Environmental Engineering Reference
In-Depth Information
r
eq
¼
DF
zB
A
B
þ
DM
xB
W
xB
þ
DM
yB
W
yB
1629
:
23
1
:
46
10
3
þ
6
:
75
3
:
036
10
6
þ
25
:
55
1
:
527
10
5
¼
¼
3
:
51 MPa
ð
9
:
57
Þ
For the main shaft, Eqs.
9.42
-
9.44
and the equations in the last column of
Table
9.6
give:
s
DF
x
shaft
A
shaft
2
2
þ
DM
shaft
W
shaft
DM
x
shaft
2W
b
r
eq
¼
þ
3
s
118
:
55
4
:
909
10
4
þ
2
2
21
:
20
1
:
534
10
6
11
:
70
2
1
:
534
10
6
¼
þ
3
¼
15
:
53 MPa
ð
9
:
58
Þ
In Eqs.
9.57
and
9.58
, the equivalent stress was calculated from the peak-to-
peak variation in the fatigue load. However, S,N-diagrams for fatigue show the
amplitude of the maximum stress versus the number of cycles for use in Miner's
Rule. Thus the results from (
9.57
) and (
9.58
) must be divided by 2. Since
0.5 9 15.53 = 7.77 MPa is well below the endurance limit for steel, the shaft
seems safe in fatigue. But there is a further complication: Miner's Rule, Eq.
9.32
,
assumes no average stress, whereas there will be mean equivalent stresses for Load
Case A and this reduces fatigue strength. Even though IEC 61400-2 states that
''mean values of the load ranges can be ignored'' it is advisable to check the effect
of the mean stress. This equals the equivalent stress for the peak-to-peak loads for
the turbine cycling between 50 and 150% of the design speed. Then it is possible to
use Gerber's relation, see, for example, Eq. 6.4 of Schijve [
7
] to estimate the
maximum stress r
eq,max
for a particular number of cycles which will be less than
the value if there were no mean stress. Assuming n is large enough for the
endurance limit stress, r
l
, to be applicable then the equation for r
eq,max
which must
replace r
l
,is
þ
r
eq
;
max
F
y
r
eq
;
max
r
l
¼
1
ð
9
:
59a
Þ
or
0
@
s
F
y
r
l
1
A
2
þ
4
r
eq
;
max
¼
F
y
2
F
y
r
l
ð
9
:
59b
Þ
where F
y
is the yield stress equal to 350 MPa in this case. If r
l
= 200 MPa, then
(
9.59b
) gives r
eq,max
= 158 MPa. Using the material load factor of 1.25, the
maximum allowable stress is 158/1.25 = 127 MPa, so the shaft is easily safe.
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