# Effectiveness of Electrode Design Methodologies for Fast EDM Slotting of Thick Silicon Wafers
## 3 Results and Discussion
### Effect of Electrode Arrays on Machining Speed with Varied Electrode Leg Heights
#### 3.1.4 Analysis of Tool Wear Ratio  
The tool wear rate (TWR) is the volume of material removed from the tool electrode for the unit time during machining. The commonly used unit for the TWR is mm\({}^{3}\)/min. In our cases, the tool wear rate was negative due to the addition of foreign material (mostly carbon from the graphite electrode and the decomposition of hydrocarbon oil) on the tool electrode. The accumulation of foreign material is due to the migration and deposition of carbon from the hydrocarbon dielectric fluid on the electrode surface facing the workpiece. This phenomenon is not unique to our experiments and can be seen in different instances. [PERSON] [38] investigated black layer characterization and the electrode wear ratio for machining BS 4695 D2 (a high carbon, high chromium tool steel) using a tungsten copper electrode (W/Cu) through EDM. Before machining, EDS-SEM (Energy Dispersive X-ray Spectroscopy-Scanning Electron Microscope) (Model: Zeiss Supra V5, Carl Zeiss AG, Oberkochen, Germany) shows that the electrode (W/Cu) only contains tungsten and copper. But later, during machining, tool electrodes accumulated C, Fe, Cr, V, and Mo from the workpiece and dielectric oil. Higher elemental migration and a higher carbon presence were observed in the low EWR (0.26%) conditions, while a higher EWR (3.48%) showed lower carbon and fewer migrated elements at the end of the machining. [PERSON] et al. [39] investigated tool wear in graphite using various dielectrics, including deionized water, EDM oil, an emulsion (a mixture of EDM oil and deionized water), and Polyethylene Glycol (PEG) solution (a combination of deionized water and PEG). It was found that dielectrics with a higher carbon content led to a reduction in the tool wear rate due to increased carbon deposition on the electrode. [PERSON] et al. [40] also found similar results in micro-EDM; carbon migration on tool electrodes was evident through EDS analysis. They also noted that both the amount of migrated material and the black layer increased with longer discharge durations and higher discharge currents. Additionally, [PERSON] et al. [41] mentioned that the porous nature of graphite electrodes allowed them to absorb some EDM oil during machining, which lead to an increase in their weight. Figure 15a-c depicts the carbon deposition on the graphite electrodes after machining silicon for arrays of electrodes 1 \(\times\) 4, 2 \(\times\) 4, and 3 \(\times\) 4 with a leg height of 0.2\(\arcsec\). It is clear that for 1 \(\times\) 4 arrays, carbon deposition is higher and quite uniform across all legs. However, for 2 \(\times\) 4 arrays, carbon accumulation mainly occurs on the left and rightmost columns for row-1 and row-2. The probable explanation for this phenomenon is that the velocity of the dielectric fluid at the first column and fourth column is lesser than at other columns as those are entry and exit points for 2 \(\times\) 4 arrays of electrodes. When it comes to 3 \(\times\) 4 arrays, carbon deposits mostly appear in row-1 (top) and row-3 (bottom), respectively. The reason for decreased carbon deposition on electrode legs in the middle row is that there is a high-velocity flow of dielectric fluid on channels on both sides of the middle row compared to one side's high velocity of dielectric flow for row-1 and row-3. Figure 15d-f depicts carbon deposition for higher arrays of electrodes (4 \(\times\) 4, 5 \(\times\) 4, and 6 \(\times\) 4); it can be observed that for higher arrays of electrodes, there is significantly less carbon deposition than for lower arrays of electrodes. All of the higher arrays of electrodes have a similar pattern, and carbon deposition mostly occurs at the entry point of the dielectric fluid, where velocity is the lowest. Figure 16 and Table 9 show the amount of carbon deposition per electrode leg for various arrays of electrodes with a leg height of 0.2\(\arcsec\).