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