Multi-objective micro-geometry optimization of gear tooth supported by response surface methodology

This paper shows the application of response surface methodology for gear optimization using micro-geometry profile modifications. The suitability of three distinct metamodeling techniques is studied in this paper: Gaussian Process (stochastic), Shepard k-Nearest (nonparametric deterministic) and Polynomial (parametric deterministic). The described optimization strategy is implemented and tested on a case study consisting of a pair of identical spur gears, in which the goal is to find optimal micro-geometry modifications of tooth profile, providing decreased values of peak-to-peak transmission error and maximal contact stress along the meshing cycle, while maintaining the safety coefficient linked to tooth bending fatigue above a required threshold. The gear pair is analyzed under three different loading scenarios. It is shown that the described optimization strategy allows finding optimal micro-geometry modifications of tooth profile that enable significant improvements in all the observed performance indices with respect to the unmodified gear design, as confirmed by detailed numerical simulations of the optimal gears.