Minimizing the Cross-Sectional Area and Maximizing Efficiency in Split-Input Two-Stage Gearboxes via NSGA-II with SAW-Guided Choice
Received: 19 September 2025 | Revised: 18 November 2025 and 10 December 2025 | Accepted: 11 December 2025 | Online: 9 February 2026
Corresponding author: Tam Thi Do
Abstract
Split-input two-stage helical gearboxes must balance a compact footprint with high transmission efficiency. This study proposes a preference-aware multi-objective framework that couples NSGA-II with Simple Additive Weighting (SAW) to design split-input two-stage gearboxes under constraints. A parameterized gearbox model is formulated using the key design variables, including the first-stage gear ratio u1 and the face-width coefficients of the first and second stages, Xba1 and Xba2. The model is optimized with two objectives: minimizing the gearbox cross-sectional area and maximizing the overall efficiency ηgb. For each target overall transmission ratio, uh, NSGA-II is employed to generate the corresponding Pareto front, after which the SAW method ranks the non-dominated solutions based on user-specified preferences to identify a best-compromise design. The post-processing identified simple design rules: u1 scales approximately linearly with uh (fit R2 > 0.95); Xba1 decreases with uh and plateaus at its lower bound for higher uh, while Xba2 remains nearly constant. The resulting fronts show the footprint–efficiency trade-off, and trend analysis demonstrates increasing area and slightly declining efficiency as uh grows—guiding early sizing. The proposed NSGA-II + SAW workflow delivers reproducible, preference-aware selections and interpretable parametric relations, providing practical decision support for compact, high-efficiency split-input two-stage gearbox design.
Keywords:
split-input two-stage gearbox, helical gearbox, multi-objective optimization, NSGA-II, Pareto front, SAW, cross-sectional area, gearbox efficiencyDownloads
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Copyright (c) 2025 Binh Duc Vu, Giang Ngoc Tran, Van Thanh Dinh, Hien Thanh Bui, Tam Thi Do
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