Fatigue Design of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 674

illustrated in Figure 12-8. In this case, a log-normal distribution is the best it to the design
data, which indicates that there is a random distribution of the logarithm of the load param-
eter. The governing equations are as follows:

2

m

ln( L F ) -

(12-2a)

n = 490exp -0.5

s

(12-2b)

PDF = n /50

where

n = bin cycle count (cycles/hr/bin)
ln( ) = natural logarithm of ( )
L F = flatwise cyclic bending moment load (kN-m)
m = 5.705, natural logarithm of median flatwise blade cyclic load L F
s = 0.35, natural logarithm of standard deviation of L F
PDF = probability density function (cycles/hr/kN-m)

Using these log-normal curve-fit parameters, the median size of the flatwise cyclic load is
exp (m) = 300 kN-m, and the 98 th percentile cyclic load is exp (m + 2s) = 605 kN-m.

1,000.000

Log-Normal Curve-Fit:
n' cycles/hr/bin

100.000

10.000

1.000

0.100

PDF cycles/hr/kN-m

0.010

Design Spectrum: 9.0 h; 19,107 Cycles

0.001

0 200 400 600 800 1,000 1,200 ,400

Blade Flatwise Cyclic Load, L F (kN-m)

Figure 12-8. Curve-fitting of a Mod-2 blade flatwise cyclic load spectrum with a log-
normal distribution, and calculation of the related probability density function.