## 4 The Simulation and Analysis of CBN Grain Movement Behavior
### The Simulation Results and Analysis of CBN Abrasive Grain Movement Behavior
#### 4.2.3 Analysis of CBN Grain Movement Behavior
However, compared to the case where no ultrasonic vibration assistance is applied, the CBN abrasive grains no longer move in the direction of the circumference of the molten metal fluid but begin to tend to flow above the melt pool. This indicates that the force generated by the ultrasonic vibration is comparable to the drag force of the metal fluid, which changes the combined force on the CBN abrasive grains and their moving direction. As shown in Figure 12c, the final arrangement of the CBN abrasive grains also changed, from a state of being distributed at the bottom of both sides of the printing layer to an overall diffusion towards the top of the printing layer. When the ultrasonic amplitude continues to increase to 20 \(\upmu\)m, 30 \(\upmu\)m, and 40 \(\upmu\)m, the movement of the CBN abrasive grains is gradually changed from molten metal fluid circumference-dominated to ultrasonic vibration-dominated upward movement. This leads to a great change in the final arrangement of the CBN abrasive grains on the printing layer. The distribution of the CBN abrasive grains under different ultrasonic amplitudes can be seen in Figure 13.  
With the increase in amplitude, the CBN abrasive grain distribution gradually spreads to the top of the printing layer. As shown in Figure 13c, when the amplitude A = 20 \(\upmu\)m, the CBN abrasive grains are more evenly distributed on the boundary of the printing layer. As the amplitude continues to increase, the effect of ultrasonic vibration on the CBN abrasive grains gradually exceeds the effect of other forces, and the number of the CBN abrasive grains distributed on the top of the printing layer increases. For the grinding wheel, the top of the printing layer is first involved in grinding, and the uniform distribution of the CBN abrasive grains is conducive to improving the grinding quality, so it is necessary to reasonably select the amplitude of the ultrasonic vibration. Ultrasonic amplitude not only affects the direction of the CBN grain movement and the final distribution but also has a greater impact on the speed of the CBN grain move \begin{table}
\begin{tabular}{c c c c c} \hline
**No.** & **Laser Power** & **Scanning Speed** & **Vibration Frequency** & **Amplification** \\
**(W)** & **(mm/s)** & **(kHz)** & **(\(\upmu\)m)** \\ \hline
1 & & & & 0 \\
2 & & & & 10 \\
3 & 250 & 4.5 & 20 & 20 \\
4 & & & & 30 \\
5 & & & & 40 \\ \hline \end{tabular}
\end{table} 
Table 8: The process parameters in the simulation. ment. Because the velocity of abrasive grains at different positions at different moments is different, the time taken by all CBN abrasive grains from the beginning of their movement to the boundary of the printing layer is calculated to reflect the movement velocity of the CBN abrasive grains. The time for all CBN abrasive grains from the beginning of movement to the boundary of the printing layer at different amplitudes can be seen in Figure 14. The duration of the movement of the CBN abrasive grains decreases gradually as the amplitude increases. Among them, when the amplitude is from 0 \(\upmu\)m to 10 \(\upmu\)m, the movement duration of the CBN abrasive grains decreases steeply, which is related to the decrease in the movement distance of the CBN abrasive grains as well as the increase in the velocity. As shown in Figure 15, the movement path of the CBN grains with metal fluid circumference is larger than that of the CBN grains applied by ultrasonic vibration. The velocity of the CBN abrasive grains with ultrasonic vibration is larger than that of the CBN abrasive grains without ultrasonic vibration. The combined effect of these two factors resulted in a steep reduction in the traveling time of the abrasive grains. When the ultrasonic amplitude gradually increases from 10 \(\upmu\)m to 40 \(\upmu\)m, the difference in the movement trajectory is not significant. Velocity is the main factor affecting the duration of the CBN grains. Therefore, with the increase in ultrasonic vibration amplitude, the moving speed of the CBN abrasive grains also increases gradually.