Environmental Engineering Reference
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frequency. As for large turbines, see Sect. 7.9.2 of Burton et al. [ 15 ], this matching
is almost guaranteed for small wind turbines whose blade speed, X, is often
controlled to match the wind speed to keep the tip speed ratio constant. For
example, the two-bladed 5 kW turbine considered here has a rated blade speed of
320 r.p.m. = 5.3 Hz and a blade passing frequency, denoted 1P, of 10.6 Hz. Thus
it is almost certain that the turbine will excite the tower natural frequency during
some part of its operation. Fortunately, the turbine thrust at a speed corresponding
to about 1 Hz is low so that a suitably stiff tower should not show significant
resonance and the blades will be stationary when the maximum turbine thrust
occurs under Load Case H of IEC 61400-2. Furthermore, wind speed and other
variations will usually cause X to vary rapidly, so the tower will not have much
opportunity to lock-into a perturbation at its lowest natural frequency.
The natural frequency is also required in order to determine whether a static or
''dynamic'' analysis is required. AS1170.2 [ 12 ], for example, allows a static
analysis for structures with n 1 [ 1 Hz but mandates a modified analysis for lower
values using increased wind loads. This often requires stiffening the tower.
The discussion and analysis so far has ignored any fatigue loading on the tower,
which in the IEC SLM, can only be from Load Case A: Normal Operation. The
5 kW turbine has a design wind speed of 10.5 m/s, and a tip radius of 2.5 m. Using
the SLM to determine the magnitude of the variations in shaft thrust gives, with the
notation from Chap. 9 :
DF x shaft ¼ 3k design Q design
2R
¼ 3 7 : 98 238 : 73
2 2 : 5
¼ 1143N
ð 10 : 21 Þ
see Eq. 9.7 . Following Eq. 9.33 , the total number of cycles, n, for a 20 year life, is
n ¼ NX design T d 60
¼ 2 320 20 365 24 60 60 = 60 ¼ 6 : 73 10 9
ð 10 : 22 Þ
As mentioned in Chap. 9 , Load Case A considers the turbine cycling between 50
and 150% of the design speed. Thus the average thrust is 1143 N and the maximum
is 1715 N. The Excel spreadsheet SLM.xls gives the shaft moment against the first
turbine bearing as 526 Nm and it will be assumed that this is M 0 acting on the tower
throughout the fatigue cycles. The following Matlab session shows the calculation of
the stresses resulting from the maximum and mean of the cyclic load for SLM Load
Case A (with the thickness and natural frequency lines removed);
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