## 3 Results
### Acceleration Signal Properties  
Figure 9 shows the effect of wear on the acceleration spectrum. The shaft frequency is clearly visible in Figure 9a; \(GMF_{1}\) and \(GMF_{2}\) are visible in Figure 9a,b and all at the frequencies shown in Table 5. The shaft frequency dominates the spectrum of the ISM. However, with BBS, the shaft frequency is low. \(GMF_{1}\) is the dominant frequency. For both sensors, \(GMF_{2}\) is still visible. The amplitude of the higher \(GMF_{i}\) is too low compared to the rest of the spectrum to be visible. As wear progresses, the lower frequencies under 2 kHz increase the most. \(GMF_{1}\) and its sidebands almost double after 2 \(\times\) 10\({}^{5}\) cycles for the ISM. The sidebands reach almost half the intensity of the GMF. For the BBS, the increase of the \(GMF_{1}\) is even greater. However, the sidebands are less than half of the \(GMF_{1}\). Therefore, the sidebands relative to the \(GMF_{1}\) of the BBS are smaller than those of the ISM. In addition, two harmonics increase between the shaft frequency and the \(GMF_{1}\) at frequencies of 366.7 Hz and 550 Hz. The further increase up to 15.6 \(\times\) 10\({}^{5}\) cycles of the \(GMF_{i}\) and their sidebands is very small. Instead, the harmonics between the shaft frequency and the \(GMF_{1}\), which first increased, have now shifted from 366.7 Hz and 550 Hz to 200 Hz and 716.7 Hz, respectively. For both sensor types, it appears that the first GMF increases with wear but the second decreases. The amplitude of the measured acceleration by the ISM is generally much lower compared to the amplitude of the BBS. In the case of \(GMF_{1}\) and \(GMF_{2}\), the amplitudes of the ISM are about one tenth of the amplitudes of the two \(GMF_{i}\) for the BBS.  
An analysis of the amplitude of the \(GMF_{1}\) confirms these findings. Figure 10 shows that the acceleration amplitude at the \(GMF_{1}\) at 916.7 Hz increases for both gears and both sensor types (ISM, BBS). It shows that there are two phases. Up to about 2 \(\times\) 10\({}^{5}\) cycles, the amplitude increases steeply. After that, the amplitude remains approximately constant for the BBS. However, the amplitude of the ISM drops at the start of several two-hour sequences. This drop does not appear in the amplitude of the cepstrum which represents the sidebands. The amplitude of the ISM \(GMF_{1}\) is about a factor of 10 lower than the amplitudes of the BBS \(GMF_{1}\).  
Figure 9: Acceleration spectrum of gear 1: (a) ISM; (b) BBS.  
Figure 11 shows that the cepstrum of the \(GMF_{1}\) decreases first. After this first phase, the cepstrum starts to fluctuate and slowly decreases. The amplitudes of the ISM sideband are about a factor of 2 lower than the amplitudes of the BBS sideband. Therefore, the relative height of the sidebands to the GMFs is higher for the ISM than for the BBS. The failure of gear 2 is clearly visible as the amplitude of the \(GMF_{1}\) rapidly decreases and the amplitude of the sideband rises. Figure 12 shows the maximum amplitudes of the vibration signal. It can be observed that the amplitudes measured using the BBS are much higher. Due to an error while saving the data, the ISM data for gear 1 are missing from 0.6 \(\times\) 10\({}^{5}\) to 1 \(\times\) 10\({}^{5}\) cycles in Figures 10a, 11a and 12.  
Figure 11: Amplitude of the cepstrum of the first GMF: **(a)** ISM; **(b)** BBS.  
Figure 10: Amplitude of the spectrum of the first GMF: **(a)** ISM with the beginning of each two-hour sequence marked in black; **(b)** BBS.