Dynamic analysis of a geared rotor-bearing system with translational motion due to shaft deformation under residual shaft bow effect

Abstract

In this paper, the dynamic response of a spur geared rotor-bearing system has been studied when the gear set has translational motion due to shaft deformation and residual shaft bow effect. A new dynamic model for the geared rotor-bearing system, considering translational motion and residual shaft bow effect, is proposed, in which the distance between the centers of two gears varies with time. Therefore, the proposed model regards gear pressure angle and contact ratio as time-varying variables, while the previous model regards them as constant. A finite element model of the geared rotor-bearing system developed, the equations of motion are obtained by applying Lagrange's equation. After deriving nonlinear equations of motion for the geared rotor-bearing system, the dynamic responses are computed by applying the fourth-order Runge-Kutta numerical method. The dynamic response including lateral response of two gears, gear pressure angle and contact ratio with different phase angle between two residual shafts are investigated. The results show that the magnitude of the residual shaft bow, the phase angle between two residual shafts will significantly affect gear pressure angle and contact ratio. This new model produces more accurate dynamic responses in comparison to those of the previous model.