Multi-Objective Optimization of Two-Stage Helical Gearboxes using Non-Dominated Sorting Generic Algorithm II (NSGA-II): Minimizing Mass and Volume while Maximizing Efficiency.

Abstract

This study presents an NSGA-II-based multi-objective optimization framework for two-stage helical gearboxes. The novelty of this work is the simultaneous optimization in case of three conflicting objectives: minimizing gearbox mass, minimizing gearbox volume, and maximizing transmission efficiency. The study does not merely optimize for a fixed set of values but examines the variation of the Pareto solution set across a very wide range of gear ratios, from 5 to 35, taking into account the gearbox volume was calculated as V=L×H×B₁, and the total transmission ratio u_h. The optimization was implemented in MATLAB, and Pareto fronts were generated for different transmission ratios. Hypervolume, spacing, spread, and the number of Pareto solutions were used to ensure robust algorithm convergence and solution diversity. The results show unique mechanical trade-offs. While raising the total transmission ratio reduces overall gearbox bulk, it also increases necessary volume and decreases transmission efficiency. The suggested method efficiently discovers balanced Pareto-optimal solutions and provides a practical tool for designing compact and high-efficiency two-stage systems.