Fatigue Design of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 698

a

æ

I
å 1 n i s -1/

a

ê

i

S maxmax = S 1

(12-12)

N f

I
å 1 n i

è

This value of S maxmax becomes the allowable fatigue stress for the loading condition repre-
sented by L maxmax in Table 12-1. The structural-dynamic analysis of loads has been converted
into a static structural design problem by this method.

Laminated Wood Blade Fatigue

To illustrate the S-N linear damage method for calculating the effect of spectrum load-
ing on fatigue strength, consider the following problem: A HAWT blade is to be manufac-
tured from laminated Douglas fir/epoxy material, whose fatigue strength is known to depend
strongly on the maximum stresses in the applied fatigue cycles. The design spectrum for the
blade is composed of the layers and numbers of cycles in Table 12-1, and the stress ratios
in each layer are the same as the load ratios listed in this table. Each spectrum represents
nine hours of operation, and the blade is to be designed for a 30-yr lifetime running continu-
ously.
The laboratory fatigue data for the laminated wood material are shown in Figure 12-
17 [Spera et al. 1990]. The veneer grade is assumed to be A +, veneer-to-veneer joints are
scarfed, and large-volume properties are to be used, to account for the size effect present in
this material. The lowest S-N curve in Figure 12-17(a) is the appropriate one for the material
requirements in this problem, and its empirical exponent α is equal to -0.0676. The empiri-
cal coefficient S 1 must be determined using the Goodman diagram in Figure 12-17(b), since
the S-N curves shown are for an R-ratio of 0.1 whereas the average R-ratio in Table 12-1 is
0.37. The line along which combinations of the cyclic stress and the average stress produce
a constant R-ratio of 0.37 is shown in the figure. Its slope is calculated as

S cyc
S avg

= (1 - 0.37)/ 2

(12-13a)

(1 + 0.37)/ 2 = 0.46

The stress cycle parameters at the intersection of this R-ratio line and the fatigue strength
line for 10 7 cycles to failure of the specified material are

S cyc = 1,650 psi (11,380 kN/m 2 )

S avg = 3,600 psi (24,820 kN/m 2 )

S max = 5,250 psi (36,200 kN/m 2 )

The S-N curve for the average fatigue strength of laboratory specimens with an R-ratio of
0.37 then becomes

- 0.0676

N
10 7

= 15, 610 N - 0.0676

S max = 5, 250

(12-13b)