Environmental Engineering Reference
In-Depth Information
mode corresponds to the natural frequency of the blades while the asymmetric are
coupled modes; one is coupled with the tower torsion and concerns the yawing of
the rotor while the other is coupled with the tower bending and concerns the tilting
of the rotor. Because the tower modes are low, the coupled modes will be lower as
compared to the symmetric one. In most designs the symmetric mode appears near
4p for three bladed rotors so that there is some margin to accommodate the cou-
pled modes. In purely structural terms one would desire a stiffer blade, but this
would increase the cost which is, in the case of wind turbines the most important
design driver. Finally as regards the lead-lag (or edgewise) motion, due to higher
stiffness the fi rst stand still fi rst mode should appear in the vicinity of 6p so that
when in operation, the coupled modes are at 5 and 7p and thus 6p is avoided.
The quality of structural models based on beam theory can be quite good.
In Table 1 predictions obtained for a commercial wind turbine are compared to
measurements indicating a maximum error of 7%.
8.2 Dynamic simulations
Dynamic simulations refer to situations in which the excitation is time varying.
Dynamic excitation on wind turbines is caused by the wind infl ow and can be either
periodic or non-periodic (the latter are usually referred to as stochastic). Typical
periodic excitations are generated by the mean wind shear, the yaw misalignment,
the blade-tower interaction and possibly the control. Non-periodic excitations are
related to the turbulent character of the wind. Strictly speaking in practice the
wind turbine is always stochastically excited. However it is possible to extract the
periodic part of the response by averaging with respect to the azimuth angle. Azi-
muthal averaging can be performed with measurements and simulations. A result
of this type is given in Fig. 10. The azimuthal variation of the predicted fl apwise
bending moment at blade root (left) and of the shaft tilting moment are compared
Table 1: Natural frequencies of the machine at standstill [30].
Natural frequency (Hz)
Difference
(%)
Mode
Measured
Predictions
1
First lateral tower bending
0.437
0.439
0.5
2
First longitudinal tower bending
0.444
0.448
0.9
3
First shaft torsion
0.668
0.674
0.9
4
First asymmetric fl ap/yaw
0.839
0.828
-1.3
5
First asymmetric fl ap/tilt
0.895
0.886
-1.0
6
First symmetric fl ap
0.955
1.024
7.2
7
First vertical edgewise
1.838
1.909
3.9
8
First horizontal edgewise
1.853
1.928
4.0
9
Second asymmetric fl ap/yaw
2.135
2.149
0.7
10
Second asymmetric fl ap/tilt
2.401
2.314
-3.6
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