Page 431 - Wind Energy Handbook

BLADES 405

machines of 40 m diameter and above, the fatigue equivalent load for in-plane
bending at the blade root is typically greater than that for out-of-plane bending.
Over most of the blade length, the chord dimension is much larger than the blade
thickness, so the section modulus for edgewise bending will generally exceed that
for flapwise bending. However, for blades attached to the hub or pitch-bearing by a
circular ring of bolts, which is the normal arrangement, the blade structure adjacent
to the root is a cylindrical shell, which will have the same section modulus about
both axes if the wall thickness is uniform. As a consequence, the blade root is the
first area that should be checked for in-plane fatigue loading.
The procedure can be illustrated for a 20 m tip radius TR blade in GFRP, designed
for an extreme static root moment of 750 kNm at 0.5 m radius. Taking the gravity
8
moment at the root as 124 kNm, and assuming 2:6 3 10 revolutions over the
machine lifetime, the notional one cycle in-plane bending equivalent load range,
8 0:1
M eq(n¼1) , becomes 248(2:6 3 10 ) ¼ 1720 kNm and ó eq(n¼1) =ó ext ¼ 1720=750 ¼ 2:3.
This is less than the minimum value of 2.7 of the right-hand expression in the
inequality (7.11), so in-plane fatigue loading does not govern. In practice, the
cylinder wall thickness would have to be increased significantly to prevent buck-
ling, rendering fatigue less critical still at this diameter.
It may be concluded from the above example that in-plane fatigue loadings are
not a significant consideration in the design of stall-regulated blades constructed in
GFRP or wood laminates, until much larger diameters are reached. They cannot be
ignored entirely, because of blade twist and because they add to the fatigue stress
ranges due to flapwise bending at points on the cross section away from the neutral
axis for edgewise bending. In-plane fatigue loadings are of more significance for
pitch-regulated machines because gravity loadings will contribute increasingly to
flapwise loadings as the pitch angle increases.

Tip deflection

Under extreme operating conditions, tip deflections of up to about 10 percent of
blade radius can occur, so care is needed to avoid the risk of blade/tower collisions
in the case of upwind machines. GL specify that the quasi-static tip deflection under
the extreme unfactored operational loading is not to exceed 50 percent of the
clearance without blade deflection, which implies a safety factor of 2. IEC, on the
other hand, require no blade/tower contact when the extreme loads are multiplied
by the combined partial safety factors for loads and the blade material.
It is instructive to compare the tip deflections for similar blades designed in
different materials. If the skin thickness distributions are chosen so that the design
compression strength of each material is fully mobilized under the extreme load
case, then the tip deflection will be proportional to the design compression strength
to Young’s Modulus ratio, ó cd =E, of the blade material. These ratios are compared
for different materials in Table 7.4.
It is clear from the table that a GFRP blade will be about twice as flexible as
blades in the other materials (apart from steel), provided that the spar is stocky
enough for buckling not to govern the design, e.g., as in Figure 7.4. In the case of
thin-walled cross sections, however, such as that in Figure 7.3, the GFRP compres-