Hertzian contact analysis in planetary gear transmissions

Abstract

This work evaluates the accuracy of the Weber-Banaschek formulation, implemented in a 2D hybrid model, for the resolution of the contact between gears of a planetary transmission. This formulation considers the Hertzian contact between active flanks in external (sun-planet) and internal gears (planet-ring). This approach presents some limitations regarding the resolution of both the external, and internal gear contact. The latter can be characterized as conformal whenever the curvature radii of the contact points are similar, as it happens in the wheel-rail contact. Thus, this analysis involves both contacts. In order to perform this assessment a new 3D finiteelement model is developed, which including some geometrical simplifications to reduce the computational effort.

Both models simulate analogous meshing scenarios in a planetary transmission with just one planet. The results of both the hybrid and finite element models are compared in terms of the magnitude of the meshing forces and length of the contact area. The contact forces show a significant agreement for all scenarios, while the length of the contact area depicts a better agreement for internal contacts.