A Multi-Objective Optimization Solution for Two-Stage Helical Gearbox Design with a New Method NSGA-II: Compromising Efficiency and Structural Compactness
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1
Faculty of Mechanical Engineering, East Asia University of Technology, Viet Nam
 
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School of Engineering Technology, Duy Tan University, Viet Nam
 
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Faculty of Mechanical Engineering, Thai Nguyen University of Technology, Viet Nam
 
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Faculty of Mechanical Engineering, Viet Tri University of Industry, Viet Nam
 
 
Submission date: 2025-08-14
 
 
Final revision date: 2026-02-24
 
 
Acceptance date: 2026-02-24
 
 
Online publication date: 2026-04-16
 
 
Corresponding author
duong vu   

School of Engineering Technology, Duy Tan University, 3 Quang Trung, Hai Chau, 550000, Da Nang, Viet Nam
 
 
 
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ABSTRACT
The design of two-stage helical gearboxes inherently involves trade-offs between structural compactness and transmission efficiency. Traditional design methods often fail to capture these competing objectives simultaneously. This study presents a comprehensive multi-objective optimization approach using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to identify optimal trade-offs between minimizing the cross-sectional area and maximizing the efficiency of a two-stage helical gearbox. Drawing from the strengths of evolutionary algorithms and integrating insights from prior literature on hybrid and decision-making-based optimization methods, the proposed model formulates the gearbox design problem with realistic constraints and evaluates the Pareto front of optimal solutions. The results demonstrate that NSGA-II provides a well-distributed set of non-dominated solutions, offering engineers greater flexibility in balancing performance and structural requirements. Comparative analysis with existing approaches highlights the effectiveness of the proposed method in simultaneously achieving compactness and energy efficiency in gearbox systems.
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