Page 480 - Wind Energy Handbook

454 COMPONENT DESIGN

site, which has not normally proved economic. Accordingly, this section concen-
trates on the two types of steel towers – tubular and lattice. The restrictions on first-
mode natural frequency are considered first.

7.9.2 Constraints on first-mode natural frequency

As noted in Section 6.14, it is important to avoid the excitation of resonant tower
oscillations by rotor thrust fluctuations at blade-passing frequency or, to a lesser
extent, at rotational frequency. Dynamic magnification impacts directly on fatigue
loads, so the further the first-mode tower natural frequency is from the exciting
frequencies, the better. Unfortunately, it is generally the case that the natural
frequency of a tower designed to be of adequate strength for extreme loads is of the
same order of magnitude as the blade-passing frequency.
In the case of machines operating at one of two fixed speeds, the latitude
available for the selection of the tower natural frequency is more restricted. Figure
7.38 shows the variation of dynamic magnification factor with tower natural
frequency for excitation at upper and lower blade-passing and rotational frequen-
cies for a three-bladed machine with a 3:2 ratio between the upper and lower
speeds. The curves are plotted for a damping ratio of zero, but the difference if the
curves were plotted for a realistic damping ratio of about 2 percent would be
imperceptible. The figure also shows the tower natural frequency bands available if
the dynamic magnification ratio were to be limited to 4 for all four sources of
excitation. It is apparent that the minimum dynamic magnification ratio obtain-
able with a tower natural frequency between the upper and lower blade-
passing frequencies is 2.6, for a tower natural frequency of 0.85 times the upper
blade-passing frequency. However, in view of the fact that the rotor thrust load

10
Excitation at upper
rotational frequency Excitation at upper
9 blade-passing frequency
8
Excitation
Excitation at
at lower passing frequency
lower blade-
Dynamic magnification factor 6 5 4 frequency) frequency)
7
rotational
frequency
(= 2/3 x upper
(= 2/3 x upper
2 3

1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
Tower natural frequency/Upper blade-passing frequency
Figure 7.38 Variation of Dynamic Magnification Factor with Tower Natural Frequency for a
Two-speed, Three-bladed Machine