Holistic Optimal Design of Face-Milled Hypoid Gearsets

Abstract

The aim of this paper is to present a holistic framework to design optimized spiral bevel and hypoid gearsets with accurate finite element simulations in the loop. Starting from the basic transmission data, we first size gear and pinion blanks, and then we synthesize the basic machine-tool settings required to generate the two toothed members. This first step represents the macro-geometry design phase and its outcome is a conjugate spiral bevel or hypoid gearset. The second design phase is represented by the definition of the optimal pinion micro-geometry. This is formulated as a multi-objective optimization problem (MOOP) where the obtained optimal ease-off is guaranteed to be manufacturable. To this end, an original strategy is proposed where the search for the pinion optimal tooth surface happens in the space of the coefficients of a polynomial representation of its micro-topography. However, thanks to a fast identification algorithm that can handle all the higher-order motions, the ideal ease-off is projected onto set of machine-tool settings, thus ensuring manufacturability from the outset. It is worth remarking that the objective functions in the MOOP are evaluated by calling as a back-end solver one of the most accurate loaded tooth contact analysis software available on the market. A dedicated parallel implementation of such MOOP allows to maintain computation times within very reasonable limits. A fully worked out numerical test case clearly demonstrates that the whole procedure far surpasses the current state of the art.