Fatigue Design of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 666

tip speed of 90 m/s and an on-line time of 7,000 hours per year. On this basis, a rotor 60 m in
diameter will experience over 350 million reversals of its dead weight in a 30-year lifetime.
This number varies inversely with rotor diameter, for a constant tip speed.
Limit and Stiffness Design Requirements
Limit strength requirements are usually critical when a wind turbine is acted upon by the
specified extreme wind (see Chapter 8). This is not an operating condition, so limit-strength
design of a wind turbine is normally a conventional problem of wind loading on a static
structure. Furthermore, conventional finite-element models with centrifugal stiffening are
suitable for determining stiffness requirements, so that natural vibration frequencies will fall
within allowable ranges. Because structural engineers are able to apply conventional design
methods to meet both limit and stiffness requirements, only fatigue loads and fatigue design
methods will be addressed here.
Fatigue Load and Stress Spectra
In a structure with highly-variable loading, such as a wind turbine, fatigue damage is de-
termined by the amplitudes and frequencies of stress cycles or stress spectra at critical loca-
tions. These cycles are normally idealized into a time sequence of alternating minimum and
maximum values connected by straight lines. In other words, the shape of the path between a
given minimum and the next maximum is usually disregarded, and only the size and number
of the minimum and maximum stresses are modeled.
Sample Stress Spectra
Figure 12-3 is an example of an idealized stress spectrum for a conventional non-rotating
structure subject to fatigue loading. In this case the structure is a wing of a bomber aircraft,
the B-52G-H , undergoing a full-scale, ground fatigue test in the 1960s. The spectrum rep-
resents a typical stress history at one location in the structure, with loads applied to simulate
a four-hour flight. We may think of this graph as the idealization of the output of a strain
gage mounted on the wing at this point. In defining patterns of stress or load, it is common
to normalize the data, in this case by dividing all values by the maximum of all the stress- or
load-maxima of the cycles in the spectrum. This is often referred to as the maxmax value of
the spectrum. The minmin value is similarly defined.
During its simulated four-hour flight, our sample airplane wing experienced about 100
measurable and significant cycles of fatigue loading, which is an average rate of only 0.4
cpm. Thus, significant loading cycles are separated by periods of relatively steady stress. A
partial reversal of gravity loads occurs only once per flight and, with its transient stresses,
causes the so-called ground-air-ground (GAG) cycle. The GAG amplitude is equal to one-
half the difference between the maxmax and minmin stresses. Amplitudes of intermediate
load cycles are generally small fractions of the GAG amplitude.
Figure 12-4 illustrates a time-history of stress that is common to wind turbines, with the
data again normalized by the maxmax value in the spectrum. The graph presents data for a
six-hour run, in which the wind speed was low at startup, became high and gusty halfway
through the run, and then dropped prior to shutdown. In contrast to Figure 12-3, there would
typically be about 5,000 to 20,000 measurable fatigue stress cycles during this period, the
number varying inversely with rotor diameter for a given blade tip speed. These estimates of
wind turbine life requirements are based on cycling rates from 15 to 60 cpm, far larger than
that of the sample bomber wing.