Page 321 - Wind Energy Handbook

HUB AND LOW-SPEED SHAFT LOADING 295

Blade 1

M ZS

M Y1 ψ 1
M Y3

M YS
O
Blade 2

M Y2

Blade 3

M Y2
O

Figure 5.40 Shaft Bending Moments, with Rotating Axis System Referred to Blade 1

blade, but with differing phase angles. The blade root out-of-plane bending
moments due to the first component will be in equilibrium, and will apply a
‘dishing’ moment to the hub which will result in tensile stresses in the front and
compression stresses in the rear. These stresses will be uniaxial for a two bladed
rotor, and biaxial for a three-bladed rotor.
The fluctuations in out-of-plane blade root bending moment due to wind shear,
shaft tilt and yaw misalignment will often be approximately sinusoidal, with a
frequency equal to the rotational frequency. Using Equations (5.118), it is easily
shown that, for a sinusoidally varying blade root bending moment with amplitude
M o , the amplitude of the resulting shaft bending moment is 1:5M o for a three-
bladed machine and 2M o for a rigid hub two-bladed machine.
In the case of wind shear conforming to a power law, the loading on a horizontal
blade is always greater than the average of the loadings on blades pointing
vertically upwards and downwards, so the loading departs significantly from
sinusoidal. The shaft bending moment fluctuations due to wind shear with a 0.2