This study presents a multi-objective design optimization of split-stage two-stage helical gearboxes using the Multi-Objective Evolutionary Algorithm based on Decomposition with Differential Evolution (MOEA/D-DE). The gearbox configuration features a dual-gear first stage, which allows for flexible distribution of the overall transmission ratio and contributes to enhanced design versatility. Two conflicting objectives are simultaneously addressed: minimization of the gearbox cross-sectional area, representing structural compactness, and maximization of mechanical efficiency, reflecting energy transmission effectiveness. To achieve this, an optimization framework is developed incorporating analytical models for gear geometry, strength, and power loss. A segmented linear fitting approach is employed to establish the relationship between the overall transmission ratio and the optimal gear ratio in the first stage. Optimization results reveal the trade-off characteristics between volume and efficiency across varying transmission ratios. Pareto-optimal solutions provide insightful guidelines for selecting appropriate design parameters based on specific engineering priorities. The proposed method demonstrates the effectiveness of MOEA/D-DE in identifying diverse and high-quality design alternatives for compact and efficient helical gearbox systems.

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Multi-objective Optimization of Split-Stage Two-Stage Helical Gearboxes Using MOEA/D-DE: Minimizing Cross-Sectional Area and Maximizing Efficiency

  • Dinh Van Thanh,
  • Hoang Xuan Tu,
  • Vu Duong,
  • Le Thi Phuong Thao,
  • Bui Thanh Hien

摘要

This study presents a multi-objective design optimization of split-stage two-stage helical gearboxes using the Multi-Objective Evolutionary Algorithm based on Decomposition with Differential Evolution (MOEA/D-DE). The gearbox configuration features a dual-gear first stage, which allows for flexible distribution of the overall transmission ratio and contributes to enhanced design versatility. Two conflicting objectives are simultaneously addressed: minimization of the gearbox cross-sectional area, representing structural compactness, and maximization of mechanical efficiency, reflecting energy transmission effectiveness. To achieve this, an optimization framework is developed incorporating analytical models for gear geometry, strength, and power loss. A segmented linear fitting approach is employed to establish the relationship between the overall transmission ratio and the optimal gear ratio in the first stage. Optimization results reveal the trade-off characteristics between volume and efficiency across varying transmission ratios. Pareto-optimal solutions provide insightful guidelines for selecting appropriate design parameters based on specific engineering priorities. The proposed method demonstrates the effectiveness of MOEA/D-DE in identifying diverse and high-quality design alternatives for compact and efficient helical gearbox systems.