Helical planetary gear transmission was applied more extensively in high-speed and heavy load situations

as the vibration mode and dynamic characteristic had significant influence on vibration and noise reduction. Targeting the helical planetary gear transmission system

co-moving coordinate system was conducted

the multi-degree of freedom nonlinear dynamical equations including gyroscopic effect and backlash was derived

and the natural characteristic of the system was solved. The results show that helical planetary gear train has three typical vibration modes: axial translational-rotational coupled vibration mode (multiplicity r=1)

translational vibration mode (multiplicity r=2) and planet vibration mode(multiplicity r=N－3

N>3); in consideration of mesh stiffness

backlash

general errors and external load

influence laws of mesh phase difference and excitation ways to dynamical coefficient have been studied

showing that mesh phase difference makes the dynamical coefficient increase; when stiffness fluctuation coefficient ζ=1.723

the system is bifurcated into 2-period sub-harmonic response

with the changes of excitation parameters

internal engagement turning into the chaotic state is earlier than external engagement.