## 4 Conclusions  
The work was focused on an analysis of the influence of the relative position of the face mill towards the workpiece on the milling dynamics and technological effects of the process. The conducted research revealed the following conclusions:  
1. The changes in radial immersion of the face mill towards the workpiece, described by the \(a^{\prime}\) factor, despite the selected constant values of axial depths of cut \(a_{p}\) and milling widths \(B\), affect the active number of teeth engaged in the workpiece. Consequently, it leads to the variations in maximal instant forces per consecutive teeth and can affect the milling vibration values and surface roughness. 2. The value of \(a^{\prime}\) factor directly characterizes the face milling process kinematics. The growth of \(a^{\prime}\) value reduces the contribution of up milling kinematics in the whole face milling process towards the contribution of down milling. Conducted studies clearly show that in the case of \(a^{\prime}=0\) (predominantly up milling), the lowest forces (in X and Z directions) and vibrations (in Y  
Figure 6: The partial and total desirability functions for the \(a^{\prime}\) factor. direction) are reached, which is attributed to the gradual immersion of the tool into the workpiece (and thus the gradual increase of uncut chip thickness in function of tool rotation angle). 3. Initiation of chip formation during face milling with higher \(a^{\prime}\) values occurs at relatively high uncut chip thicknesses. Therefore, the dynamic contact between the tooth and workpiece can cause some forced vibrations, contributing to the growth of cutting force dynamic components. This relation has been confirmed by measurements of vibrations, which revealed the increasing trend of acceleration of vibration in \(Y\) direction together with the growth of \(a^{\prime}\) factor. 4. The performed multicriteria optimization, based on determination of total desirability function, enabled the obtainment of optimal \(a^{\prime}\) factor, and equaled to 3.15 mm. The face milling with the selection of optimal \(a^{\prime}\) factor affects the reduction of cutting forces, vibrations, and surface roughness parameters. Therefore, these findings can be implemented in industrial applications. To put this another way, the selection of optimal tool radial immersion towards the workpiece \(a^{\prime}\_opt\) during flat face milling with the milling width \(B\) lower than the cutter's diameter \(D\) can contribute to improvements in process economics (resulting from the reduction of surface roughness and milling power). Conceptualization, D.Y.P., A.H., and S.W. ; methodology, D.Y.P., A.H., and S.W. ; software, A.H., A.M., S.W., and D.I.S. ; validation, A.H., A.M., and D.I.S. ; formal analysis, A.H., A.M., S.W., and D.I.S. ; investigation, A.H., A.M., S.W., and D.I.S. ; resources, A.H., A.M., S.W., and D.I.S. ; data curation, A.H., A.M., S.W., and D.I.S. ; writing-original draft preparation, D.Y.P., A.H., S.W., M.M., A.M., D.I.S., A.B., G.K., and M.K.G. ; writing-review and editing, D.Y.P., A.H., S.W., M.M., A.M., D.I.S., A.B., G.K., and M.K.G. ; visualization, A.H., A.M., S.W., and D.I.S. ; supervision, D.Y.P., S.W., M.M., M.K.G., G.K., and M.K.G. ; project administration, D.Y.P. and A.H.; funding acquisition, D.Y.P. and A.H. The study was supported under Act 211 Government of the Russian Federation, contract Nr. 02.A03.21.0011. The authors  
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