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Research Papers

Coupled Dynamic Characteristics of Wind Turbine Gearbox Driven by Ring Gear Considering Gravity

[+] Author and Article Information
Aiqiang Zhang

State Key Laboratory of Mechanical
Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: zaq_sklmt@163.com

Jing Wei

State Key Laboratory of Mechanical
Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: weijing_slmt@163.com

Datong Qin

State Key Laboratory of Mechanical
Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: dtqin@cqu.edu.cn

Shaoshuai Hou

State Key Laboratory of Mechanical
Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: hou_shaoshuai@163.com

Teik C. Lim

Office of The Provost,
University of Texas Arlington,
701 South Nedderman Drive Davis Hall,
Suite 321,
Arlington, TX 19118
e-mail: teik.lim@uta.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received August 24, 2017; final manuscript received February 6, 2018; published online April 9, 2018. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 140(9), 091009 (Apr 09, 2018) (15 pages) Paper No: DS-17-1423; doi: 10.1115/1.4039482 History: Received August 24, 2017; Revised February 06, 2018

Gravity is usually neglected in the dynamic modeling and analysis of the transmission system, especially in some relatively lightweight equipment. The weight of wind turbine gearbox is up to tens of tons or even hundreds of tons, and the effects of gravity have not been explored and quantified. In order to obtain accurate vibration response predictions to understand the coupled dynamic characteristics of the wind turbine gear transmission system, a comprehensive, fully coupled, dynamic model is established by the node finite element method with gravity considered. Both time-domain and frequency-domain dynamic responses are calculated using the precise integration method with various excitations being taken into account. The results indicate that gravity has a significant impact on the vibration equilibrium position of central floating components, but the changing trends are different. Gravity does not change the composition of the excitation frequency, but will have a certain impact on the distribution ratio of the frequency components. And the high frequency vibrations are hardly affected by gravity. In addition, the load sharing coefficient is greater when gravity is taken into account, both of internal gearing and of external gearing system. When the planet gears have a certain position error in accordance with certain rules, the load sharing performance of the system will be better.

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References

Lin, J. , and Parker, R. G. , 1999, “ Sensitivity of Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters,” J. Sound Vib., 228(1), pp. 109–128. [CrossRef]
Lin, J. , and Parker, R. G. , 2000, “ Structured Vibration Characteristics of Planetary Gears With Unequally Spaced Planets,” J. Sound Vib., 233(5), pp. 921–928. [CrossRef]
Inalpolat, M. , and Kahraman, A. , 2008, “ Dynamic Modelling of Planetary Gears of Automatic Transmissions,” Proc. Inst. Mech. Eng. Part K, 222(3), pp. 229–242.
Qin, D. , Wang, J. , and Lim, T. C. , 2009, “ Flexible Multibody Dynamic Modeling of a Horizontal Wind Turbine Drivetrain System,” ASME J. Mech. Des., 131(11), p. 114501. [CrossRef]
Abousleiman, V. , Velex, P. , and Becquerelle, S. , 2007, “ Modeling of Spur and Helical Gear Planetary Drives With Flexible Ring Gears and Planet Carriers,” ASME J. Mech. Des., 129(1), pp. 95–106.
Abousleiman, V. , and Velex, P. , 2006, “ A Hybrid 3D Finite Element/Lumped Parameter Model for Quasi-Static and Dynamic Analyses of Planetary/Epicyclic Gear Sets,” Mech. Mach. Theory, 41(6), pp. 725–748. [CrossRef]
Lin, J. , and Parker, R. G. , 2002, “ Planetary Gear Parametric Instability Caused by Mesh Stiffness Vibration,” J. Sound Vib., 249(1), pp. 129–145. [CrossRef]
Liu, C. , Qin, D. , and Lim, T. C. , 2014, “ Dynamic Characteristics of the Herringbone Planetary Gear Set During the Variable Speed Process,” J. Sound Vib., 333(24), pp. 6498–6515. [CrossRef]
Sun, T. , and Hu, H. Y. , 2003, “ Nonlinear Dynamics of a Planetary Gear System With Multiple Clearances,” Mech. Mach. Theory, 38(12), pp. 1371–1390. [CrossRef]
Bahk, C. J. , and Parker, R. G. , 2011, “ Analytical Solution for the Nonlinear Dynamics of Planetary Gears,” ASME J. Comput. Nonlinear Dyn., 6(2), p. 021007.
Kim, W. , Ji, Y. L. , and Chung, J. , 2012, “ Dynamic Analysis for a Planetary Gear With Time-Varying Pressure Angles and Contact Ratios,” J. Sound Vib., 331(4), pp. 883–901. [CrossRef]
Montestruc, A. N. , 2010, “ Influence of Planet Pin Stiffness on Load Sharing in Planetary Gear Drives,” ASME J. Mech. Des., 133(1), p. 014501.
Singh, A. , 2010, “ Load Sharing Behavior in Epicyclic Gears: Physical Explanation and Generalized Formulation,” Mech. Mach. Theory, 45(3), pp. 511–530. [CrossRef]
Kahraman, A. , 1994, “ Load Sharing Characteristics of Planetary Transmissions,” Mech. Mach. Theory, 29(8), pp. 1151–1165. [CrossRef]
Gu, X. , and Velex, P. , 2012, “ A Dynamic Model to Study the Influence of Planet Position Errors in Planetary Gears,” J. Sound Vib., 331(20), pp. 4554–4574. [CrossRef]
Guo, Y. , Keller, J. , and Lacava, W. , 2012, “ Combined Effects of Gravity, Bending Moment, Bearing Clearance, and Input Torque on Wind Turbine Planetary Gear Load Sharing,” American Gear Manufacturers Association Fall Technical Meeting, Dearborn, MI, Oct. 28–30, pp. 53–68.
Guo, Y. , Keller, J. , and Parker, R. G. , 2014, “ Nonlinear Dynamics and Stability of Wind Turbine Planetary Gear Sets Under Gravity Effects,” Eur. J. Mech. A, 47, pp. 45–57. [CrossRef]
Guo, Y. , Keller, J. , and Parker, R. G. , 2012, “ Dynamic Analysis of Wind Turbine Planetary Gears Using an Extended Harmonic Balance Approach,” International Conference on Noise and Vibration Engineering, Leuven, Belgium, Sept. 17–19, pp. 4329–4342.
Wei, J. , and Zhang, A. , 2017, “ A Coupling Dynamics Analysis Method for a Multistage Planetary Gear System,” Mech. Mach. Theory, 110, pp. 27–49. [CrossRef]
Hua, X. , and Lim, T. C. , 2012, “ Dynamic Analysis of Spiral Bevel Geared Rotor Systems Applying Finite Elements and Enhanced Lumped Parameters,” Int. J. Automot. Technol., 13(1), pp. 97–107. [CrossRef]
Ren, Y. , Zhang, Y. , and Zhang, X. , 2015, “ Vibration and Stability of Internally Damped Rotating Composite Timoshenko Shaft,” J. Vibroengineering, 17(8), pp. 4404–4420.
Franciosi, C. , and Mecca, M. , 1998, “ Some Finite Elements for the Static Analysis of Beams With Varying Cross Section,” Comput. Struct., 69(2), pp. 191–196. [CrossRef]
Cui, C. , Liu, J. , and Chen, Y. , 2015, “ Simulating Nonlinear Aeroelastic Responses of an Airfoil With Freeplay Based on Precise Integration Method,” Commun. Nonlinear Sci. Numer. Simul., 22(1–3), pp. 933–942. [CrossRef]
Ma, H. , and Song, R. , 2014, “ Time-Varying Mesh Stiffness Calculation of Cracked Spur Gears,” Eng. Failure Anal., 44(5), pp. 179–194. [CrossRef]
Sun, W. , and Li, X. , 2015, “ A Study on Load-Sharing Structure of Multi-Stage Planetary Transmission System,” J. Mech. Sci. Technol., 29(4), pp. 1501–1511. [CrossRef]

Figures

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Fig. 1

Wind turbine gearbox transmission system: (a) transmission principle and (b) division of shafting elements

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Fig. 2

Example of an equivalent virtual shaft segment: (a) ring gear and (b) gear shaft

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Fig. 3

Shaft segment of (a) uniform cross section and (b) variable cross section

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Fig. 4

Connecting element

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Fig. 6

Mesh element: (a) internal gearing and (b) external gearing

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Fig. 7

The generalized coordinate system of the transmission system

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Fig. 8

Node finite element model and node number of the overall system

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Fig. 9

Time-varying mesh stiffness of (a) the first stage, (b) the second stage, and (c) the third stage

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Fig. 10

Motion trajectories of key node: (a) the ring gear, node 17, (b) the planet gear, node 21, (c) the sun gear, node 42, and (d) the pinion, node 63

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Fig. 11

Analysis diagram of force transmission

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Fig. 12

Mesh forces of the first stage and second stage, (a)–(c) are R-P11, R-P12, and R-P13, respectively, and (d)–(f) are P21-S, P22-S, and P23-S, respectively

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Fig. 13

Acceleration root-mean-square (RMS) value under different loading: (a) X direction, (b) Y direction, and (c) rate of change after considering gravity

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Fig. 14

Mesh force RMS value under different loading: (a) variation trend and (b) rate of change after considering gravity

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Fig. 15

Vibration displacement RMS value at different speeds: (a) variation trend and (b) rate of change after considering gravity

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Fig. 16

Vibration acceleration RMS value at different speeds: (a) the ring gear node and the sun gear node, (b) the pinion node, and (c) rate of change after considering gravity

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Fig. 17

Mesh force RMS value at different speeds: (a) variation trend and (b) rate of change after considering gravity

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Fig. 18

Frequency-domain response of displacement of the sun gear node in Y direction: (a) w/o gravity, (b) w/gravity, and (c) rate of change after considering gravity

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Fig. 19

Frequency-domain response of acceleration of the sun gear node in Y direction: (a) w/o gravity, (b) w/gravity, and (c) rate of change after considering gravity

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Fig. 20

Frequency-domain response of mesh force of P21-S: (a) w/o gravity, (b) w/gravity, and (c) rate of change after considering gravity

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Fig. 21

Effect of gravity under different bearing stiffness of the input shaft: (a) equilibrium position, (b) mesh force, and (c) rate of change of mesh force after considering gravity

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Fig. 22

Effect of gravity under different bearing stiffness of the output shaft: (a) equilibrium position, (b) change value of equilibrium position after considering gravity, and (c) mesh force

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Fig. 23

Effect of gravity under different mesh stiffness of the first stage: (a) equilibrium position, (b) mesh force, and (c) rate of change of mesh force after considering gravity

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Fig. 24

Effect of gravity under different mesh stiffness of the third stage: (a) equilibrium position, (b) change value of equilibrium position after considering gravity, and (c) mesh force

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Fig. 25

Load sharing coefficient of (a) internal gearing and (b) external gearing, without gravity considered

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Fig. 26

Load sharing coefficient of (a) internal gearing and (b) external gearing, with gravity considered

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Fig. 27

Load sharing coefficient of each planet gear of internal gearing when the position error exists in (a) P11, (b) P12, and (c) P13, without gravity considered

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Fig. 28

Load sharing coefficient of each planet gear of external gearing when the position error exists in (a) P21, (b) P22, and (c) P23, without gravity considered

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Fig. 29

Load sharing coefficient of each planet gear of internal gearing when the position error exists in (a) P11, (b) P12, and (c) P13, with gravity considered

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Fig. 30

Load sharing coefficient of each planet gear of external gearing when the position error exists in (a) P21, (b) P22, and (c) P23, with gravity considered

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Fig. 31

Variation rule of load sharing coefficient of (a) internal gearing and (b) external gearing, with position error

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