Holistic Optimal Design of Face-Milled Hypoid Gearsets

The aim of this paper is to showcase a holistic approach to design optimized spiral bevel and hypoid gearsets. The first step is the definition of the gear and pinion blanks starting from the basic transmission data. The second step is to synthesize the basic machine-tool settings required to cut the two toothed members. The gear machine-tool settings are obtained first, whereas the basic pinion settings are identified by minimizing the deviations of the pinion tooth surface from the gear conjugate member accounting for the presence of misalignments. The proposed novel identification strategy can handle all the higher-order motions while offering a remarkable speedup with respect to existing techniques. The result of the macro-geometry design phase is a conjugate spiral bevel or hypoid gearset. As a last step, the design of the pinion micro-geometry is formulated as a multi-objective optimization problem where the obtained optimal ease-off is guaranteed to be manufacturable. To this end, an original strategy is devised where the search for the optimal tooth surface is driven by the coefficients of a free-form polynomial representation of its micro-topography. However, the tooth geometry evaluated by the loaded tooth contact solver is actually its closest manufacturable analogue. A fully worked out numerical test case substantiates the whole method.