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, a preferred design of a heavy-duty planetary gear three-stage transmission system, with the volume of the gearing system as the optimization objective, was proposed to address problems such as the difficulty in coordinating the transmission ratios of the heavy-duty planetary gear multi-stage gearing system, the challenging balance between lightweight design and load-carrying capacity, and the low space utilization rate. Firstly, based on the sequential quadratic programming algorithm, eight kinds of transmission ratio preferential assignments were 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 were both reduced and the ratio of the tertiary stage was increased, was 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 was established. The reasonableness of the initial selection scheme was verified by solving the response surface objective function, and the optimal allocation result was obtained. This result was allocated as follows: The primary transmission ratio was 1.5635, the secondary transmission ratio was 5.7158, and the tertiary transmission ratio was 4.8800. The volume under this allocation was 5.32573 × 108 mm³, which decreased by 7.75% compared to the maximum volume of 5.77307 × 108 mm³ among all lightweighting schemes. The lightweight design of the heavy-duty planetary gear three-stage transmission system was realized. The results could provide helpful references for the lightweight design and optimization of planetary gear transmission systems, the coordinated distribution of transmission ratios, and the improvement of space utilization in transmission systems.