# Gear Fault Detection Method Based on Convex Hull Clustering of Autoencoder's Latent Space
## 2 Materials and Methods
### Experiment Setup
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{4}{c}{**Gear Pair I (Quenched and Tempered + Gas-Nitrided)**} \\ \hline \hline \multirow{2}{*}{**Load Stage**} & **Pinion Torque,** & **Pinion Revolutions,** & **Number of Pinion** & **Load Stage** \\  & **Nm** & **rev/min** & **Load Cycles** & **Duration Time** \\ \hline
0 & 42 & 2500 & \(1.5\cdot 10^{5}\) & 1 h \\
1 & 455 & 2500 & \(1.5\cdot 10^{6}\) & 10 h \\
2 & 455 & 2500 & \(1.5\cdot 10^{6}\) & 10 h \\
3 & 455 & 2500 & \(1.5\cdot 10^{6}\) & 10 h \\
4 & 455 & 2500 & \(1.5\cdot 10^{6}\) & 10 h \\
5 & 455 & 2500 & \(1.5\cdot 10^{6}\) & 10 h \\
6 & 455 & 2500 & \(1.5\cdot 10^{6}\) & 10 h \\
7 & 455 & 2500 & \(1.5\cdot 10^{6}\) & 10 h \\
8 & 455 & 2500 & \(1.5\cdot 10^{6}\) & 10 h \\ \hline \hline \multicolumn{4}{c}{**Gear Pair II (Quenched and Tempered Only)**} \\ \hline \hline \multirow{2}{*}{**Load Stage**} & **Pinion Torque,** & **Pinion Revolutions,** & **Number of Pinion** & **Load Stage** \\  & **Nm** & **rev/min** & **Load Cycles** & **Duration Time** \\ \hline
0 & 42 & 2500 & \(1.5\cdot 10^{5}\) & 1 h \\
1 & 138 & 2500 & \(2.5\cdot 10^{6}\) & 16 h 40 min \\
2 & 244 & 2500 & \(2.5\cdot 10^{6}\) & 16 h 40 min \\
3 & 342 & 2500 & \(2.5\cdot 10^{6}\) & 16 h 40 min \\
4 & 455 & 2500 & \(2.5\cdot 10^{6}\) & 16 h 40 min \\
5 & 455 & 2500 & \(2.5\cdot 10^{6}\) & 16 h 40 min \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Load stages for the tested gear pairs. particles in oil [26], or the use of image processing [27] and vision measurements [28]. In this paper, after each load, the stage gears were inspected for any sign of damage. If failure occurred, it was captured as a photograph, and then the image was processed to evaluate the percentage area of pitting damage. The details of the image processing algorithm for the calculation of the percentage area of pitting are given in [29]. For gear pair I, no sign of damage was detected. A macro photograph of the tooth surfaces after the eighth load stage is shown in Figure 3.  
The pitting rate for the quenched and tempered gear pair (gear pair II) after each load cycle is presented in Figure 4.  
The first sign of failure occurred after the second load stage on the pinion tooth surfaces. Next, the pitting progressively increased, leading to heavy damage to surfaces after the fifth load stage (Figure 5). Figure 4: Percentage damage of tooth surface after each load stage for gear pair II (quenched and tempered only). Figure 3: Macro photograph of tooth surfaces of the gas-nitrided gear pair (gear pair I) after tests: (**a**) pinion tooth surface; (**b**) gear tooth surface. More information about this kind of damage and the nature of pitting formation can be found in [29]. Moreover, at the beginning and end of each load cycle, the horizontal (perpendicular to the plane of the shaft) vibrations of the tested gear case were acquired with the aid of a 3-axis piezoelectric sensor (PCB Piezoelectric ICP 356B21) and data acquisition module (National Instruments NI9234). The sampling frequency was 25 kHz while the signal duration was 1 s, which gives 25,000 samples for each measurement.