# Simulation Analysis of Nanosecond Laser Processing of Titanium Alloy Based on Helical Trepanning
## 3 Results and Discussion
### Experimental Results  
To verify the validity of the simulation model, a nanosecond laser (Light Conversion l17771) was used to process titanium alloy samples of 60 \(\upmu\)m under three sets of laser processing parameters. The three-dimensional micro hole's shape was measured by a confocal laser microscope (OLS4100, Olympus Corporation, Wenzhou, China). The measured  
Figure 8: Effect of scanning path on micro hole shape: (**a**) depth; (**b**) width.  
Figure 7: Effect of scanning speed on micro hole shape: (**a**) width; (**b**) depth.  
results were compared with the simulation results obtained under the same parameters. The parameters of the three simulation cases are shown in Table 2.  
The comparison diagram of actual processing results, simulation results and the three-dimensional scanning graph are shown in Figure 9. The simulation results showed that there was a bulge in the center of the micro hole's shape, which denoted the residual materials after laser processing. In actual processing, these residual materials will remain on the substrate due to the lack of support. There was an error of approximately 25% in the width direction, but the wall of the micro hole's shape and the radian at the laser inlet were similar, which could be caused by a machining mechanical error. For case c (Table 2), the radius of the outermost scanning path reached 116 \(\upmu\)m, but the actual diameter was only 96 \(\upmu\)m. This could be attributed to the scanning path deviation caused by an installation error of the machining platform. By comparing the combination of the simulated phase transition interface and the temperature gradient map with the actual machined 3D topography, it was found that the taper of the actual micro hole's shape was related to the thickness of the region from the solid-liquid transition line to the gas-liquid transition line in the simulated temperature gradient. This indicated that the taper of the micro hole's shape was caused by the flow of the molten metal that was not cooled down after the laser processing. This conclusion is consistent with the conclusion of [PERSON] et al. [21] obtained on the basis of experimental results of picosecond single-line repeated processing. They found that when the repeated time number reached a certain value, the increase in the processing times or energy density could lead to a rapid increase in the width, but the depth of the micro hole's shape would decrease gradually.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Serial Number** & **Power (W)** & **Scanning Speed** & **Path End Angle (\({}^{\circ}\))** & **Defocusing Distance** & **Pulse Repetition Rate (kHz)** & **Spot Size (\(\upmu\)m)** \\ \hline a & 18 & 2400 & 4.3 & 0 & 100 & 27 \\ b & 13.5 & 2400 & 5.3 & 0 & 100 & 27 \\ c & 13.5 & 2400 & 6.3 & 0 & 100 & 27 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental sample and the corresponding processing parameters.  
Figure 9: Comparison of the simulation and actual results under three laser parameter setups shown in Table 2. (**a**) No. a; (**b**) No. b; (**c**) No. c; (**d**) experimental results for the 3D micro hole’s shape.