# Investigations into the Recognisability of Gear Damage
## 3 Data Analysis
### Recognisability of Gear Damage in the Time Domain
Noticeably, the block from \(S_{1}\) to \(S_{1}\) shows a very high overall correlation. This can be explained by the more distinctive, recurring vibration signal that occurs due to the damage. Furthermore, the blocks between \(S_{3}\) and \(S_{4}\) to \(S_{1}\) show very low correlations overall and thus little similarity to the vibration signal of the damaged meshing. A slightly increased similarity occurs between \(S_{2}\) and \(S_{1}\). In order to make a better statement about the behaviour of the individual damage classes in relation to each other, the correlation coefficients of the individual blocks are averaged. Furthermore, these correlation matrices are determined for all investigated rotational speeds. These matrices are also averaged. Figure 10 shows the correlation matrices of the measurements of the gearbox with damage at gear \(z_{1}\) (left) and gear \(z_{3}\) (right) averaged over the speeds. In addition, the mean correlation coefficients are shown in the blocks. The main diagonals of both correlation matrices show the highest values of the respective damage levels in this observation. This can be explained by the high similarity of the periodically occurring gear meshing. Overall, the mean correlation coefficients of the gearbox with damage to gear \(z_{1}\) show significantly higher correlation coefficients than those of the gearbox with damage to gear \(z_{3}\), due to the longer signal length caused by the slower rotational speed. For the correlation matrix of the measurement series on the gearbox with damage to \(z_{1}\), it can be seen that the damage level \(S_{1}\) clearly distinguishes itself from the others. It shows an increased correlation of 0.71 to the signals among each other. Furthermore, \(S_{1}\) clearly differs from \(S_{0}\), \(S_{3}\) and \(S_{4}\). The slight similarity of \(S_{2}\) to \(S_{1}\) indicates that the damage level \(S_{2}\) also exhibits recognisable characteristics. The damages \(S_{3}\) and \(S_{4}\) show the highest similarity to the reference signal \(S_{0}\). From this it is concluded that these two signals do not show clear distinguishability and thus the damage level cannot be detected. The correlation matrix of the measurement series on the gearbox with damage to \(z_{3}\) shows a comparable pattern. Here, especially damages \(S_{1}\) and \(S_{2}\), stand out from the other damages and show an increased correlation to each other. Furthermore, damage \(S_{1}\) shows the highest correlation among the signals, due to the distinctive signal behaviour already recognised in the spectrograms. Since damages \(S_{3}\) and \(S_{4}\) show the greatest similarity to the reference signals \(S_{0}\), no distinguishability of the damages appears to be possible. Overall, based on this investigation, damages \(S_{1}\) and \(S_{2}\) show a recognisable behaviour in the time domain for both gears, since they stand out due to their increased correlation  
Figure 10: Maximum correlation coefficients of the cross-correlation for the gearbox with damage to gear \(z_{1}\) (**left**) and for the gearbox with damage to \(z_{3}\) (**right**) averaged over equal damage sizes. Figure 9: Maximum correlation coefficients of the cross-correlation of all signals for the gearbox with damage at gear \(z_{1}\). to each other and also due to their lower correlation to damages \(S_{3}\) and \(S_{4}\), as well as the signals of the intact tooth meshing \(S_{0}\).