A universal algorithm for spur gear optimization based on selective search: Numerical methodology and applications

Abstract

This paper presents a universal methodology for the numerical optimization of spur gear parameters based on the selective search method. Unlike heuristic or commercial approaches, the proposed algorithm is deterministic, easy to implement in any numerical environment, and guarantees full coverage of the feasible design space. The developed mathematical model precisely describes the tooth geometry, including the involute flank and the extended root transition curve, and was validated against CAD simulations of the generating cutting process. A novel numerical procedure was introduced to calculate tooth root stresses with sub-micron resolution, achieving excellent agreement with FEM (maximum error below 1.7%) while maintaining negligible computational cost. The main novelty of this study lies in combining simplicity and universality with high numerical accuracy. Compared to existing optimization strategies, the algorithm offers faster convergence, lower error margins, and flexibility to integrate additional constraints and decision variables. Beyond gear design, the proposed approach can be applied to lightweight mechanical structures, sustainable manufacturing, and AI-assisted digital twins. The results demonstrate that the method enables rapid and cost-effective optimization, making it suitable for early design stages where FEM-only optimization would be too expensive and time-consuming.