## 4 Conclusions  
EDM of tungsten carbide; WC (famously considered as a difficult-to-machine material), was carried out using various tool designs to produce cylindrical holes of 4 mm depth with 8 mm diameter. The tool designs include the conventional cylindrical design (D\({}_{\text{C}}\)), relief angle design (D\({}_{\text{R}}\)) containing four relief angles (10, 20, 30, and 45\({}^{\circ}\)), and relief angle with a land design (D\({}_{\text{RL}}\)) consisting of five relief angles (10, 20, 30, 45, and 90\({}^{\circ}\)) with a land of 1 mm thickness. The performance was gauged through evaluating the machining time (MT), hole taper angle (\(\omega\)), radial overcut at the hole entrance (ROC_en), radial undercut at the hole exit plane (RUC_ex), longitudinal tool wear (LTW), and the surface roughness (SR) of the inner walls of the machined holes. By considering machining outcomes, erosion phenomenon, and comparative analysis of tool designs' performances, the following conclusions might be inferred:  
1. [label=., ref=.  
* Regarding the hole taper angle (\(\varphi\)), as the relief angle increased the corresponding taperness in holes' sidewalls also increased. The tool having 10 degree relief with a land thickness of 1 mm (D\({}_{\text{RL10}}\)) produced the hole with minimum taper angle amounting to 3.84\({}^{\circ}\).
* There was a clear difference in the radial overcut at the hole entrance when the modified tool designs were employed. The tools with relief angle (D\({}_{\text{R}}\)) were found to be better than the conventional cylindrical tool in order to get the smaller overcut at the hole entrance. On the other, the undercut at the exit plane of the hole was smallest in the case of conventional tool design (D\({}_{\text{C}}\)).
* Longitudinal tool wear (LTW) of modified tool designs was found to be substantially less than the tool wear in the case of the conventional tool design (D\({}_{\text{C}}\)). The minimum longitudinal tool wear was observed in the case of the 10 degree relief angle (D\({}_{\text{R10}}\)) with an amount of 790 \(\upmu\)m.
* There was close competition among the performance of all the electrode designs in the case of the roughness of the inner surfaces of the machined holes. However, the modified tool designs produced the surfaces with smaller roughness as compared to the roughness caused by the conventional tool design (D\({}_{\text{C}}\)). Moreover, the minimum roughness of R\({}_{\text{a}}\) 4.42 \(\upmu\)m resulted again by the tool D\({}_{\text{RL10}}\), i.e., tool having a relief angle of 10\({}^{\circ}\) with a land thickness of 1 mm.
* The tool design D\({}_{\text{RL10}}\) could be considered as the most appropriate tool design capable of resulting significantly improved results for most of the five performance characteristics taken in this study.  
Conceptualization, N.A.M.; Data curation, M.R.; Formal analysis, N.A.M., M.R. and N.A.; Funding acquisition, N.A. and A.M.A.-A.; Investigation, M.R. and A.H.; Methodology, N.A. and M.Q.S.; Project administration, A.M.A.-A.; Resources, N.A.M. and A.H.; Software, M.Q.S.; Supervision, N.A.M.; Validation, M.Q.S. and A.M.A.-A.; Writing - original draft, N.A.M., M.R. and N.A.; Writing - review & editing, A.H. and A.M.A.-A. All authors have read and agreed the published version of this manuscript.  
Raytheon Chair for Systems Engineering, King Saud University, Riyadh, Saudi Arabia.  
The authors are grateful to the Raytheon Chair for Systems Engineering, King Saud University for funding.  
The authors declare no conflict of interest.