A misaligned formulation for planetary gears with analytical 3D contact characterization

In the study of planetary drivetrains the substantially high transmitted loads lead to significant deflections in the supporting gear structures, which directly impact the gear pair alignment and alter the gear meshing. This contribution proposes an analytical formulation to model misaligned planetary gears by means of distributed gear contact forces. The presented model relies on a thin-sliced approach for the computation of misaligned contact forces, where the two main nonlinear phenomena affecting contact force accuracy are: (1) variable contact stiffness, and (2) contact detection and compression assessment. With regard to the former, this contribution proposes an internal gear extension of the analytical contact compliance approach previously developed by the authors for external gears. With regard to the latter, this contribution proposes a novel technique for analytical misaligned contact detection for three-dimensional helical gear contact. The model is validated with quasi-static simulations, including gear microgeometry modifications and misalignments, by comparison to numerical results. The computational efficiency of the presented method is enhanced by two kinds of contributions: a linearization of the compliance model to speed up the contact force computation, and an analytical contact Jacobian formulation. The availability of an efficient planetary gear contact model uncovers many interesting applications in the design and operational phases merged with digital twins frameworks.