A torsional and translational nonlinear vibration mathematical model was established to predict the dynamic characteristics of the star gearing system.The time-varying mesh stiffness

gear composite errors

run-out errors and gear backlashes were considered.A numerical method was applied to solving the large parametrically excited nonlinear multi-DOF dynamic system.A numerical example was also presented.From the results

the influences of the time-varying meshing stiffness

run-out errors and backlashes on the dynamic responses and dynamic gear tooth loads were investigated respectively.The dynamic load equalizations among star gears were also analyzed under the existence of gear run-out errors.In comparison with some calculated results from the literature

the numerical results presented show a good agreement.