## 3 Results and Discussion  
### Experimental Results  
Under lubrication with both oils considered, the value of the COF increased with decreasing oil pressure. This conclusion is valid for all the nominal pressures analyzed. This confirms the correctness of the concept of the device for reducing friction in the flange area of the drawpiece. In general, the higher the nominal pressure value, the smaller the difference between the COF determined for different oil pressures. When the sheet is heavily loaded, the nominal pressure and mechanical cooperation of the summits of the surface asperities have a dominant influence on the friction phenomena. Under these conditions, the oil, even under high pressure, is not able to effectively reduce the COF. The developed concept of pressurised lubrication is most effective at relatively small nominal pressures of 2-4 MPa. Such pressure values correspond to the actual pressures applied during the deep-drawing of steel sheets [2; 33]. Under conditions of dry friction, the values obtained for the COF rise above 0.3, while under conditions of lubrication, even without pressure-assisted lubrication, the COF values do not exceed 0.2 (Figure 9). The value of the COF initially increases in the nominal pressure range of 2-6 MPa and decreases after reaching the maximum value. This is a phenomenon also observed by other authors [37; 38; 39]: after exceeding a certain pressure value, the relationship between the friction force and the contact force is not proportional, and consequently, the value of the COF decreases. It should be remembered that in SMF, a very hard tool and a relatively soft sheet come into contact. So, the friction phenomena are more intense than in machine nodes. Oil lubrication significantly affects the stability of the friction process and reduces error bars. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Range of Variability** \\ \hline p\({}_{0}\) (MPa) & 2–8 \\ \hline p\({}_{0}\) (MPa) & 0.6–1.8 \\ \hline n\({}_{\text{k}}\) (mm\({}^{2}\)/s) & 0–1135 * \\ \hline Sa (\(\mu\)m) & 1.07–1.96 \\ \hline Sq (\(\mu\)m) & 1.33–2.42 \\ \hline Sku & 2.5-3.0 \\ \hline Ssk & \(-\)0.0967–0.395 \\ \hline \hline \end{tabular}  
* * \(-\)n\({}_{\text{k}}=0\) is assumed for dry friction conditions (without lubrication).  
\end{table} 
Table 3: The range for each input and output parameter. It seems crucial to determine the effect of lubrication on the change in the COF in relation to the conditions of conventional lubrication (without pressurised lubricant). For this purpose, the coefficient of lubrication efficiency (CLE), defined as follows, has been introduced:  
\[\text{CLE}=\frac{\mu_{\text{p}}-\mu_{\text{p0}}}{\mu_{\text{p}}}\cdot 100\% \tag{1}\]  
where \(\mu_{\text{p}}\) is the COF determined at pressure-assisted conditions and \(\mu_{\text{p0}}\) is the COF determined at conventional lubrication (p\({}_{\text{o}}\) = 0 MPa). Figure 10 confirms that pressure lubrication is most effective at low nominal pressures. Lubrication efficiency increases with increasing oil pressure. A liquid medium placed between two rubbing surfaces acts as a cushion. Oil pressure-assisted lubrication ensures better oil filling of all valleys in the surface topography. Under these conditions, the summits of the surface asperities are not flattened, and the surface topography is characterised by valleys with a large volume holding the lubricant. The lubrication efficiency of both oils, S100+ (Figure 10a) and S300 (Figure 10b), is similar, and for the nominal pressure of 2 MPa, it is about 15-50% depending on the oil pressure. As the nominal pressure is further increased, the value of the CLE decreases exponentially. At the highest tested nominal pressure of 8 MPa, the value of the CLE does not exceed 3-15%. The lubrication efficiency clearly decreases with the value of the oil pressure.