## 2 Materials and Methods
### Description of the Experiment, Its Design Variables, and the Equipment Used  
For the purposes of the laboratory experiment, a special fixture was designed and manufactured to perform the technological test of the drawing of seamless tubes (see Figure 2). Subsequently, the cold tube drawing experiment was performed in laboratory conditions using the EU 40 hydraulic testing machine with a nominal force of 400 kN (see Figure 3a). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Factors’ Levels** & \\
**Factor, Measurement Unit** & **Low Value (\(-1\))** & **High Value (\(1\))** \\ \hline \(A\) (diameter of the pre-tube, mm) & \(16\) & \(18\) \\ \(B\) (wall thickness of the pre-tube, mm) & \(1\) & \(2\) \\ \(C\) (diameter of the die, mm) & \(12\) & \(14\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: General experiment design table for the case of the response variable \(y_{1}\) (the final outer diameter of the tube)—factors’ levels. As it can be interpreted from Figure 2, the drawing fixture consisted of individual components such as a clamping shank and a clamping plate, and also other technological parts such as a base plate in which the drawing die is centrally mounted. A detailed representation of the shape and dimensions of the drawing die used in the experiment is shown in Figure 2b. On the other hand, the fixture was structurally designed for clamping onto the workspace of the tensile testing machine. The method of clamping the fixture to the EU 40 testing machine is also documented in Figure 3. Here, it is possible to appreciate that the tube is firmly clamped in the chuck of the table of the hydraulic testing machine (by the swaged part of the tube) (see Figure 4), and the moveable cross-head displaces upwards with the fixture, i.e., with the drawing die (see Figure 3b,c). This way, in the experimental drawing, the drawing die moves instead of the tube. Figure 3: Hydraulic tensile testing machine EU 40 with a clamping fixture for cold tube drawing: (**a**) view of the whole testing machine with the fixture; (**b**) detailed view of the fixture with the tube before the experimental drawing; (**c**) view of the fixture with the tube after the experimental drawing (the tube is clamped in the chuck of the table and does not move while the fixture moves upward along with the drawing die). Figure 2: The equipment used for the cold tube drawing experiment. (**a**) The fixture for the cold tube drawing experiment: (1) clamping shank; (2) rod; (3) screw nut; (4) clamping plate; (5) die; (6) base plate. (**b**) The shape and dimensions of the drawing die. Moreover, as part of the cold tube drawing experiment of seamless tubes, all test tubes were rotary swaged, numbered, and then used for direct drawing production (single-operation production). The drawing speed in each case was 60 mm/min, and a liquid lubricant mineral oil was applied to reduce the effect of friction. As it can already be inferred from Tables 5-8, during the experiment, a total of 8 test specimens were produced by the cold drawing process. Specimens 1 and 3 were drawn through the die to a final outer diameter of \(\mathcal{O}\)12 mm, using draft tubes with values of the outer diameter of \(\mathcal{O}\)16 mm for both and having wall thicknesses of 1 and 2 mm, respectively. Specimens 5 and 7 were also drawn through the die to a final diameter of \(\mathcal{O}\)12 mm, while the dimension of the draft tubes' outer diameter was \(\mathcal{O}\)18 mm for both, and the wall thicknesses had values of 1 and 2 mm, respectively. In the case of specimens 2 and 4, these were drawn using a die of \(\mathcal{O}\)14 mm, both being pre-tubes of \(\mathcal{O}\)16 mm and having wall thicknesses of 2 and 1 mm, respectively. The final two specimens, 6 and 8, were also drawn using a die of \(\mathcal{O}\)14 mm, both being pre-tubes of \(\mathcal{O}\)18 mm and having wall thicknesses of 1 and 2 mm, respectively. As mentioned before, all of these elements constituted the factors engaged in the factorial experiments and their respective levels.