# 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  
The machining time required for slotting silicon in the case of block electrodes and hollow electrodes with different thicknesses was investigated. The outer shape of all the electrodes was the same, which was square with a length and width of 1\({}^{\prime\prime}\) and 1\({}^{\prime\prime}\), respectively. The depth of hollow electrodes was 0.2\({}^{\prime\prime}\). Figure 19 shows the average machining time of through-hole machining on silicon workpieces for block and hollow electrodes with various wall thicknesses. The machining time for block electrodes (1\({}^{\prime\prime}\) square) and hollow electrodes with 0.12\({}^{\prime\prime}\), 0.08\({}^{\prime\prime}\), and 0.04\({}^{\prime\prime}\) wall thicknesses were 68.867, 51.5, 36.128, and 22.200 min, respectively. From Figure 19, it can be seen that with the decrease in the wall thickness from 1\({}^{\prime\prime}\) (solid block electrode) to the hollow electrode of a 0.04\({}^{\prime\prime}\) wall thickness, the machining time decreased from 68.867 min to 22.20 min, which is a significant leap in terms of improving productivity. It was found that for machining the same size through a square hole (1 in \(\times\) 1 in), hollow electrodes are more effective in terms of the machining speed, compared to solid block electrodes. For each case of wall thickness, the hollow electrode performs better than the solid electrode. This can be explained using the carbon accumulation phenomenon discussed in the earlier section. The solid block electrode has a large surface area facing the workpiece during machining, although in EDM, there is no direct contact between the workpiece and the electrode. However, the amount of carbon accumulation was significantly higher in the solid block electrode due to the higher surface area compared to the hollow electrode. This carbon accumulation causes secondary sparking and arcing, thus increasing the number of ineffective pulses during machining, and increasing the machining time [43]. The discharge energy for each spark in EDM is as follows:  
\[\text{E}=\text{V}\times\text{I}\times\text{T}_{\text{on}}\]  
where V = discharge voltage, I = discharge current, and T\({}_{\text{on}}\) = Pulse on time. Furthermore, in an ideal scenario in EDM, where the machining parameters, dielectric oil, material of tool electrode, and workpiece are the same, the number of sparks (n) for a given period will be identical. So, the spark energy density for the same period will be as follows:  
\[\text{E}_{\text{S}}=\frac{\text{V}\times\text{I}\times\text{T}_{\text{on}}}{ \text{A}}\] \begin{table}
\begin{tabular}{c c c c c} \hline
**Electrode** & **Sample** & **Length (\(\upmu\)m)** & **Width (\(\upmu\)m)** & **Thickness (\(\upmu\)m)** \\ \hline \multirow{2}{*}{Block} & Sample-1 & 25,463.50 & 25,476.20 & - \\  & Sample-2 & 25,463.50 & 25,463.50 & - \\  & Sample-3 & 25,463.50 & 25,463.50 & - \\ \hline \multirow{2}{*}{0.12\({}^{\prime\prime}\) Hollow} & Sample-1 & 25,463.50 & 25,476.20 & 3018.841 \\  & Sample-2 & 25,463.50 & 25,476.20 & 2981.047 \\  & Sample-3 & 25,476.20 & 25,463.50 & 2981.286 \\ \hline \multirow{2}{*}{0.08\({}^{\prime\prime}\) Hollow} & Sample-1 & 25,476.20 & 25,463.50 & 2056.545 \\  & Sample-2 & 25,476.20 & 25,463.50 & 1962.208 \\ \hline \multirow{2}{*}{0.04\({}^{\prime\prime}\) Hollow} & Sample-3 & 25,463.50 & 25,476.20 & 1056.742 \\  & Sample-2 & 25,463.50 & 25,476.20 & 1113.336 \\ \hline \multirow{2}{*}{0.08\({}^{\prime\prime}\) Hollow} & Sample-3 & 25,476.20 & 25,463.50 & 1094.308 \\ \hline \end{tabular}
\end{table} 
Table 11: Dimensional characterizations of arrays of block and hollow electrodes. where A = effective discharge/ machining area. So, for the same amount of discharge energy, the smaller the effective area (A), the higher the energy density will be. So, hollow electrodes will have a higher spark energy density compared to block electrodes.