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Technical Briefs

Flexible Multibody Dynamic Modeling of a Horizontal Wind Turbine Drivetrain System

[+] Author and Article Information
Datong Qin

State Key Lab for Mechanical Transmission, Chongqing University, Chongqing 400044, P.R.C.dtqin@cqu.edu.cn

Jianhong Wang1

State Key Lab for Mechanical Transmission, Chongqing University, Chongqing 400044, P.R.C.jhwang@cqu.edu.cn

Teik C. Lim

Department of Mechanical Engineering, University of Cincinnati, 598 Rhodes Hall, P.O. Box 210072, Cincinnati, OH 45221teik.lim@uc.edu

1

Corresponding author.

J. Mech. Des 131(11), 114501 (Oct 06, 2009) (8 pages) doi:10.1115/1.3211094 History: Received October 10, 2008; Revised July 28, 2009; Published October 06, 2009

A mathematical model of a horizontal wind turbine drivetrain is developed by applying the flexible multibody dynamics theory based on the Lagrange formulation. The proposed model accounts for the variation in the number of teeth in contact and support bearing elasticity, which are known to influence the dynamic behavior of drivetrain significantly. The derivation of the system governing equation by Lagrange equations requires the formulations of the kinetic energy terms of both orbiting and rotating gears, the potential energy terms of time-varying tooth stiffness and bearing compliance, and the work from input torque. From the resultant governing equations, the natural frequencies and modes of interest are calculated, and the effect of bearing stiffness on those modes is examined. The rotational vibrations of the sun gears as well as the tooth contact forces between the sun and planet and the ring and planet are analyzed in detail. Result of the dynamic transmission error as a function of gearbox speed is also predicted to understand the overall dynamic behavior of the drivetrain system.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

The kinematical motion and deformation of a flexible body with the initial position denoted by a nonsolid dashed double-dotted line

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Figure 2

A typical drive train assembly of interest applied in wind turbine applications

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Figure 3

Planetary gear set deformed coordinates

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Figure 4

Final drive pinion and gear deformed coordinates

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Figure 5

Displacements of bearings 2 and 3, sun gear, and input gear of final drive set along the y direction

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Figure 6

First mode of shaft 1 assembly at f=797 Hz

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Figure 7

Rotational mode of planetary set at f=15,647 Hz

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Figure 8

The influence of the stiffnesses of bearings 2 and 3 on the first natural frequencies of the shaft 1 assembly in the z direction response

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Figure 9

The influence of the stiffnesses of bearings 2 and 3 on the third natural frequency of shaft 1 assembly in the z direction response

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Figure 10

Sun gears floating in 30 s: (a) sun gear displacement in the y direction and (b) sun gear displacement in the z direction

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Figure 11

Tooth contact force: (a) ring and planet gear mesh; (b) sun and planet gear mesh

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Figure 12

rms amplitude Arms: (a) rms of DTE at the ring and planet gear mesh; (b) rms of DTE at the sun and planet gear mesh

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