A Refined Dynamic Model for the Planetary Gear Set Considering the Time-Varying Nonlinear Support Stiffness of Ball Bearing

Dynamics models of planetary gear sets (PGSs) are usually established to predict their dynamic behavior and load-sharing characteristics. The accurate modeling of bearing support stiffness is essential to study their dynamics. However, in most of the existing PGS dynamic models, the effect of characteristics coupling the rolling bearing time-varying nonlinear stiffness with the translational property of PGSs on the dynamic responses was completely neglected. To investigate this problem, a refined dynamic model for PGSs is proposed considering the coupled relationship between the radial translation of the rotating components and the time-varying nonlinear support stiffness of the ball bearing. The refined dynamic model simultaneously considers the coupled effect of the time-varying characteristic caused by the orbital motion of the rolling elements and the nonlinear characteristic caused by Hertzian contact between the rolling elements and raceways of the ball bearing. Comparisons between the simulations and experimental results are presented, which indicate that the PGS vibration spectrums yielded by the proposed time-varying nonlinear stiffness model are much closer to the actual scenarios than those of traditional models. The analysis results provide theoretical guidance for fault monitoring and diagnosis of the rolling bearings used in the PGS.