The current research of wind turbine drivetrain is mainly concentrated in dynamic characteristics of gearbox with a specific suspension of main shaft, such as one-point and two-point suspension. However, little attention is paid to the effects of these suspension configurations on the dynamic responses of wind turbine gearbox. This paper investigates the influences of suspension configurations of main shaft on the dynamic characteristics of drivetrain. For evaluating the dynamic behaviors of drivetrain with multi-stage transmission system more realistically, a dynamic modeling approach of drivetrain is proposed based on Timoshenko beam theory and Lagrange's equation. Considering the flexibility and different suspension configurations of main shaft, time-varying mesh stiffness excitation, time-varying transmission error excitation and gravity excitation, etc., a three-dimensional dynamic model of drivetrain is developed, and the dynamic responses of drivetrain are investigated. Results show that with the one-point suspension of main shaft, the resonance frequencies in gearbox, especially at the low-speed stage, obviously shift to the higher frequency range compared to the gearbox without main shaft, but this trend could be inversed by increasing main shaft length. Meanwhile, the loads in main shaft, main shaft bearing and carrier bearing are greatly sensitive to the main shaft length. Hence, the load sharing is further disrupted by main shaft, but this effect could be alleviated by larger load torque. Comparing to the one-point suspension of main shaft, there occurs the obvious load reduction at the low-speed stage with two-point suspension of main shaft. However, those advantages greatly depend on the distance between two main bearings, and come at the expense of increased load in upwind main shaft unit and the corresponding main bearing. Finally, a wind field test is conducted to verify the proposed drivetrain model. This study develops a numerical model of drivetrain which is able to evaluate the effects of different suspension configurations of main shaft on gearbox.
The current research of wind turbine drivetrain is mainly concentrated in dynamic characteristics of gearbox with a specific suspension of main shaft, such as one-point and two-point suspension. However, little attention is paid to the effects of these suspension configurations on the dynamic responses of wind turbine gearbox. This paper investigates the influences of suspension configurations of main shaft on the dynamic characteristics of drivetrain. For evaluating the dynamic behaviors of drivetrain with multi-stage transmission system more realistically, a dynamic modeling approach of drivetrain is proposed based on Timoshenko beam theory and Lagrange's equation. Considering the flexibility and different suspension configurations of main shaft, time-varying mesh stiffness excitation, time-varying transmission error excitation and gravity excitation, etc., a three-dimensional dynamic model of drivetrain is developed, and the dynamic responses of drivetrain are investigated. Results show that with the one-point suspension of main shaft, the resonance frequencies in gearbox, especially at the low-speed stage, obviously shift to the higher frequency range compared to the gearbox without main shaft, but this trend could be inversed by increasing main shaft length. Meanwhile, the loads in main shaft, main shaft bearing and carrier bearing are greatly sensitive to the main shaft length. Hence, the load sharing is further disrupted by main shaft, but this effect could be alleviated by larger load torque. Comparing to the one-point suspension of main shaft, there occurs the obvious load reduction at the low-speed stage with two-point suspension of main shaft. However, those advantages greatly depend on the distance between two main bearings, and come at the expense of increased load in upwind main shaft unit and the corresponding main bearing. Finally, a wind field test is conducted to verify the proposed drivetrain model. This study develops a numerical model of drivetrain which is able to evaluate the effects of different suspension configurations of main shaft on gearbox.
[1] Y Guo, J Keller, La Cava W, et al. Recommendations on model fidelity for wind turbine gearbox simulations. United States:National Renewable Energy Lab, Golden, CO, 2015.
[2] J Helsen, P Peeters, K Vanslambrouck, et al. The dynamic behavior induced by different wind turbine gearbox suspension methods assessed by means of the flexible multibody technique. Renewable Energy, 2014, 69:336-346.
[3] J Helsen, F Vanhollebeke, F D Coninck, et al. Insights in wind turbine drive train dynamics gathered by validating advanced models on a newly developed 13.2 MW dynamically controlled test-rig. Mechatronics, 2011, 21(4):737-752.
[4] J Helsen, F Vanhollebeke, B Marrant, et al. Multibody modelling of varying complexity for modal behavior analysis of wind turbine gearboxes. Renewable Energy, 2011, 36(11):3098-3113.
[5] J Peeters, D Vandepitte, P Sas. Multibody simulation of a three-stage planetary gearbox in a wind turbine. Proceedings of the 7th German Wind Energy Conference, German, 2004.
[6] J L Peeters, D Vandepitte, P Sas. Analysis of internal drive train dynamics in a wind turbine. Wind Energy, 2006, 9(1-2):141-161.
[7] Y Guo, J Keller, W Lacava. Combined effects of gravity, bending moment, bearing clearance, and input torque on wind turbine planetary gear load sharing. AGMA Fall Technical Meeting, Dearborn, USA, 2012.
[8] R Schkoda, A Bibo, Y Guo, et al. Characterizing the influence of abstraction in full-scale wind turbine nacelle testing. ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, USA, 2016.
[9] C C Zhu, S Chen, C S Song, et al. Dynamic analysis of a megawatt wind turbine drive train. Journal of Mechanical Science and Technology, 2015, 29(5):1913-1919.
[10] C C Zhu, S Chen, H J Liu, et al. Dynamic analysis of the drive train of a wind turbine based upon the measured load spectrum. Journal of Mechanical Science and Technology, 2014, 28(6):2033-2040.
[11] S L Zhang, C C Zhu, C S Song, et al. Natural characteristic analysis of wind turbine drivetrain considering flexible supporting. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2017:0954406217692006.
[12] V K Ambarisha, R G Parker. Nonlinear dynamics of planetary gears using analytical and finite element models. Journal of Sound and Vibration, 2007, 302(3):577-595.
[13] T M Ericson, R G Parker. Planetary gear modal vibration experiments and correlation against lumped-parameter and finite element models. Journal of Sound and Vibration, 2013, 332(9):2350-2375.
[14] W Shi, C W Kim, C W Chung, et al. Dynamic modeling and analysis of a wind turbine drivetrain using the torsional dynamic model. International Journal of Precision Engineering & Manufacturing, 2013, 14(1):153-159.
[15] M Zhao, J C Ji. Nonlinear torsional vibrations of a wind turbine gearbox. Applied Mathematical Modelling, 2015, 39(16):4928-4950.
[16] P Srikanth, A S Sekhar. Wind turbine drive train dynamic characterization using vibration and torque signals. Mechanism & Machine Theory, 2016, 98:2-20.
[17] S Wei, Q Han, Z Peng, et al. Dynamic analysis of parametrically excited system under uncertainties and multi-frequency excitations. Mechanical Systems & Signal Processing, 2016, 72:762-784.
[18] C C Zhu, X Y Xu, H J Liu, et al. Research on dynamical characteristics of wind turbine gearboxes with flexible pins. Renewable Energy, 2014, 68:724-732.
[19] C C Zhu, X Y Xu, T C Lim, et al. Effect of flexible pin on the dynamic behaviors of wind turbine planetary gear drives. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2013, 227(1):74-86.
[20] H F Zhai, C C Zhu, C S Song, et al. Dynamic modeling and analysis for transmission system of high-power wind turbine gearbox. Journal of Mechanical Science and Technology, 2015, 29(10):4073-4082.
[21] Y Xing, M Karimirad, T Moan. Modelling and analysis of floating spar-type wind turbine drivetrain. Wind Energy, 2014, 17(4):565-587.
[22] L Sethuraman, Y Guo, S Sheng. Main bearing dynamics in three-point suspension drivetrains for wind turbines. American Wind Energy Association Conference & Exhibition, USA, 2015.
[23] X Liang. Dynamic characteristics research based on load spectrum of megawatt level wind turbine gearbox. Chongqing:Chongqing University, 2013. (in Chinese)
[24] J S Rao, T N Shiau, J R Chang. Theoretical analysis of lateral response due to torsional excitation of geared rotors. Mechanism & Machine Theory, 1998, 33(6):761-783.
[25] Z X Fei. Research on finite element modeling and dynamic behaviors of complex multi-rotor coupled systems. Hangzhou:Zhejiang University, 2013. (in Chinese)
[26] J J Tan, C C Zhu, C C Song, et al. Study on the dynamic modeling and natural characteristics of wind turbine drivetrain considering electromagnetic stiffness. Mechanism and Machine Theory, 2019, 134:541-561.
[27] Y Guo, R G Parker. Dynamic modeling and analysis of a spur planetary gear involving tooth wedging and bearing clearance nonlinearity. European Journal of Mechanics-A/Solids, 2010, 29(6):1022-1033.
[28] J A Keller, Y Guo, L Sethuraman. Gearbox reliability collaborative investigation of gearbox motion and high-speed-shaft loads, United States:National Renewable Energy Lab, Golden, CO, 2016.
[29] Y Guo, R G Parker. Dynamic analysis of planetary gears with bearing clearance. Journal of Computational & Nonlinear Dynamics, 2012, 7(4):041002.
[30] S S Wang. Research on dynamic characteristics of wind power transmission system considering non-torque loads. Chongqing:Chongqing University, 2017. (in Chinese)
[31] SKF:WindCon by SKF condition monitoring for wind turbine systems,[2019-03-13].https://www.skf.com/group/industry-solutions/wind-energy/applications/index.html.