A set of linear equations describing the motion of an operating 3-bladed HAWT is obtained from the dynamic characteristics of the stationary turbine by adding rotating frame effects. The approach makes use of the Coleman multi-blade transformation to present all results relative to the fixed frame. The formulation is in terms of a selected number of stationary, real mode shapes. The formulation is applied to the expression of both the aerodynamic loading and the displacement response in terms of the complex operating mode shapes. The technique is demonstrated on a hypothetical 46-m wind turbine subject to vertical wind shear. The principal objective of the paper is to enable the characteristics of the inflow to be related to the nature of the response. A second objective is to illustrate a method of extracting linearized models from general aeroelastic codes such as ADAMS™.

Issue Section:
Technical Papers
Keywords:
wind turbines, aerodynamics
Topics:
Blades, Inflow, Stress, Turbines, Wind shear, Wind turbines, Equations of motion, Horizontal axis wind turbines, Mode shapes
1.
Sutherland, H. J., 2001, “Preliminary Analysis of the Structural and Inflow Data From the LIST Program,” Proc. of AIAA/ASME Wind Energy Symp., Reno, NV, pp. 173–183.
2.
Meirovitch, L., 1980, Computational Methods in Structural Dynamics, Sijthoff & Nordhoff.
3.
Meirovitch
,
L.
,
1975
, “
A Modal Analysis for the Response of Linear Gyroscopic Systems
,”
ASME J. Appl. Mech.
,
42
(
2
), pp.
446
–
450
.
4.
Malcolm, D. J., 2001, “Aerodynamic Loads on HAWTs in Terms of Structural Modes,” Proc. of AIAA/ASME Wind Energy Symp., Reno, NV, pp. 411–418.
5.
Coleman, R. P., and Feingold, A. M., 1958, “Theory of Self-Excited Mechanical Oscillations of Helicopter Rotors With Hinged Blades,” NACA Tech. Report TR 1351.
6.
Dugundji, J., and Wendell, J. H., 1981, “Review of Analysis Methods for Rotating Systems With Periodic Coefficients,” Proc. of Wind Turbine Dynamics, NASA Conf. Pub. 2185, DOE Pub. CONF-810226, Cleveland, OH.
7.
Malcolm, D. J., and James, G. H., 1996, “Identification of Natural Operating Modes of HAWTs From Modeling Data,” Proc. of ASME Wind Energy Symp., Houston, TX, pp. 24–31.
8.
Kelley, N. D., Hand, M., Larwood, S., and McKenna, E., 2002, “The NREL Large Scale Turbine Inflow and Response Experiment-Preliminary Results,” Proc. of ASME/AIAA Wind Energy Symp., Reno, NV, pp. 412–426.
9.
Kelley, N. D., Osgood, R., Bialasiewicz, J., and Jakubowski, A., 2000, “Using Time-Frequency and Wavelet Analysis to Assess Turbulence/Rotor Interactions,” Proc. of ASME/AIAA Wind Energy Symp., Reno, NV, pp. 130–149.
10.
Mechanical Dynamics Inc., 1994, ADAMS/Solver Reference Manual, Version 8.0, Ann Arbor, MI.
11.
Patil, M., Lee, D., and Hodges, D., 2001, “Multi-Flexible-Body Dynamic Analysis of Horizontal Axis Wind Turbines,” Proc. ASME/AIAA Wind Energy Symp., Reno, NV, pp. 369–399.
12.
Lee, D., and Hodges, D., 2002, “A Framework for Dynamic and Aeroelastic Analysis of Horizontal Axis Wind Turbines,” Proc. of ASME/AIAA Wind Energy Symp., Reno, NV, pp. 223–236.
13.
Bir, G., and Stol, K., 2000, “Modal Analysis of a Teetered-Rotor Turbine Using the Floquet Approach,” Proc. of AIAA/ASME Wind Energy Symp., Reno, NV, pp. 23–33.
Copyright © 2002
 by American Institute of Physics
You do not currently have access to this content.