## 4 Results and Discussion  
### Cutting Force Signal and Feature Extraction  
The force signals in the process of continuous milling have been collected through Test I, and the force signal waveforms of three different tool wear states are shown in Figure 10. The spindle rotational period can be divided into two stages, as labeled in Figure 10, where Stage I is the cutting process of the cutter and Stage II is the idle process in which the cutter has been separated from the workpiece. Thus, the cutting force is nearly 0 N in Stage II. For the milling process, RMS of the cutting force in the feed direction and the vertical radial direction is extracted as the common feature. To create a dataset reflecting the statistical correlation with tool wear, cutting force signals are partitioned into segments with a length of six spindle rotational periods. Thus, 3500 samples corresponding to the 35 cuttings are obtained, including 1600 samples of initial wear, 1300 samples of middle wear and 600 samples of severe wear. The scatter of samples is shown in Figure 11 and parts of the cuttings are marked. Since the tool wear  
Figure 10: Raw cutting force signals in Test I: (**a**) force in feed direction under initial wear, (**b**) force in vertical radial direction under initial wear, (**c**) force in feed direction under middle wear, (**d**) force in vertical radial direction under middle wear, (**e**) force in feed direction under severe wear, (**f**) force in vertical radial direction under severe wear. values increase gradually from NO. 1 to NO. 35, the samples with different tool wear states highly overlap with each other. In addition, the tendency that the within-class scatter increases with tool wear is visible. Compared with the force signal waveforms in Test I, the cutting processes fill up the whole spindle rotational period since four cutters are used in Test II. The stages from I to IV, marked in Figure 12, correspond to cutting processes of four cutters, respectively. Without loss of generality, the same features with Test I are extracted. Due to the disturbance factors such as spindle runout, there is a difference in cutting force waveform between the cutting processes of different cutters, as shown in Figure 12. To eliminate the above influence, a sufficiently long sample length should be chosen. However, limited cutting force signals are collected in this test. Therefore, a proper balance should be struck between the sample length and the number of samples, and the length of a spindle rotational period is used for partitioning cutting force signals. As the result, 1080 samples corresponding to the 12 cuttings are obtained, the scatter of samples is shown in Figure 13 and parts of the cuttings are marked. The samples of NO. 1 to NO. 3 and NO. 9 to NO. 11, corresponding to initial wear, have a concentrated distribution in the bottom-left of Figure 13. The samples of NO. 4 to NO. 8 correspond to middle wear and the samples NO. 12 correspond to the severe wear. The tendency that the within-class scatter increases with tool wear appears again as shown in Figure 13. However, the samples corresponding to middle wear and severe wear are distributed in different regions because of different cutting parameters. For example, the samples of NO. 1 to NO. 3 (Test ID: A) and NO. 6 to NO. 7 (Test ID: B) are separated, for which both correspond to initial wear. In addition, the samples of NO. 4 (Test ID: A) and NO. 8 (Test ID: B) are separated, for which both correspond to middle wear. In Test III the force signals in five cutting processes including initial wear (NO. 1, NO. 2), middle wear (NO. 3, NO. 4) and severe wear (NO. 5) are collected, respectively. Figure 14 shows waveforms of three different tool wear states. It can be seen that no periodicity can be found from the cutting force waveforms of the turning process. Thus, features different from the milling process should be used. In this study, STD of the cutting force in the feed direction and the vertical radial direction is extracted as the common feature.