## 2 Methodology of Experimental Research
A record of the drawing and blankholding forces is shown in Figure 4. From experimentally-measured values of the drawing and blankholding forces the friction coefficient can be determined in the area under the blankholder and on the die drawing edge as well. Two methods were applied for evaluation of friction coefficient in the area under the blankholder. In the first method the regression analysis was used [5, 18, 19, 20]. The relation between the blankholding force and drawing force can be described as follows:  
\[\Delta\text{F}_{p(\text{f3}=0)}=\text{Intercept}+\Delta\text{F}_{\text{N1},2}( \text{Slope}) \tag{1}\]  
where \(\Delta\text{F}_{\text{p(f3}=0)}\) is the difference of drawing forces versus the difference of blankholding forces; \(\Delta\text{F}_{\text{N1},2}\) is difference of the blankholding forces F\({}_{\text{N2}}\)--F\({}_{\text{N1}}\), F\({}_{\text{N2}}\)? F\({}_{\text{N1}}\); (F\({}_{\text{N2}}\)--blankholding force for current measurement, F\({}_{\text{N1}}\)--blankholding force for previous measurement; for the first measurement it is not possible to calculate). Figure 3: The friction simulator photo and CAD model—strip drawing test. 1—base plate; 2—middle plate; 3—upper plate; 4—hydraulic clamping cylinder; 5—upper grip; 6—lower grip; 7—dynamometer for measurement of blankholding force; 8—roller; 9—ball bearings; 10— brake mechanism of the roller; 11-strip. It is known that increasing the blankholding force results in an increase of the drawing force. Thus, the friction coefficient f1,2 is calculated as half value of slope:  
\[\text{f}_{1,2}=\frac{\text{Slope}}{2} \tag{2}\]  
where f1,2--mean friction coefficient between die and strip. The second method emerges from analytical models based on the measurement of forces during the strip drawing test [19]. When the roller on the friction simulator is not blocked (friction model under the blankholder), the friction coefficient f1,2 is calculated as follows:  
\[\text{f}_{1,2}=\frac{\text{F}_{\text{p2(f3=0)}}-\text{F}_{\text{p1,ref(f3=0)}} }{2(\text{F}_{\text{N2}}-\text{F}_{\text{N1,ref}})}=\Delta\text{F}_{\text{p1,2 (f3=0)}}/(2\Delta\text{F}_{\text{N1,2}}) \tag{3}\]  
where F\({}_{\text{bA}}\) is the bending force, F\({}_{\text{N1,ref}}\) = 2 kN, F\({}_{\text{N2}}\) is the blankholding force (F\({}_{\text{N1,ref}}\) < F\({}_{\text{N2}}\)), F\({}_{\text{p2(f3=0)}}\) is drawing force generated by the blankholding force F\({}_{\text{N2}}\), F\({}_{\text{p1,ref(f3=0)}}\) is the drawing force generated by the blankholding force F\({}_{\text{N1,ref}}\). When the roller on the friction simulator is blocked (friction model on the die drawing edge), the friction coefficient f3 is calculated as follows:  
\[\text{f}_{3}=\text{In}\left(\frac{\text{F}_{\text{p(f3>0)}}}{\text{F}_{\text{ p(f3=0)}}}\right)\frac{2}{\pi} \tag{4}\]  
where F\({}_{\text{p(f3=0)}}\) is the drawing force generated by a rotating roller, F\({}_{\text{p(f3>0)}}\) is the drawing force generated by a fixed roller, and f3 is the friction coefficient in the die drawing edge. The cup test was performed on a hydraulic machine RM-501 LVH-1. The test parameters were as follows: the punch diameter d = 32.85 mm, the punch radius r\({}_{\text{p}}\) = 4.5 mm, the die radius r\({}_{\text{d}}\) = 4.5 mm, the roughness of the die and blankholder Ra = 0.4 \(\mu\)m, and the amount of lubricant was 2 g\(\cdot\)m\({}^{-2}\). Sheet blanks with diameter D\({}_{0}\) = 60 mm were used for studying various contact conditions. Blankholder forces F\({}_{\text{N}}\) were set as follows: F\({}_{\text{N}}\) = 2; 5; 10, 20, and 30 kN. The drawing force measurement under the same conditions was performed on five specimens (Figure 5). Figure 4: Record of the drawing and blankholding forces in the strip drawing test. To verify the measured values of the friction coefficient, numerical simulation of the cup test was done in Pam Stamp 2G software (ESI Group, Rungis, France). The friction coefficients in the simulations were set as calculated by analytical models based on the results of the strip drawing test.