Page 438 - Wind Energy Handbook

412 COMPONENT DESIGN

They concluded that the fundamental cause of edgewise blade oscillations that had
been observed on some stall-regulated machines of 40 m diameter and over was
negative aerodynamic damping, but found that the use of dynamic stall models
improved the level of agreement with measurements.

Coupling of edgewise blade mode and rotor whirl modes

A further important finding was that, on one machine subject to stall-induced
vibrations which was investigated in detail, there was coupling between the blade
first edgewise mode and one of the second rotor whirl modes. The rotor whirl
modes arise from the combination of simultaneous nodding and yawing oscillations
of the rotor shaft, which occur at the same frequency during operation due to
gyroscopic effects. As a result, the rotor hub traces out a circular or elliptical path,
running either in the same direction as rotor rotation or in reverse, which explains
the existence of two first and second modes.
The explanation for the coupling was as follows. When a pair of blades vibrate in
the edgewise direction in anti-phase, they impart a sinusoidally varying in-plane
force to the rotor hub even though their edgewise root bending moments cancel
out. The direction of this oscillating force rotates with the rotor, so it has horizontal
and vertical components of the form sin(ø 1 t þ ç):sin Ùt and sin(ø 1 t þ ç):cos Ùt,
where ø 1 is the frequency of the blade first edgewise mod, and Ù is the speed of
rotor rotation. With respect to stationary axes the in-plane loads on the hub
therefore act at two frequencies – namely ø 1 þ Ù and ø 1 Ù. In the case of the
machine investigated by Petersen et al., the upper frequency of 2:9 þ 0:5 ¼ 3:4Hz
coincided with the backward second rotor whirl mode, allowing interaction be-
tween this mode and the blade first edgewise mode.
Simulations were carried out on an aeroelastic model of the turbine at various
wind speeds and satisfactory agreement obtained between simulated and measured
behaviour. In particular, the simulation at 23.2 m/s predicted the build up of large
blade root edgewise moment oscillations at the first mode frequency, as observed
on the real machine at this wind speed. Significantly, when the latter simulation
was repeated with the rotor shaft stiffness increased sufficiently to increase the
backward second rotor whirl mode frequency to 3.6 Hz, the predicted blade root
edgewise moment oscillations were negligible by comparison.

Mechanical damping

An alternative strategy for preventing damaging edgewise vibrations is the incor-
poration of a tuned mass damper inside the blade towards the tip. The performance
of such a damper on a 22 m tip radius blade is reported by Anderson, Heerkes and
Yemm (1998). It was found that the fitting of a damper tuned to the first mode
edgewise frequency, and weighing only 0.4 percent of the total blade weight,
effectively suppressed the edgewise vibrations which had previously been ob-
served during high wind speed operation.