Spur gear teeth profile optimization through tensor-based kinematics: integrating the Reuleaux method with differential evolution

This paper presents a novel method for spur gear tooth profile optimization, addressing the challenge of designing gears with improved performance. Traditional gear designs often compromise between contact stress, wear, and noise. This research explores a wider design space to identify gear profiles offering a better balance. The proposed approach leverages tensor-based kinematics combined with the Reuleaux method for conjugate profile generation, creating a robust framework for exploring potential designs. This framework defines an objective function considering multiple performance criteria. Differential evolution is employed to search for novel tooth profiles minimizing this function. The performance of optimized profiles is compared against existing designs, including involute, S-gears, and cosine gears. Key performance indicators include Hertz contact and subsurface shear stresses, normal force, sliding factor, specific sliding, contact ratio, and gear mesh stiffness. Results demonstrate the method’s effectiveness in generating improved tooth profiles. Optimized solutions exhibited contact and shear stress reductions comparable to 30-degree involute and S-gears, suggesting improved pitting resistance and wear. Some designs showed substantial specific sliding reductions, indicating the potential for reduced heat generation and surface wear. While cosine gears showed reduced contact stress, they also exhibited lower contact ratios, potentially increasing dynamic loads. These optimized solutions offer a promising path towards designing high-performance gears tailored to specific applications. The method effectively explores the vast solution space and generates tooth profiles fulfilling desired optimization trade-offs, paving the way for future research incorporating additional performance criteria and exploring more complex gear geometries.