A novel modelling method is proposed for rigid-flexible coupled planetary gear transmission systems that consist of rigid gear subsystems and elastic ring gear subsystems. The model for rigid gear subsystems is established by using the lumped parameter method and the model for elastic ring gear subsystems is established by using the FEA method. The natural frequency and vibration modes are deter-mined according to the compatible state of deformation between mesh force and ring gear deformation
and the distribution of the natural frequency for the coupled system is described. It is based on the vibration characteristics of the system that the vibration modes are classified into six kinds of modes. The effects of system rigidity to the sensitivities of natural frequency with different orders are calculated
and can be used as the bases for planetary transmission system vibration suppression. The influences of torsional stiffness of sun gear and the mesh stiffness between sun gear and planetary gears to the torsional vibration of the system are analyzed. The influences of the gear rim thickness to the system natural frequency distribution
to the subsystem coupling order time and to the vibration mode are discussed. It is found that the natural frequency appears in the position of the gear subsystem torsional vibration frequency
but the ring gear vibration mode is gradually reduced from the high-order section diameter and the first order vibration mode of the system is changed from a circle section diameter vibration mode into a gear ring rigid vibration mode as the thickness of the ring gear increase.
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