Mechanical Modelling and Dynamic Characterization of Multi-Rigid-Flexible Planetary Systems: Multi-Rigid-Flexible Planetary Systems

Planetary transmission gears are widely used in the aerospace field, yet there is a scarcity of analysis and design tools specifically for planetary systems. In this paper, a three-dimensional dynamic gear tooth mesh load distribution model for planetary gear systems is proposed, which can take into account the influence of factors such as tooth side clearance, gear support stiffness, and tooth surface load distribution on the dynamic root stress of the system. A numerical integration strategy is combined with an elastic contact iteration algorithm to solve the multi-body dynamics solution problem. This approach inherently captures mesh stiffness fluctuations without the need for an empirical mesh stiffness formulation or transfer error excitation of the system. The dynamic root stress response of the parametrically excited system under different gear meshing phase conditions is investigated using this model. The results discussed not only demonstrate that the model in this paper can provide the necessary information for fatigue failure analysis and reliability prediction of planetary systems with multi-scale geometrical variables, but also reinforce the need for such computationally efficient models for design purposes.