Environmental Engineering Reference
In-Depth Information
Coupling between teeter motion and blade pitch angle is introduced when the axis of
the teeter hinge is skewed from being perpendicular to the blade axis by a so-called d 3
angle , as illustrated in Figure 10-4. As a
rotor blade teeters upwind and downwind
of the plane of revolution, the d 3 angle
causes the blade to twist on its longitudi-
nal axis and change pitch in proportion
to the teeter angle. Thus, a d 3 angle intro-
duces cyclic pitch in a two-bladed rotor,
which means that the pitch on one blade
increases while the pitch on the second
blade decreases. The purpose of having
a d 3 hinge in a wind turbine hub is to re-
strain the amplitude of teetering by
means of an aerodynamic “spring.”
However, the resulting feedback from
teetering to blade pitch creates negative
aerodynamic damping of the first unsym-
metrical flatwise bending mode. This im-
portant mode is superimposed on the rigid-
body teeter motion. Under typical design
conditions, a d 3 angle can reduce the aero-
dynamic damping of this mode from a
normal 3 percent to 1 percent of critical. If
the rotor is to run at an unusually high
rotational speed, it may be necessary to
reduce or eliminate the d 3 angle to keep
this bending mode from becoming unsta-
ble.
Figure 10-4. The so-called d 3 angle intro-
duced into a teetered hub to restrain the
teeter motion. However, a d 3 angle also re-
duces aerodynamic damping.
HAWT Nacelle/Tower Instability
In the absence of corrective control system action, there are aeroelastic instabilities that
may be encountered as motions of the nacelle and tower of a HAWT. There are two modes
of importance, each essentially driven by a disturbance of the direction the rotor thrust
vector relative to the rotor shaft axis.
First, a whirl mode instability can occur in which the shaft moves through a conical
locus, with the tower deflecting and the hub moving in a nearly circular path. This mode
requires approximately equal stiffness of shaft restraint in the vertical and lateral directions
before it will become unstable, which is not difficult to avoid in a practical design. Bend-
ing coupling between the rotor and the shaft, which is present in hingeless hubs, exacerbates
the prospect of a whirl mode instability and warrants careful analytical investigation.
A second vibration mode involving yaw angle oscillations of the turbine shaft is inher-
ently unstable for downwind rotors and stable for upwind rotors. When the center of
gravity of the nacelle/rotor combination is not on the tower centerline and the yaw drive is
soft or disengaged, there will be cyclic angular motion of the shaft centerline in a horizontal
plane whenever there is lateral bending motion. The rotor thrust vector will lag behind the
shaft angular motion because of teetering action, resulting in a periodic lateral thrust
component that can feed the lateral tower bending. In the upwind-rotor configuration, the
result is positive damping of this mode. However, in the downwind configuration the result
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