## 3 Case Study
### Active Boring Bar Design  
Once chatter conditions were detected, and maximum cutting forces were measured, the active boring bar was designed in accordance with the proposed methodology. NOLIAC SCMAP-NCE46-10-10-2-200-H36-C01 actuator was found to be the best compromise between force that can be provided, dimensions and response time. In particular, since it is not provided with preload mechanism and case, its size is reduced to \(10\times 10\times 36\) mm, compliant with the available space. Moreover, the selected actuator is made of hard-doped ceramic that reduces self-heating issues arising at high frequencies. Its characteristics are reported in Table 3.  
Actuation section was placed near the tool tip in order to allow the use of the tool with different overhangs. Considering the selected configuration (Section 2.2) maximum slots depth along radial direction, that respect the radial size limit, was found to be 6.5 mm. The difference in terms of thickness between slots on tool insert side and the opposite one, which guarantees section centroid alignment, was found to be 1 mm (Figure 12). Preload required was calculated following the approach presented in Section 2.4, using MSC Nastran(r) FE solver. The boring bar FE model is showed in Figure 13.  
Figure 11: Cutting forces shown in (**a**) time history and (**b**) frequency spectrum. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Piezoelectric** \\ **Material** \\ \end{tabular} } & \multicolumn{3}{c}{**Dimensions**} & \multirow{2}{*}{\begin{tabular}{c} **Free Stroke** \\ **(\(\mathbf{\mu}\)m)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Estimated** \\ **Blocking** \\ **Force [N]** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Unloaded** \\ **Resonant** \\ **Frequency** \\ **[kHz]** \\ \end{tabular} } \\ \cline{1-1} \cline{2-5}  & NCE46 & 10 & 10 & 36 & 32.3 & 3200 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Selected actuator characteristics. Figure 12: Slots radial dimensions. In accordance with Table 4, maximum relative displacement between slot section was predicted to be 8 \(\upmu\)m at the measured chatter frequency (463 Hz). The preload that allows to compensate this distancing was estimated in 4 kN. Global required preload is then 5 kN. Covers are supposed to be jointed to the tool body by means of hexagon socket head cap screws able to provide an adequate force for placing. Hole position was chosen spaced enough from the contact area, where contact stress is less than 0.1% of maximum contact stress. As a result, slot length is obtained as the sum of insert length and actuators length (Figure 14). Using the model presented in Section 2.4, interference was estimated for selected preload, based on the equivalent stiffness. Boring bar FE model is shown in Figure 15. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Force Direction** & **Displacement Direction** & **Maximum Displacement** & **Correspondent Frequency** \\  & & **[mm]** & **[Hz]** \\ \hline X & Z & 0.024 & 463 \\ Y & Z & 0.008 & 463 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum distancing of slots sections. Figure 14: Slots dimensions. Figure 13: Boring bar model for slots surfaces distancing estimation. In Table 5, measured stiffness of actuator and estimated contact stiffness and boring bar stiffness are reported. Resulting interference was found to be 0.133 mm. By means of the FE model shown in Figure 16, according with approach presented in Section 2.5, cover thickness, that guarantees the compensation of material removed for actuators housing, was found to be 1.5 mm (for the two covers on insert side) and 1.8 mm (for the other two covers). In Table 6 properties of the section, in correspondence of actuators, of the different models are reported in terms of cross sectional area (\(A\)) and second moment of area with respect to central axis of inertia \(\chi\) and \(y\) (\(J_{x}\) and \(J_{y}\), respectively).