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Determining Fatigue Load
Parameters (Flowchart A)
Reliability Analysis based on S-N
curves model-Miner Rule
a) FORM Method b) MCS Method
Determining Fatigue Strength
Parameters
1- Simulation of traffic flow based on Railway data of
Iran2- Crossing simulated loads over the finite element
model
3-Determining time history of Displacement applied to
spring clips type vossloh Skl144- Applied time history of displacement to spring clips
type vossloh Skl14
5- Applying obtained time history of displacement to
finite element model of spring clips6- Determination time history of stress in critical
element of spring clips
8- Cycle counting with "rain flow" method 7-Time history of stress in critical element of spring clips
Calculate Sre Is the number of
analyzes enough?
NO
Yes
Selection 20
wagons
Form Train
Random Speed
Train passing over finite
element model
Selection Random
Axial load
Determining equivalent stress range per Crossing every train and repeat the
steps above to determining the probability distribution function
9 6 0
9 8 0
1 0 00
1 0 20
1 0 40
1 0 60
1 0 80
1 1 00
1 1 20
0.02
0.38
0.74 1.1
1.46
1.82
2.18
2.54 2.9
3.26
3.62
3.98
4.34 4.7
5.06
5.42
5.78
6.14 6.5
6.86
Stress(Mpa)
Tim e (S)
Stre ss -Tim e
-0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
0
0.2
0.4
0.6
0.8 1
1.2
1.4
1.6
1.8 2
2.2
2.4
2.6
2.8 3
3.2
3.4
3.6
3.8 4
Deflection(m)
Time(s)
Deflection-Time
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 2 4 6 8 10
Co
nta
ct f
orc
e f
act
or
Time (ms)
Experiment Data from Newton & Clark (1979)
Current Calculation
Start
t < Tendt = t + dt End
No
Yes
Stop process
No
Insert the following parameters and information:
- Track- Train- Rail-wheelset contact- Ending process time (Tend)- Time rate (dt)
Determine the track roughness function
Start processt=0
Form matrixes of mass, stiffness and damping of track,
train and force vectors
Determinate the train position
Assuming the quantity of linear Hertzian spring stiffness based
on latest step
Form a new stiffness matrix
Form new forces vector
Calculation of displacement based of Newmark method
Is wheel set separatefrom rail?
Are the all wheel sets separated?
The Hertzian stiffness in separated wheelsets = 0
Yes
The system is unstableCalculate the quantity of linear Hertzian spring stiffness
No
Is convergencein amount of Hertzian spring
stiffness?
Yes
Yes No
Save the results of displacement in time “t”
0
100
200
300
400
500
600
700
800
900
1000
0 2 4 6 8 10 12
Fo
rce
(k
g)
Displacement (mm)
Sample 5
Sample 1
Sample 4
FEM
Sample 2
Sample 7
Sample 3
Sample 6
( )g Z R L
( ) ( ( ) 0)P f P g Z
1( ( ))P f
m
fA N S
1i
fi
DN
1 1
1mn ni
i ifi
SD
N A
1
nm
i
i
S
1
n m
iiS
1
nm m
i i
i
E S E n E S
0
100
200
300
400
500
600
700
800
900
1000
14 16 19 22 24 27 30 33 35 38 41 43 46 49 52 54 57 60 62 65
Nu
mb
er
Equivalent Stress Range (MPa)
1 m
iD E n E SA
( , )g X t eD
( , )
m
ren Sg X t e
A
1
1
0
( ) )
m
mi
T otal
n m m
re ri re sNS S or S S f s ds
1 2,X X A 4 reX S
3 41
2
( )mX X
g X X nX
2
2.5
3
3.5
4
4.5
5
5.5
6
0 5 10 15 20 25 30 35 40 45
Re
lia
bil
ity
ind
ex
Time (year)
1827
3827
5827
7827
9827
13827
17827
21827
23827
Nu
mb
er
of
da
ily
cy
cle
0
1
2
3
4
5
6
7
8
1 5 10 15 20 25 30 35 40
Re
lia
bil
ity
In
de
x
Time (year)
30 40 50
60 70 80
Equivalent Stress Range (MPa)
( )M X C X K X F t
1 2 1 2
& &
& &
[ ]
[ ]
[ ]
[ ]
[ ] ( , , , , , , , , , )
[ ] ( , , ..., ) [ ] ( , , ..., )NS NS
Carbody Bogie W heel
Rail
Sleeper
BallastT DOF T DOF
Carbody Bogie W heel c c t t t t w w w w
Sleeper s s s Ballast b b b
M
MM
M
M
M diag M J M J M J M M M M
M diag M M M M diag M M M
2 2
1
2
156 22 54 13
4 13 3[ ] [ ] [ ]
156 22420
. 4
i i
NE i i ii i r i
Rail Rail Rail
ii
i
L L
L L Lm LM M M
L
sy L
& & /
/ & /
/ /
/ /
/
[ ] [ ]
[ ] [ ] [ ]
[ ] [ ] [ ]
[ ] [ ] [ ]
[ ] [ ]
Carbody Bogie C B W
W C B W heel W R
R W Rail R S
S R Sleeper S B
B S BallastT DOF T DOF
K K
K K K
K K KK
K K K
K K
2
& 2
2
2 0 0 0
2 0 0
2 0 0 0[ ]
2 0 0
2 0
2
t t t
t c t c t c
t w
Carbody Bogie
w t
t w
w t
k k k
k L k L k L
k kK
k L
k k
k L
1 2 3 4
& /
0 0 0 0
0 0 0 0
0 0[ ]
0 0
0 0
0 0
[ ] ( , , , ) ( , , , )
1 0
0
j j j
j
w w
C B W
w t w t
w w
w t w t
W heel w w w w w H w H w H w H
x x w
w
k kK
k L k L
k k
k L k L
K diag k k k k diag I k I k I k I k
if X R XI
else
1 1 2 2 1 1 2 2
1
2
1
/
2
[ ] ( , , ..., ) [ ] ( , , ..., )
0
0 0 0
0 0
0 0 0
0 0 0
NS NS NS NS
NS
NS
Sleeper b p b p b p Ballast b f b f b f
p
p
S R
p
pNS NJ
K diag k k k k k k K diag k k k k k k
k
k
K
k
k
1
2
1
1
/ /
0 0
2
2
0
0 0
0
0
0 0
NS
NS
i
NS
b f sh sh
sh b f sh sh
Ballast
sh b f sh sh
sh b f shNS NS
b
bS B B S
bNS NS
k k k k
k k k k k
K
k k k k k
k k k k
k
kK K
k
2 2
31
2
12 6 12 6
4 6 2[ ] [ ] [ ]
12 6
. 4
i i
NE i i ii i
Rail Rail Rail
ii i
i
L L
L L LEIK K K
LL
sy L
،
& & /
/ &
/
/ /
/
[ ] [ ]
[ ] [ ]
[ ] [ ]
[ ] [ ] [ ]
[ ] [ ]
Carbody Bogie C B W
W C B W heel
Rail R S
S R Sleeper S B
B S BallastT DOF T DOF
C C
C C
C CC
C C C
C C
[ ]Rail Rail RailC M K
10 1
2 1
2 1
( )
( ) ( )
0
W agon
Rail NJ
NS
F t
F t F t
1 1
2 2
3 3
4 4
0
0 0
0
00
0( )
00
c
b
b
W agon
H xw
H xw
H xw
H xw
M g
M g
M gF t
K RM g
K RM g
K RM g
K RM g
j
i
1 j
iNW NE2 ji ii
Rail H j Rail Railj jij 1 i 13 j
i
4 j
(a )
(a )F (t) k IR(a ) F F
(a )
(a )
3 / 2
1/ 2
( )
( ) ( ) ( )
j j j j j
j j j j j j j j j j j
Contact H x x w
H x x w x x w H x x w
F C X R X
C X R X X R X K X R X