Page 374 - Wind Energy Handbook

348 CONCEPTUAL DESIGN OF HORIZONTAL-AXIS TURBINES

is normally dominated by the cyclic gravity moment due to the cantilevered
rotor mass. On a rigid hub machine, the shaft moment ‘Damage Equivalent
Load’ or DEL (defined in Section 5.12.6) due to deterministic and stochastic
rotor out-of-plane loadings combined can be of similar magnitude, so the
insertion of a teeter hinge can produce a substantial reduction in overall shaft
moment DEL. It should be noted, however, that the cyclic shaft moment due to
wind shear relieves that due to gravity on a rigid hub machine, so teetering is
not beneficial in respect of this load component.
A rough estimate of the overall shaft moment DEL on a rigid-hub machine,
excluding yaw error and tower shadow effects, can be obtained by taking the
square root of the sum of the squares of the shaft moment DEL due to stochastic
loads and that due to the combined cyclic loads due to gravity, wind shear and
shaft tilt.
(c) Nacelle structure. The provision of a teeter hinge should eliminate nodding and
yawing moments on the nacelle completely during operation, leaving only rotor
torque, thrust and in-plane loadings. This will benefit the fatigue design of the
nacelle structure considerably, but not the extreme load design, for the reasons
already explained.

(d) Yaw bearing and yaw drive. Rigid-hub machines experience severe yaw moments
due to both deterministic and stochastic loads, which were underestimated on
many early designs. The introduction of a teeter hinge dramatically reduces
yaw moments during operation by eliminating rotor out-of-plane moments on
the hub, but yaw moments due to in-plane loads on the rotor still remain.
The relative magnitude of the yaw moments due to in-plane as opposed to
out-of-plane loads on a rigid-hub rotor can be appreciated by comparing the
effect of wind speed fluctuation, u, on the in-plane and out-of-plane loads on a
blade element. Assuming that the blade is not stalled and that ö is small, the in-
plane load per unit length is, from Equation (5.131a), given approximately by:

F Y ¼ 1 rÙ dC l c(r)ru C l þ sin ö (6:12)
2 dÆ dC l =dÆ

whereas the out-of-plane load per unit length is, from Equation (5.25) approxi-
mately

dC l
1
F X ¼ rÙ c(r)ru (6:13)
2 dÆ
Defining the distance between the hub centre and the tower centre-line as e,itis
seen that the yaw moment due to the in-plane rotor load is

e C l þ sin ö
r dC l =dÆ