Nonlinear Dynamic Model of Planetary Gear Train

A nonlinear dynamic model of a single-stage planetary gear train is established. Factors, such as the floating motion of the centroid of the sun gear, time-varying mesh stiffness, gear meshing transmission errors and gear backlashes, are considered. In the model, the sun gear has three degrees of freedom: two transverse and one rotation. The planets and ring gear have one rotational degree of freedom, respectively. Thus, the system has N+4 degrees of freedom (DOF). Due to the semi-definite characteristic of the system, the relative displacements are selected as generalized coordinates to eliminate the influence of rigid body displacement. The dimensionless nonlinear differential equations, which are easy to be solved by the method of numerical integration, are obtained in the end. This model can be employed to further investigate the dynamic behavior of planetary gear train.