Abstract
Vibration sensors are, generally, fixed on the housing of planetary gearboxes for vibration monitoring. When a local fault occurred on the tooth of a planet gear, along with the system operating, the faulty tooth will mesh with the ring gear or sun gear at different positions referring to the fixed sensor. With consideration of the attenuation effect, the amplitudes of the fault-induced vibrations will be time-varying due to the time-varying transfer paths. These variations in signals are valuable information to identify the fault existence as well as the severity and types. However, the fault-meshing positions are time-varying and elusive due to the complicated kinematics or the compound motion behaviors of the internal rotating components. It is tough to accurately determine every fault meshing position though acquiring information from multi-sensors. However, there should exist some specific patterns of the fault meshing positions referring to the single sensor. To thoroughly investigate these motion patterns make effective fault diagnosis feasible merely by a single sensor. Unfortunately, so far few pieces of literature explicitly demonstrate these motion patterns in this regard. This article proposes a method to derive the motion periods of the fault-meshing positions with a faulty planet gear tooth, in which two conditions are considered: 1. The fault-meshing position initially occurs at the ring gear; 2. The fault-meshing position initially occurs at the sun gear. For each scenario, we derive the mathematical expression of the motion period in terms of rotational angles. These motion periods are, in essence, based on the teeth number of gears of a given planetary gearbox. Finally, the application of these motion periods for fault diagnosis is explored with experimental studies. The minimal required data length of a single sensor for effective fault diagnosis is revealed based on the motion periods.