## 3 Results and Discussion
### Effect of Electrode Design on Taper Angle (\(\mathbf{o}\))  
The effects of tool designs and various relief angles on the degree of taperness of the machined holes have been presented in Figure 7. By the use of conventional design (\(\mathrm{D_{CR0}}\)), in which the sides of the tool are straight and parallel to the axis of the hole, the taper angle of 3.94\({}^{\circ}\) was observed. The second design type (\(\mathrm{D_{R}}\)), in which relief angles were provided and the sidewalls of the tool were not parallel to the hole axis, the taper angle was found to be larger than the taper angle in the case of the conventional tool design (\(\mathrm{D_{CR0}}\)). Furthermore, as the relief angle in the tool increased the taperness in the sidewalls of the machined hole also increased as can be observed from the red callout mentioned in Figure 7.  
As the erosion progressed, the tool wear was experienced at the bottom and consequently the tool length mainly reduced. The wear in tool length reduced the diameter of the tool at the bottom end because of the presence of relief angle. The exit diameter of the machined hole became smaller. Thus, the difference in hole diameters (at the entrance and exit) resulted in a taper angle. This difference in diameters became more and more as the relief angle was increased from 10 to 45\({}^{\circ}\). Consequently, the taper angle in the sidewalls of the hole increased. Among the tools designed under the category of \(\mathrm{D_{R}}\) the tool having a relief angle of 10\({}^{\circ}\) produced the minimum taper angle (4.21\({}^{\circ}\)) in the machined hole. A similar pattern of the hole taper angle was noticed in the case of third design type (\(\mathrm{D_{CR}}\)) in which relief angles were given after the 1 mm land thickness. In this design type, the side walls of the  
Figure 7: The effect of different design types on the hole taper angle after the EDM of WC.  
tool, at a height of 1 mm from the tool bottom, were parallel to the hole axis whereas after 1 mm the sides became inclined due to the presence of the relief angle. The maximum surface area available for the sparking remained constant for all the design variants of D\({}_{\mathrm{RL}}\) because of a 1 mm land thickness. The total surface area for sparking is the summation of the bottom surface area and surface area of circular land of 1 mm thickness (\(\pi\times 4^{2}+2\pi\times 4\times 1=75.4\) mm\({}^{2}\)). In this way, the total surface area was 75.4 mm\({}^{2}\), which theoretically remained constant in the case of D\({}_{\mathrm{RL}}\) tools. Therefore, ideally the hole taper angle should remain constant but in actual the taper angle increased as the relief angle increased. The cause of this increase could be the change in current characteristics occurred due to the relief angles. As in the case of a 90 degree relief angle, it is possible that the behavior of the discharge current became erratic and the resulted taper of the hole reached a maximum value of 21.11\({}^{\circ}\). Since EDM is a complex phenomenon and the prediction of discharge current and other parametric behaviors is difficult [23], therefore further research is needed to understand the change in current performance when a relief angle of 90\({}^{\circ}\) is provided. Hence, land with a relief of 90\({}^{\circ}\) was the worst design in terms of the hole taper angle. The minimum taper angle under the category of D\({}_{\mathrm{RL}}\) was found to be in case of 10 degree relief with 1 mm land (D\({}_{\mathrm{RL}10}\)). As a whole, if we compared the taper angles of all the ten designs, the minimum taper angle of 3.84\({}^{\circ}\) was achieved using the tool D\({}_{\mathrm{RL}10}\) in which the relief of 10\({}^{\circ}\) was provided with 1 mm land. Thus, D\({}_{\mathrm{RL}10}\) was the most appropriate tool to have the machined hole with a minimum taper angle.