## 2 Materials and Methods
It includes the machining time (MT), taper angle (\(\upomega\)), radial overcut (ROC), radial undercut  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & & & \multicolumn{6}{c}{**Design Dimensions**} \\ \cline{4-10}
**Design** & **Design Name** & **Design** & **Angle** & & & **Height** & & **Diameter** \\ \cline{3-10}
**Type** & **Design Name** & **Symbol** & **Relief** & **Land** & **Face** & **Shank** & **Total** & **Face** & **Shank** \\  & & & **Angle;** & **Height;** & **Height;** & **Height;** & **Height;** & **Diameter;** & **Diameter;** \\  & & & & **(deg)** & **LH** & **FH** & **SH** & **H** & **FD** & **SD** \\ \hline
**D\({}_{\text{C}}\)** & **Conventional** & \(\text{D}_{\text{CR0}}\) & 0 & 0 & 0 & 50.00 & 50 & 8 & 8 \\ \hline \multirow{4}{*}{**D\({}_{\text{R}}\)**} & \multirow{4}{*}{**Relief angle**} & \(\text{D}_{\text{R10}}\) & 10 & 0 & 8.50 & 41.50 & 50 & 8 & 5 \\  & & \(\text{D}_{\text{R20}}\) & 20 & 0 & 4.12 & 45.87 & 50 & 8 & 5 \\  & & \(\text{D}_{\text{R30}}\) & 30 & 0 & 2.60 & 47.40 & 50 & 8 & 5 \\  & & \(\text{D}_{\text{R45}}\) & 45 & 0 & 1.50 & 48.50 & 50 & 8 & 5 \\ \hline \multirow{4}{*}{**D\({}_{\text{RL}}\)**} & \multirow{4}{*}{**Relief angle**} & \(\text{D}_{\text{RL10}}\) & 10 & 1 & 8.50 & 40.50 & 50 & 8 & 5 \\  & & \(\text{D}_{\text{RL20}}\) & 20 & 1 & 4.12 & 44.87 & 50 & 8 & 5 \\  & & \(\text{D}_{\text{RL30}}\) & 30 & 1 & 2.60 & 46.40 & 50 & 8 & 5 \\  & & \(\text{D}_{\text{RL45(RUC), longitudinal tool wear (LTW), and surface roughness (SR). Generally, the deep machining (milling or drilling) was considered as difficult and the sidewalls of the resulting feature (cavity or hole) did not remain parallel. As a result the tapered feature was produced. With reference to the drilled/milled holes, the difference in diameters of the hole at the entry and exit positions caused the taperness in sidewalls as schematically shown in Figure 2a. Therefore, in this study the taper angle was taken as one of the important performance characteristics, which was calculated using Equations (1) and (2). \[Half\;diff\;ference\;in\;diameters\;(\Delta D)=1/2(D_{en}-D_{ex}) \tag{1}\]  
\[Taper\;angle\;(\varnothing)=Tan^{-1}(\Delta D/L) \tag{2}\]  
where,  
\(D_{en}\) is the diameter at the hole entrance;  
\(D_{ex}\) is the diameter at the hole exit;  
\(\Delta D\) is the half of the difference between both the diamters (\(D_{en}\) and \(D_{ex}\));  
\(L\) is the hole length. By comparing the diameters of tool and the machined hole, EDM produces oversized hole, in general. The phenomenon is well-reported by the term \"overcut\". It is being noticed that at the entrance of the hole, the machined diameter is larger than the tool diameter whereas the exit diameter of the hole is found to be less than the tool diameter. Thus, at the hole entrance the radial overcut (ROC_en) and at the hole exit the radial undercut (RUC_ex) are taken as response characteristics as schematically depicted in Figure 2b. The radial overcut and undercut were calculated using Equations (3) and (4), respectively. \[Radial\;overcut\;(ROC)=1/2(D_{en}-D_{load}) \tag{3}\]  
\[Radial\;undercut\;(RUC)=1/2(D_{load}-D_{ex}) \tag{4}\]  
where,  
\(D_{en}\) is the diameter of machined hole at the entrance;  
\(D_{ex}\) is the diameter of hole at the exit;  
\(D_{tool}\) is the diameter of the tool electrode. With reference to the measurements of each of the experimental runs, the machining time was carefully noted. The calculations of taper angle, radial overcut, and radial undercut primarily involve  
Figure 2: Schematic of hole dimensions: (**a**) taper angle and (**b**) radial overcut and undercut. the measurements of different diameters (tool electrode, hole entry, and hole exit). All the diameters associated with each of the experimental runs were measured on coordinate measuring machine; CMM (CE-450 DV, CHIEN WEI Precise Technology Co., LTD. Taiwan) with a 1 \(\upmu\)m measurement accuracy. For each diameter, 8-points measurement was planned around the periphery of the circle as shown in Figure 3a.