Environmental Engineering Reference
In-Depth Information
where m
r
is the rotor mass, and the rotor eccentricity, e
r
, is to be taken
as 0.005R unless it can be proven otherwise. e
r
was defined and discussed in
Sect. 7.7
. L
rb
is the distance from the rotor to the first bearing, usually on the front
end of the generator. The loads on the blades and shaft that comprise this Load
Case will be transmitted to the tower. They are considered in
Chap. 10
on tower
design.
9.2.2 Load Case B: Yawing
The equation for the maximum blade root bending moment, M
yB
,is
12
M
yB
¼
m
B
x
2
max
L
rt
R
cog
þ
2x
max
J
B
X
þ
R
9
DF
x
shaft
ð
9
:
10
Þ
where L
rt
is the distance from the rotor to the yaw (tower) axis, the maximum yaw
rate is determined from (
9.3
), and DF
x-shaft
comes from (
9.7
). The first term is the
centrifugal term. The second term gives the amplitude of the cyclic gyroscopic
load; the actual moment is the amplitude multiplied by the cosine of the azimuthal
angle measured from the vertically upward position of the blade. Note that this
term provides the ''envelope'' shown on the measured blade root bending moment
in Fig.
8.1
. The last term approximates the effect of wind shear. A glaring
omission is a term accounting for the blade thrust. For two-bladed turbines, the
shaft loading is
13
:
M
shaft
¼
4x
max
XJ
B
þ
m
r
gL
rb
þ
R
6
DF
x
shaft
ð
9
:
11
Þ
For a three or more bladed turbine with N blades
14
:
M
shaft
¼
Nx
yaw
XJ
B
þ
m
r
gL
rb
þ
R
6
DF
x
shaft
ð
9
:
12
Þ
For N [ 1, there is no contribution from the average blade thrust to the shaft
moment. Experience has shown that the gyroscopic terms involving x
max
are
dominant. The difference between (
9.11
) and (
9.12
) implies a significant difference
between a two-bladed (N = 2) and other multi-bladed turbines—recall that the
standard specifically excludes single blade rotors. The difference arises because the
rotor's moment of inertia about the yaw axis must depend on the azimuthal
position of the blades as considered in Exercise 8.1. This is most easily seen for
a two-bladed rotor by considering the yaw inertia for the two extreme cases.
12
(IEC 28).
13
(IEC 29).
14
(IEC 30).
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