## 4 Results and Discussions  
### Rolling Element Analysis  
Two identical tapered roller bearing with different induced faults were used in this setup. The first roller bearing was damaged on its both outer races and the second roller bearing was scuffed on the roller surface as shown in Figure 5. Each scuffed roller was placed in one of the bearing races. The recorded signal from these bearings was also expected to be contaminated with some noise originating from the AC motor, pulley, belt and other nearby bearings used in the test-rig itself. The characteristic frequencies of the rolling element used for the experiments using the customised test rig at the University of Birmingham are summarised in Table 1.  
Figure 4: The radial vibration sensor installed near the planetary gear on the left and both axial and radial vibration sensors installed on the generator drive end on the right.  
Figure 5: The induced scuffing on the bearing outer race (**left**) and the roller (**right**).  
In each case, it is expected to observe the presence of the bearing characteristic frequency corresponding to the induced fault. In the case of the first bearing, the Ball Pass Frequency of Outer race (BPFO) is expected to be dominant. For the second bearing, the Ball Spin Frequency (BSF) that indicates the frequency of which the roller is turning can be used to identify the fault. However, as the rollers turn, the scuffed area will hit both the inner and outer race in each revolution. Thus, the observed defect frequency is expected to be twice the BSF frequency.  
The Cyclic Spectral Coherence was calculated over 4 s of the vibration data. As it can be seen in Figure 6, the BPFO frequency is clearly visible. Alongside the BPFO frequency, some modulations at the BSF frequency are also present which indicate damage in the rolling elements. This was confirmed by inspection of the rollers after testing. The outer race damage and heavy load on the bearing caused the surface of the rollers to degrade. However, the degradation was not significant.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Speed**} & \multicolumn{4}{c}{**Characteristic Frequency (Hz)**} \\ \hline
**PRM** & **Hz** & **FTF** & **BPFO** & **BPFI** & **BSF** \\ \hline
600 & 10 & 4.4 & 92.3 & 117.7 & 40.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the characteristic frequencies of the rolling element used for the experiment. Here, FTF stands for Fundamental Train Frequency, BPFO and BPFI are Ball Pass Frequency of Outer and Inner race respectively; and BSF is Ball Spin Frequency.  
Figure 6: Cyclic Spectral Coherence of the first bearing; top figure shows the BPFO frequency (92.4 Hz) and the BSF (\(\sim\)38 Hz) modulation and the bottom figure shows a slice of the top figure at 7.5 kHz.  
Similar to the first bearing, 4 s of vibration data were recorded from the second bearing and then used to calculate the Cyclic Spectral Coherence as shown in Figure 7.  
As it was mentioned earlier, the fault frequency (2 \(\times\) BSF) was observed in the Cyclic Spectral Coherence. However, unlike the first bearing frequency, it was more spread across the frequency spectrum. This could have been caused due to two damaged rollers or slight change in the bearing speed during the test arising from the load imposed.  
As it can be seen in Figure 7, the fundamental train frequency (4.4 Hz) is also very dominant. This was assumed to be due to the interaction between the damaged roller and the cage. However, after inspection, it was found that one of the damaged rollers led to fracture of the cage of the second bearing.