## 3 Time Domain Analysis of Characteristic Signal
The grinding efficiency of the difficult grinding directions is (0-2) \(\times 10^{-5}/\left[\upmu\text{m}^{3}\cdot\left(N\cdot m\cdot s^{-1}\right)^{-1}\right]\), the grinding direction with a grinding efficiency greater than 2 is considered the non-difficult grinding direction. The relationship between sharpening direction and sharpening efficiency is shown in Table 3. In order to determine the relationship between the characteristic parameters and the grinding direction, an experimental study was carried out. First, the tool was oriented off-line using a crystal orientation instrument, the non-difficult grinding direction or difficult grinding direction of the grinding surface to the grinding speed direction was adjusted, and the acoustic emission signals of the non-difficult grinding directions and the difficult grinding directions, respectively, were collected. The crystal orientation instrument uses an MWL110 crystal orientation instrument purchased from Multiwire laboratories. Ltd of US by Changchun Institute of Optics, Fine Mechanics and Physics of China, the light source of the orientation instrument is X-ray, the orientation instrument from Multiwire laboratories. Ltd of US is designed according to the Laue principle, which can be oriented to a single crystal, the orientation accuracy is 0.25 degrees. The photos obtained during orientation were marked and compared with the actual crystal surface. Among them, the photo of the single-crystal diamond tool shows that the tool bar is perpendicular to the paper surface, and the direction of the blade line is longitudinal. The orientation instrument object, orientation instrument structure, single-crystal diamond tool, and crystal direction figure are shown in Figure 3a-d. In the experiment, the grinding wheel is made of high phosphorus cast iron for grinding diamonds, whose shape, size, and proportion of pores in the material structure are optimized. The surface of the grinding disc is inlaid with diamond grinding powder, and the particle size can be smaller than 1 \(\upmu\)m to 40 \(\upmu\)m. The grinding disc has a diameter of approximately 300 mm, the grinding wheel speed is 7200 r/min, and the collected acoustic emission signals and the collected vibration signals are analyzed in the time domain according to Formulas (7)-(11), and the results are shown in Tables 4 and 5. \begin{table}
\begin{tabular}{c c} \hline \hline \multirow{2}{*}{**Ginding Direction**} & **Ginding Efficiency \(K\)** \\  & \(\times 10^{-5}/\left[\upmu\text{m}^{3}\cdot\left(N\cdot m\cdot s^{-1}\right)^{-1}\right]\) \\ \hline Difficult grinding direction & 0–2 \\ The direction between difficult grinding and easy grinding & 2–4 \\ Easy grinding direction & 4–6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The relationship between sharpening direction and sharpening efficiency. Figure 2: The angle relationship of 100, 110, 111 typical crystal surface. As can be seen from Table 4, the statistical results of mean value and variance for acoustic emission signals in the different grinding directions have little difference, and the skewness has no obvious regularity. The kurtosis is approximately 3 in the non-difficult grinding direction and significantly greater than 3 in the difficult grinding direction, which has obvious non-Gaussian characteristics and a strong correlation with the grinding direction. Similarly, as can be seen from Table 5, the skewness and kurtosis of the vibration signal have obvious law and strong correlation with the grinding direction, which is consistent with the fact that the vibration signal is not a strong correlation with the grinding direction.