Gears Design with Shape Uncertainties using Monte-Carlo Simulations and Kriging

Rodolphe Le Riche (1, 2, 3, 4, 5, 6) , Victor Picheny (1, 2) , David Ginsbourger (1, 2) , André Meyer , Nam-Ho Kim

1 3MI-ENSMSE - Département Méthodes et Modèles Mathématiques pour l'Industrie
2 Mines Saint-Étienne MSE - École des Mines de Saint-Étienne
3 SITE-ENSMSE - Centre Sciences, Information et Technologies pour l'Environnement
4 DEMO-ENSMSE - Département Décision en Entreprise : Modélisation, Optimisation
5 CNRS - Centre National de la Recherche Scientifique
6 LCG-ENSMSE - UMR 5146 - Laboratoire Claude Goux

This article presents an approach to the optimization of helical involute gears for geometrical feasibility, contact ratio, teeth sliding velocity, stresses and static transmission error (STE). The teeth shape is subject to random perturbations due to wear (a randomized Archard's wear). The consequences of shape inaccuracies are statistically expressed as a 90% percentile of the STE variation, which is optimized. However, estimating a 90% STE percentile by a Monte Carlo method is computationally too demanding to be included in the optimization iterations. A method is proposed where the Monte Carlo simulations are replaced by a kriging metamodel during the optimization. An originality of the method is that the noise in the empirical percentile, which is inherent to any statistical estimation, is taken into account in the kriging metamodel through an adequately sized nugget effect. The kriging approach is compared to a second method where the STE variation for an average wear profile replaces the percentile estimation.

Domaines: Mécanique [physics.med-ph]

Rodolphe Le Riche, Victor Picheny, David Ginsbourger, André Meyer, Nam-Ho Kim. Gears Design with Shape Uncertainties using Monte-Carlo Simulations and Kriging. 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, May 2009, Palm Springs (California), United States. ⟨10.2514/6.2009-2257⟩. ⟨hal-00409760⟩