Influence of Fixed Ring Gear Structural Compliance on the Quasi-Static and Dynamic Response of Epicyclic Gear Sets

The structural compliance of annular ring gear can significantly influence the quasi-static and dynamic performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. The current paper will study the impact of ring gear compliance on the dynamic response of epicyclic gear sets in fixed ring kinematic configuration. To achieve this objective, the current study will incorporate a finite element-based ring gear formulation into the three-dimensional planetary load distribution model of Ryali and Talbot (2021, "A Dynamic Load Distribution Model of Planetary Gear Sets," Mech. Mach. Theory, 158, p. 104229). The proposed model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several components and system-level design variations. The developed formulation is used to conduct parametric studies involving different planetary gear designs, ring gear fixtures (bolted vs. splined), and operating conditions (quasi-static, dynamic). In the case of a splined ring gear fixture, an external splined tooth contact model is developed, which will be used to validate the model against the quasi-static experiments of Kahraman et al. (2010, "Influence of Ring Gear Rim Thickness on Planetary Gear Set Behavior," ASME J. Mech. Des., 132(2), pp. 0210021-0210028). The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears with thin annular ring gears.