# Effectiveness of Electrode Design Methodologies for Fast EDM Slotting of Thick Silicon Wafers
## 3 Results and Discussion
### Effects of Hollow Electrodes on Machining Speed with Varied Wall Thickness
#### 3.2.2 Analysis of Machining Time and Material Removal Rate
In addition, the equation for the material removal rate (MRR) is as follows:  
\[\mathrm{MRR}=\mathrm{k}\frac{\mathrm{E_{s}}}{\mathrm{T_{P}}}\]  
where T\({}_{\mathrm{P}}\) = pulse time duration and k = coefficient related to parameters such as polarity, electrode, dielectric, flushing condition, etc. In our case, everything is identical except the effective machining area, so for both hollow and block electrodes, the MRR is proportional to Es. As the 0.04\({}^{\prime\prime}\) wall thickness has the highest energy spark density, it will have the highest MRR [44; 45]. From Figure 20, it can be observed that there is an increase in the MRR values with the reduction in the wall thickness of hollow electrodes. The values of the MRR are 36.098, 48.012, 68.529, and 111.419 mm\({}^{3}\)/min for the block electrode and the 0.12\({}^{\prime\prime}\)-, 0.08\({}^{\prime\prime}\)-, and 0.04\({}^{\prime\prime}\)-thick hollow electrodes, respectively. In the case of the 0.04\({}^{\prime\prime}\)-thick hollow electrode, the MRR is around 3 times more than for the solid block electrode, approximately 2.5 times more than for the 0.12\({}^{\prime\prime}\)-thick hollow electrode, and around 1.5 times more than for the 0.08\({}^{\prime\prime}\)-thick hollow electrode. During machining with square block electrodes, the area of the silicon workpiece melts and vaporizes, which is equal to the bottom surface area of block electrodes. However, for hollow electrodes, only the wall thickness area caused sparking over the silicon workpiece and was responsible for machining. As a result, the hollow electrode cut through a biscuit-shaped block equal to the inner cross-section of the hollow electrode, while leaving a square through slot on the silicon workpiece. This significantly reduces the sparking surface area and thus the energy consumption during machining. As a result, the energy per area of the lower-thickness electrode will be higher than that of block electrode and higher-wall-thickness hollow electrode. As a result of that, the 0.04\({}^{\prime\prime}\)-thick hollow electrode depicts a higher MRR compared to the 0.12\({}^{\prime\prime}\) and 0.08\({}^{\prime\prime}\) wall thickness hollow electrodes and the solid block electrode. The portion of the workpiece that is inside the hollow electrode was dropped as a square biscuit of silicon, while for machining with a block electrode with a 1 in \(\times\) 1 in cross-section, the entire material is removed in the form of small craters via continuous sparking. These crater sizes can be controlled by the selection of parameters, thus controlling the discharge energy per pulse [46]. Advanced pulse generators using a Resistance-Capacitance-type (RC) pulse generators are found to produce smaller craters due to their capability of using lesser discharge energy per pulse  
Figure 19: Average machining time for block and hollow electrodes with different thicknesses. during machining, and can be useful for improving the dimensional accuracy of silicon in EDM [47]. However, smaller craters will create a lot of powdery debris, which must be removed from the electrode-workpiece gap, thus slowing down the machining process. This biscuit-shaped silicon produced as a result of machining using a hollow electrode can be used for another purpose, if needed, thus minimizing the wastage of silicon material.