Dynamic modeling of the planetary gear set considering the effects of positioning errors on the mesh position and the corner contact

The positioning errors of a gear pair will directly affect the mesh position and the corner contact (via the tooth pair separation distance) which should be considered for correctly modeling the gear time-varying mesh stiffness and dynamic responses. This phenomenon is more complex for a planetary gear set as it includes both the external gear pairs (sun-planets mesh) and internal gear pairs (ring gear-planets mesh). However, in the literature, these effects have not been studied in the dynamic modeling of planetary gear sets possibly due to their complexities. To fill this gap, the actual mesh position and the separation distance considering the gear positioning errors for both the external and internal gear pair are derived via geometric analysis. The mesh stiffness models for both the internal and external gear pairs are established through the load coordination equation considering the corner contact induced by the tooth pair separation distance and the position-dependent Hertzian contact deformation. Finally, the dynamic model for a planetary gear set with position errors is built based on the proposed mesh stiffness models. The load sharing characteristics simulated by the proposed model are compared with the traditional model which only considers the effect of positioning errors on the contact ratio and pressure angle and ignores their effects on the mesh position and the separation distance for both the external and internal gear pairs. The results indicate that the difference of the load sharing characteristics between the proposed model and the traditional models is significant under heavy external load. The simulation results also show that suitable positioning errors can improve the load sharing condition by 10% if the amount of positioning errors is changed from 0.1 to 0.2 mm.