## 4 Results and Discussion
### Influence of Machining Parameters on Surface Roughness
When the feeding rate exceeded 8 \(\upmu\)m/min, the surface roughness worsened, partly due to the accelerated appearance of a glazing film with the increase in feeding rate, which blocked the abrasives and weakened the reaction, and partly due to the accelerated accumulation of frictional heat, which weakened the holding ability of the binder. This led to the abrasives falling off prematurely, resulting in a significant fluctuation in the friction coefficient between the workpiece and the abrasive tool, which harmed the surface roughness of the sapphire. Figure 10a shows the relationship between feeding rate and material removal rate. It can be seen that, with the increase in feeding rate, the material removal rate showed an upward trend. When the feeding rate was low, the chemical and mechanical effects were both weak. With the increase in feeding rate, the temperature of the interaction area gradually increased, thereby promoting the solid-phase chemical reaction; hence, the material removal rate increased. Figure 10: Influence of feeding rate on the (**a**) surface roughness, MRR, and (**b**) machining temperature (average temperature in the contact area after machining for 5 min). Figure 12a shows the relationship between grinding depth and surface roughness, while Figure 12b shows the influence of grinding depth on the machining temperature. Figure 13 shows the surface topography of sapphire under different grinding depths. In this paper, the grinding depth referred to the feeding distance of the tool when it first touched the sapphire; due to abrasive tool wear, the grinding depth was slightly less than the theoretical value. It can be seen from Figure 14 that the surface roughness of sapphire decreased with the increase in grinding depth and then increased. When the grinding depth was low, the pressure between the abrasive tool and sapphire was slight, and it can be seen from Figure 13a that only some shallow grinding traces were left on the sapphire. Furthermore, from Figure 12b, it can be seen that the machining temperature was low in the contact area, which was not conducive to the solid-phase chemical reaction. Upon increasing the grinding depth, the contact area of the grinding zone increased, the number of abrasive particles participating in the grinding per unit area increased, and the heat accumulation caused the temperature of the grinding zone to rise rapidly [19]. Within a certain temperature range, an increase in temperature was beneficial to increase the solid-phase chemical reaction rate, which increased the plastic removal ratio of the abrasive tool and improved the surface quality of the sapphire. When the grinding depth was further increased, the volume of material removed by the abrasive tool increased, while the friction area increased gradually, the grinding force perpendicular to the surface of the workpiece increased, the grinding force required by a single abrasive particle increased, and the mechanical effect of the abrasive tool began to dominate, which increased the surface roughness. Figure 12a shows the relationship between the grinding depth and the material removal rate. As the grinding depth increased, the contact area between the abrasive tool and the workpiece increased, the rate of frictional heat accumulation increased, and the material removal rate of the abrasive tool increased, as the increase in temperature could promote the solid-phase chemical reaction. When the grinding depth was further increased, the rapid accumulation of frictional heat led to rapid glazing of the abrasive tool, causing a reduction in the chemical and mechanical effects, and the material removal rate accordingly began decreasing. Figure 12: Influence of grinding depth on the (**a**) surface roughness, MRR, and (**b**) machining temperature (average temperature in the contact area after machining 5 min).