## 3 Results and Discussion
### Metallographic Analysis of Mild Steel to Reveal the Thermal Energy Deposition
This effect is significantly more predominant at higher amplitudes (Figure 9c). At a cutting speed comparable to static beam shaping (0.5 m/min), the interaction time extends to 253%. The fast laser beam motion for high oscillation frequencies (Figure 9d) has a similar interaction time as shown in Figure 9b. However, it creates a more homogenous intensity profile, comparable to static beam shaping. Static beam shaping has the lowest interaction time in Figure 9 and reaches the slowest cutting speed in Figure 3a. Beam oscillation with 500 \(\upmu\)m amplitude and 250 Hz frequency exhibit the longest interaction time and achieves the fastest cutting speed (see Figure 3a). As the total amount of energy deposition is equal for all charts in Figure 9, a correlation is suggested between interaction time, the corresponding pulse-like intensity profile, and the resulting cutting speed. Figure 8: Beam diagnostic visualizes the interaction area and average intensity distribution of: **(a)** Static beam shaping; **(b)** Linear beam oscillation; **(c)** The laser beam velocity is constant for static beam shaping and alternates in case of longitudinal, linear beam oscillation. Figure 9: Schematic comparison of the local intensity profile and energy deposition for one certain material position along the cut path as function of the time for: **(a)** Static laser beam shaping; and different values of the longitudinal, linear beam oscillation parameters: **(b)** 60 \(\upmu\)m amplitude and 250 Hz frequency; **(c)** 500 \(\upmu\)m amplitude and 250 Hz frequency; **(d)** 60 \(\upmu\)m amplitude and 4000 Hz frequency. All axes of the four charts are scaled equally. Cutting speed and focal plane are constant and heat conduction and melt ejection have been disregard. To increase the cutting speed, more material has to melt per time. This requires high heat conduction rates through the melt film up to the solid phase. Heat conduction depends mainly on the material constants, the temperature difference within the melt film, and the melt film thickness. The laser beam affects only the latter two. Increasing the temperature difference and decreasing the melt film thickness raises the heat conduction rate. According to the state of the art, a pulsed energy deposition is a common way to achieve a high heat conduction rate combined with minimized heat conduction losses for LBFC of thin sheets [43]. Because beam oscillation creates a similar intensity sequence as a pulse regime (Figure 9), similar effects to the cutting process are also expected. One is an improved heat conduction rate. Beam oscillation is assumed to generate this by a significant volatile temperature profile, with high peaks, but also frequent heat dissipation. This enables a thin, but punctually hot melt film with high heat conduction rate, which in turn enables the obtained high cutting speeds (see Figure 3). Further investigations have to confirm this assumption by analyzing the temperature profile during the cutting process. The second effect to explain is the considerable improved cut edge quality at high amplitudes. The high heat conduction rate in combination with the extended interaction time for optimized beam oscillation parameters (Figure 9c) is expected to improve the melt ejection. Indications deliver the HAZ and recast layer analysis (Figure 7). Previous investigations obtained burr-free and smooth cut edges when the material has a small HAZ and recast layer width [3; 11; 19; 42]. Furthermore, for static beam shaping, the HAZ area decreases, whereas the recast layer width grows at an accelerating cutting speed [11; 19; 42; 44; 45; 46]. However, referring to the results shown in Figures 3 and 7, a significant correlation has been observed between the amplitude, cutting speed, HAZ area, burr height, and surface roughness for beam oscillation. The average recast layer width decreases with an increasing amplitude, respectively, cutting speed. This is contrary to static beam shaping. Again, the interaction time is the cause.