## 3 Results
### Clamping Screw Tightening Torque Selection  
In order to prepare a hybrid simulation model, for the purpose of clamping screw tightening torque selection, the parameters of this model must be determined. It is achieved by performing simulations for a nominal clamping condition and searching for the set of parameters \(k_{dl}\), \(\mu_{l2}\), and \(\mu_{l3}\) that provide a good agreement between simulation and real cutting results, which is to say, a similar level of vibration expressed as the RMS of displacements. For the presented experimental case, such compliance was achieved for \(k_{dl}=5800\) N/mm\({}^{2}\), \(\mu_{l2}=0.4\), and \(\mu_{l3}=0.66\).  
At the nominal clamping condition, the screw tightening torque of 90 Nm was selected. Next, using these parameters, a series of simulations for screw settings of 50, 70, 110, and 130 Nm were performed. For each setting, the appropriate dominant natural frequencies, modal damping coefficients (Table 1), and accompanying normal modes identified by EMA were applied in the simulation model for the selected settings. The results of the simulations are presented in Figures 6 and 7 and Table 2. The RMS relative vibration displacements between the tool and the workpiece for point S are calculated for selected time intervals. The selection will be justified and explained in the next section of the paper.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \
\begin{tabular}{c} **Tightening** \\ **Torque [Nm]** \\ \end{tabular} & \multicolumn{6}{c}{**Mode**} \\ \cline{2-7}  &
\begin{tabular}{c} **1** \\ \end{tabular} & **2** & **3** & **4** & **5** & **6** \\ \hline Frequency [Hz] & 50 & 187.36 & 230.91 & 245.68 & 324.68 & 371.00 & 423.41 \\ Modal damping [\%] & 50 & 1.66 & 3.04 & 2.91 & 1.57 & 1.48 & 1.35 \\ \hline Frequency [Hz] & 70 & 186.71 & 233.54 & 249.81 & 323.15 & 374.03 & 426.08 \\ Modal damping [\%] & 70 & 2.07 & 3.46 & 3.16 & 0.98 & 1.02 & 1.68 \\ \hline Frequency [Hz] & 90 & 187.84 & 234.70 & 251.43 & 323.75 & 377.47 & 422.26 \\ Modal damping [\%] & 1.55 & 3.85 & 2.55 & 1.98 & 1.16 & 2.79 \\ \hline Frequency [Hz] & 110 & 187.80 & 235.49 & 255.49 & 326.04 & 377.99 & 421.72 \\ Modal damping [\%] & 1.03 & 3.44 & 2.42 & 1.66 & 1.39 & 2.78 \\ \hline Frequency [Hz] & 130 & 186.35 & 235.96 & 249.44 & 325.23 & 380.11 & 423.88 \\ Modal damping [\%] & 130 & 2.26 & 4.17 & 2.92 & 0.76 & 1.16 & 2.35 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Identified natural frequencies and modal damping coefficients.  
Figure 5: Workpiece amplitude gains of frequency response functions (FRFs) and coherences for screw tightening torques: (**a**) 50 Nm, (**b**) 70 Nm, (**c**) 90 Nm, (**d**) 110 Nm, and (**e**) 130 Nm.  
According to the EAOVP procedure, simulation results should allow for the selection of the best clamping condition for vibration reduction. The results predict that setting the clamping screws with the torque of 50 Nm should result in the lowest vibration during milling, and setting them with the torque of 70, 90, or 110 Nm should result in a high level of vibration. For the selected workpiece, vibration in its middle part is the highest; thus, it is most important to reduce vibrations in this part. Taking this into account, it is apparent that a setting of 90 Nm should be treated as the worst, and 50 Nm as the best one.