Abstract
A coupled flexible multibody dynamic model of planetary gear is presented to investigate the dynamic performance of the planetary gear and its supporting bearings. The bearing's and gear's kinematical deformation are first defined, the bearing has two degrees of freedom with respect to each axis of the coordinates, that is, the translation in the axis and rotation around the axis; the gear within the planetary gear has degrees of freedom of translations and rotation around its center. Because the carrier and shaft are assumed to have no bending deformation, the deformation freedom of bearing and gear are coupled together by algebraic equations. According to the bearing's and gear's constraints in the system, the corresponding constraints are set. After calculating the kinetic energy, potential energy as well as virtual work of external force, the system's governing equations are obtained by applying Lagrange function. Using the governing equation, the system's deformation modes are analyzed, planetary gear's dynamic performance is simulated during a carrier cycle and finally the bearing's dynamic behaviors are illustrated.
