Dynamic modelling of planetary gears of automatic transmissions

In this paper, a generalized dynamic model for multi-stage planetary gear trains of automotive automatic transmissions is proposed. The planetary gear train is formed by N number of planetary gear sets of different types (single-planet, double-planet, or complex-compound), connected to each other in any given kinematic configuration. In addition, each planetary stage can have any number of parallel planet branches. A generalized power flow formulation and a gear mesh load distribution model are used to determine the stiffnesses, displacement excitations, and fundamental frequencies at the gear mesh interfaces. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. At the end, the model is applied to a three-stage planetary gear train representative of an automotive automatic transmission application to demonstrate the influence of coupling stiffnesses and the kinematic configurations on the natural modes and the dynamic response.