Effect of residual shaft bow on the dynamic analysis of a double-stage geared rotor-bearing system with translational motion due to shaft deformation

In this study, the dynamic responses of a double-stage geared rotor-bearing system with translational motion due to the effects of rotating shaft deformation were examined, which was lacking in past research. Residual shaft bow has been neglected in most geared rotor-bearing system models. In this study, the dynamic response of a double-stage geared rotor-bearing system whose gear set underwent translational motion was examined when the shaft was deformed (residual shaft bow). The proposed model considers contact ratio and pressure angle of gear pair as time-dependent variables, whereas in other models, they are constants. A finite element model of a double-stage geared rotor-bearing system with residual shaft bow was developed, and equations of motion were obtained by applying the Lagrange's equation. System equations of motion are solved by Runge-Kutta numerical method. The dynamic response was investigated, including lateral response, contact ratio and pressure angle of gear pair with different residual shaft bow magnitudes and gear positions. The results show that residual shaft bow raises the amplitudes of lateral displacement, contact ratio and phase angle of gear pairs in the system. This study demonstrated that the residual shaft bow effect is too considerable to ignore when it becomes sufficiently large.