For a helicopter transmission system which consists of spiral bevel gears and planetary gear train

the purely torsional vibration model was established

and the non-linear dynamical equations containing backlash was built using the lumped-parameter method. Through the finite element method

the time-varying mesh stiffness was obtained

and the dynamical equations were solved by the 4-5 order Runge-Kutta algorithm with variable time step; by means of dynamic load coefficient

phase plane plots

Poincaré maps and fast Fourier transform spectra

the dynamic characteristics of transmission system were studied under various excitations of the time-varying mesh stiffness

backlash

general transmission errors and external load. The results show that mesh stiffness has the greatest effect on the transmission system

with the maximum dynamic load coefficient of 1.5; backlash has a limited effect on the response characteristics; to some extent

mesh errors can suppress the vibration of the gear system; external load fluctuation has various effects on different speed stages

and the maximum dynamic load coefficient is stemmed from the combined drive gears.