# A Simple Model to Predict Machined Depth and Surface Profile for Picosecond Laser Surface Texturing
## 3 Results and Discussion
### LST of Micro-Channels via Changing Scanning Speed  
In order to reduce the calculation time, the computational length of the micro-channel was chosen as 110 \(\upmu\)m, while the width was set as 60 \(\upmu\)m. The mesh sizes in both directions were set as 50 nm. The effect of scanning speed on the fabrication of the micro-channel was investigated using Equation (4) by changing scanning speed from 1 mm/s to 5 mm/s with a fixed adjacent interval of 3 \(\upmu\)m. For a fixed pulse energy of 8 \(\upmu\)J and an overscan number of 8, \(D_{\text{max}}(N)\) utilized was 0.50 \(\upmu\)m which was determined by linear fitting based on the ablation depths from 2 and 20 pulses. The scale factor \(k\) was equal to 1.5, which was obtained on the above simulation of micro-craters. The predicted depths were compared to the actual experimental results, as shown in Figure 5. As can be observed, excellent agreement is obtained for the predicted depths from 1 mm/s to 5 mm/s, and the error is negligible. A low scanning speed of 1 mm/s leads to higher overlapping of consecutive craters in longitudinal direction, resulting in a greater mean depth up to 11.1 \(\upmu\)m. Then, an increase in scanning speed from 1 mm/s to 5 mm/s significantly decreases the longitudinal overlap, leading to the decrease of the machined depth of the micro-channel.  
Figure 4: Comparison between experimental and predicted micro-craters for different pulses: (**a**) measured micro-craters, (**b**) comparison of cross-sectional profiles, and (**c**) predicted micro-craters.  
To show the advantage of the developed model, not only the machined depths of the created micro-channels but also the profiles were compared. The computationally predicted and experimental results of micro-channels with three different scanning speeds are presented in Figure 6. The experimentally measured surface topologies are shown in Figure 6a, while the predicted 3D channels are presented in Figure 6c. The comparison between the experimental and simulated cross-sectional profiles are plotted in Figure 6b. As the figure indicates, the machined depth of the micro-channel decreases with the increasing scanning speed, while the width keeps almost unchanged at around 50 \(\upmu\)m. The profile made with lower scanning speed has a shaper transition on the edges and has a higher aspect ratio. Moreover, the experimental and simulated profiles are in very close agreement for the scanning speed of 3 mm/s and 5 mm/s. However, for scanning speed of 1 mm/s there is a little discrepancy, which is likely due to the material redeposition resulting from heat accumulation at a high overlap. The random position of resolidification leads to the asymmetric profile at the bottom of the created micro-channel, as shown in the upper panel of Figure 6a,b.  
Figure 5: Effect of scanning speed on machined depth of micro-channels.  
Figure 6: The comparison between experimental and predicted micro-channels for different scanning speeds: (**a**) measured micro-channels, (**b**) comparison of cross-sectional profiles, and (**c**) predicted micro-channels.