Environmental Engineering Reference
In-Depth Information
percentile levels for all 13 cases in Figures 12-11, the following empirical equations result:
d
M
y
,
n
=
a
M
g
sin
q
+ 432 (1 + 1.47
a
)
cd
(
g
+ 0.012
b
)
x
(12-7a)
(0.134
n
) (
D
/100 )
4
U
n
(1 -
s
)
exp
(0.276
n
)(
D
/100 )
3
d
M
z
,
n
=
e
M
g
+ 46.8
cd
(
g
+ 0.100
b
)
U
n
(1 -
s
)
exp
(12-7b)
d
P
n
/
A
= 6.4 + (0.014
P
R
/
A
+ 4
a
)
exp
{0.807 [1 + 0.0027
b
(
D
- 37)]
n
}
(12-7c)
d
T
n
/
A
= 2.91(1 + 1.47
a
)
cd
(
g
+ 0.012
b
)
U
n
exp
(0.140
n
)(
D
/100)
(12-7d)
where
d
M
y
=
blade cyclic flatwise bending load (kN-m)
n =
number of standard deviations, s, from the mean in a
log-normal
probabil-
ity distribution:
= 0 for the 50th percentile load, = 1 for the 84th percentile load
= 2 for the 98th percentile load, = 3 for the 99.9th percentile load
M
g
=
blade maximum static gravity moment (kN-m)
Q
=
hub coning angle (deg)
s =
blade station at which loads are measured, as a fraction of span
U
n
=
wind speed at hub elevation that is
n
s from the mean in a log-normal prob-
ability distribution (m/s)
d
M
z
=
blade cyclic chordwise bending load (kN-m)
d
P/A =
generator cyclic power density (W/m
2
)
A =
rotor swept area (m
2
)
P
R
=
generator rated power (W)
d
T/A =
rotor cyclic thrust density (N/m
2
)
For convenience, cyclic shaft torque and tower bending have been replaced by cyclic power
and cyclic rotor thrust. The first terms in Equations (12-7a) and (12-7b) are the effects of
gravity with undamped dynamic amplification in the chordwise direction. All other terms are
wind effects. The exponential terms define the load probability distributions.
Correlation between Calculated and Measured Fatigue Loads
As listed in Table 12-6,
coefficients of variation
(
i.e.,
ratios of standard deviation to the
mean value of the variable) of about 12 percent can be expected between cyclic loads in ser-
vice and those calculated in accordance with Equations (12-7a) to (12-7d). These range from
5 percent for blade cyclic chordwise moment to 20 percent for generator cyclic power den-
sity. A typical correlation graph is shown in Figure 12-13, in which measured blade cyclic
flatwise moments at the 50th and 98th percentile levels are plotted
vs
. calculated values. The
standard deviation for this fatigue load is 10 percent, and calculations within one standard
deviation of perfect correlation fall in the shaded band.
Deviations between calculated and measured fatigue loads are caused by several factors.
First, the empirical equations are
idealized models
and as such do not contain all the param-
eters affecting cyclic loads. Two of these that are under the control of the design engineer
are (a) airfoil properties such as maximum lift coefficient and stall behavior, and (b) flexible
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