# Simulative and Experimental Investigation of Vibration Transfer Path at Gearboxes
## 5 Results and Discussion
### Experimental Results
The gravitation and amplitude modulation cannot affect this signal. Figure 9 shows the frequency spectrum of the signal after post-processing. The amplitude at 8.3 Hz decreases from 7.8 mm/s\({}^{2}\) (Figure 8) to 1.3 mm/s\({}^{2}\) (Figure 9), which means that the effect of the gravitation is eliminated. Additionally, the peaks beside the gear mesh frequency also become smaller. To evaluate a good position of the sensors for condition monitoring, the peak-to-mean ratios of the signals from the sensors at the pinion and at the housing are evaluated at different rotational speeds and an applied torque of 500 Nm. Further data on this test are listed in Table 3. The peak-to-mean ratio can be presented as the peak-to-mean value, calculated with Equation (1). As shown in Table 3, the peak-to-mean value of the signal after post-processing is larger than the signal from Channel 2 because the gravitation and sideband of the gear mesh frequency are eliminated through post-processing. The peak-to-mean value from Channel 1 is larger than the post-processing signal because Channel 1 meas  
Figure 10: The schematic representation of the positions and measurement directions of the accelerometers on the pinion also depicted in Figure 7a. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **500 rpm** & **1000 rpm** & **1500 rpm** & **2000 rpm** & **2500 rpm** & **3000 rpm** \\ \hline Channel 1 & 132 & 707 & 176 & 159 & 53 & 93 \\ Channel 2 & 7 & 87 & 42 & 47 & 24 & 52 \\ Signal after post-processing & 89 & 583 & 147 & 134 & 32 & 31 \\ Channel 4 & 7 & 156 & 128 & 190 & 43 & 170 \\ Channel 5 & 16 & 183 & 158 & 236 & 154 & 369 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Peak-to-mean values of signals from different sensors at 500 Nm and different rotational speeds (dimensionless ratio). the radial and tangential accelerations. Hence, this signal has a larger amplitude at the gear mesh frequency. Additionally, the peak-to-mean values of the signals from both housing sensors have an increasing trend when the rotational speed increases. The reason for this can be explained in Figures 11 and 12. Figure 11 shows the frequency spectrum of the signal from the housing sensor at 500 rpm. The amplitude at the gear mesh frequency (183.9 Hz) is 0.036. This value is much smaller than 0.745, which is the amplitude at the gear mesh frequency (916.8 Hz) at 2500 rpm, as shown in Figure 12. At the same time, the vibration of the housing sensor with the Outer Race Defect frequency does not change as much as the vibration with the gear mesh frequency, when the rotational speed increases from 500 rpm to 2500 rpm. That means that, at a high rotational speed, the vibration of the housing with the gear mesh frequency can be more dominant than the other noise. To compare the peak-to-mean ratios from the rotating sensors at the gear and housing sensors, the value r is calculated through Equation (14), and the peak-to-mean values from Table 3 are used. \[r=\frac{\text{peak}-\text{to}-\text{mean}(\text{signalafterpostcessing})}{ \text{peak}-\text{to}-\text{mean}(\text{signalfromhousingsensorofpinionshaft})} \tag{14}\]  
Figure 11: Frequency spectrum of signal from housing sensor (pinion shaft) at 500 rpm and 500 Nm. Figure 12: Frequency spectrum of signal from housing sensor (pinion shaft) at 2500 rpm and 500 Nm. The calculated values \(r\) at different rotational speeds and a constant torque are shown in Figure 13. The larger this ratio \(r\) rises, the greater the peak-to-mean ratio of the signal from the rotating sensor. As shown in Figure 13, this ratio decreases when the rotational speed increases. This means that the rotating sensor at the gear for condition monitoring has an advantage at low rotational speeds. When the rotational speed is large, the housing sensor probably has better performance relative to the cost of implementation.