## 4 In-Process Tool Wear Prediction and Hole Depth Control  
A comparison between data-driven and traditional approaches is carried out by implementing a control strategy for in-process tool wear prediction (Figure 2). The control strategy, which is programmed in G-code language, enables to select one of the three regression models for predicting the TWR. The selection of the predictive models must be done by the machine user before starting the drilling process.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{8}{c}{**Explanatory Variables**} \\ \cline{2-10}  & \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & \(\mathbf{X_{4}}\) & \(\mathbf{X_{5}}\) & \(\mathbf{X_{6}}\) & \(\mathbf{X_{7}}\) & \(\mathbf{X_{8}}\) \\ \hline PP & \(T_{\text{on}}\) & \(U_{\text{o}}\) & \(F\) & \(K\) & \(U_{\text{e}}\) & - & - & - \\ DD & \(F_{\text{P}}\) & \(V_{\text{f}}\) & \(U\) & - & - & - & - & - \\ PP + DD & \(T_{\text{on}}\) & \(U_{\text{o}}\) & \(F\) & \(K\) & \(U_{\text{e}}\) & \(F_{\text{P}}\) & \(V_{\text{f}}\) & \(U\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Explanatory variables used in each predictive model.  
The regression equations of the predictive models, as computed using MATLAB software, are implemented in the G-code. When selecting the DD or PP + DD model, the system embedded in the control unit of the SARIX(r) machine tool is used for monitoring \(f_{p}\), \(v_{f}\), and \(u\). These three quantities are monitored at regular steps of 50 \(\upmu\)m until a drilling depth (\(Z\)) equal to the target drilling depth (\(H_{t}\)) is reached. The average values of \(f_{p}\), \(v_{f}\), and \(u\) are computed when \(Z=H_{t}\). Since the tool electrode is inevitably wearing during the drilling process, this condition guarantees that a hole having a depth lower than \(H_{t}\) has been drilled if \(Z=H_{t}\), while at the same time it also allows to obtain a reliable estimation of the average values of the monitored quantities (\(F_{p}\), \(V_{f}\), and \(U\)). The MLR models are used for predicting the MRR and TWR. From the predicted values of the TWR and MRR (\(TWR_{p}\) and MRR\({}_{p}\)), the target drilling depth (\(Z_{t}\)), which needs to be reached to drill a hole of depth equal to \(H_{t}\), is calculated as:  
\[Z_{t}\ =\ H_{t}+\frac{V_{t}}{A_{t}}\ =\ H_{t}+\frac{TWR_{p}\ast T_{p}}{A_{t}} \tag{6}\]  
where \(A_{t}\) is the cross sectional area of the tool electrode and \(T_{p}\) is the monitored drilling time at \(Z=H_{t}\). The value of \(Z_{t}\) is computed when \(Z=H_{t}\) if the DD or DD + PP predictive models are chosen, while \(Z_{t}\) is computed at the start of the drilling process when selecting the PP predictive model. After computing \(Z_{t}\), the drilling process is continued until \(Z=Z_{t}\) is reached.  
In order to test the control strategy, micro-EDM drilling experiments are carried out for blind holes into specimens composed of two parts. The two parts are obtained by wire-EDM cutting of a Ti6 Al4V plate. Two sets of experiments are carried out by varying the target hole depth: 1.5 mm and 2.5 mm. During the experiments, the specimens are placed into the workpiece clamp as in Figure 3. The drilling experiments are performed along the intersection line of the two parts. This allows easy  
Figure 2: Flowchart of the control strategy for hole depth control based on in-process wear prediction.  
inspection of the holes after drilling. For every drilled hole, after measuring the actual hole depth (\(H_{a}\)), the depth error (\(\Delta H\)) is computed as in Equation (7).  
\[\Delta H\ =\ \ |H_{a}-H_{t}\ | \tag{7}\]