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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