# Simulation Analysis of Nanosecond Laser Processing of Titanium Alloy Based on Helical Trepanning
## 3 Results and Discussion
### Simulation Results
#### 3.2.4 Effects of Processing Parameters on Micro Hole  
The effect of the laser power on the micro hole was analyzed by changing the laser power from 15 W to 17.5 W while keeping the other parameters unchanged. The time-varying curves of the micro hole depth and width at different laser powers are presented in Figure 5. As shown in Figure 5, when the laser power reached the ablation threshold, the depth of the micro hole increased with the laser power, but its width increased only slightly. This shows that increasing the laser power can increase the material removal speed in the depth direction and only slightly affect the width direction. This is because the energy of the Gaussian beam is concentrated in the center of the laser spot, and changing the energy will have a greater impact on the energy peak of the center of the laser spot and a smaller impact on the energy of the spot boundary. The influence of different laser powers on the material temperature distribution at the same laser processing time is shown in Figure 6. The green line indicates the isotherm of the melting temperature (1670 k) of the material, and the material between the isotherm and the dark blue (air) is the material still in the molten state at the current time. It can be seen from Figure 6 that the thickness of the molten pool near the center of the spot at 17.5 W laser power was slightly thinner than that at 15 W laser power. This happens because the laser power at 17.5 W makes the removal speed of the material in the center of the spot greater than that at 15 W. There is not much difference in the thermal diffusion rate between the two because the center temperature is close to the evaporation temperature of the material.  
Figure 4: Fluid velocity change with laser processing time: (**a**) \(t\) = 0.034961 ms; (**b**) \(t\) = 0.10367 ms.  
The laser scanning speed effect was examined by changing the scanning speed from 1200 mm/s to 3600 mm/s while keeping the remaining parameters unchanged. Figure 7 shows the time-varying curves of the depth and width at different scanning speeds. As shown in Figure 7, with the increase in the scanning speed, the width of the micro hole increased, but the depth of the micro hole decreased slightly. This was because when other conditions remained the same, the increase in the scanning speed reduced the beam overlapping of the laser on the material surface and the removal rate. At the same time, the decrease in the laser energy density on the micro hole wall reduced the increase in width caused by the thermal effect.  
Figure 5: Effect of laser power on the micro hole: (**a**) width; (**b**) depth.  
Figure 6: Simulation results for the temperature and micro hole shape at \(t\) = 0.12 ms under different laser powers: (**a**) 15 W; (**b**) 17.5 W.  
The effect of the scanning path was investigated through simulations under the same simulation conditions, and the same initial position of the scanning path, by changing the end path position from 70 \(\upmu\)m to 110 \(\upmu\)m of the scanning radius. Figure 8 shows the time-varying curves of the depth and width for different scanning path ends. The results indicated that with the increase in the path length, the final width of the micro hole's shape increased, while the depth of the increasing speed of the micro hole's shape decreased. This was because, with the change in the end position of the path, the final position of the laser processing also changed, which increased the final forming width. As the path became sparse, the laser energy density acting on the material decreased, which reduced the removal speed in the depth direction.  
According to the above simulation data, the formulas related to the increase in speed of micropore width and depth, power and scanning speed were fitted. The specific formulas are as follows:  
\[V_{w}=-32.6857P+194.1667V+8.3333 PV+30.4457\frac{P}{V}, \tag{7}\]  
\[V_{h}=-21.6571P-352.500V+29.3333 PV+53.8971\frac{P}{V}. \tag{8}\]