the load output from the universal material testing machine is converted into voltage. Load Cell X measures the load in the direction of roller travel, while Load Cell Y measures the load perpendicular to the roller travel direction. Calibration for each load condition (50 kgf, 100 kgf, 150 kgf, and 200 kgf) was conducted three times, and the average value was utilized as the calibration value, representing the load per 1 V.  
Figure 5: Schematic of the roller hemming experiments system. (**a**) Vertically articulated robot. (**b**) Robot roller hemming tool. (**c**) External force measuring tool model in the tangential direction. (**d**) Measurement of normal force device. (**e**) Schematic diagram of the load measurement system. Based on the data shown in Figure 5(b), the following Equation (5) obtained Equations (6) and (7). In this section, the results for Load Cell X and Load Cell Y are depicted in Figure 4(c). Load Cell X registered a measurement of 669.51 N per 1 V, while Load Cell Y recorded 365.38 N per 1 V.  
\[A{=}F/V_{Lc} \tag{8}\]  
A: Load per 1V [N/V]; F: Load [N], measured by tensile/compression tester; \(V_{Lc}\): Voltage [V], measured by data logger. \[F_{LcX}[N]=669.51\left[\frac{N}{V}\right]\times V_{LcX}[V] \tag{9}\]  
\[F_{LcY}[N]=365.38\left[\frac{N}{V}\right]\times V_{LcY}[V] \tag{10}\]  
The experimental conditions for both the tensile and compression testing machines, as well as load calibration details, are presented in Table 5. Figure 5(a) depicts the experimental setup, illustrating the relationship between the tensile/compression testing machine and the associated tools. The load and voltage values were recorded for each stroke during the first and second measurements under different set pressures. Calibration experiments on the \(Z\) direction load cell for measuring the normal external load on the rollers were conducted using a tensile/compression testing machine. The machine operated at a speed of 0.1 mm/min, with a travel distance of 1.1 mm. Air pressure, regulated by an air regulator, was set at 0.05 MPa, 0.10 MPa, and 0.20 MPa for each measurement, with each setting tested twice.