## 3 Results and Discussion
### Fast Fourier Transform (FFT) Analysis  
Acceleration signals acquired during machining were analysed in the frequency domain by applying a Fast Fourier Transform (FFT). This enables the determination of the frequencies at which the components of the vibration signal occur. This approach facilitates the detection of chatter vibration that is a potential risk during the milling process. The analysis was carried out for signals obtained when changing the cutting speed (Figures 13-15) and feed per tooth (Figures 16-18). Tooth passing frequencies and harmonics, which are multiplications of tooth passing frequencies, were marked on the obtained diagrams and are presented in Table 1.  
Figure 13: FFT for a cutting speed of (**a**) 400 m/min, (**b**) 600 m/min, (**c**) 800 m/min, and (**d**) 1000 m/min, applying the ER toolholder. Figure 14: FFT for a cutting speed of (**a**) 400 m/min, (**b**) 600 m/min, (**c**) 800 m/min, and (**d**) 1000 m/min, applying the shrinkfit toolholder. Figure 15: FFT for a cutting speed of (**a**) 400 m/min, (**b**) 600 m/min, (**c**) 800 m/min, and (**d**) 1000 m/min, applying the hydraulic toolholder. On the waveforms achieved for milling with the ER toolholder (Figure 13), the largest peaks occurred at frequencies corresponding to harmonics. These are multiples of the tooth passing frequencies, which correspond to the considered cutting speeds, namely, 265, 398, 531, and 663 Hz, respectively. At a lower cutting speed \(v_{c}\) = 400-600 m/min, an initial decrease in harmonics amplitude height was observed, followed by a subsequent increase. This indicates some instability in the process and a tendency towards self-excited vibration. At a higher cutting speed \(v_{c}\) = 800-1000 m/min, harmonics were gradually extinguished, but the amplitudes at other frequencies also increased. However, their values were not very high, so machining can be considered fairly stable. When increasing cutting speed, the amplitude of vibration magnitude also increased. Figure 16: FFT for a feed of (**a**) 0.05 mm/tooth, (**b**) 0.1 mm/tooth, (**c**) 0.15 mm/tooth, (**d**) 0.2 mm/tooth, (**e**) 0.25 mm/tooth, and (**f**) 0.3 mm/tooth, applying the ER toolholder. The harmonics were dominant again when machining was performed with the tool clamped in the shrinkfit toolholder (Figure 14), except \(v_{c}\) = 800 m/min, where the passing frequency had the highest peak. Their amplitudes gradually decreased at higher frequencies. The exception was the harmonics at \(v_{c}\) = 400 m/min, where the amplitudes again increased around 3 kHz, but the increase was relatively slight. Within the range \(v_{c}\) = 800-1000 m/min, peaks also appeared at frequencies other than the harmonics and their values were lower than the harmonics. However, they were higher than the results obtained when using the ER holder. There was no clear effect of changing the cutting speed on the magnitude of the vibration as the maximum amplitudes were comparable at cutting speeds \(v_{c}\) = 600 and 1000 m/min, which may be associated with the fact that these speeds were in the unstable machining area of the SLD. The amplitude decreased at \(v_{c}\) = 800 m/min, as that speed was at the limit of the stable machining area. Figure 17: FFT for a feed of (**a**) 0.05 mm/tooth, (**b**) 0.1 mm/tooth, (**c**) 0.15 mm/tooth, (**d**) 0.2 mm/tooth, (**e**) 0.25 mm/tooth, and (**f**) 0.3 mm/tooth, applying the shrinkfit toolholder. In the case of the hydraulic toolholder (Figure 15), the greatest difference could be seen at the lowest cutting speed, where the number of frequencies at which chatter occurred was considerably higher compared to the other toolholders. This indicates a fairly high susceptibility to the chatter vibration occurrence. Machining stability considerably improved at the other cutting speed \(v_{c}\), where vibration occurred at fewer frequencies and was gradually weakened. At a cutting speed \(v_{c}\) = 800-1000 m/min, amplitudes at