## 4 Milling Cutter Wear Experiment and Analysis of Recognition Results  
The milling cutter wear experiment was conducted on a vertical CNC milling machine, using an uncoated high-speed steel end mill with a straight shank. The geometric parameters of the milling cutter are shown in Table 1. The workpiece was made of 45 modulated steel, measuring 100 mm \(\times\) 100 mm \(\times\) 80 mm. To effectively capture the vibration signals during milling, an accelerometer was mounted on one side of the workpiece. A Dytran 3097A2 model accelerometer, with a range of \(\pm\)50 g and sensitivity of 100 mV/g, was selected to collect vibration signals in the X, Y, and Z directions. The accompanying SIRIUSi 8 XACC data acquisition card was used, with a sampling rate set to 10,000 Hz. The digital microscope consists of an LED light source, a 0.7\(\times\) to 5\(\times\) parfocal lens, and a charge-coupled device camera. The magnification ranges from 20\(\times\) to 180\(\times\) with a working distance of 105 mm. It is used to measure the central width of the main rear face of milling cutters. The milling tool wear experiment setup is shown in Figure 10.  
Figure 9: The structure diagram for recognizing the wear state of milling cutters under variable conditions based on optimized SDP. Under dry cutting operations, experiments were conducted under six different conditions, with a full lifecycle wear experiment for the milling cutter in each condition, as shown in Table 2. To gather data related to the evolution of cutter wear states, signals were collected online, and wear was measured offline. The experiment used peripheral milling along the X-axis direction of the milling machine, with each cut spanning 100 mm. After every ten cuts, the wear of the milling cutter was measured to ensure the collected vibration signals corresponded to the cutter's wear state. Due to the potential for installation state changes when the tool is removed, wear measurement was conducted on the machine. The primary flank wear volume of the milling cutter was assessed to evaluate the tool wear state, calculating the difference between the initial and current values in the central zone of the blade's flank as the current wear volume for that blade. The average current wear volume of the three blades was determined as the current wear volume \(VB\) of the milling cutter. According to the machining handbook, \(VB\) less than 0.05 mm indicates the initial wear stage, between 0.05 to 0.3 mm indicates normal wear, and more than 0.3 mm indicates severe wear. The new milling cutter and three different states of worn milling cutters are shown in Figure 11. Taking condition 1 as an example, the milling cutter wear curve is shown in Figure 12. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Case** & \(a_{\text{P}}\) **(mm)** & \(a_{\text{e}}\) **(mm)** & \(f_{\text{z}}\) **(mm/z)** & \(v_{\text{e}}\) **(m/min)** \\ \hline
1 & 5 & 0.3 & 0.15 & 23 \\
2 & 4 & 0.3 & 0.07 & 17 \\
3 & 3 & 0.5 & 0.07 & 23 \\
4 & 5 & 0.5 & 0.03 & 29 \\
5 & 4 & 0.4 & 0.03 & 23 \\
6 & 3 & 0.2 & 0.03 & 17 \\ \hline \end{tabular}
\end{table} 
Table 2: Milling process parameters. Figure 10: Milling tool wear experiment setup. This experiment is able to collect vibration signals from the X, Y, and Z axes of the workpiece. After data processing, the SDP transform is used to merge the multi-channel signals into a visual image, which intuitively represents the characteristics of the three-axis vibration signals. This approach leverages the complementarity and redundancy among the signals to better characterize the information related to tool wear. The SDP transformation effect is limited by the preset parameters: the number of mirrors \(m\), the lag coefficient \(l\), and the aperture gain \(\xi\), where the number of mirrors \(m\) depends on the number of merged signals, thus \(m=3\), making the starting angles \(\Theta^{\prime}\) of the vibration signals in the X, Y, and Z directions \(120^{\circ}\), \(240^{\circ}\), and \(360^{\circ}\), respectively.