Environmental Engineering Reference
In-Depth Information
divided by the distance from the centroid to the point of maximum stress. This is
the furthest point on the component from the neutral axis, which runs through the
centre of mass. Use can then be made of the formulae in Table
9.6
to evaluate the
stresses. For example, r
shaft
, the radius of the rotor shaft is 12.5 mm, so A
shaft
=
4.909 9 10
-4
m
2
.
The
second
moment
of
inertia
for
the
circular
shaft
is
W
shaft
= 1.9175 9 10
-8
/0.0125 = 1.534 9
pr
shaft
=
4
¼
1
:
918
10
8
m
4
;
and
10
-6
m
3
.
The corresponding information for the blade is harder to obtain. The blade root
area, A
B
, was taken as the smallest cross-sectional area in the root region as
determined from a CAD model of the blade. This gave A
B
= 0.00146 m
2
.This
occurred just above the 0.095 m (in the chord direction) by 0.105 m (radial) by
0.025 m thick rectangular attachment section.
The CAD software was used to determine the other moments about the axes
defined in Appendix 2 of IEC 61400-2:
I
xx
¼
2
:
79
10
8
m
4
I
yy
¼
1
:
199
10
6
m
4
and
ð
9
:
55
Þ
and the respective distances from the stress points were found to be
c
xB
¼
0
:
00919 m
and
c
yB
¼
0
:
00778 m
ð
9
:
56
Þ
W
xB
= 2.79 9 10
-8
/0.00919 = 3.0359 9 10
-6
m
3
Thus
and
W
yB
= 1.19 9
10
-6
/0.00778 = 1.527 9 10
-4
m
3
.
The ultimate material strength, denoted f
k
in (
9.30
), of the timber blades is
123 MPa, Peterson and Clausen [
6
]. The generator shaft is assumed to be made
from mild steel for which f
k
= 250 MPa.
The next subsections show the calculations of the equivalent stresses. It is
assumed that the shaft and other metal components are made from structural steel
with a yield stress of 350 MPa and the timber blades have a yield stress of
120 MPa [
6
]. Both materials are assumed to be well characterised so that the
appropriate material safety factors are 1.25 for fatigue and 1.1 for ultimate
strength. Using the load safety factor of 3 for the ultimate strength, the blades will
be safe in ultimate loads if the equivalent stress is less than 36.4 MPa, and the steel
components if the stress is less than 106.1 MPa.
9.5.1 Equivalent Stress for Case A: Normal Operation
Load case A is the only fatigue load. However, it will be shown below that the
equivalent average stress level is still required to complete the analysis. The
equivalent stress in the blade root is found using Eqs.
9.39
-
9.41
inclusive. Since
the root area of the blade in Fig.
6.1
is more rectangular than circular, the equa-
tions in the second column of Table
9.6
will be used. Thus
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