Modeling and Vibration Analysis of a Gear Rotor-Bearing System with a Shaft Crack

This paper aims to investigate the vibration characteristics of a geared rotor-bearing system (GRS) with a shaft crack. Firstly, a lateral–torsional coupling model is proposed. In the dynamic model, the rotating shafts of the GRS are modeled as Timoshenko beams; the meshing gear is modeled as a pair of rigid disks connected by a spring–damper with time-varying mesh stiffness; the opening and closing behavior of the crack is analyzed based on strain energy release rate theory and stress intensity factor theory. Then, this dynamic model is utilized to analyze the vibration characteristic of the GRS with a shaft crack. The results show that the most significant effect of a crack on the GRS is amplitude modulation of vibration signals. Not all the natural frequencies of the GRS can be affected by the crack. In addition, the feature frequencies of the GRS will also show some unique characteristics. This study provides a theoretical basis for the analysis and diagnosis of a GRS with a shaft crack.