Co-design of mechanical and electrical parameters in wind turbine gearbox-generator systems

  • Ruibo Chen orcid

    Drilling Technology Research Institute of Shengli Petroleum Engineering Corporation, Sinopec, Dongying 257017, China; Department of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin 150001, China; State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University, Chongqing 400044, China

  • Zhonghua Wu orcid

    Drilling Technology Research Institute of Shengli Petroleum Engineering Corporation, Sinopec, Dongying 257017, China

  • Jinwei Sun orcid

    Department of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin 150001, China

  • Datong Qin orcid

    State Key Laboratory of Mechanical Transmission for Advanced Equipment, Chongqing University, Chongqing 400044, China

  • Chuanwei Zhao orcid

    Drilling Technology Research Institute of Shengli Petroleum Engineering Corporation, Sinopec, Dongying 257017, China

Article ID: 4262
Keywords: wind turbine transmission system; electromechanical coupling dynamic model; electromechanical coupling dynamic characteristics; electromechanical integration design

Abstract

Conventional design practices for wind turbine drivetrains commonly adopt a segregated workflow where the gearbox and electrical machine are developed independently. Such a decoupled strategy overlooks inherent electromechanical coupling constraints, thereby imposing fundamental limits on attainable power density and dynamic behavior of the entire transmission assembly. To mitigate these limitations, this work presents a hierarchical integrated parameter co-design framework for wind turbine gearbox–generator systems, which implements progressive optimization from system-level to component-level, while synchronously satisfying static performance and dynamic response requirements. In the first design stage, an integrated initial parameterization scheme is formulated via finite element analysis (FEA) and numerical computation, with objectives to elevate system power density and suppress amplitudes of internal dynamic excitations. The optimized parameters from this stage serve as baseline inputs for the second stage. An electromechanically coupled dynamic model is then established to quantify correlations between key mechanical structural parameters (gearbox bearings, hollow shafts, splines, ring gear bolt stiffness) and generator electromagnetic/structural parameters, as well as overall system dynamic characteristics. Sensitive design variables are identified via correlation analysis, and a Kriging surrogate model is constructed to approximate nonlinear input–output relationships efficiently. Multi-objective component optimization is subsequently performed using the surrogate model. Finally, vibration attenuation and load reduction performances of the baseline and optimized drivetrain configurations are systematically compared under rated and variable operating conditions.

Published
2026-07-20
How to Cite
Chen, R., Wu, Z., Sun, J., Qin, D., & Zhao, C. (2026). Co-design of mechanical and electrical parameters in wind turbine gearbox-generator systems. Sound & Vibration, 60(4). https://doi.org/10.59400/sv4262
Section
Article

References

[1]Rubio F, Llopis-Albert C, Pedrosa AM. Analysis of the Influence of Calculation Parameters on the Design of the Gearbox of a High-Power Wind Turbine. Mathematics. 2023; 11(19): 4137. doi: 10.3390/math11194137

[2]Llopis-Albert C, Rubio F, Devece C, et al. Digital Twin-Based Approach for a Multi-Objective Optimal Design of Wind Turbine Gearboxes. Mathematics. 2024; 12(9): 1383. doi: 10.3390/math12091383

[3]Wang C. Study on dynamic performance and optimal design for differential gear train in wind turbine gearbox. Renewable Energy. 2024; 221: 119776. doi: 10.1016/j.renene.2023.119776

[4]Bußkamp P, Jacobs G, Röder J. Multiobjective wind turbine gearbox design optimization to reduce component damage risk during grid faults. Forschung im Ingenieurwesen. 2025; 89(1): 48. doi: 10.1007/s10010-025-00821-2

[5]Zhou L, An X, Chen H. Multi-objective Optimization Design of Gearbox with Helical Cylindrical Gear Drive. Journal of Mechanical Transmission. 2016; 40(3): 62–65. Available online: https://www.jxcd.net.cn/thesisDetails#10.16578/j.issn.1004.2539.2016.03.013&lang=zh (in Chinese)

[6]Savsani V, Rao RV, Vakharia DP. Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms. Mechanism and Machine Theory. 2010; 45(3): 531–541. doi: 10.1016/j.mechmachtheory.2009.10.010

[7]Gologlu C, Zeyveli M. A genetic approach to automate preliminary design of gear drives. Computers & Industrial Engineering. 2009; 57(3): 1043–1051. doi: 10.1016/j.cie.2009.04.006

[8]Chen J, Wu S, Hsieh C. Design of optimal weight for a gear transmission system using hybrid taguchi-genetic algorithm. Wuhan University Journal of Natural Sciences. 2012; 17(4): 331–336. (in Chinese)

[9]Wei J, Yang P, Qin D, et al. Equal-strength optimization design method for heavy-duty planetary gear transmissions. Journal of Beijing University of Technology. 2018; 44(7): 979–986. Available online: https://journal.bjut.edu.cn/bjgydxxb/cn/article/doi/10.11936/bjutxb2017050047 (in Chinese)

[10]Liang M, Hu J, Li S, et al. Topology optimization of transmission gearbox under multiple working loads. Advances in Mechanical Engineering. 2018; 10(11). doi: 10.1177/1687814018813454

[11]Lv X, Ruan X, Zhong J, et al. Study on Design of Elastic Support for Wind Turbine. E3S Web of Conferences. 2020; 194: 03017. doi: 10.1051/e3sconf/202019403017

[12]Lei Y, Hou L, Fu Y, et al. Research on vibration and noise reduction of electric bus gearbox based on multi-objective optimization. Applied Acoustics. 2020; 158: 107037. doi: 10.1016/j.apacoust.2019.107037

[13]Jouilel N, Radouani M, El Fahime B. Wind Turbine’s Gearbox Aided Design Approach Using Bond Graph Methodology and Monte Carlo Simulation. International Journal of Precision Engineering and Manufacturing-Green Technology. 2021; 8(1): 89–101. doi: 10.1007/s40684-019-00170-w

[14]Bozca M. Transmission error model-based optimisation of the geometric design parameters of an automotive transmission gearbox to reduce gear-rattle noise. Applied Acoustics. 2018; 130: 247–259. doi: 10.1016/j.apacoust.2017.10.005

[15]Garambois P, Perret-Liaudet J, Rigaud E. NVH robust optimization of gear macro and microgeometries using an efficient tooth contact model. Mechanism and Machine Theory. 2017; 117: 78–95. doi: 10.1016/j.mechmachtheory.2017.07.008

[16]Liu G, Liu H, Zhu C, et al. Design optimization of a wind turbine gear transmission based on fatigue reliability sensitivity. Frontiers of Mechanical Engineering. 2021; 16(1): 61–79. doi: 10.1007/s11465-020-0611-5

[17]Zhang Y, Ji JC, Ren Z, et al. Digital twin-driven partial domain adaptation network for intelligent fault diagnosis of rolling bearing. Reliability Engineering & System Safety. 2023; 234: 109186. doi: 10.1016/j.ress.2023.109186

[18]Liu X, Jiang D, Tao B, et al. A systematic review of digital twin about physical entities, virtual models, twin data, and applications. Advanced Engineering Informatics. 2023; 55: 101876. doi: 10.1016/j.aei.2023.101876

[19]Zhou Y, Zhou J, Cui Q, et al. Digital twin‐driven online intelligent assessment of wind turbine gearbox. Wind Energy. 2024; 27(8): 797–815. doi: 10.1002/we.2912

[20]Öztürk N, Dalcalı A, Çelik E, et al. Cogging torque reduction by optimal design of PM synchronous generator for wind turbines. International Journal of Hydrogen Energy. 2017; 42(28): 17593–17600. doi: 10.1016/j.ijhydene.2017.02.093

[21]Abdoos A, Moazzen ME, Ebadi A. Optimal Design of a Radial-Flux Permanent Magnet Generator with Outer-Rotor for Direct-Drive Wind Turbines. Computational Intelligence in Electrical Engineering. 2020; 11(4). doi: 10.22108/isee.2020.117057.1227 (in Persian)

[22]Alemi-Rostami M, Rezazadeh G, Alipour-Sarabi R, et al. Design and Optimization of a Large-Scale Permanent Magnet Synchronous Generator. Scientia Iranica. 2019; 29(1). doi: 10.24200/sci.2019.53569.3314

[23]Jin F, Si J, Cheng Z, et al. Optimization Design of A Novel Toroidal-Winding Permanent Magnet Synchronous Generator. In: Proceedings of the 2019 22nd International Conference on Electrical Machines and Systems (ICEMS); 11–14 August 2019; Harbin, China. pp. 1–5. doi: 10.1109/ICEMS.2019.8921858

[24]Emami SP, Mahmoudi A, Kahourzade S. Robust Optimization of a Wind Generator based on an Analytical Model and Wind data of a Site. In: Proceedings of the 2020 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES); 16–19 December 2020; Jaipur, India. pp. 1–6. doi: 10.1109/PEDES49360.2020.9379720

[25]Mohd-Shafri SA, Tiang TL, Ishak D, et al. Optimal Design of SMPMSM Using Genetic Algorithm Based on Finite Element Model. In: Proceedings of the 11th International Conference on Robotics, Vision, Signal Processing and Power Applications. Springer; 2022. pp. 721–726. doi: 10.1007/978-981-16-8129-5_110

[26]Mohd-Shafri SA, Tiang TL, Tan CJ, et al. Optimal Design of SMPMSM Using SD-model based on Genetic Algorithm. In: Proceedings of the 2021 IEEE International Magnetic Conference (INTERMAG); 26–30 April 2021; Lyon, France. pp. 1–7. doi: 10.1109/INTERMAG42984.2021.9579622

[27]Sindhya K, Manninen A, Miettinen K, et al. Design of a Permanent Magnet Synchronous Generator Using Interactive Multiobjective Optimization. IEEE Transactions on Industrial Electronics. 2017; 64(12): 9776–9783. doi: 10.1109/TIE.2017.2708038

[28]Dang L, Samb SO, Bernard N. Design optimization of a direct-drive PMSG considering the torque-speed profile Application for Offshore wind energy. In: Proceedings of the 2020 International Conference on Electrical Machines (ICEM); 23–26 August 2020; Gothenburg, Sweden. pp. 1875–1881. doi: 10.1109/ICEM49940.2020.9271034

[29]Dang L, Samb SO, Sadou R, et al. Co-Design Optimization of Direct Drive PMSGs for Offshore Wind Turbines Based on Wind Speed Profile. Energies. 2021; 14(15): 4486. doi: 10.3390/en14154486

[30]Asef P, Perpina RB, Barzegaran MR, et al. Multiobjective Design Optimization Using Dual-Level Response Surface Methodology and Booth’s Algorithm for Permanent Magnet Synchronous Generators. IEEE Transactions on Energy Conversion. 2018; 33(2): 652–659. doi: 10.1109/TEC.2017.2777397

[31]Jaen-Sola P, McDonald AS, Oterkus E. Lightweight design of direct-drive wind turbine electrical generators: A comparison between steel and composite material structures. Ocean Engineering. 2019; 181: 330–341. doi: 10.1016/j.oceaneng.2019.03.053

[32]Chen R, Qin D, Liu C. Dynamic modelling and dynamic characteristics of wind turbine transmission gearbox-generator system electromechanical-rigid-flexible coupling. Alexandria Engineering Journal. 2023; 65: 307–325. doi: 10.1016/j.aej.2022.10.036

[33]He Y. Research on Uniformity and Orthogonality of Latin Hypercube Design [PhD Thesis]. Peking University; 2011. Available online: https://d.wanfangdata.com.cn/thesis/Y2024797 (in Chinese)