## 2 Materials and Method  
To get actual surface roughness data for the validation of the model attained through artificial intelligence, machining experiments were carried out. Several passes with different milling cutter position (\(a^{\prime}\)) related to the workpiece were done. During the tests, milling forces (3 directions) and vibrations (2 directions) were acquired. After each pass, the surface roughness was measured. The experiments were carried out on Mori Seiki SV-40 (Nagoya, Japan), a 3 axis CNC (Computer Numeric Control) vertical machining center with 22 kW of power and a maximum rotational speed of 12,000 rpm. The setup is presented in the Figure 1a; the workpiece and a dynamometer are over the machine tool table, as well as the accelerometers. The cutting forces were measured using a Kistler 9257 BA Winterthur, Switzerland) stationary dynamometer connected to a Kistler 5019B signal conditioner. After this, a computer with a National Instruments PCI-6025E (Austin, TX, USA) A/D acquisition board and National Instruments LabVIEW 8.5 software were responsible for the acquisition and saving of the force signals. The data acquisition rate was 3 kHz/channel. The vibrations were measured using accelerometers attached to the workpiece (as shown in Figure 1a). The measurements were conducted in two orthogonal directions (+x and +y in the experiment). At the same time, the signal of acceleration was recorded using Bruel and Kjaer Photon+ (Narum, Denmark) dynamic signal analyzer. It had \(1\) kHz sampling rate with default setting for anti-aliasing and phase-distortion filters. The material used for the workpiece was SAE 1045. Its chemical composition is presented in Table 1.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & \\ \multirow{2}{*}{ \begin{tabular}{c} **Workpiece** \\ **Material** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Vickers** \\ **Hardness,** \\ **HV** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Vickers** \\ **Hardness,** \\ **HV** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Hardness,** \\ **HV** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Vickers** \\ **Hardness,** \\ **HV** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Hardness,** \\ **HV** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **Hardness,** \\ **HV** \\ \end{tabular}  } & \multirow{2}{*}{
\begin{tabular}  
The hardness of the workpiece was established at HV 184 using a Struers (Westlake, OK, USA) Vickers indenter with a load of 30 kgf. The workpiece has the geometry and dimensions presented in Figure 1b. The width of the workpiece was determined according to the milling cutter diameter and the length to fit into the dynamometer. Two screws (M8) were used to attach the workpiece in the dynamometer. Dry machining tests were carried out using a Walter (Tubingen, Germany) LNGX 130708 R-L55 insert (insert shape rectangular, rake angle 0\({}^{\circ}\), edge length 13 mm, insert width 11 mm, insert thickness 7 mm, tool nose radius 0.8 mm) grade WKP 25 (recommended for machining of steels). The milling cutter, also a Walter (Tubingen, Germany), was a F 4041.B.063.Z06 13. After the indexable inserts were attached to the milling cutter, the tool geometry consisted of the following angles: radial rake angle + 50\({}^{\circ}\), axial rake angle + 20\({}^{\circ}\), clearance angle + 5\({}^{\circ}\) in both main and secondary cutting edges, and lead angle 90\({}^{\circ}\). This geometry was chosen because the 90\({}^{\circ}\) lead angle tends to generate a higher effort in the plane of the surface being machined. This would increase the trend of vibration and highlight the benefits of the methodology being proposed in the present work. It is worth mentioning that this kind of tool is used in face milling, especially when a 90\({}^{\circ}\) shoulder is necessary. The characteristics of the used tools are specified in Table 2. The milling cutter can be seen in Figure 1c.