## 2 Modulation Effects and Dynamics Symptom of Planet Gear Fault  
### Vibration Transfer Paths and Modulation Effect in Planetary Gearbox  
Usually, vibration sensors are mounted on the gearbox casing. When the planetary gearbox runs, planet gears will not only move around sun gear but also rotate around their own center. As a result, the position of the planet meshing area changes periodically relative to the vibration sensors, which will bring in modulation effect in the monitoring signal caught by vibration sensors. As shown in Figure 1, there are three dominate paths for vibration signals to transfer from planet-ring gear meshing area to accelerometer sensor. Vibration signal transfers to sensor directly in path 1. Undeniable, vibration signal could also transfer to sensor through the major arc, but the signal caught by sensor is much weaker apparently. In path 2, vibration signal firstly transfers to planet-sun meshing area, after transferring back to planet-ring meshing area that is closest to the sensor (as point B shown in Figure 1), vibration signal transfers to sensor eventually. Path 3 is more complicate, vibration signal transfers to planet carrier through gear body of planet gear, planet gear bearing, planet bearing shaft, after transferring back to planet-ring meshing area, which is closest to the sensor (as point B shown in Figure 1), through a reversed path, vibration signal transfers to sensor eventually. There are also other potential paths to transfer vibration signal from planet-ring meshing area to sensor, however, they are obviously much longer than the three paths mentioned above, which will result in signal attenuation gradually. Comparing with path 1, path 2 and path 3 are relatively longer, in addition, more parts and components are involved during signal transferring. Considering meshing clearance, damping and other influence factors, signal attenuation caused by path 2 and path 3 will be much heavier. What's more, as vibration signal will pass through other meshing areas, signal intensity of which is as high as the signal source of interest, attenuated vibration signal will be overwhelmed by the meshing areas they pass through. Thus, vibration signal transferring through path 1 is more reliable than others, and should be mainly considered. Shown in Figure 2 is how the dominate signal transfer path changes in a carrier cycle as planetary gearbox runs. When planet gear and ring gear meshes at the sensor, as shown in Figure 2a, signal transferring path is shortest, and there will be no signal attenuation. On the contrast, when planet gear and ring gear meshes at the radial opposite position of sensor, signal transferring path is longest, and there will be the severest signal attenuation. Dynamically, as planet-ring gear meshing area departs from the sensor, which is shown in Figure 2a-c, signal transferring path will become longer and longer until planet gear and ring gear meshes at the radial opposite position of sensor. As a result, vibration signal caught by sensor will be weaker. As planet-ring gear meshing area draws near to the sensor, which is shown in Figure 2d-f, signal transferring path will become shorter and shorter until planet gear and ring gear meshes at the sensor, vibration signal caught by sensor will be stronger as well. Variation period of signal transferring path is identical with rotating period of carrier. Figure 1: Signal transfer paths in planetary gearbox. Figure 2: Signal transfer path in a carrier cycle. Unique planetary movement in planetary gearbox brings in difficulties to research on signal modeling and fault diagnosis method; [PERSON] [5; 37] and [PERSON] [11] proposed a Hanning function-based model to describe the transmission path; [PERSON] [38] improved this model by reconsidering the influence of planet gear when it is in the farthest location. Figure 3a shows the Hanning function-based model of signal transfer path.