Optimal Design of a Two-Stage Helical Gearbox Using NSGA-II and MAIRCA: A Trade-Off between Performance and Axial Length - Dinh, Van Thanh; Vu, Duc Binh; Vu, Ngoc Pi; Nguyen, Manh Cuong (Engineering, technology & applied science research, 2025)
This study presents a Multi-Objective Optimization (MOO) approach for the design of a two-stage helical gearbox, aiming to simultaneously maximize the transmission efficiency and minimize the overall axial length. The optimization framework integrates the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to generate a diverse Pareto front of optimal solutions, and the Multi-Attribute Ideal-Real Comparative Analysis (MAIRCA) method to support decision-making by ranking the Pareto-optimal alternatives. A physics-based mathematical model of gearbox geometry, load capacity, and efficiency was established to evaluate the performance of each candidate design. The design variables include the gear ratio distribution between the stages and the face width coefficients, subject to practical constraints, such as the gear strength and contact ratios. The results show a clear trade-off between performance and compactness, and demonstrate the effectiveness of combining NSGA-II with MAIRCA for identifying optimal gearbox designs under conflicting objectives. This approach offers valuable insights for gearbox designers aiming to balance performance and spatial constraints in modern mechanical systems. This is the first study to apply a combined NSGA-II and MAIRCA technique for the bi-objective optimization of a two-stage helical gearbox with the goals of maximizing efficiency and minimizing the length. The proposed method successfully determines the optimal design parameters across a range of transmission ratios, thereby facilitating the early-stage selection of suitable gear ratios in preliminary gearbox design.