Robust optimization of the loaded contact pattern in hypoid gears with uncertain misalignments

This paper presents an automatic procedure to optimize the loaded tooth contact pattern of face-milled hypoid gears with misalignments varying within prescribed ranges. A two-step ap- proach is proposed to solve the problem: in the first step, the pinion tooth micro-topography is automatically modified to bring the perturbed contact patterns (as the assembly errors are varied within the tolerance limits) match a target area of the tooth, while keeping them off the edges; in the second step, a subset of the machine-tool settings is identified to obtain the required topog- raphy modifications. Both steps are formulated and solved as un- constrained nonlinear optimization problems. While the general methodology is similar to the one recently proposed by the same authors for the optimization at nominal conditions, here the ro- bustness issues with respect to misalignment variations are con- sidered and directly included in the optimization procedure: no a posteriori check for robustness is therefore required. Numerical tests show that nominally satisfactory and globally robust hypoid pairs can be designed by a direct process and within a unified framework, thus avoiding tiresome trial-and-error loops.