Abstract
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.
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Funding
This work is also supported by the Anhui Provincial Key Project of Natural Science—Research and Application of High-Efficiency Hybrid Vehicle Transmission Technology (2025AHGXZK31129).
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Qiong Zhang: Writing-original draft, review and editing. Cuifeng Ren: Formal analysis, Methodology, Validation. Haixia Niu: Review, supervision. All authors reviewed the manuscript.
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Zhang, Q., Ren, C. & Niu, H. Transmission ratio-efficiency coupled modeling and high-efficiency zone design for multi-row planetary gear transmission of hybrid electric vehicles. Sci Rep (2026). https://doi.org/10.1038/s41598-026-37023-x
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DOI: https://doi.org/10.1038/s41598-026-37023-x
