Determining Fatigue Load Parameters (Flowchart A)
Reliability Analysis based on S-N curves model-Miner Rule
a) FORM Method b) MCS Method
1- Simulation of traffic flow based on Railway data of
Iran 2- Crossing simulated loads over the finite element
model
3-Determining time history of Displacement applied to spring clips type vossloh Skl14
4- Applied time history of displacement to spring clips type vossloh Skl14
5- Applying obtained time history of displacement to
finite element model of spring clips 6- 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
F orm 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 0 0 1 0 2 0 1 0 4 0 1 0 6 0 1 0 8 0 1 1 0 0 1 1 2 0
0 .0 2 0 .3 8 0 .7 4 1 .1 1 .4 6 1 .8 2 2 .1 8 2 .5 4 2 .9 3 .2 6 3 .6 2 3 .9 8 4 .3 4 4 .7 5 .0 6 5 .4 2 5 .7 8 6 .1 4 6 .5 6 .8 6
St
re
ss
(M
pa
)
T i m e ( S )
S tr e s s -T i m e
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0
2
4
6
8
10
C
o
n
ta
c
t
fo
rc
e
f
a
c
to
r
Time (ms)
Start
t < Tend
t = 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 process
t=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 separate from rail?
Are the all wheel sets separated? The Hertzian stiffness in separated wheelsets = 0
Yes
The system is unstable Calculate the quantity of linear
Hertzian spring stiffness
No
Is convergence in amount of Hertzian spring
stiffness?
Yes
Yes No
Save the results of displacement
0 100 200 300 400 500 600 700 800 900 1000
0 2 4 6 8 10 12
F
o
rc
e
(
k
g
)
Displacement (mm)
( )
g Z
R
L
( )
( ( )
0)
P f
P g Z
1m f
A
N S
1
i fi
D
N
1 1
1
mn n
i
i fi i
S
D
N
A
1 n
m i i
S
1
n m
i i
S
1 n
m 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
N
u
m
b
er
1
mi
D
E n E S
A
( , )
g X t
eD
( , )
m r e
n S
g X t
e
A
1 1
0
( )
)
m mi T otal
n m m
r e N r i r e s
S
S
or S
S f s ds
1
,
2X
X
A
X
4
S
r e3 4
1
2
( )
m
X X
g X
X
n
X
2 2.5 3 3.5 4 4.5 5 5.5 6
0 5 10 15 20 25 30 35 40 45
R e li a b il it y i n d e x Time (year) 1827 3827 5827 7827 9827 13827 17827 21827 23827 N u m b e r o f d a il y c y c le
0
1
2
3
4
5
6
7
8
1
5
10
15
20
25
30
35
40
R
e
li
a
b
il
it
y
I
n
d
e
x
Time (year)
M
X
C
X
K
X
F t
( )
1 2 1 2
& & & &
[
]
[
]
[
]
[
]
[
]
(
,
,
,
,
,
,
,
,
,
)
[
]
(
,
, ...,
)
[
]
(
,
, ...,
)
NS NSC a r body Bogie W heel
R a il
Sleeper
Ba lla st
T DO F T DO F C a r body Bogie W heel c c t t t t w w w w
Sleeper s s s Ba lla st b b b
M
M
M
M
M
M
dia g M
J
M J
M J
M
M
M
M
M
dia g M
M
M
M
dia g M
M
M
2 2 1 2156
22
54
13
4
13
3
[
]
[
]
[
]
156
22
420
.
4
i i
NE i i i
i i r i
R a il R a il R a il
i i
i
L
L
L
L
L
m L
M
M
M
L
sy
L
& & /
/ & /
/ / / / /
[
]
[
]
[
]
[
]
[
]
[
]
[
]
[
]
[
]
[
]
[
]
[
]
[
]
Ca r body Bogie C B W
W C B W heel W R
R W R a il R S
S R Sleeper S B
B S Ba lla st
T DOF T DOF
K
K
K
K
K
K
K
K
K
K
K
K
K
K
2 & 2 22
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
C a r body Bogie
w t
t w
w t
k
k
k
k L
k L
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
k
K
k L
k L
k
k
k L
k L
K
dia g k
k
k
k
dia g I
k
I
k
I
k
I
k
if X
R
X
I
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 Ba lla st b f b f b f
p p S R p p NS NJ
K
dia g k
k
k
k
k
k
K
dia g 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 NSb f sh sh
sh b f sh sh
Ba lla st
sh b f sh sh
sh b f sh
NS NS
b
b
S B B S
b
NS NS
k
k
k
k
k
k
k
k
k
K
k
k
k
k
k
k
k
k
k
k
k
K
K
k
2 2 3 1 212
6
12
6
4
6
2
[ ]
[ ]
[ ]
12
6
.
4
i i
NE i i i
i i
R a il R a il R a il
i
i i
i
L
L
L
L
L
EI
K
K
K
،
& & /
/ & / / / /
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
[ ]
C a r body Bogie C B W
W C B W heel
R a il R S
S R Sleeper S B
B S Ba lla st
T DOF T DOF
C
C
C
C
C
C
C
C
C
C
C
C
[ ]
C
R a il
M
R a il
K
R a il
10 1 2 1 2 1( )
( )
( )
0
W a gon
R a il NJ
NS
F
t
F t
F
t
1 1 2 2 3 3 4 40
0
0
0
0
0
0
( )
0
0
c b b W a gonH x w H x w H x w H x w
M g
M g
M g
F
t
K
R
M g
K
R
M g
K
R
M g
K
R
M g
j
i
1 j
i
NW NE
2 j
i i i
Rail j H j i Rail Rail j
j 1 i 1
3 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
