This paper presents a multi-objective optimization approach for the design of a two-stage helical gearbox using the Multi-Objective Evolutionary Algorithm based on Decomposition with Differential Evolution (MOEA/D-DE). The design problem is formulated with two conflicting objectives: minimizing the total axial length of the gearbox to ensure compactness, and maximizing mechanical efficiency to enhance energy transmission performance. A series of optimization runs were conducted across a range of overall transmission ratios (uh​). The MOEA/D-DE algorithm successfully generated well-distributed Pareto-optimal solutions that reflect the trade-offs between size and efficiency. Two post-analysis strategies were employed to explore design tendencies: (1) selecting solutions with minimum gearbox length, and (2) selecting solutions with the highest efficiency-to-length ratio. Results show clear trends in gear ratio distribution and face width coefficients, along with strong linear correlations between stage 1 gear ratio u1​ and total transmission ratio uhuh​, offering useful design heuristics. The findings demonstrate the effectiveness of MOEA/D-DE in navigating complex trade-offs and providing diverse optimal solutions for gearbox design, even in the absence of a decision-making layer. This study serves as a foundation for further research integrating performance-based selection and multi-criteria decision techniques.

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Multi-objective Optimization of Two-Stage Helical Gearbox Design Using MOEA/D-DE with Objectives of Compactness and Efficiency

  • Vu Duc Binh,
  • Vu Ngoc Pi,
  • Dinh Van Thanh,
  • Le Xuan Hung,
  • Tran Thi Phuong Thao

摘要

This paper presents a multi-objective optimization approach for the design of a two-stage helical gearbox using the Multi-Objective Evolutionary Algorithm based on Decomposition with Differential Evolution (MOEA/D-DE). The design problem is formulated with two conflicting objectives: minimizing the total axial length of the gearbox to ensure compactness, and maximizing mechanical efficiency to enhance energy transmission performance. A series of optimization runs were conducted across a range of overall transmission ratios (uh​). The MOEA/D-DE algorithm successfully generated well-distributed Pareto-optimal solutions that reflect the trade-offs between size and efficiency. Two post-analysis strategies were employed to explore design tendencies: (1) selecting solutions with minimum gearbox length, and (2) selecting solutions with the highest efficiency-to-length ratio. Results show clear trends in gear ratio distribution and face width coefficients, along with strong linear correlations between stage 1 gear ratio u1​ and total transmission ratio uhuh​, offering useful design heuristics. The findings demonstrate the effectiveness of MOEA/D-DE in navigating complex trade-offs and providing diverse optimal solutions for gearbox design, even in the absence of a decision-making layer. This study serves as a foundation for further research integrating performance-based selection and multi-criteria decision techniques.