## 5 Experimental Signal Analysis
### Sun Fear Fault  
Experimental Signal Analysis  
Sun gear wear signals are analyzed to verify that the spectral analysis can be used to diagnose faults in planetary gearboxes using the theoretical derivation, and to show the effectiveness with which faults are detected and located for different operating conditions. Artificially seeded wear simulates local gear damage and the spectral peaks are assessed using the characteristic frequency. For all cases, the meshing frequency \(f_{m}\) is dominant at 1200 rpm, and \(f_{m}+2f_{s}-f_{H}\) is dominant at other input speeds.  
Figures 20-22 show the time domain waveform and the frequency domain spectra of the wear signals for different input speeds and output loads. The dashed lines show the meshing frequency and  
Figure 21: Waveform for a broken sun gear, Fourier spectrum and enlarged Fourier spectrum for an input speed of 2100 rpm and a load of: (**a**) 32 N-m, (**b**) 56 N-m and (**c**) 80 N-m.  
Figure 22: Waveform for a broken sun gear, Fourier spectrum and enlarged Fourier spectrum for an input speed of 3000 rpm and a load of: (**a**) 32 N-m, (**b**) 56 N-m and (**c**) 80 N-m.  
For a health signal, the illustrations show that there are some sidebands at frequencies of \(f_{m}\pm kf_{s}\) and \(f_{m}\pm kf_{s}\pm f_{H}\) (where \(k\in Z\)), but their amplitude is small. Gear production and gearbox assembly involve errors that result in sidebands, even for normal gears.  
Compared to the health signal for 1200 rpm and loads 32 N-m, 56 N-m and 80 N-m, the vibration signal for sun gear wear has different frequency domain spectra, as shown in Figure 20. The spectral peaks occur at the same frequencies of \(f_{m}\pm kf_{s}\) and \(f_{m}\pm kf_{s}\pm f_{H}\) (where \(k\in Z\)) as those for the health signal. The meshing frequency (\(f_{m}\)) is 216 Hz, the distributed damage frequency of sun gear (\(f_{s}\)) is 18 Hz and the rotating frequency of the planet carrier (\(f_{H}\)) is 2 Hz. The amplitude of the characteristic frequency and the corresponding sidebands increase significantly with sun gear wear, so this study uses sidebands to detect gear faults, rather than the meshing frequency \(f_{m}\) and rotation frequency of the planet carrier minus and plus the meshing frequency \(f_{m}\pm f_{H}\).  
Figure 20 shows an enlarged image of the Fourier spectrum for a wear signal. The sidebands at frequencies of \(f_{m}-f_{s}-f_{H}\), \(f_{m}-f_{s}\) and \(f_{m}-f_{s}+f_{H}\) have much larger amplitudes than those for the health signal, so the gearbox is faulty, and the wear is on the sun gear.  
For a vibration signal of less than 2100 rpm and loads of 32 N-m, 56 N-m and 80 N-m, the meshing frequency (\(f_{m}\)) is 378 Hz, the distributed damage frequency for the sun gear (\(f_{s}\)) is 31.5 Hz and the rotating frequency of the planet carrier (\(f_{H}\)) is 3.5 Hz. The sidebands at frequencies of \(f_{m}+f_{s}-f_{H}\), \(f_{m}+f_{s}\) and \(f_{m}+f_{s}+f_{H}\) have larger amplitudes than those of the health signal, as shown in Figure 21.  
For a vibration signal of less than 3000 rpm and loads of 32 N-m, 56 N-m and 80 N-m, the meshing frequency (\(f_{m}\)) is 540 Hz, the distributed damage frequency for the sun gear (\(f_{s}\)) is 45 Hz and the rotating frequency for the planet carrier (\(f_{H}\)) is 5 Hz. The sidebands at frequencies of \(f_{m}-f_{s}-f_{H}\) and \(f_{m}-f_{s}+2f_{H}\) have significantly larger amplitudes than those of the health signal, as shown in Figure 22.