Fatigue Design of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 673

Statistical Analysis of Examples of Fatigue Load Spectra

After the individual fatigue cycles in the spectrum have been identified and the param-
eters of each have been tabulated, a statistical analysis is usually required to convert the
resulting time-history data into fatigue design information. Depending on the damage mecha-
nism assumed in the fatigue model, fatigue life may be expressed as a function of maximum
stresses, cyclic stresses, or a combination of cyclic and average stresses. In the examples that
follow, cyclic stress has been selected as the key fatigue-damage parameter, and three differ-
ent distributions of fatigue cycle rates with respect to loads are illustrated.

Example 1: Log-Normal Distribution of Blade Flatwise Loads

Normalized blade load design spectra for the Mod-2 2.5-MW wind turbine were listed
in Table 12-1, in time-series order [Boeing 1979]. These same data are now converted to a
dimensional format based on an assumed maxmax load of 1,800 kN-m. Cyclic loads are then
sorted into bins each 50 kN-m in width. The bins and their populations are tabulated in the
irst four columns of Table 12-3. The 1-hr count data from Table 12-3 are then curve-it as

Table 12-3. Calculation of Probability Density Function for Flatwise Blade Fatigue
Loads on the Mod-2 2.5-MW Wind Turbine

9.0-hr Design Spectrum Data Sorted into
Load Bins 50-kN-m Wide

Log-Normal
Curve-Fit of
1-hr Count

Probability
Density
Function

Bin No. Cyclic

Load
L F,mid
(kN-m)

9-hr Count 1-hr Count

n'
(cyc/bin)

n
(cyc/hr/bin)

n
(cyc/hr/bin)

PDF
(cyc/hr/kN-m)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22

1,275
1,225
1,175
1,125
1,075
1,025
975
925
875
825
775
725
675
625
575
525
475
425
375
325
275
225

1 0.11 0.11

0.17
0.27
0.43
0.70
1.13
1.83
2.97
4.85
7.93
12.97
21.18
34.45
55.55
88.38
137.65
207.63
298.43
398.79
476.42
476.61
354.96

0.0022
0.0034
0.0054
0.0087
0.0140
0.0225
0.0365
0.0594
0.0970
0.1586
0.2594
0.4237
0.6889
1.1110
1.7675
2.7531
4.1526
5.9686
7.9757
9.5284
9.5322
7.0992

3 0.33

10 1.11

12
37
36
118
130

1.33
4.11
4.00
13.11
14.44

562
139
356
675
1,875
2,605
3,194
4,164
2,600
2,590

62.44
15.44
39.56
75.00
208.33
289.44
354.89
462.67
288.89
287.78

Totals 19,107 2,123 2,583 cycles/hr