Fatigue Design of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 670

wind speed, maximum load, and minimum load are relatively constant. A shortcoming of
this simple counting scheme is that identifying Type II cycles requires some judgment.
Three parameters which appear in almost all models of the fatigue cycles are as fol-
lows:

L cyc = 0.5 ( L max - L min ) (12-1a)

(12-1b)

L avg = 0.5 ( L max + L min )

R f = L min / L max (12-1c)

where
L max , L min = maximum and minimum loads in one fatigue cycle (kN or kN-m)

L cyc = cyclic, alternating , or half-range load; also load amplitude (kN or kN-m)

L avg = average, mean , or mid-range load (kN or kN-m)

R f = fatigue cycle shape parameter; also called R-ratio

Rainflow Model for Counting Fatigue Cycles

Other models have now been developed that automatically include the cyclic effects
of transient wind conditions and control changes. A very useful one is the rainflow model
[Matsuiski and Endo 1969, Downing and Socie 1982, Rychlik 1987, Sutherland and Schluter
1989 and 1990, Schluter 1991, Endo Memorial Volume 1991, ASTM 2005], which is often
included in the software of data systems used to monitor loads and stresses because it can be
applied reliably to a general spectrum. The rainflow model is currently the most common
algorithm used for counting fatigue cycles when analyzing test data from wind turbines.
A major advantage of using the rainflow counting algorithm to define wind turbine fa-
tigue spectra is that cycle counting is de-coupled from the rotational rate of the turbine. In
this way, fatigue cycles caused by wind turbulence can be captured at whatever frequency
they occur. Often, large numbers of smaller-amplitude load cycles are counted by rainflow
algorithms that were not recognized in earlier, simpler counting methods.
There are at least two ways to diagram the rainflow cycle counting algorithm, which
for convenience we may term the drain and drip methods. Figure 12-6 illustrates the drain
method (Cosmos 2005). The time axis of a 6-cycle idealized time-series of fatigue loads (or
stresses) is oriented horizontally, and the series is figuratively filled with water. Water is
then assumed to be drained from the lowest point in the series, at an elapsed time of approxi-
mately 7 seconds. The resulting change in water level above this point defines the maximum
and minimum loads in Cycle 1, which are 600 and - 200 kN-m in this example. Applying
Equations (12-1), average and cyclic loads for Cycle 1 are calculated to be 200 and 400 kN-
m, respectively, and its R-ratio is - 3.00. The same parameters for Cycles 2 through 6 are
obtained by successively draining water from progressively higher minimum points. The
cycle-counting results for this example are listed in Table 12-2.