# Real-Time Estimation for Cutting Tool Wear Based on Modal Analysis of Monitored Signals
## 3 Experimental Study
### Feature Extraction of Test Data  
A cutting test is one of the frequently used methods to monitor tool condition in the milling process. With the increase of tool wear, the cutting edge is passive and inevitably leads to the change of cutting vibration. As there are many reasons affecting the milling process, the milling vibration is not stable especially with wearing condition increment, but both of them have a larger correlation. In many components of cutting vibration, the influence of tool wear on the vibration is obvious. Anyhow, the cutting vibration increases with cutting tool wear despite some fluctuation. It is mainly related to some factors such as material properties, built-up edge, and measurement error that accumulate in the cutting process. However, the influence on the overall upward trend of cutting vibration is small. By analyzing vibration signals of training set in the milling process, we find that its amplitude increases with wearing stage, which can be used as a characteristic for tool condition analysis. Decomposing signals and obtaining IMFs, we plotted the frequency spectrums of IMFs. What is interesting in these frequency spectrums of the first IMF, called IMF1, is the phenomenal change of amplitude in three frequency bands at the different stage. It is obvious that frequency amplitude increases with wearing stage as the tool is not sharp between 11.2 KHz and 11.4 KHz approximately. The peak located at 16 KHz is always existed and the peak between 17 KHz and 19 KHz is in the middle and late processing. Figure 5 shows frequency domain analysis for the first IMF of cutting vibration in different tool stages. Figure 5a is the cutting vibration in \(X\) direction at the initial stage. \begin{table}
\begin{tabular}{c c c c} \hline
**Groups** & **In \(X\) Direction** & **In \(Y\) Direction** & **In \(Z\) Direction** \\ \hline
1 & 0.9605 & 0.9574 & 0.9337 \\
2 & 0.9328 & 0.9278 & 0.9467 \\
3 & 0.9370 & 0.9406 & 0.9220 \\ \hline \end{tabular}
\end{table} 
Table 1: Correlation coefficients for vibration with tool wear. Figure 4: Vibration signals of tool in the milling process. Figure 5b is cutting vibration in \(X\) direction at the middle stage. Figure 5c is cutting vibration in \(X\) direction at the late stage. A possible explanation for the trend may be that the tool wear changes its natural mode of vibration in the first intrinsic mode function between 11.2 KHz and 11.4 KHz, so amplitude varies with the tool wear. The peak located at 16 KHz, is probably related to resonant frequency of sensor, so there is no significant change in amplitude. The peak between 17 KHz and 19 KHz may be related to the different stages of tool wear. It can be seen from the frequency spectrum that the energy between 11.2 KHz and 11.4 KHz is distributed at the early stage of tool cutting with less amplitude, while the energy widely concentrates in between 11.2 KHz and 11.4 KHz at the late stage with more amplitude, therefore the frequency band is extracted to estimate tool wear. In future work, studies about other frequency bands will be considered. To show the feature trend with the number of milling significantly, feature value Gn is introduced in this paper, that can be calculated using  
\[Gn(j)=\sum_{f=11.2\text{ K}Hz}^{f=11.4\text{ K}Hz}A_{j}(f)\ \ j=1,2,\cdots,P \tag{15}\]  
where \(j\) is the number of cut, and P = 315 in Figure 6. \(A_{j}(f)\) shows the frequency spectrum amplitude of IMF1 decomposed from vibration signals at the \(j\)th milling in \(f\) Hz. The results obtained from preliminary calculation of Gn in the milling process are shown in Figure 6. In spite of the fluctuations in the amplitude, the amplitude of Gn is expected to continue increasing with time in the milling process, and the results of the correlational analysis between Gn and the tool wear show that there is a high correlation between the feature value and the tool wear. Figure 5: The first IMF frequency spectrum of vibration signals at the different stage.