## 4 Results and Discussion
### Influence of Machining Parameters on Surface Roughness  
The material removal rate was calculated as a function of the thickness change of the sapphire. Figure 8a shows the relationship between spindle speed and surface roughness, while Figure 8b shows the influence of spindle speed on the machining temperature. Figure 9 shows the surface topography of the sapphire under different spindle speeds. It can be seen that the roughness of sapphire first decreased and then increased with the change in spindle speed. On the one hand, this was due to the fact that, as the spindle speed increased, the linear speed of the grinding abrasive increased, the quantity of abrasive involved in the grinding increased, and the grinding force and depth requirement of a single abrasive decreased; accordingly, the workpiece's plastic deformation also decreased, resulting in a decrease in surface roughness [30]. On the other hand, with the increase in spindle speed, more coolant entered the same area simultaneously, which could reduce  
Figure 6: Residual map of the surface roughness. Figure 7: Influence of different machining parameter on the surface roughness Ra: (**a**) spindle speed; (**b**) feeding rate; (**c**) grinding depth. the temperature of the grinding area and prevent damage and glazing of the abrasive tool g. The number of abrasives involved in grinding became excessive as the spindle speed increased, making it difficult to remove the resulting debris from the processing region on time, causing abrasive debris to clog the pores and overheat the abrasive tool, and decreasing the mechanical effect of the abrasive tool. Adhesive wear reduced the surface quality of the sapphire substrate. Figure 8a shows the relationship between the rotational speed and the material removal rate. It can be seen that the material removal rate increased first and then decreased with the increase in spindle speed. The number of abrasives involved in grinding increased with spindle speed, as did the material removal rate. Nevertheless, when the spindle speed was too high, the number of abrasives involved in grinding decreased, while the abrasive tool tended to glaze, which reduced its ability to self-sharpen; accordingly, the rate of material removal decreased. Figure 10a shows the relationship between feeding rate and surface roughness, while Figure 10b shows the influence of feeding rate on the machining temperature. Figure 11 shows the surface topography of sapphire under different feeding rates. It can be seen that, with the increase in feeding rate, the roughness of sapphire initially decreased and then increased. When the feeding rate was 4 \(\upmu\)m/min, the surface roughness was highest. On the one hand, the tangential grinding force of the tool was small, and the grinding traces could hardly be observed from Figure 11a, indicating a poor mechanical effect of the abrasive tool. On the other hand, it can be seen from Figure 10b that the temperature of the contact area was low; since the solid-phase chemical reaction is closely related to the temperature [26], when the feeding rate was too low, the temperature struggled to increase with the effect of coolant. When the feeding rate increased, the temperature  
Figure 8: Influence of spindle speed on the (**a**) surface roughness, MRR, and (**b**) machining temperature (average temperature in the contact area after machining for 5 min). Figure 9: Surface topography of sapphire under different spindle speeds: (**a**) 750 rpm; (**b**) 800 rpm; (**c**) 850 rpm; (**d**) 900 rpm; (**e**) 950 rpm. also increased due to the increase in pressure between the sapphire and the abrasive tool, thereby promoting solid-phase chemical reactions; hence, the surface roughness presented a descending trend.