## 3 Results and Discussion
### Metallographic Analysis of Mild Steel to Reveal the Thermal Energy Deposition
Compared with the static beam shaping, both the HAZ area and average recast layer width reduces at all oscillation parameters (see reference values in  
Figure 6: Microscopically images of polished and etched cross-sections of 12 mm laser beam fusion cut mild steel using different oscillation parameters: (**a**) 60 \(\upmu\)m amplitude and 250 Hz frequency; (**b**) 60 \(\upmu\)m amplitude and 4000 Hz frequency; (**c**) 500 \(\upmu\)m amplitude and 250 Hz frequency. Figure 7). The best cut quality (marked with a star in Figure 7) was achieved at frequencies below 1 kHz using amplitudes above 200 \(\upmu\)m. In this case, the HAZ area and the recast layer width decreases by 55% and 75%, respectively, compared to static beam shaping. According to the obtained results presented in Figures 3 and 7, two main effects were observed when using beam oscillation, compared to static beam shaping: (i) The cutting speed increases significantly and (ii) The cut edge quality improves considerable. A simplified model for the beam oscillation during LBFC suggests an explanation for both effects. Explanatory Approach of the Process Improvements Due to Beam Oscillation Based on an Energetic Consideration  
In fact, the cutting speed depends on the energy balance in the cutting process [15]. A change of the cutting speed at constant laser power requires a different energy deposition as function of time. Figure 8 illustrates which requirements beam oscillation meet to increase the cutting speed. In the case of static beam shaping, the energy deposits continuously while the laser beam passes once a certain position at a constant cutting speed. In contrast, with beam oscillation, the laser beam does not move uniformly. Furthermore, large amplitudes increase the interaction area of the laser beam with the material, compared to static beam shaping. This represents the beam diagnostic in Figure 8a,b. The indicated interaction area for beam oscillation (Figure 8b) is valid, when the measuring time is longer than one oscillation period. Figure 8c points out that the alternating laser beam velocity causes the intensity distribution of beam oscillation in Figure 8b. At the inflection points, where the oscillation speed is zero, the intensity is maximal. In addition, for large amplitudes, the laser beam reaches a higher velocity and the intensity distribution covers a larger interaction area during one oscillation period. The laser beam velocity also speeds up at an increasing frequency; however, the interaction area remains constant. Accordingly, not only does the cutting speed determine the interaction time of laser beam and material, but also the oscillation parameters. A low amount of laser energy deposits locally due to the fast laser beam velocity of beam oscillation. Thus, the complete melting of the material requires multiple passes over a certain position. The energy input is therefore gradual, instead of continuous as in static beam shaping. Figure 9 illustrates that by plotting both the local intensity profile as well as the energy deposition for a certain position along the cut path. Considered are the static beam shaping and three different beam oscillations, whereby the cutting speed and focal plane is equal within all four scenarios. The interaction time of the laser beam at a fixed position corresponds to the time until the intensity has dropped to zero. Figure 7: Contour plots of: (**a**) HAZ area; (**b**) Average recast layer width for 12 mm mild steel as a function of the oscillation frequency and amplitude. The stars denote the best cutting result. The reference values (Ref) correspond to the values obtained with static beam shaping. The shortest interaction time obtains static beam shaping in Figure 9a. In contrast, the combination of small amplitude and low frequency (Figure 9b) illustrates a cyclic time-dependency for the laser beam intensity. This causes a gradual energy input, and thus, a 15% longer interaction time compared with static beam shaping.