Vibration Analysis of Two-Stage Helical Gear Transmission with Cracked Fault Based on an Improved Mesh Stiffness Model

The crack fault has an important influence on the vibration characteristics of the transmission system. This paper is devoted to analyzing fault mechanism and dynamic characteristics of transmission with gear crack, which provides the basis for crack diagnosis and monitoring of helical gear in two-stage transmission system. For this purpose, an improved calculation method of time-varying meshing stiffness with crack fault is proposed considering the axial force of the helical gear. The influence of crack depths and angles on stiffness is analyzed. Based on this, the dynamic model of the two-stage helical gear transmission system is established using the lumped mass method. The influence of crack parameters on the characteristics of the transmission system is studied. In order to better diagnose the crack fault of the helical gear, the statistical index in time domain is calculated and the sensitivity to crack fault is analyzed. It is shown that the stiffness decreases by 25%, and the vibration acceleration increases by 8.3% after the axial force component is considered into the stiffness of the crack gear pair. The meshing stiffness decreases with the increase of crack depths and crack angles. The dynamic model is verified by rig test. Periodic impact exists in the system. The time of entering meshing of the cracked tooth and the time of complete disengagement is observed in the residual signal. In the frequency domain, there appear sidebands on the mesh frequency of the first gear pairs and its harmonics, the second gear mesh frequency and its harmonic frequencies. There is a little influence on the vibration acceleration of the driven gear of the second-stage. According to the signals in the frequency domain and the time domain, we can tell at which stage the gear is cracked. While through the time required for the crack tooth from engagement to disengagement completely, we can tell which gear is cracked. The sensitivity of skewness, impulse factor and kurtosis to crack fault decreases successively. The results provide theoretical basis for crack fault diagnosis of a two-stage helical gear transmission system.