Transmission ratio-efficiency coupled modeling and high-efficiency zone design for multi-row planetary gear transmission of hybrid electric vehicles

To overcome the efficiency degradation caused by independently designing transmission ratios and evaluating mechanical losses in hybrid electric vehicle drivetrains, this study proposes a unified transmission ratio-efficiency coupled modeling and optimization framework for multi-row planetary gear transmissions. An improved kinematic model based on topological analysis is integrated with a refined multi-source loss model for meshing, bearing, churning, and windage losses. The resulting nonlinear coupled system is solved using a Newton-Raphson method with adaptive step-size regulation. This approach enables the prediction of speed distribution, torque balance, and transmission efficiency under varying operating conditions. An enhanced multi-objective particle swarm optimization (MOPSO) algorithm is then employed to identify high-efficiency zones and to optimize key structural and lubrication parameters. Bench-test verification is conducted through efficiency MAP measurements, thermal endurance tests, and dynamic response evaluations. The results indicate a mean efficiency prediction error of 1.38% and stable thermal and transient behavior. After optimization, the high-efficiency zone coverage increases from 68.5% to 78.6%, and the comprehensive efficiency rises from 92.8% to 95.6%. Overall, the proposed framework provides a computationally efficient and engineering-applicable approach for the systematic design and optimization of planetary gear transmissions.