## 4 Results and Discussion
### Tool Chatter Behavior in Micro-Milling  
Experiments and corresponding FE simulations of micro-milling with a DOC of 2 \(\mu\)m, a spindle speed of 12,000 r/min and a feed speed of 10 mm/s are conducted to investigate the tool chatter behavior. The variation in the simulated feed force with time in the micro-milling of the Cu workpiece is shown in Figure 4, which demonstrates that the feed force is irregular fluctuations. Figure 4c plots the corresponding experimental feed force-time curve within a time of 0.1 s, which indicates that the feed force shows long-range periodicities. Figure 4a,c indicate that the fluctuations of the simulated feed force and the experimental feed force are both in the range of \(-\)0.3 to 0.3 N, which also demonstrates the high prediction accuracy of the established FE model of diamond micro-milling. Figure 3: Schematic illustration of the tool chatter impact on the transient DOC in micro-milling. To reveal the intrinsic characteristics of tool chatter, Figure 4b,d present the amplitude-frequency of the simulated and experimental feed force by fast Fourier transform analysis (FFT), respectively. Figure 4b shows that the frequency of the simulated feed force is in the range of 0-80 kHz, with a peak at 3.33 kHz. Figure 4d indicates that the main frequency of the experimental feed force is 1.65 kHz, with a frequency range of 0-5 kHz. The differences in the fluctuation characteristics of the feed force between the FE simulation and experiment are mainly caused by the low sensitivity of the experimentally utilized dynamometer, which is insufficient to capture the tool chatter-induced feed force variations with a high frequency; similar conclusions have also been illustrated by [PERSON] et al. [22]. Figure 5 shows the FE simulation results of the milling process for the first two rotation cycles considering tool chatter. As shown in Figure 5a1, in the initial stage of the milling process, contact stress originates in the local contact area between the milling tool edge and workpiece. The transient DOC is the theoretical maximum value accompanied by the largest amount of material removal at this point of the initial contact between the milling tool and workpiece; thus, the milling tool deformation is the largest in the thrust direction. As shown in Figure 5a2, the material removal volume increases gradually with the feed of the milling tool, and chips start to form and subsequently flow along the rake face of the milling tool. Accompanied by the increase in the deformation and chatter of the milling tool, the stress concentration in the workpiece is also increased. As shown in Figure 5a3, with the further feeding of the milling tool, the accumulated chips are curled, and the tool chatter accompanied by the tool deformation causes irregular fluctuations on the machined surface morphology. Figure 5b1 shows the configuration of the milling tool cutting into the workpiece in the second rotation cycle in the milling process. The milling tool first contacts with both sides of the groove formed by the first rotation cycle, accompanied by stress concentrations formed on both sides. As shown in Figure 5b2, as the milling tool continues to feed, the material removal gradually increases, and chips are gradually formed after the tool cuts through the groove formed by the first rotation cycle. The machined surface morphology shown in Figure 5b3 demonstrates that the transient DOC has an increasing trend at first but then decreases when it reaches a critical value, at which point the milling tool rebounds  
Figure 4: Variation in feed force with time in (**a**) FE and (**c**) experiment simulation of micro-milling; FFT analysis of feed force in (**b**) FE simulation and (**d**) experiment. sharply due to the increased extrusion effect of the workpiece on the milling tool, resulting in a steep groove at the end of milling. Figure 6a,b show a chip profile obtained in the FE simulation and the experiment of diamond micro-milling of the Cu workpiece, respectively.