## 5 Experimental Signal Analysis
### Comparison of an Accelerometer and an Embedded Sensor  
To verify the accuracy of the embedded sensor, the gearbox housing contains a commercially available wired accelerometer as a vibration reference index, as shown in Figure 17. The wired accelerometer specifications are shown in Table 6.  
The spectrum for the three-axis vector measurement is not significantly different for the Y direction, so a planetary gearbox with sun gear wear is used, and the test rig uses an input drive motor at 1200 rpm and a load motor at 80 N-m.  
The gearbox is run for a time and a segment of vibration signal is collected. Figure 18 shows the time domain and frequency spectrum for the signal in the wired accelerometer and the embedded sensor. The signal for the wired accelerometer has a larger amplitude than that for the embedded sensor, possibly because the wired accelerometer is attached to the surface of the gearbox and the gearbox is sufficiently rigid that the surface amplitude is greater than the amplitude inside. The root mean square (RMS) and peak values are calculated using the time domain signal and are used to determine the condition of the gearbox. The RMS value is 0.258 g, and the peak value is 1.619 g for the wired accelerometer. The RMS value is 0.233 g, and the peak value is 1.393 g for the wireless embedded sensor. These results show that the error in the RMS value is less than 10%, and the error in the peak value is less than 14%. The Fourier spectrum shows that the theoretical meshing frequency for this scenario is 216 Hz, and there is a significant peak in both spectra. The error for the wired accelerometer is 0.032 Hz, and the error for the embedded sensor is 0.861 Hz.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sun Gear Teeth Number** & **Planet Gear Teeth Number** & **Ring Gear Teeth Number** & **The Number of Planet Gears** \\ \hline
12 & 47 & 108 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters for the planetary gearbox.  
Figure 16: Different faulty gear in the gearbox: (**a**) sun gear; (**b**) planet gear; (**c**) ring gear.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Meshing Frequency**} & \multicolumn{3}{c}{**Rotating Frequency**} & \multicolumn{3}{c}{**Distributed Damage**} & \multicolumn{3}{c}{**Local Damage**} \\ \cline{2-9}  & **Sun** & **Carrier** & **Planet** & **Sun** & **Ring** & **Planet** & **Sun** & **Ring** \\ \hline
216 & 20 & 2 & 4.6 & 18 & 2 & 4.6 & 54 & 6 \\ \hline
378 & 35 & 3.5 & 8 & 31.5 & 3.5 & 8 & 94.5 & 10.5 \\ \hline
540 & 50 & 5 & 11.5 & 45 & 5 & 11.5 & 135 & 15 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Values of characteristic frequencies (Hz).  
The time domain and spectrum are similar for the signal in the wired accelerometer and the embedded sensor. Any difference is due to an error in the placement position, the stability of the test rig and the sampling frequency rate difference. The signal analysis for the embedded sensor in the Y direction is used to validate that the spectral analysis can be used to diagnose planetary gearbox faults using the theoretical derivation.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Parameter Value** \\ \hline Model & 356A15 \\ \hline Supply Voltage & 20 to 30 VDC \\ \hline Input Range & \(\pm\)50 g \\ \hline Sensitivity & 100 mV/g \\ \hline Broadband Resolution & 0.0002 g rms \\ \hline Resonant Frequency & \textgreater{}25 kHz \\ \hline \hline \end{tabular}
\end{table}
Table 6: Wired accelerometer specifications.  
Figure 17: Planetary gearbox sensor locations.  
Figure 18: Waveform and Fourier spectrum signal for a wired accelerometer and an embedded sensor.  
Data are logged on an Internet database file, as shown in Figure 19. When the recording stops, the uploading button is used to run the script to upload the measurement data. An offline analysis uses PC data-log text files or Internet database files.