## 3 Fault Diagnosis Method of Planet Gear Based on CVS and MED
### Continuous Vibration Separation for Planet Gear  
Vibration separation technique is a signal processing algorithm to separate dynamic responses of each gear using an extracting and mapping strategy. It takes advantage of the modulation effect to extract a segment of signal for each planet gear when planet gear meshes at the sensor and mapping the signal segments back to normal tooth number order according to mapping index. There are 3 stages in VS: acquisition/interpolation, extraction, and assembly. The acquisition/interpolation stage encompasses the synchronously collected vibration data and tachometer data, divides vibration data into each shaft cycle according to the tachometer data, and then interpolates data after filtering. Extraction stage extracts a predetermined number of data points from every shaft cycle according to extraction index, which presents the moment when planet gear is aligned with the vibration sensor. The extracted data are stored in a structured matrix called the assembly family. Assembly stage recovers dynamic responses of each gear component by assigning a mapping index to the extracted data in assembly family. The mapping index depends on the planet gear tooth engaged in meshing at the time when the data are extracted. Similar to TSA, the dynamic responses  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c} \hline \hline
**Carrier Cycle** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** & **13** & **14** & **15** & **16** & **17** & **18** & **—** \\ \hline \multirow{4}{*}{**Tooth**} & P1 & **8** & 2 & 30 & 24 & 18 & 12 & 6 & 34 & 28 & 22 & 16 & 10 & 4 & 32 & 26 & 20 & 14 & **8** & **—** \\  & P2 & **32** & 26 & 20 & 14 & 8 & 2 & 30 & 24 & 18 & 12 & 6 & 34 & 28 & 22 & 16 & 10 & 4 & **32**  
recovered using VS covers a full cycle of planet gear. Detailed and step by step procedure can be found in Refs. [31; 32; 33]. Since result of VS contains only one cycle of dynamic responses of the planet gear, fault-induced impulses, if exists, will appear only once in the resultant signal of VS, which brings in inconvenience for further signal processing and fault detection. To address this problem, a continuous vibration separation method is proposed to separate dynamic responses of planet gear while keeping signal periodicity. Figure 7 shows procedure of CVS where similar to VS, 3 stages (namely, acquisition and resampling, extraction, and MCT (mapping, combining, and TSMA)) are included in CVS. In first stage, vibration signal is resampled to eliminate speed fluctuations after filtering. The vibration signal must be collected with tachometer signal synchronously. Additionally, resampling rate \(L\) should be an integer multiple of ring gear tooth number for data extraction and mapping in the following stages. Second stage of CVS is data extraction. A series of window functions are used to extract data segments that are less modulated by the planetary movements from the resampled signal. Two parameters should be deliberated, namely, window center and window width. In terms of window center, several alternative approaches were given in Refs. [13; 33; 35]. In terms of window width, a large window width is not suitable since modulated signals will be extracted, but it must be wide enough to cover all planet gear teeth. In Table 2, half of the planet gear tooth aligns with the sensor while the other half does not. The window width should be larger than \(N_{p}\)/P\({}_{\text{HTR}}\). Last stage of CVS mainly consists of mapping, combining, and TSMA (MCT). Detailed process of MCT can be found in Ref. [23]. MCT rebuilds dynamic responses of planet gears by mapping the extracted data segments to Assembly Holding Matrix (AHM), then combination signal is constructed by lining up signals rebuilt from each AHM, and after that, TSMA is applied to combination to depress noises and asynchronous signal components within combination signal, which helps highlight fault-related signals.