## 4 Results and Discussion
### Sensitivity Analysis of Signal Features to Tool Wear  
The frequency response of the X\(-\)direction vibration signal corresponding to three types of cutting paths, with a 0.27-s sampling length, is shown in Figure 11, along with the corresponding scatter index J calculated for each frequency (bandwidth 60 Hz) based on 5 sharp and worn datasets. The frequency domain feature with the higher index value J will be considered more sensitive to the tool condition change and is usually selected as the input vector for the designed classifier. Based on the analysis in Figure 11, the frequency features which hold the highest sensitivity to the increase in tool wear in each type of cutting path were observed to be different from each other. For example, in the case of straight line cutting, the energy of the frequency features at 2.4 kHz, 4 kHz, and 5.6 kHz for the worn tool case is higher than for the sharp tool case (Figure 11a). In contrast, the energy of features at 1 kHz, 4.2 kHz, and 5.8 kHz collected from the worn tool examples are lower than for the sharp tool samples. However, this result will not match the cases in the square and circle path cutting conditions, except for features higher than 5.4 kHz. In the frequency range lower than 3.2 kHz, the features in straight line cutting have a relatively higher-value scatter index J (Figure 11b) than in the square and circle path cutting situations. In contrast, the high-frequency features play a much more important role in detecting tool conditions in the square and circle path cutting conditions, and they might also be good features, since the scatter value in the high-frequency range is also sufficiently high in the straight line cutting situation. These results suggest that selecting the lower frequency features as the input to the classifier, based on the results obtained from straight line cutting, will lead to failure in monitoring the tool wear condition when the cutting path consists of all three types of cutting paths. The frequency response of the AE signals and the scatter index J for each frequency feature is also investigated and is shown in Figure 12. Different from the vibration signal in the x-direction, the patterns of its energy distribution over the frequency for three types of cutting paths are similar to each other. The AE signal energy concentrates on the frequency range from 50 kHz to 220 kHz for all three types of cutting paths. By investigating the scatter index for each frequency feature, the one located around 170 kHz has the highest value J for all types of paths. These results suggest that the AE signal features might not be significantly affected by changing the cutting paths compared to the vibration signals. Figure 10: Time domain AE signal: (**a**) sharp tool; (**b**) worn tool. Figure 11: Frequency domain vibration signal in the x-direction and scatter index for sharp and worn tools: (**a**) frequency domain signals; (**b**) classification index J (60 Hz). Figure 12: Frequency domain AE signal and classification index for sharp and worn tools: (**a**) frequency domain signals; (**b**) classification index J (6 kHz). by the variation material propety, tool-material engagement, and machine tool peformance, not by the cutting path direction change. For the frequency features, the bandwidth chosen to generate them is usually expected to affect their sensitivity to the monitoring target and the noise/disturbance. Therefore, the effect of the bandwidth size for frequency features on the scatter index is analyzed here. An example of the frequency response of an X-direction vibration signal, with bandwidth sizes of 150 Hz and 300 Hz, is shown in Figure 15. The corresponding scatter-index J of each frequency feature calculated, based on repeated tests, is shown in Figure 16. By investigating the index J for all three types of cutting paths, shown in Figure 16, no significant change could be observed when changing the bandwidth of the frequency features from 150 Hz to 300 Hz.