Effects of tooth-crack-induced mesh stiffness on fault signals of a planetary gear train

The early fault of tooth crack in a planetary gearbox is difficult to be detected duo to its weak yet complex effects on the system's vibration signals. In order to identify fault signals aroused from small tooth crack of the sun gear in a planetary gear train, a lateral-rotational-coupled nonlinear dynamic model that incorporates the tooth-crack-induced time-varying mesh stiffness is proposed. A three-dimensional finite element model of gear pair is established to formulate the mesh stiffness of the gear pair with and without tooth crack. Based on the proposed nonlinear dynamic model, the vibration signals of a planetary gear system in both healthy and tooth-cracked conditions are predicted. Though a distinct reduction in the time-varying mesh stiffness of the sun-planet gear pair can be observed after introducing the effects of tooth crack, the time-domain vibration signals for both healthy and fault conditions are almost the same. However, the vibration signals in frequency-domain under two conditions are quite different in that multiplicities of sidebands spaced by characteristic frequency of the sun gear around the harmonics of mesh frequencies can be observed in the fault condition. Hence, from the perspective of fault diagnosis, the dynamic-model-based frequency spectra can be used to detect the early fault of tooth crack in a planetary gear train.