A methodology for simulation-based, multiobjective gear design optimization

Design optimization of geared transmissions has become more of a necessity than ever before. Typically, conflicting design goals must be concurrently achieved. The difficulty of such a multiobjective design optimization problem is exacerbated by the fact that modern design practices rely on increasingly sophisticated, computationally-expensive simulation tools for tooth contact analysis. Their intrinsic nonlinearities add complexity to the problem, hampering gear designers’ efforts to obtain globally optimal solutions. Practical optimization problems of this class have often been solved by evolutionary algorithms, but their computational burden may well be inappropriate for CPU-intensive simulation models. The present work details an algorithmic framework inspired by deterministic multiobjective optimization methods, specially combined with a direct-search global optimization algorithm to obtain globally Pareto-optimal solutions. Nonlinear constraints are enforced through an exact penalty formulation. A comprehensive description of all theoretical and algorithmic details is provided, with the intention of enabling gear designers to implement or adapt the proposed methodology to their design optimization purposes. Two tests on a challenging gear design problem, namely ease-off topography optimization of a hypoid gear set for maximum efficiency and minimum contact stress, demonstrate that the proposed method can efficiently obtain solutions belonging to the global Pareto front.