## 5 Experimental Research of the Planet Tooth Breakage
The frequency distribution of the simulated vibration signal in Figure 8 is similar to the experimental results in Figure 14c. One of the main difference between the experiment results in Figure 9 and the simulation results in Figure 8 is the effect of the gear mesh on the gearbox vibration. In the healthy gear simulation, the mesh impact is the only excitation source, and the damping is simplified, which make the low frequency region of the spectrum clean and the octaves of mesh frequency outstanding. In the experiment, other excitations, caused by shaft misalignment, bending, etc., exist at the same time, which reduce the effect of the gear mesh. Figure 15 shows the partial enlarged view of the spectra. It can be found that the carrier rotational frequency and the sun gear rotational frequency can be observed from the spectrum directly; however, the fault characteristic frequency cannot be observed from the low frequency region of the spectrum directly. According to the simulation results, demodulation is needed to detect the tooth breakage fault. Resonance demodulation analysis (DRA) is used here. At first, a band-pass filter is used to process the vibration signal with the frequency range chosen as 1700 to 2500 Hz, then the envelope spectrum of the filtered signal is calculated. Figure 9 shows the envelope spectrum of the three signals at 0 to 50 Hz. The rotational frequency of the carrier \(f_{c}=4\) Hz, the rotational frequency of the sun gear \(f_{s}=14\) Hz and their octaves can be found in all of these spectra. No other frequencies exist when the gear is healthy, shown as Figure 16a. For the half tooth breakage fault in Figure 16b, the fault characteristic frequency \(f_{p}=13\) Hz and its octaves can be clearly observed. For the whole tooth breakage fault in Figure 16c, a difference-frequency between \(f_{c}\) and \(f_{m}\) can also be found. Consequently, the simulation result that sum- and difference-frequency between \(f_{c}\) and \(f_{p}\) exist in the envelope spectrum of the fault gear vibration signal is validated by the experiment. Figure 11: Planet gears with: (**a**) half tooth breakage fault; (**b**) the whole tooth breakage fault. Figure 12: RMS of the experimental ring vertical acceleration varying with rotational speed. Figure 10: Structure of the test rig: (**a**) structure diagram, where G is the gearbox, M is the motor, V is the variable frequency drive, P is the signal pre-processors, C is the collector, 1 to 7 are sensors, 1 is the rotational speed sensor and 6 is the gearbox vertical acceleration sensor; (**b**) picture of the test rig. Figure 14: Spectrum of the experimental ring vertical acceleration of the (**a**) healthy gear, (**b**) half tooth breakage fault gear and (**c**) the whole tooth breakage fault. Figure 13: Envelope spectrum of the experimental ring vertical acceleration of the (**a**) healthy gear, (**b**) half tooth breakage fault gear and (**c**) the whole tooth breakage fault. Figure 16: Envelope spectrum of the experimental ring vertical acceleration of the (**a**) healthy gear, (**b**) half tooth breakage fault gear and (**c**) the whole tooth breakage fault. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \(C\) & \(f_{\mathbf{c}}\) & \(f_{\mathbf{s}}\) & \(f_{\mathbf{m}}\) & \(f_{\mathbf{p}}\) \\  & **(rpm)** & **(Hz)** & **(Hz)** & **(Hz)** & **(Hz)** \\ \hline
1 & 77 & 1.28 & 4.59 & 85.98 & 4.3 \\
2 & 117 & 1.95 & 6.98 & 130.7 & 6.53 \\
3 & 157 & 2.62 & 9.36 & 175.3 & 8.77 \\
4 & 197 & 3.28 & 11.7 & 220.0 & 11.0 \\
5 & 237 & 3.95 & 14.1 & 264.7 & 13.2 \\
6 & 277 & 4.62 & 16.5 & 309.3 & 15.5 \\
7 & 317 & 5.28 & 18.9 & 354.0 & 17.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of the planetary gear. Figure 15: Partial enlarged view of the experimental spectrum of the ring vertical acceleration of the (**a**) healthy gear, (**b**) half tooth breakage fault gear and (**c**) the whole tooth breakage fault.