Design optimization of a wind turbine gear transmission based on fatigue reliability sensitivity

Abstract

Fatigue failure of gear transmission is one of the key factors that restrict the performance and service life of wind turbines. One of the major concerns in gear transmission under random loading conditions is the disregard of dynamic fatigue reliability in conventional design methods. Various issues, such as overweight structure or insufficient fatigue reliability, require continuous improvements in the reliability-based design optimization (RBDO) methodology. In this work, a novel gear transmission optimization model based on dynamic fatigue reliability sensitivity is developed to predict the optimal structural parameters of a wind turbine gear transmission. In the model, the dynamic fatigue reliability of the gear transmission is evaluated based on stress–strength interference theory. Design variables are determined based on the reliability sensitivity and correlation coefficient of the initial design parameters. The optimal structural parameters with the minimum volume are identified using the genetic algorithm in consideration of the dynamic fatigue reliability constraints. Comparison of the initial and optimized structures shows that the volume decreases by 3.58% while ensuring fatigue reliability. This work provides new insights into the RBDO of transmission systems from the perspective of reliability sensitivity.

Keywords

gear transmission / fatigue reliability / reliabi-lity sensitivity / parameter optimization

References

[1] He H F, Liu H J, Zhu C C, Study on the gear fatigue behavior considering the effect of residual stress based on the continuum damage approach. Engineering Failure Analysis, 2019, 104: 531–544

[2] Zhou Y, Zhu C C, Liu H J. A micropitting study considering rough sliding and mild wear. Coatings, 2019, 9(10): 639

[3] Yuan M, Liu Y, Yan D H, Probabilistic fatigue life prediction for concrete bridges using Bayesian inference. Advances in Structural Engineering, 2019, 22(3): 765–778

[4] Zhou J, Roshanmanesh S, Hayati F, Improving the reliability of industrial multi-MW wind turbines. Insight–Non-Destructive Testing and Condition Monitoring, 2017, 59(4): 189–195

[5] Yi P X, Hu P, Shi T. Numerical analysis and experimental investigation of modal properties for the gearbox in wind turbine. Frontiers of Mechanical Engineering, 2016, 11(4): 388–402

[6] Chen H T, Fan J K, Jing S X, Probabilistic design optimization of wind turbine gear transmission system based on dynamic reliability. Journal of Mechanical Science and Technology, 2019, 33(2): 579–589

[7] Nejad A R, Gao Z, Moan T. On long-term fatigue damage and reliability analysis of gears under wind loads in offshore wind turbine drivetrains. International Journal of Fatigue, 2014, 61: 116–128

[8] Chen H T, Wang X H, Gao H C, Dynamic characteristics of wind turbine gear transmission system with random wind and the effect of random backlash on system stability. Proceedings of the Institution of Mechanical Engineers. Part C, Journal of Mechanical Engineering Science, 2017, 231(14): 2590–2597

[9] Zhu S P, Liu Q, Lei Q, Probabilistic fatigue life prediction and reliability assessment of a high pressure turbine disc considering load variations. International Journal of Damage Mechanics, 2018, 27(10): 1569–1588

[10] Zhu S P, Liu Q, Peng W W, Computational–experimental approaches for fatigue reliability assessment of turbine bladed disks. International Journal of Mechanical Sciences, 2018, 142–143: 502–517

[11] Lu C, Feng Y W, Fei C W. Weighted regression-based extremum response surface method for structural dynamic fuzzy reliability analysis. Energies, 2019, 12(9): 1588

[12] Zhu S P, Liu Q, Zhou J, Fatigue reliability assessment of turbine discs under multi-source uncertainties. Fatigue & Fracture of Engineering Materials & Structures, 2018, 41(6): 1291–1305

[13] Mishra S K, Roy B K, Chakraborty S. Reliability-based-design-optimization of base isolated buildings considering stochastic system parameters subjected to random earthquakes. International Journal of Mechanical Sciences, 2013, 75: 123–133

[14] Zhou D, Zhang X F, Zhang Y M. Dynamic reliability analysis for planetary gear system in shearer mechanisms. Mechanism and Machine Theory, 2016, 105: 244–259

[15] Xie L Y, Wu N X, Qian W X. Time domain series system definition and gear set reliability modeling. Reliability Engineering & System Safety, 2016, 155: 97–104

[16] Wang L, Shen T, Chen C, Dynamic reliability analysis of gear transmission system of wind turbine in consideration of randomness of loadings and parameters. Mathematical Problems in Engineering, 2014, 2014: 261767

[17] Tan X F, Xie L Y. Fatigue reliability evaluation method of a gear transmission system under variable amplitude loading. IEEE Transactions on Reliability, 2019, 68(2): 599–608

[18] Yan Y Y. Load characteristic analysis and fatigue reliability prediction of wind turbine gear transmission system. International Journal of Fatigue, 2020, 130: 105259

[19] Han W, Zhang X L, Huang X S, A time-dependent reliability estimation method based on Gaussian process regression. In: Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Quebec City: ASME, 2018, V02AT03A056

[20] Wei F, Lin H. Multi-objective optimization of process parameters for the helical gear precision forging by using Taguchi method. Journal of Mechanical Science and Technology, 2011, 25(6): 1519–1527

[21] Korta J A, Mundo D. Multi-objective micro-geometry optimization of gear tooth supported by response surface methodology. Mechanism and Machine Theory, 2017, 109: 278–295

[22] Savsani V, Rao R V, Vakharia D P. Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms. Mechanism and Machine Theory, 2010, 45(3): 531–541

[23] Zhu C C, Xu X Y, Lu B, Fuzzy reliability optimization for transmission system of high-power marine gearbox. Journal of Ship Mechanics, 2010, 14(8): 915–921 (in Chinese)

[24] Qin D T, Xing Z, Wang J. Optimization design of system parameters of the gear transmission of wind turbine based on dynamics and reliability. Chinese Journal of Mechanical Engineering, 2008, 44(7): 24–31

[25] Zhang G Y, Wang G Q, Li X F, Global optimization of reliability design for large ball mill gear transmission based on the Kriging model and genetic algorithm. Mechanism and Machine Theory, 2013, 69: 321–336

[26] Wang Q Q, Wang H. Reliability optimization design of the gear modification coefficient based on the meshing stiffness. In: Proceedings of the 2nd International Conference on Advances in Materials, Machinery, Electronics. Xi’an: AMME, 2018, 1955: 030015

[27] Tong C, Tian Z. Optimization design of gear reducer based on multi-attribute decision making and reliability sensitivity. In: Proceedings of the International Conference on Optoelectronic Science and Materials. Hefei: IOP, 2020, 711: 012045

[28] Spinato F, Tavner P J, van Bussel G J W, Reliability of wind turbine subassemblies. IET Renewable Power Generation, 2009, 3(4): 387–401

[29] Li Y, Zhu C C, Tao Y C, Research status and development tendency of wind turbine reliability. China Mechanical Engineering, 2017, 28(9): 1125–1133 (in Chinese)

[30] Wang W, Liu H J, Zhu C C, Effect of the residual stress on contact fatigue of a wind turbine carburized gear with multiaxial fatigue criteria. International Journal of Mechanical Sciences, 2018, 151: 263–273

[31] Qin D T, Zhou Z G, Yang J, Time-dependent reliability analysis of gear transmission system of wind turbine under stochastic wind load. Chinese Journal of Mechanical Engineering, 2012, 48(3): 1–8

[32] International Electrotechnical Commission. IEC 61400-4:2012. Wind Turbines—Part 4: Design Requirements for Wind Turbine Gearboxes. 2012

[33] Sun W, Li X, Wei J. An approximate solution method of dynamic reliability for wind turbine gear transmission with parameters of uncertain distribution type. International Journal of Precision Engineering and Manufacturing, 2018, 19(6): 849–857

[34] Gao J X, An Z. A new probability model of residual strength of material based on interference theory. International Journal of Fatigue, 2019, 118: 202–208

[35] Lin X, Wei J, Lai Y, Gear residual strength model and dynamic reliability. Journal of Harbin Engineering University, 2017, 38(9): 1476–1483 (in Chinese)

[36] He H F, Liu H J, Zhu C C, Study of rolling contact fatigue behavior of a wind turbine gear based on damage-coupled elastic-plastic model. International Journal of Mechanical Sciences, 2018, 141: 512–519

[37] Schaff J R, Davidson B D. Life prediction methodology for composite structures. Part I—Constant amplitude and two-stress level fatigue. Journal of Composite Materials, 1997, 31(2): 128–157

[38] International Organization for Standardization. ISO 6336-2-2019. Calculation of Load Capacity of Spur and Helical Gears—Part 2: Calculation of Surface Durability (pitting). 2019

[39] International Organization for Standardization. ISO 6336-3-2019. Calculation of Load Capacity of Spur and Helical Gears—Part 3: Calculation of Tooth Bending Strength. 2019

[40] Evans M H. White structure flaking (WSF) in wind turbine gearbox bearings: Effect of ‘butterflies’ and white etching cracks (WECs). Materials Science and Technology, 2012, 28(1): 3–22

[41] Li M, Xie L, Ding L. Load sharing analysis and reliability prediction for planetary gear train of helicopter. Mechanism and Machine Theory, 2017, 115: 97–113

[42] Wei J, Pan Z, Lin X Y, Copula-function-based analysis model and dynamic reliability of a gear transmission system considering failure correlations. Fatigue & Fracture of Engineering Materials & Structures, 2019, 42(1): 114–128

[43] International Organization for Standardization. ISO 6336-5: Calculation of Load Capacity of Spur and Helical Gears—Part 5: Strength and Quality of Materials. 2017

[44] Aghili S J, Hajian-Hoseinabadi H. The reliability investigation considering data uncertainty; an application of fuzzy transformation method in substation protection. International Journal of Electrical Power & Energy Systems, 2014, 63: 988–999

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grant No. U1864210).

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2021 Higher Education Press