As a part of coupled transmission with load sharing system based on wind turbine gearboxes,a multi-stage transmission system with two-stage planetary gear train and one-stage parallel-shaft gear train was considered.A dynamic mechanical model for three stage gear train was presented using lumped-parameter method.Many factors were taken into account,such as mesh stiffness and mesh damping of gear pairs of the transmission system,errors of gear pairs,torsional coupling stiffness of the connecting section, and the inertia of the system.The natural frequencies and vibration modes of the system were obtained through solution of the associated eigenvalue problem by using the related parameters. Based on the properties of the transmission system,the vibration modes of the system were classified into eight categories,which were coupling vibration mode between the first stage and the second stage,coupling vibration mode between the second stage and the third stage,overall rotational mode of the system,planet mode of the first stage,planet mode of the second stage, single-stage vibration mode of the first planetary gears,single-stage vibration mode of the second planetary gears and single-stage vibration mode of the parallel-shaft gears,respectively.Moreover,the influences of the coupling stiffness between the carrier of the first stage and the ring of the second stage on the natural characteristics were studied. The analysis showed that vibration modes of multi-stage planetary transmission system are more diverse and complex than that of single-stage system.
