A lightweight design scheme for a heavy-duty planetary gear three-stage transmission system based on the SQP algorithm and the response surface method

Abstract Within a certain range of total transmission ratios, the heavy-duty planetary gear multi-stage transmission system faces challenges such as difficulty in coordinating transmission ratios, balancing lightweight design with load-carrying capacity, and low space utilization. To address these issues, this study proposes an optimized design for a heavy-duty planetary gear three-stage transmission system, with the volume of the gearing system as the optimization objective. Firstly, based on the sequential quadratic programming algorithm, eight kinds of transmission ratio preferential assignments are made for the heavy-duty planetary gear three-stage transmission system. By analyzing the results of the volume optimization, the preliminary transmission scheme for the heavy-duty planetary gear three-stage transmission system, in which the ratios of the first two stages are both reduced and the ratio of the tertiary stage is increased, is preferred. Secondly, on this basis, and in combination with the response surface method, the second-order response model for the relationship between the transmission ratios of all stages of the heavy-duty planetary gear three-stage transmission system and the total volume of the system is established. The reasonableness of the initial selection scheme is verified by solving the response surface objective function, and the optimal allocation result is obtained. This result is allocated as follows: The primary transmission ratio is 1.5635, the secondary transmission ratio is 5.7158, and the tertiary transmission ratio is 4.8800. The volume under this allocation is 5.32573 × 10 8 mm 3 , which decreases by 7.75% compared to the maximum volume of 5.77307 × 10 8 mm 3 among all lightweighting schemes. The lightweight design of the heavy-duty planetary gear three-stage transmission system is realized. The results of the study provide helpful references for the lightweight design and optimization of transmission systems, the coordinated distribution of transmission ratios, and the improvement of space utilization in transmission systems.