An Integrated NSGA-II and EAMR Approach for the Optimal Design of a Two-Stage Gear Transmission
Received: 18 April 2025 | Revised: 1 June 2025 | Accepted: 6 June 2025 | Online: 2 August 2025
Corresponding author: Luu Anh Tung
Abstract
This paper presents a Multi-Objective Optimization Problem (MOOP) for the design of a two-stage gear reducer using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The optimization simultaneously targets the minimization of the gearbox volume and the maximization of the mechanical efficiency. Three key design variables are considered: the gear ratio of the high-speed stage (u1), the Face Width Coefficient (FWC) of the high-speed stage (Xba1), and that of the low-speed stage (Xba2). A physics-based model is developed to compute the gearbox volume and efficiency from these design parameters. NSGA-II was employed to generate Pareto-optimal solutions, and the Evaluation based on Distance from Average Solution Ranking (EAMR) method was deployed to identify the most balanced design for each transmission ratio (uh). The results showed that as uh increases from 5 to 35, the gearbox volume rises from 237.08 dm3 to 272.72 dm³, while the efficiency decreases from 95.84% to 90.82%. A strong linear relationship (R2 = 0.9941) between u1 and uₕ was discovered, enabling deriving a general design rule for the gear ratio allocation in preliminary gearbox design.
Keywords:
two-stage gearbox, multi-objective optimization, NSGA-II, gear ratio, face width coefficient, efficiency, volume, design trade-offDownloads
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Copyright (c) 2025 Dinh Van Thanh, Khac Minh Nguyen, Ngoc Pi Vu, Luu Anh Tung
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