## 2 Methodology of Experimental Research  
Two steels were used during experiments: uncoated cold rolled extra deep drawing quality DC 05 with thickness a\({}_{0}\) = 0.8 mm and austenitic stainless steel AISI 304 with thickness a\({}_{0}\) = 0.8 mm (Table 1). Surface roughness parameters Ra, Rz, and RPc (peak count per cm) were measured according to the ISO 4287 standard in 10 different places on the sheet by a Mitutoyo Surftest SJ-301 device (Mitutoyo, Kawasaki, Kanagawa, Japan) in the rolling direction according to ISO 4287 with input values set to \(\lambda\)c = 0.25 mm and \(n\) = 5. Average values and the standard deviation for each parameter are shown in Table 1. The roughness profile and Abbott-Firestone curve (bearing area curve) are shown in Figure 2. \begin{table}
\begin{tabular}{c c c c} \hline  & **Ra (\(\mu\)m)** & **Rz (\(\mu\)m)** & **RPc (cm\({}^{-1}\))** \\ \hline DC 05 & 0.71 \(\pm\) 0.135 & 5.04 \(\pm\) 0.604 & 120.7 \(\pm\) 35.2 \\ \hline AISI 304 & 0.07 \(\pm\) 0.020 & 0.60 \(\pm\) 0.189 & 241.1 \(\pm\) 72.3 \\ \hline \end{tabular}
\end{table} 
Table 1: Surface roughness parameters for steels DC 05 and AISI 304. Mechanical properties were measured by ISO 6892-1, normal anisotropy ratios by ISO 10 113 at a strain level of 20%, and strain-hardening exponents by ISO 10275 within the strain range 5-20%. A PC-controlled TiraTEST 2300 (TIRA GmbH, Schalkau, Germany) testing machine with extensometers for length and width measurement was used with automated evaluation of the properties shown in Table 2. The chemical composition of both materials is in Table 3.  
The friction simulator shown in Figure 3 was used to study the friction in a stamping process. This simulator enables modelling the stress state of flat (Figure 1a) and curved regions (Figure 1b). Processes on the contact areas can be investigated separately or combined. The roller can be fixed or free rotated. If the movement of the roller is not blocked, the loading of the die contact areas under the blankholder between flat surfaces is being modelled (Figure 1a). In the case the roller is fixed, the loading of the curved contact areas on the die drawing edge is being modelled (Figure 1b). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Title 1**} & **Dir** & **R\({}_{\text{po-2}}\)** & **Rm** & **K** & **n** & **r** \\  & **(°)** & **(MPa)** & **(MPa)** & **(MPa)** & **(-)** & **(-)** & **(-)** \\ \hline \multirow{3}{*}{DC 05} & 0 & 164 & 299 & 505 & 0.23 & 1.9 \\  & 45 & 172 & 309 & 531 & 0.219 & 1.5 \\  & 90 & 166 & 296 & 511 & 0.221 & 2.2 \\ \hline \multirow{3}{*}{AISI 304} & 0 & 267 & 634 & 1523 & 0.517 & 0.98 \\  & 45 & 262 & 615 & 1469 & 0.519 & 1.03 \\  & 90 & 273 & 629 & 1491 & 0.515 & 0.99 \\ \hline \end{tabular}  
* **Notes:** Dir—rolling direction; R\({}_{\text{po-2}}\)—yield stress; Rm—ultimate tensile stress; K—strength constant; n—strainhardening exponent; r—plastic strain ratio.  
\end{table} 
Table 2: Mechanical properties of steels. Figure 2: Roughness profile and Abbot–Firestone curve; (**a**) DC 05, and (**b**) AISI 304. Drawing conditions were as follows: Blankholding forces F\({}_{\text{N}}\) = 2, 3, 4, 6, and 8 kN, strip drawing speed v = 10 mm/s, strip width 50 mm, grips' contact area 20 \(\times\) 50 mm. Both, grips and roller of friction tester were made from tool steel 1.2379, hardened to 63 HRc and polished to Ra = 0.32 \(\pm\) 0.05 \(\upmu\)m. The surface of the sheet strip was lubricated with Anticorit Prelube 3802-39 S lubricant with a kinematic viscosity of 60 mm\({}^{2}\cdot\)s\({}^{-1}\) at 40 \({}^{\circ}\)C in the amount of 2 g\(\cdot\)m\({}^{-2}\). During the strip drawing test, drawing force and blankholding force were measured. The measuring system consisted of KAS 20 and KF 20 K force load cells, a QuantumX MX440A tensorite unit (HBM, Darmstadt, Germany) and Catman Easy software (HBM, Darmstadt, Germany).