## 4 Method Validations Using Simulations and Experiments
### Experiment Signal Analysis  
To verify effectiveness of the proposed method practically, experiments were conducted to collect signals under planet fault condition, as well as health condition. Laboratory experiments were conducted on a planetary gearbox test rig. Figure 16a,b shows its mechanical schematic. The test rig mainly includes driving motor, bevel stage, first and second  
Figure 14: CVS signal: (**a**) signal waveform; (**b**) envelope order spectrum. Figure 13: Raw simulation signal: (**a**) signal waveform; (**b**) envelope order spectrum. Figure 15: MED signal: (**a**) signal waveform; (**b**) envelope order spectrum. planetary stage, speed-up gearbox, and load motor. Experiments can be carried out on level stage and two planetary stage to explore fault mechanism and response of gears; speed-up gearbox is used to match running speed and torque between driving motor and load motor. Parameters of test rig are listed in Table 3.  
Fault-seeded and baseline experiments were conducted on the test rig, a broken plane gear is used to simulate planet gear damage on second planetary stage. The damaged planet gear is shown in Figure 17. Piece of planet gear tooth was cut off to imitate planet gear fault using wire-electrode cutting machine. Figure 18 shows the vibration sensors that were used to collect vibration signals during the test. Two sensors were installed on each planetary stage in vertical and horizontal direction, respectively. Sampling rate is 5.12 kHz. Signal collected in the vertical direction is used for further analysis; the sensor is highlighted with a red circle in Figure 18. Tachometer is located at the carrier shaft to collect once-per-revolution tachometer signal. During the experiments, driving motor running speed was 1200 r/min and torque is 41.2 Nm. Accordingly, rotating speed of second stage planet carrier was 30.10 r/min. For that, 198.4 s data were collected during each test. Shown in Figure 19 is vibration and tachometer signal from 4 to 20 s collected during a test. Figure 16: Planetary gearbox test rig: (**a**) test rig image; (**b**) test rig schematic diagram. Figure 17: Planet gear with tooth broken fault. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Bevel Stage** & **First Planetary Stage** & **Second Planetary Stage** \\ \hline
**Gear No.** & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 9 \\ Teeth number & 18 & 36 & 32 & 40(3) & 112 & 28 & 34(4) & 96 \\ Transmission ratio & 2 & & 4.5 & & & 4.4286 & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameters of test rig. Data manipulating process has been described step by step in detail when processing simulation signals. Demonstration of how signal changes after each step will not be covered in this section. We focus on comparison of signals under fault condition and health condition to validate effectiveness on fault diagnosis of planet gear, and then, VS method is used to process experimental data for a comparative study. DPT was set as 50 when resampling and processing experimental signals. Figure 20 shows raw experimental signal and its envelope order spectrum. The waveform of raw signal under health and fault condition tells no apparent difference caused by planet gear fault since heavy noise exists within the signal. The envelope order spectrum reveals that amplitudes at fault characteristic order and its multiples increases. However, the fault feature is very weak. Additionally, other frequency components interfere diagnosis of planet gear fault. Figure 19: Laboratory experiment signal. Figure 20: Raw signal: (**a**) health condition waveform, (**b**) health condition envelope order spectrum, (**c**) fault condition waveform, and (**d**) fault condition envelope order spectrum. Figure 21 shows the resultant signal using the proposed CVS-MED method. The collected data covers 97 full carrier cycles, and the P\({}_{\text{HTR}}\) is 17. As a result, MED signal covers 5 cycles of planet gear.