Finite Element/Contact Mechanics Calculation Of Quasi-Static Response,Tooth Root Stress,And Load Sharing In Planetary Gears With Rolling Element Bearings

This study uses a state-of-the-art finite element/contact mechanics(FE/CM) method to investigate quasistatic central member response, planet load sharing, planet bearing and rim deformation, and tooth root stress in planetary gears with rolling element planet bearings. The FE/CM method has been widely used in past research to accurately predict elastic contact at the tooth mesh. Most existing planetary gear models use lumped stiffnesses to represent rolling element planet bearings.A two-dimensional bearing model based on a production bearing is created using FE/CM method.The bearing model is analyzed quasi-statically in an isolated environment to understand its stiffness and deflection properties. Periodicity in bearing stiffness and bearing deflection properties are dependent on the kinematic motion of the rolling elements. The bearing stiffness is nonlinear with both applied load and radial clearance.A two-dimensional FE/CM planetary gear model based on a helicopter application is created and analyzed quasi-statically with both stiffness matrix and full contact bearing models. Errors in mean value of central member degrees of freedom caused by nonlinearity in bearing stiffness when using stiffness matrix bearing model is identified. In models with full contact bearings, additional low frequency content in carrier rotational response occurs as a result of fluctuation in bearing deflection. PG models with full contact bearings have modulation in the planet bearing forces due to fluctuations in rolling element bearing stiffness. Parametric studies on bearing clearance and planetary gear torque reveals that in many conditions low frequency content in carrier rotational response and modulation in planet load sharing are significant. Planet pin position error causes uneven load sharing, which however is not sensitive to bearing modeling method.A three-dimensional planetary gear model based on the same application is created using FE/CM method and analyzed statically at two typical bearing contact conditions to characterize bearing race deformation, tooth root stress, tooth contact pressure,static transmission error, and planet load sharing, when stiffness matrix and full contact bearing models are used respectively. The model with full contact bearings are found to provide more accurate result for bearing race deformation. The combined effect from bearing race deformation and rolling element contact causes location and maximum of tooth root stress to be distinct from that calculated in model with stiffness matrix bearings. By tuning bearing race thickness,tooth root stress in three-dimensional planetary gear model with full contact bearings can be approximated using three-dimensional or two-dimensional planetary gear model with stiffness matrix bearings.