Page 265 - Wind Energy Handbook

BLADE LOADS DURING OPERATION 239

ð ð
R R
2
M Y ¼ 2Ù¸zrm(r)dr ¼ 2Ù¸ cos ł r m(r)dr ¼ 2Ù¸ cos łI B (5:23)
0 0
where I B is the blade inertia about the root.
As an example, consider a 40 m machine with ‘TR’ blades yawing at one degree
2
per second during operation at 30 r:p:m. The blade root inertia is 153 Tm , so the
maximum value of M Y is 2ð(0:0175)153 ¼ 17 kNm. This is only about 5 percent of
the maximum out-of-plane moment due to aerodynamic loads.

Braking loads

Rotor deceleration due to mechanical braking introduces edgewise blade bending
moments which are additive to the gravity moments on a descending blade.

Teeter loads

Blade out-of-plane root bending moments can be eliminated entirely by mounting
each blade on a hinge so that it is free to rotate in the fore–aft direction. Although
centrifugal forces are effective in controlling the cone angle of each blade at normal
operating speeds, the need for alternative restraints during start-up and shut-down
means that such hinges are rarely used. However, in the case of two bladed
machines, it is convenient to mount the whole rotor on a single shaft hinge allowing
fore–aft rotation or ‘teetering’, and this arrangement is frequently adopted in order
to reduce out-of-plane bending moment fluctuations at the blade root, and to
prevent the transmission of blade out-of-plane moments to the low speed shaft. As
teetering is essentially a dynamic phenomenon, consideration of teeter behaviour is
deferred to Section 5.8.

5.7.5 Stochastic aerodynamic loads – analysis in the frequency
domain

As noted in Section 5.7.1, the random loadings on the blade due to short-term wind
speed fluctuations are known as stochastic aerodynamic loads. The wind speed
fluctuations about the mean at a fixed point in space are characterized by a
probability distribution – which, for most purposes, can be assumed to be normal –
and by a power spectrum which describes how the energy of the fluctuations is
distributed between different frequencies (see Sections 2.6.3 and 2.6.4).
The stochastic loads are most conveniently analysed in the frequency domain
but, in order to facilitate this, it is usual to assume a linear relation between the
fluctuation, u, of the wind speed incident on the aerofoil and the resultant loadings.
This is a reasonable assumption at high tip speed ratio, as will be shown. The
2
1
fluctuating quasisteady aerodynamic lift per unit length, L,is rW C l c, where W is
2
the air velocity relative to the blade, C l is the lift coefficient and the drag term is