## 3 Results and Discussion
### The Normal Force per Grit vs. Maximum Undeformed Chip Thickness  
Figure 5 shows the trend of normal force per grit with the increase of maximum undeformed chip thickness (\(H_{\text{max}}\)). Single grit normal force increases until reaches a maximum value at the point of \(H_{\text{max}}\) = 3.32 \(\upmu\)m, then starts to decrease sharply, and at last fluctuates in a small range with the increasing \(H_{\text{max}}\). When \(H_{\text{max}}\) equals 0.78 \(\upmu\)m, the force of grit on 120# wheel is bigger than the force of 180# wheel (see Figure 5a). Figure 5b-d are separate views of Figure 5a under different wheel conditions. In Figure 5b, using 60# wheel shows that when \(H_{\text{max}}\) is smaller than 3.32 \(\upmu\)m, a larger \(H_{\text{max}}\) resulted from increasing \(a_{\text{p}}\) leads to an increase of single grit normal force. When \(H_{\text{max}}\) is bigger than 3.32 \(\upmu\)m, no obvious pattern about the specific normal force is obtained as a function of \(H_{\text{max}}\). At the range of 3.32 to 4.7 \(\upmu\)m, the normal force per grit declines due to the decreasing \(V_{\text{s}}\) (wheel speed). The specific normal force is proved to be growing with \(V_{\text{w}}\) when \(H_{\text{max}}\) ranges from 4.7 to 6.64 \(\upmu\)m and is reduced as a result of declining \(V_{\text{s}}\) between 6.64 and 7.94 \(\upmu\)m of \(H_{\text{max}}\). In other words, the normal force per grit is affected by grinding parameters. Figure 5c shows that an increase in maximum undeformed chip thickness, whether it is resulted from \(a_{\text{p}}\) or \(V_{\text{w}}\), leads to a larger normal force per grit. A similar trend is seen in Figure 5d: that an increase of maximum undeformed chip thickness results in a larger normal force per grit. The change of \(a_{\text{p}}\) leads to the increasing \(H_{\text{max}}\). Figure 5: (**a**) is the normal grinding force per grit of alumina as a function of the maximum undeformed chip thickness with different wheels. In picture (**b**), the mesh size of wheel is 60#. In picture (**c**), it is 120#. In picture (**d**), it is 180#. In Figure 7a, the normal force per grit is fluctuating with increasing maximum undeformed chip thickness when using the 60\(\#\) wheel and 120\(\#\) wheel, while, it is rising under the 180\(\#\) wheel condition. Figure 7b shows that when \(H_{\text{max}}\) is less than 4.7 \(\upmu\)m, \(F_{\text{gn}}\) is increasing with the increasing \(V\)s, while when \(H_{\text{max}}\) is bigger than 6.64, \(F_{\text{gn}}\) is decreasing with the increasing \(V\)s. A similar regular pattern, that \(F_{\text{gn}}\) is reduced when \(H_{\text{max}}\) is smaller than 4.07 \(\upmu\)m and rising when \(H_{\text{max}}\) is larger than 4.07 \(\upmu\)m, was obtained as a function of \(a_{\text{p}}\). Figure 7c reflects the influences of \(V\)w and \(a_{\text{p}}\) on \(F_{\text{gn}}\). The normal force per grit is decreasing at first, and then going up with increasing \(H_{\text{max}}\) resulted from \(V\)w. At last, the opposite trend is coming up with increasing \(H_{\text{max}}\) resulted from increasing \(a_{\text{p}}\). Not until \(H_{\text{max}}\) is less than 0.78 \(\upmu\)m, which is smaller than brittle-ductile cutting depth (1.03 \(\upmu\)m) of this fused silica, \(F_{\text{gn}}\) increases as a function of \(H_{\text{max}}\). In Figure 7d, the changing \(H_{\text{max}}\) is resulted from \(a_{\text{p}}\). In summary, the predictive grinding force model does not correspond with Figure 7b,c conditions. As we all know, most predictive grinding force models were derived based on crystal ceramics, while Fused silica is a non-crystalline ceramic, which is significantly different from crystals. From this experiment, we can see that microstructure plays an important role in determining grinding force models. Figure 7: **(a)** The normal grinding force per grit of fused silica as a function of the maximum undeformed chip thickness with different wheels. In picture **(b)**, the mesh size of wheel is 60\(\#\). In picture **(c)**, it is 120\(\#\).