Optimization of the Transmission Ratio in a Two-Stage Spur-Helical Gearbox Using Sequential Quadratic Programming Algorithm

Abstract

Two-stage gear reducers are widely used in industrial power transmission systems due to their ability to reduce speed, increase torque, and maintain high mechanical efficiency. This study proposes a standards-based optimization framework for two-stage gearboxes that simultaneously ensures contact fatigue strength, adequate oil-bath lubrication, and minimized gearbox volume. The optimization problem is formulated analytically and solved using the Sequential Quadratic Programming (SQP) algorithm. The main objective is to establish a practical lookup table for optimal transmission ratio ranges, enabling efficient preliminary design selection. The proposed approach improves computational efficiency while maintaining the physical interpretability of the design variables and constraints. To the best of the authors’ knowledge, this study is among the first to simultaneously integrate uniform contact strength, lubrication constraints, and volume minimization within a unified SQP-based optimization framework. The results provide a useful reference for preliminary gearbox design and can support rapid parameter selection in engineering practice, although further adjustments may be required to account for manufacturing constraints and specific operating conditions.