## 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  
From the temperature field and flow field analysis, it can be seen that the metal in the melt pool is completely melted after t = 100 ms and starts to form a more stable convection flow. In the actual laser cladding process, the number of abrasive grains on a single 2D cross-section is small. To make the simulation representative, the number of grains is increased in the particle tracking module, so that it can include the movement of most grains. The laser cladding process adopts the coaxial feeding method, and the CBN abrasive  
Figure 10: The velocity distribution of molten metal in the direction of the depth of the melt pool. Figure 9: The velocity distribution within the melt pool. grains and the metal bond powder are mixed, so the release form of the CBN abrasive grains is selected to be randomly distributed in the particle tracking module. The release time of the abrasive grains is chosen to be t = 100 ms. The boundary condition of the CBN abrasive grains with the boundary of the printing layer is set to be adhesion, while the boundary condition with the bottom of the melt pool is set to be rebound. 1. The CBN abrasive grain movement behavior analysis without ultrasonic vibration Under the condition of no ultrasonic vibration assistance, the CBN abrasive grains in the melt pool start to move under the joint action of their gravity, the buoyancy force of the molten metal, and the drag force, formed by the flow of the molten metal. As shown in Figure 10(a), when t = 100 ms, the CBN abrasive grains were released into the molten metal in the melt pool, and the position of the grains showed a random distribution. Then, the CBN abrasive grains started to move under the action of the three forces, as shown in Figure 10(b). To observe the moving direction of different CBN grains, the point style in the particle trajectory is changed to \"comet tail\", and the length of the comet tail also reflects the size of the CBN grain velocity. From Figure 10(b), it can be seen that the CBN abrasive grains located near the boundary of the printing layer have larger velocities, while those located at the bottom of the melt pool have the smallest velocities. The CBN abrasive grains move following the two molten metal circumfluences, which suggests that the molten metal flow dominates the dragging force of the CBN abrasive grains. As the flow proceeds, the CBN abrasive grains eventually accumulate on the boundaries on both sides of the printing layer, while there is no abrasive grain distribution on the top of the printing layer, as shown in Figure 10(c). Figure 11: The CBN abrasive grain movement at different moments without ultrasonic vibration: (**a**) the initial stage; (**b**) the movement stage; (**c**) the final stage. 2. The effect of ultrasonic amplitude on the movement behavior of the CBN abrasive grains in the melt pool Under the premise of unchanged laser power, scanning speed, and ultrasonic vibration frequency, the ultrasonic vibration amplitude was changed to observe the CBN abrasive grain movement pattern and the arrangement. Five sets of process parameters as shown in Table 8 were selected for simulation. The amplitude of ultrasonic vibration cannot be set directly in the software, so the amplitude needs to be converted into acceleration by Equation (9). \[a_{z}=4\pi^{2}f^{2}A\] (9)  
Firstly, ultrasonic vibration with an amplitude of 10 \(\upmu\)m was applied to the model, and the movement state of the CBN abrasive grains in the melt pool at different moments is shown in Figure 12. The CBN abrasive grains were randomly released at t = 100 ms. At this time, the CBN abrasive grains in the melt pool are subjected to the force generated by the ultrasonic vibration in addition to the gravity, buoyancy, and drag forces. As shown in Figure 12b, the CBN abrasive grains start to move.