## 5 Novel Proposed Method Application for Planetary Gearbox Fault Diagnosis  
In this section, for the novel method application, experimental signals are collected from a lab planetary gearbox test rig with implanted wear tooth faults on the sun, planet and ring gear. Figure 19 illustrates a schematic of the experimental planetary gearbox test rig. It includes a single-stage planetary gearbox, a 4-kW three-phase asynchronous motor for driving the gearbox and a magnetic powder brake for loading. The motor speed can be adjusted for different values. The load can be adjusted by a brake controller through the current of the magnetic powder brake connected to the output shaft (carrier). The NI data acquisition system consists of four IEPE accelerometers (Dytran 3056B4, Dytran Instruments Inc., Fraser, MN, USA), PXI-1031 mainframe, PXI-4472B data acquisition cards and LabVIEW software (National Instrument Inc., Austin, TX, USA). In addition, a tachometer and torque sensor is installed in the input shaft for acquiring the speed and load information. The single-stage planetary gearbox consists of the sun gear, planet gear and fixed ring gear. The sun gear is connected to the input shaft and rotates around its own center. All planet gears mesh simultaneously with the sun gear and ring gear. These planet gears not only rotate around their own centers, but also revolve around the center of the sun gear, and vibration signals picked up by a fixed sensor attached to the planetary gearbox housing differ significantly from that of fixed-axis/parallel gear systems [32]. Compared to the fixed-axis gearbox test rig in Section 4, all of the settings are the same, except the gearbox type. Single-stage planetary gearbox gear parameters are listed in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline
**Gear** & **Sun** & **Planet** & **Ring** & **Planet Number** \\ \hline Teeth number & 13 & 64 & 146 & 3 \\ \hline \end{tabular}
\end{table} 
Table 2: Gear parameters of the single-stage planetary gearbox. Figure 17: (**a**) Squared envelope spectrum after the sixth DC offset cancellation; (**b**) time-frequency contour of the squared envelope signal after the sixth DC offset cancellation. Figure 18: (**a**) Envelope spectrum of the time synchronous signal; (**b**) time-frequency contour of the envelope signal of the original signal. Wear gear faults of the planetary gearbox were implanted in one tooth of the ring gear, planet gear and sun gear, respectively, in order to validate the proposed analysis method. Figure 20 illustrates the implanted gear faults. Tooth wear faults belong to localized fault, and their fault frequencies can be calculated through the following equations [33]. The meshing frequency for the stationary ring gear \(f_{\text{mesh}}=f_{\text{carrier}}\times Z_{\text{ring}}\) equals the product of the planet carrier rotating frequency \(f_{\text{carrier}}\) and the number of ring gear teeth \(Z_{\text{ring}}\). Relative rotating frequency with respect to the planet carrier is \(f_{\text{relative}}=f_{\text{mesh}}/Z\), where \(Z\) is the total number of teeth of the gear of interest. The characteristic frequency of faulty planet gear is \(f_{\text{planet}}=f_{\text{mesh}}/Z_{\text{planet}}\), where \(Z_{\text{planet}}\) is the number of planet gear teeth. If the damage exists on both sides of the gear tooth, the damaged planet gear tooth also meshes with the other mating gear. The characteristic frequency of the faulty planet gear becomes \(f_{\text{planet}}=2\times f_{\text{mesh}}/Z_{\text{planet}}\). The characteristic frequency of the faulty sun gear equals the relative rotating frequency of the sun gear multiplied by the number of planet \(\text{gears}f_{\text{sun}}=N_{\text{planet}}\times f_{\text{mesh}}/Z_{\text {sun}}\), where \(Z_{\text{sun}}\) is the number of sun gear teeth and \(N_{\text{planet}}\) is the number of planet years. The characteristic frequency of the faulty ring gear is \(f_{\text{ring}}=N_{\text{planet}}\times f_{\text{mesh}}/Z_{\text{ring}}\).