## 3 Results and Discussion
### Evaluation of Dynamics and Surface Roughness
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Inputs**} & \multicolumn{6}{c}{**Outputs Parameters**} \\ \cline{2-13} \multirow{3}{*}{**Exp.**} & \multicolumn{3}{c}{**Parameters**} & \multicolumn{6}{c}{**Force, \(F_{x}\), N**} & \multicolumn{6}{c}{**Acceleration,**} \\  & \multicolumn{3}{c}{**Relative Position**} & \multicolumn{6}{c}{**\(F_{y}\)**} & \multicolumn{6}{c}{**\(A_{x}\), m/s\({}^{2}\)**} \\  & \multicolumn{3}{c}{**of Face Mill and Workpiece \(a^{\prime}\)**} & \multicolumn{6}{c}{\(F_{x}\)**} & \multicolumn{6}{c}{\(F_{y}\)**} & \multicolumn{6}{c}{\(A_{y}\)**} \\  & \multicolumn{3}{c}{**With \(A^{\prime}\)**} & \multicolumn{3}{c}{**After RMS**} & \multicolumn{3}{c}{**After RMS**} & \multicolumn{3}{c}{**After RMS**} & \multicolumn{3}{c}{**After RMS**} & \multicolumn{3}{c}{**After RMS**} & \multicolumn{3}{c}{**After RMS**} & \multicolumn{3}{c}{**After RMS**} \\ \hline
1 & 0 & 129.4 & 544.4 & 307.5 & 321.5 & \(-\)437 & \(-\)97.7 & \(-\)255 & 263.5 & 44 & 271 & 169.7 & 176.6 & 7.4 & 4.8 \\
2 & 0.3 & 65.9 & 576.2 & 312.1 & 331.2 & \(-\)424.8 & \(-\)1538.3 & \(-\)303.4308.5 & 83 & 300.3 & 183.7 & 188.5 & 7.89 & 5.55 \\
3 & 0.8 & 58.6 & 534.7 & 318.3 & 334.9 & \(-\)439.5 & \(-\)119.6 & \(-\)29.2399.8 & 92.8 & 268.6 & 182.9 & 188.6 & 7.93 & 6.03 \\
4 & 3.3 & 144 & 561.5 & 345.6 & 357.5 & \(-\)427.3 & \(-\)952.2 & \(-\)49.8261.2 & 48.8 & 271 & 181.4 & 186.8 & 8.73 & 6.87 \\
5 & 6.3 & 170.9 & 585.9 & 382 & 391.3 & \(-\)432.1 & \(-\)308.122.9 & 53.7 & 271 & 176.3 & 182.6 & 6.74 & 6.12 \\
6 & 9.3 & 188 & 590.8 & 40.9 & 412 & \(-\)439.534.2 & \(-\)156.5180.6 & 58.6 & 266.1 & 179.5 & 184.3 & 6.44 & 5.94 \\
7 & 11.8 & 175.8 & 625 & 408 & 416.3 & \(-\)405.368.4 & \(-\)126.7156.7 & 51.3 & 273.4 & 173.4 & 179.7 & 7.69 & 6.35 \\
8 & 12.3 & 266.1 & 605.5 & 431.5 & 435.1 & \(-\)363.890.3 & \(-\)99.6 & 141.7 & 114.8 & 297.9 & 187.8 & 191.2 & 7.42 & 6.46 \\
9 & 12.6 & 271 & 654.3 & 435.3 & 439.2 & \(-\)341.8102.5 & \(-\)92.3 & 137.8 & 105 & 295.4 & 187.8 & 191.5 & 9.4 & 6.35 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The experimental components of the cutting force \(F_{x}\), \(F_{y}\), \(F_{z}\) and the accelerations \(a_{x}\) and \(a_{y}\). the function of \(a^{\prime}\) have been determined (see Figure 4b). It can be observed that in the case of vibrations in Y direction, the increasing trend together with the \(a^{\prime}\) factor is found, which can be attributed to the relations between the initial uncut chip thicknesses \(a_{i}(\psi_{1})\) and forced vibrations in milling. In case of surface roughness parameters (Figure 5a,b), the increasing trend with the growth of \(a^{\prime}\) is found. However, local oscillations of these values, mainly in the range of \(0\leq a^{\prime}\leq 6.3\) mm, can be observed. The highest values of \(Ra\) and \(Rz\) parameters occur for the \(a^{\prime}=12.6\) mm, which also corresponds to the highest measured values of \(F_{x}\) force and \(A_{y}\) accelerations of vibrations. Therefore, the correlation between the formation of surface roughness and process dynamics can be exposed. Nevertheless, during the face milling process, the formation of the surface profile can be also strongly affected by geometrical errors in the machine-toolholder-tool system, plastic and elastic deformations of the material being cut, homogeneity of the workpiece, as well as some random factors. Figure 4: The root mean square values: (**a**) The root mean square values of cutting force \(F_{x}\) force as function of \(a^{\prime}\); (**b**) the root mean square values of acceleration of vibration \(A_{x}\) as a function of \(a^{\prime}\). Figure 3: The cutting force components’ time courses.