## 2 Experiment Details
### Grinding Experiment  
The grinding experiment was conducted on a MK9025 numerical controlled machine shown in Figure 2. The spindle is capable of running from 3000 to 6600 r/min. Resin bond diamond wheels with different sizes were used in this experiment. The wheels have an outer diameter of 100 mm, a width of 10 mm and a thickness of 5 mm. The grit surface density was obtained by a theory equation (Equation (1)) [10]. Properties of the wheels are introduced in Table 2.  
The grain dimension \(d_{g}\) is quoted in a simple way as equal to the aperture opening of the sieve according to the following relationship: \(d_{g}=15.2/M\)[10]. \(M\) is the mesh size of the wheel. \(v\) is the volume fraction of diamond in the grinding wheel. In this experiment, all wheels have the same density of 100, in other words, \(v=0.25.f\) is the fraction of diamond particles that actively cut in grinding. It is assumed that only one-half of the diamond particles on the wheel surface are actively engaged in cutting, so \(f\) = 0.5 [10]. Considering the difference between the theoretical value of Equation (1) and actual value, the grit surface density used in this study is a proximate value.  
Surface-grinding was performed on the specimen of 20 \(\times\) 10 mm\({}^{2}\) face and was employed in a down grinding mode. A geometry model for grinding was simplified as a single grit-workpiece interaction model and shown in Figure 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Mesh Size \(M\)/\#** & **Mean Grit Size/\(\upmu\)m** & **Grit Surface Density \(C\)**/\#\(\cdot\)**mm\({}^{-2}\)** \\ \hline
1 & 60 & 253 & 3.82 \\
2 & 120 & 127 & 15.15 \\
3 & 180 & 84 & 34.6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Properties of grinding wheels.  
Figure 2: MK9025 numerical controlled machine.  
Seen from Figure 3, \(r_{\text{s}}\) is the semi-diameter of wheels. \(H_{\text{max}}\) is the maximum undeformed chip thickness when depth of cut is \(a_{\text{p}}\). O is the initial position of grain track center and O\({}^{\prime}\) is the real center of the grain track. The wheel whirled to get \(V_{\text{s}}\) and at the same time had a vertical reciprocating motion to get \(V_{\text{w}}\). The wheel rotated clockwise and the workpiece was relatively moving in upper direction. Grinding width was held a constant at \(b=10\) mm and the maximum undeformed chip thickness \(H_{\text{max}}\) was obtained by Equation (2) [16], where \(V_{\text{w}}\) is the speed of workpiece and \(V_{\text{s}}\) is the speed of wheels, \(a_{\text{p}}\) is depth of cut, \(d_{\text{e}}\) is the equivalent diameter of wheels (in this experiment it is surface-grinding, so \(d_{\text{e}}\) equals wheel's diameter), \(C\) is the surface density of wheel, and \(r\) is the ratio of chip width to average undeformed chip thickness. The value of \(r\) is reported to be in the range of 10-20 [16]; \(r=4\times\tan\theta\) (\(\theta\) is the angle of wheel's grain tip) by the geometric model and \(r\) was assumed to be equal to 10 in this experiment. No grinding fluid was used in the experiment. The grinding parameters employed are shown in Table 3.  
\[H_{\text{max}}=\left(\frac{4V_{\text{w}}}{V_{s}\cdot C_{s}r}\sqrt{\frac{a_{p}} {d_{e}}}\right)^{0.5} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Mesh Size** & **Depth of Cut** & **Wheel Speed** & **Work Speed** & **Max Undeformed Chip Thickness** \\  & \# & /\(\mathbf{\mu}\mathbf{m}\) & /\(\mathbf{m}\cdot\mathbf{s}^{-1}\) & /\(\mathbf{m}\cdot\mathbf{s}^{-1}\) & \(\mathbf{H_{\text{max}}}/\mathbf{\mu}\mathbf{m}\) \\ \hline
1 & & 100 & 10.5 & 0.2 & 7.94 \\
2 & & 100 & 15