# Remaining Useful Life Prediction of Cutting Tools Using an Inverse Gaussian Process Model
## 3 Example Study
### Experiment  
Real milling experiments were performed to verify the availability and validity of the proposed approach by detecting tool wear condition. The experiment was performed on specimens of 7109 aluminum alloy by milling in the normalized state. The workpiece was cuboid with a 100-mm side length. The chemical compositions of the selected materials are specified in Table 1.  
The experiment was carried out using a flat-end milling cutter using coolant, and the characteristics of the tool are specified in Table 2. A five-axis DMG CTX gamma 2000 TC (Hamburg, Germany) with Numeric Control Siemens 840D sl (Munich, Germany) was used in the experiment. The cutting was conducted with the spindle speed of the cutter at 6000 r/min, a feed rate value of 2000 mm/min, and a cutting depth value of 1 mm. The cutter wear was measured using a Dino-Lite AM3113 microscopy system (AnMo, Shenzhen, China). The roughness of the machined surface was measured by the Mahr M1 surface roughness meter (Mahr GmbH, Esslingen am Neckar, Germany) after the cutting. The proposed approach was run on a server with a 2.40 GHz processor and 64 GB RAM.  
Milling from the lower edge of the workpiece to the upper edge of the workpiece was recorded as a cycle. After each cutting cycle, we stopped and collected the roughness data of the specimens. The roughness was measured on the flank face of the cutting surface four times, and the four measurements were averaged as the true roughness. Meanwhile, the tool wear was measured using a Dino-Lite microscopy system. The wear of tool and the roughness of workpiece were monitored and recorded, until the roughness deviated from the requirement value of 2 \(\upmu\)m. The experimental environments and measurements are shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Material** & & & & & \multicolumn{4}{c}{**Chemical Composition \%**} & \\ \hline
7109 & Si & Fe & Cu & Mn & Mg & Cr & Zn & Zr & Co & O & Ti \\
0.1 & 0.15 & 0.1 & 0.05 & 2.4 & 0.06 & 6.2 & 0.15 & 0.2 & 0.05 & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Chemical compositions of material of the cutting workpiece.  
Figure 6: Predicted value and actual value of URL with simulation data.  
Due to equipment and artificial measurement errors, there may be fluctuation errors in wear measurement results. To eliminate measurement errors, abnormal data were rejected, and the mean values of the normal data before and after were filled in. Then, the measurement data were smoothed. The tool-wearing curve is shown in Figure 8. Considering the high rate in the early stage and the severe wear in the later stage, the data of a stable wear period were applied for the modeling.  
In this experiment, it was assumed that the failure criterion of the tool is whether the surface roughness of the workpiece met 2 \(\upmu\)m. The former 40 cycles of cutting use were regarded as the historical data. The prediction results were not ideal, with a fixed failure threshold of 0.18 mm, as shown in Figure 9. Then, the failure threshold was set to [0.175 mm, 0.18 mm] and obeyed a uniform probability distribution. As shown in Figure 10,  
Figure 8: Tool-wearing curve.  
Figure 7: Experiment environment and measurement.  
the prediction results improved significantly compared to Figure 3. The PDF of the URL was drawn as shown in Figure 11.  
Figure 11: PDF of URL and its corresponding point estimation under variable degradation threshold.  
Figure 9: Predicted value and actual value of URL with fixed degradation threshold.