## 3 Results and Discussion  
### Improvement of the LBFC Due to Longitudinal, Linear Beam Oscillation  
First part of this investigation deals with the proof of a process improvement using longitudinal, linear beam oscillation. The dependencies between oscillation frequency and amplitude to the three investigated characteristics-cutting speed, burr, and surface roughness-illustrate Figure 3. Linear interpolation generates tendencies between the data points. The color scale in the images contains the reference value for static beam shaping. Empty spaces of the area charts exhibit the limited amplitude as function of the frequency. Figure 3 depicts different effects of the used beam oscillation parameters on the cutting process for stainless and mild steel. For example, the beam oscillation improves cutting speed and burr formation of stainless steel at single amplitude-frequency-combinations Figure 3a,b. Whereas, cutting speed and burr changes continuously with increasing amplitude and frequency in case of mild steel (Figure 3d,e). A steady development of the surface roughness in dependence of the oscillation parameters is obvious for both steels (Figure 3c,f). In addition, the three characteristics improve, compared to their reference values for both steels. Similar oscillation parameter achieves a faster cutting speed for both steels. However, the oscillation parameters for reaching low burr height and small surface roughness are not identical for the two investigated materials. The best result for stainless steel cut with beam oscillation has 83% faster cutting speed and 30% less burr height compared to the reference sample. However, the average surface roughness rises by 25%. A star in Figure 3 distinguishes the corresponding oscillation parameters. In case of mild steel (Figure 3d-f), all three characteristics reveal a similar dependency on the oscillation parameters. Higher amplitudes increase the cutting speed and decreasing burr as well as surface roughness. The correlation with the oscillation frequency is reverse. An increasing frequency reduces the cutting speed. In addition, burr, as well as surface roughness, exposes a non-linear dependency at higher frequencies. Both parameters increase up to about 2 kHz and slightly decrease for higher frequencies. An improvement of all three characteristics achieves a frequency below 1 kHz in combination with more than 200 um amplitude. The best result for mild steel cut with beam oscillation accomplishes 500 Hz frequency combined with a 300 um amplitude. In fact, this beam oscillation parameters increases the cutting speed by 76%, with a decreased burr height (77%) and lower surface roughness (38%) compared to the reference sample. Figure 4 depicts the cut edges optimized by the used beam oscillation compared to static beam shaping. The oscillation parameters used for this purpose are marked with a star in Figure 3. The reference cuts of stainless (Figure 4a) and mild steel (Figure 4c) exhibit distinct burr heights. Another obvious difference between the samples cut with static beam shaping and beam oscillation is the cut edge appearance (striation curvature). The cut edges of the reference samples show striations with several directional changes, whereas beam oscillation creates rather straight striations. Figure 4: Cut edges of 12 mm stainless steel (**a** and **b**) and 12 mm mild steel (**c** and **d**) with static beam shaping (**a** and **c** are references) and longitudinal, linear beam oscillation (**b** and **d**) with the oscillation parameters marked as star in Figure 3.  
Figure 3: Contour plots of evaluated cutting results for cutting speed (**a**,**d**), burr height (**b**,**e**), and surface roughness (**c**,**f**) for 12 mm stainless steel (**a**,**b**,**c**) and 12 mm mild steel (**d**,**e**,**f**) as a function of frequency and amplitude using longitudinal, linear beam oscillation. The stars denote the best cutting result. The reference values (Ref) corresponds to the values obtained with static beam shaping.