Gears Design with Shape Uncertainties using Monte Carlo Simulations and Kriging

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.