# Gear Fault Detection Method Based on Convex Hull Clustering of Autoencoder's Latent Space
## 2 Materials and Methods  
### Experiment Setup  
The experiment was conducted on a power circulation test stand for cylindrical gear fatigue testing (Figure 1). The test stand consisted of two gear pairs--the tested (item no. 1) and the stand (item no. 2). These were connected to each other using shafts (items no. 3 and 4). The torque was provided by preload applied by the load clutch (item no. 5). The electric motor (item no. 6), with the aid of belt transmission (item no. 7), covered only the power losses and provided rotational speed. The stand gear pair was designed in such a way as to have a much greater service life than the tested gears to maintain durability over all tests. A piezoelectric accelerometer (item no. 8) mounted on the case of the tested gear was used for the vibration measurements. The tested gear pairs (Figure 2) were the helical gears, and the data are listed in Table 1. The gear teeth were manufactured with a worm-shaped tool on a Koepfer EMAG 200 CNC (Koepfer gruppe, Furtwangen, Germany) gear hobbing machine from 42 CrMo4 steel. The teeth surface profile was measured on a Mahr MarSurf GD 120 measuring machine (Mahr Federal Inc., Providence, RI, USA). Measured roughness  
In the experiment, two sets of gears were used. The first set, whose teeth had been gas-nitrided (surface hardness 600-750 HV), provided the necessary data for training and testing the neural network in normal operational conditions (without damage). The second gear pair, which was only quenched and tempered (surface hardness 28-30 HRC), was used to test the ability of the neural network to detect a failure. Table 2 provides the details of the load applied and the duration time of each load stage. There are various methods for measuring the pitting damage for quantitative evaluation such as the loss of mass of gears [24], tooth profile measurements [25], measuring the \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **Pinion** & **Gear** \\ \hline \hline \multicolumn{4}{c}{Geometry} \\ \hline Normal module, mm & & \(\text{m}_{\text{n}}=3\) & \\ Number of teeth & \(\text{z}_{1}=30\) & & \(\text{z}_{2}=47\) \\ Face width, mm & & \(\text{b}=30\) & \\ Helix angle, \({}^{\circ}\) & & \(\beta=22.482\) & \\ Normal pressure angle, \({}^{\circ}\) & & \(\alpha_{\text{n}}=20\) & \\ Profile shift & & x = 0 & \\ Axes distance, mm & & a = 125 & \\ Pitch diameter, mm & \(\text{d}_{1}=97.40\) & \(\text{d}_{2}=152.59\) \\ Tip diameter, mm & \(\text{d}_{21}=103.40\) & \(\text{d}_{22}=158.59\) \\ Root diameter, mm & \(\text{d}f_{1}=89.90\) & \(\text{d}f_{2}=145.09\) \\ \hline \multicolumn{4}{c}{Accuracy} \\ \hline Total profile deviation \(F_{\alpha}\), \(\mu\)m & 13.5 & 15.1 \\ Profile form deviation \(f_{\beta\alpha}\), \(\mu\)m & 11.6 & 8.4 \\ Profile slope deviation \(f_{\beta\alpha}\), \(\mu\)m & 5.3 & \(-12.3\) \\ Total helix deviation \(F_{\beta}\), \(\mu\)m & 12.3 & 14.1 \\ Helix form deviation \(f_{\beta\gamma}\), \(\mu\)m & 7.0 & 12.7 \\ Helix slope deviation \(f_{\beta\beta}\), \(\mu\)m & 9.5 & 17.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data of the tested gear pairs.