Effect of Supported Bearing Clearance on Load-Sharing Characteristics of a Double-Row Planetary Gear System

Few studies were focused on the load-sharing characteristics of double-row planetary gear(DRPG)systems with bearings.Meanwhile,the supported bearing has an important influence on the transmission characteristics of the entire system.To overcome this problem,a multi-body dynamic(MBD)model of the DRPG system fully considering the influences of bearing parameters is established.Dynamic loads among contacting gear pairs have been obtained to calculate the load-sharing coefficient(LSC)of the system.The LSC of each gear tooth pair has been compared to study the effect of the supported bearing clearance on the load-sharing characteristics.These methods are based on Hertz contact theory.The liner stiffness and damping are used in the model.The results show that the supported bearing clearance has a greatly effect on the LSC of the DRPG system.Choosing appropriate clearance parameters of supported bearing can help suppress the uneven load distribution of the DRPG system.The results can provide some guidance to find new method to study the LSC and increase the service life of planetary gear systems.

Bifurcation and chaos study on transverse-torsional coupled 2K-H planetary gear train with multiple clearances

A new non-linear transverse-torsional coupled model was proposed for 2K-H planetary gear train, and gear's geometric eccentricity error, comprehensive transmission error, time-varying meshing stiffness, sun-planet and planet-ring gear pair's backlashes and sun gear's bearing clearance were taken into consideration. The solution of differential governing equation of motion was solved by applying variable step-size Runge-Kutta numerical integration method. The system motion state was investigated systematically and qualitatively, and exhibited diverse characteristics of bifurcation and chaos as well as non-linear behavior under different bifurcation parameters including meshing frequency, sun-planet backlash, planet-ring backlash and sun gear's bearing clearance. Analysis results show that the increasing damping could suppress the region of chaotic motion and improve the system's stability significantly. The route of crisis to chaotic motion was observed under the bifurcation parameter of meshing frequency. However, the routes of period doubling and crisis to chaos were identified under the bifurcation parameter of sun-planet backlash; besides, several different types of routes to chaos were observed and coexisted under the bifurcation parameter of planet-ring backlash including period doubling, Hopf bifurcation, 3T-periodic channel and crisis. Additionally, planet-ring backlash generated a strong coupling effect to system's non-linear behavior while the sun gear's bearing clearance produced weak coupling effect. Finally, quasi-periodic motion could be found under all above–mentioned bifurcation parameters and closely associated with the 3T-periodic motion.

Dynamic load sharing behavior of transverse-torsional coupled planetary gear train with multiple clearances

A new nonlinear transverse-torsional coupled model with backlash and bearing clearance was proposed for planetary gear set. Meanwhile, sun gear and planet's eccentricity errors, static transmission error, and time-varying meshing stiffness were taken into consideration. The differential governing equations of motion were solved by employing variable step-size Rung-Kutta numerical integration method. The behavior of dynamic load sharing characteristics affected by the system parameters including input rate, sun gear's supporting stiffness and eccentricity error, planet's eccentricity error, sun gear's bearing clearance, backlashes of sun-planet and planet-ring meshes were investigated qualitatively and systematically. Some theoretical results are summarized at last which extend the current understanding of the dynamic load sharing behavior of planet gear train, enrich the related literature and provide references for the design of planetary gear train.

Friction moment analysis of space gyroscope bearing with ribbon cage under ultra-low oscillatory motion

This paper presents the model of calculating the total friction moment of space gyroscope ball bearings which usually work under ultra-low oscillatory motion and are very sensitive to the friction moment. The aim is to know the proportion of the friction moment caused by each frictional source in the bearing＇s total friction moment, which is helpful to optimize the bearing design to deduce the friction moment. In the model, the cage dynamic equations considering six degree-of-freedom and the balls dynamic equations considering two degree-of-freedom were solved.The good trends with different loads between the measured friction moments and computational results prove that the model under constant rate was validated. The computational results show that when the speed was set at 5 r/min, the bearing＇s maximum total friction moment when oscillation occurred was obviously larger than that occurred at a constant rate. At the onset of each oscillatory motion, the proportion of the friction moment caused by cage in the bearing＇s total friction moment was very high, and it increased with the increasing speed. The analyses of different cage thicknesses and different clearances between cage pocket and ball show that smaller thickness and clearance were preferred.