# Investigations into the Recognisability of Gear Damage
## 2 Experimental Setup
### Synthetic Gear Damage  
For the investigations into the recognisability of damage levels, four teeth of each two gears were artificially damaged. Gears \(\text{z}_{1}\) (14 teeth) and \(\text{z}_{3}\) (11 teeth) of the gearbox were examined. Four teeth of the two gears were damaged with synthetic flank damage. For gear \(\text{z}_{1}\), teeth 1, 4, 7 and 10 and for gear \(\text{z}_{3}\), teeth 1, 3, 6, 9 were damaged. This synthetic flank damage was realised by removing parts of the tooth flanks. Here, the damage size was iteratively reduced so that the transition from recognisable to non-recognisable damage could be examined through the damage levels. Each of the gears were inserted into a new gearbox to ensure that only the influence of the specific gear occurs in the vibration signal. The respective gears were operated with the test rig from Figure 1. The single pitch deviation was used as a way of measuring the magnitude of the synthetic damage levels. Single pitch deviation is a common metric for gear measurement according to DIN 3960 [16]. The single pitch deviation \(f_{\text{p}}\) is shown in Figure 3.  
The circular pitch of a gear results from the pitch diameter \(d_{\text{t}}\) and the number of teeth \(n_{\text{z}}\) according to \(p_{\text{t}}=\frac{\pi d_{\text{t}}}{n_{\text{z}}}\). The single pitch deviation \(f_{\text{p}}\) describes the difference between the circular pitch \(p_{\text{t}}\) and the real pitch [18]. The single pitch deviation of the measured gears is given in \(\upmu\)m. The values of the four teeth of each gear were determined via a tactile gear measurement. Table 2 shows a listing of the measured deviations for both the synthetic damaged gears. In addition to the four damage levels \(S_{1}\)-\(S_{4}\), the average deviation of an intact gear \(S_{0}\) of the same type without damages is given as reference. \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & \(\text{z}_{1}\) & \(\text{z}_{2}\) & \(\text{z}_{3}\) & \(\text{z}_{4}\) \\ \hline Module [mm] & 3 & 3 & 4 & 4 \\ Total profile deviation [\(\upmu\)m] & 47.3 & 48.6 & 41.3 & 36.6 \\ Single pitch deviation [\(\upmu\)m] & 20.3 & 18.3 & 14.0 & 27.6 \\ Adjacent pitch deviation [\(\upmu\)m] & 35.3 & 31.1 & 27.7 & 39.8 \\ Total pitch deviation [\(\upmu\)m] & 28.7 & 56.4 & 19.9 & 74.8 \\ Accuracy grade (ISO1328-1 [15]) & 11 & 9 & 9 & 11 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of gear measurement of an intact gearbox. Figure 3: Circular pitch \(p_{\text{t}}\) and single pitch deviation \(f_{\text{p}}\) of a gear according to [17]. Since gears have a periodic meshing behaviour, signal changes in the vibration signal caused by damage also occur periodically. Figure 4a shows the theoretical occurrence of damage for gear \(z_{1}\) with 14 teeth (damage to teeth 1, 4, 7 and 10) and Figure 4b shows that for gear \(z_{3}\) with 11 teeth (damage to teeth 1, 3, 6 and 9). The period \(T_{z_{1}}\) in which the gear has rotated once results from the geometry of the gear and the rotational speed of the input shaft \(\omega(t)\). For gear \(z_{1}\), the period in seconds is given by \(T_{z_{1}}=60/\omega(t)\). For gear \(z_{3}\), the calculation for the period \(T_{z_{3}}\) additionally contains multiplication with the gear ratio \(i_{1}\), since the gear is on the second gearbox stage. Since the frequency of occurrence in the damaged tooth meshes depends significantly on the rotational speed, different speed levels were examined for each gearbox as part of these investigations. Figure 5 shows the speeds used and the theoretical occurrence of the damage. The gearbox is used to drive a chain transport floor. Preliminary investigations have shown that the rotational speed is in a range between 100 and 400 rpm. In addition, it has been shown that the rotational speed changes only very slowly during operation. Based on