## 2 Materials and Method
For each pass, a new set of inserts was used in order to eliminate tool wear as a variable. The cutting force and vibrations were acquired during milling in a dynamically stable process. After each pass, the surface roughness was measured three times in the region where the feed per tooth was at its maximum, and 10 mm after the tool entry in the middle part of the workpiece, and 10 mm before the tool exits the workpiece. Below in Figure 2a-d, the diagrams are depicted which represent the positions of the cutter and workpiece, described by the \(a^{\prime}\) factor during the flat face milling, with the milling width \(B\) lower than the cutter's diameter \(D\). The \(a^{\prime}\) parameter is defined as a translation of cutter's rotational axis in the direction perpendicular to the feed motion towards the workpiece's axis of symmetry, parallel to the feed motion. Asymmetric face milling (with positions symmetry of cutter and workpiece in direction that is transverse to feed e, e; positions the end of the cutter diameter and the beginning of the workpiece, \(a^{\prime}\)) is depicted in Figure 2a,b, whereas the symmetric face milling is presented in Figure 2c,d. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material of the Cutting Part** & **Cutter Diameter, \(D\), mm** & **Major Cutting Edge** & **Number of Teeth, \(z\)** \\ \hline PVD coated carbide (TiAlN + Al\({}_{2}\)O\({}_{3}\) on the rake face) + (ZrCN on the flank face) & 63 & 90 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of tools. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Depth of Cut, \(d\), mm** & **Cutting Speed, \(v_{c}\), m/min** & **Feed Per Tooth, \(f_{z}\), mm/tooth** & **Relative Position of the Cutter,** \\  & & **\(a^{\prime}\), mm** \\ \hline \(1\) & 100.0 & 0.1 & 0, 0.3, 0.8, 3.3, 6.3, 9.3, 11.8, 12.3, 12.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Specifications of cutting conditions. Table 4 shows the types of installation of face Up and Down milling. Note that \(a^{\prime}=0\) mm means that \(e=12.6/2=6.3\) mm and when \(a^{\prime}=12.6\) mm then \(e=-12.6/2=-6.3\) mm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**a/mm**} & \(\mathbf{\psi_{1}}\)**, inlet** & \(\mathbf{\psi_{2}}\)**, Outlet** & \(\mathbf{\psi}\)**, Contact** & \multirow{2}{*}{**\(\mathbf{\psi}\)**, Contact**} & \multirow{2}{*}{**\(\mathbf{\psi}\)**} & \multirow{2}{*}{**Scheme in**} & \multirow{2}{*}{**Description**} \\  & **Angle,°** & **Angle,°** & **Angle,°** & & & **dec tile** & \\ \hline
0 & 0 & 126.9 & 126.9 & 2.12 & Figure 2a & Asymmetric (predominantly up milling) \\
0.3 & 7.9 & 127.6 & 119.7 & 2 & Figure 2a & Asymmetric (predominantly up milling) \\
0.8 & 12.9 & 128.7 & 115.8 & 1.93 & Figure 2a & Asymmetric (predominantly up milling) \\
3.3 & 26.5 & 134.8 & 108.3 & 1.81 & Figure 2a & Asymmetric (predominantly up milling) \\
6.3 & 36.9 & 143.2 & 106.3 & 1.77 & Figure 2c & Symmetric * \\
9.3 & 45.2 & 153.6 & 108.4 & 1.81 & Figure 2b & Asymmetric (predominantly down milling) \\
118 & 51.3 & 167.1 & 115.8 & 1.93 & Figure 2b & Asymmetric (predominantly down milling) \\
12.3 & 52.5 & 172.1 & 119.6 & 1.99 & Figure 2b & Asymmetric (predominantly down milling) \\
12.6 & 53.1 & 180 & 126.9 & 2.12 & Figure 2b & Asymmetric (predominantly down milling) \\ \hline \hline \end{tabular}  
* When the milling is symmetric the operation is half up milling and half down milling. For instance, in the case of (c), the bottom part of the figure is up milling, but the up part is down milling.  
\end{table} 
Table 4: Types of installation of face Up and Down milling.