Impact of Ring Gear Dynamics on Planet Load Sharing

Abstract This paper presents an elastic continuum modelling approach for ring gears of planetary gearsets where the fixed ring gear spline supports and ring/planet gear contact stiffnesses are treated as lumped dynamic stiffnesses. The hybrid modeling approach used allows coupling of lumped discrete stiffnesses and a continuum model and their coupled solution. The ring gear is modelled as a thin-walled ring structure under the assumption that the normal stress in the direction of ring gear axis is negligible compared to stresses due to the in-plane flexural vibrations. Hamilton’s approach is used to obtain the continuum ring model equations. The spline supports are modelled as non-rotating discrete stiffnesses and the gear contact compliances are modelled as rotating discrete stiffnesses and displacement sources. The system is discretized using Galerkin’s method and Newmark’s time-step marching based integration method is used to determine transient response of the system. The proposed model is utilized to investigate the influence of number of planet gears, number of splines as well as ring gear design parameters on ring gear dynamics and its impact on planet load sharing. The case studies revealed that the planet and spline numbering have an influence on ring gear dynamics as much as ring gear design parameters.