## 4 Results and Discussion
### Classification of Tool Wear Condition for Various Cutting Paths and Sensor Directions  
Based on the analyses results in previous sections, a simple linear classifier is developed to verify the cutting path effect on the performance of a monitoring system and to investigate the benefits we could obtain by increasing the sample signal length. By considering the effect of the changing cutting direction with different cutting paths, four models were independently developed, based on each type or direction of the sensor signal. A total of 3 sets of signals collected in the straight line cutting condition were used to train and generate the model. The signals obtained from 2 sets of tests other than those used for training the model were used to verify the system, including all three types of cutting paths. The classification rates of tool wear corresponding to vibration signals in the three directions and AE signals are shown in Tables 2 and 3. The results illustrate that the classification rates for the cases with square and circle cutting are far lower than the results for the case with straight line cutting. This result are in good agreement with the signal feature analysis based on the scatter index J and could support the conclusions that the characteristics of cutting motion in the circle and square cuttings are different from the one (straight line cutting) used for developing the linear classification model. Moreover, the Z-direction vibration signal was observed to exhibit a higher capability for monitoring tool wear with the lower cutting path effect. This might be caused by the change in direction of the cutting in the circle or square path, leading to the lowest impact in the Z-direction (out of plane); the results match well with the observations in Figures 6 and 7. When considering the differences between the vibration and the AE signals, a lower classification rate for the AE signal than for the vibration signal was observed. This might be caused by the features of the signal varing randomly due to paramters other than the cutting path change. In the previous discussion, the increase in the sampled signal length could increase the value of the scatter index J and reduce the cutting path effect on the vibration signal. The classification rate for all three types of cutting paths, with various sampled signal lengths, is shown in Table 4. Four levels of sampled signal lengths were used in this study, including 0.017 s, 0.27 s, 0.82 s, and 2.18 s. for vibration signals and 0.015 s 0.22 s, 1 s, and 1.75 s. for the AE signal. The difference between the chosen signal length is caused by the different sampling rates and the easy operation of transforming the time domain signals to the frequency response. The results, as shown in Tables 4-6, demonstrate that \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Bandwidth Size** \\ **1200 Hz** \\ \end{tabular} } & \multicolumn{3}{c}{**Straight Line**} & \multicolumn{3}{c}{**Square**} & \multicolumn{3}{c}{**Circle**} \\ \cline{2-10}  & & & & & & & & \\ \hline \multirow{2}{*}{\begin{tabular}{c} **Data Length** \\ **0.27 s** \\ \end{tabular} } & \multirow{2}{*}{**Sharp**} & \multirow{2}{*}{**Worn**} & \multirow{2}{*}{**Average**} & \multirow{2}{*}{**Sharp**} & \multirow{2}{*}{**Worn**} & \multirow{2}{*}{**Average**} & \multirow{2}{*}{**Sharp**} & \multirow{2}{*}{**Worn**} & \multirow{2}{*}{**Average**} \\ \cline{1-1}  & & & & & & & & \\ \hline \multirow{2}{*}{\begin{tabular}{c} **X axis** \\ **Y axis** \\ \end{tabular} } & 89 & 100 & **93** & 75 & 100 & **88** & 69 & 100 & **84** \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} **Y axis** \\ \end{tabular} } & 86 & 100 & **93** & 31 & 100 & **66** & 38 & 100 & **69** \\ \hline \multirow{2}{*}{
\begin{tabular}{c} **Z axis** \\ \end{tabular} } & 100 & 100 & **100** & 94 & 100 & **94** & 94 & 100 & **97** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Tool wear classification rate with various axis vibration signals (model trained by line data).