10th

International Conference on Contact Mechanics

CM2015, Colorado Springs, Colorado, USA

Effects of key parameters of EMU bogie on rail gauge corner wear

Dabin Cui

a,b, Weihua Zhang

b, Li Li

c, Zefeng WEN

b, Xuesong Jin

b, Jian Wang

d, Wenjuan Ren

b

a Department of Mechanical Engineering, Emei Campus of Southwest Jiaotong University, Emei 614202, China

b State Key Laboratory of Traction Power, Southwest Jiaotong University, Chengdu 610031, China

c School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China

d School of Civil Engineering, Southwest Jiaotong University, Chengdu, Sichuan 610031, China e-mail: cdb1645@163.com

ABSTRACT

The long term investigation of wheel and rail wear condition reveals that wheel flange/rail gauge corner wear is

one serious problem of EMU vehicles and sharp curved tracks. In order to solve the problem, a EMU vehicle

dynamic model was built to simulate the vehicle dynamic behavior. The results show that under the condition of

great yaw stiffness of wheelset, the yaw angles of wheelset is not enough to pass the sharp curve, which increases

attack angle between wheel and rail. Then wheel-rail two-point contact would occur and cause serious wheel

flange/rail gauge corner wear. Effects of bogie key parameters on vehicle dynamic behavior were studied which

indicates that both the axle-box positioning stiffness and wheelbase affect the curving negotiation performance

significantly. On the premise of meeting the requirements of vehicle running behavior on tangent track, a new wheel

profile was attained by the improved parallel inverse design method to reduce wheel flange/rail gauge corner wear.

Key Word: Rail gauge corner wear; Dynamic behavior; bogie parameter; wheel profile design

1. Introduction

With the train speed increasing and various advanced

technique employed in this field, the problems of

vehicle parameters have been of great interest. It

concerns, for example, the critical speed of railway

vehicle hunting, the running stability, and the ability

of curve negotiation. Usually these factors are

difficult to achieve the optimal state in one group of

parameters of bogie simultaneously.

No’ and Hedrick [1] studied the influences on the

critical speed of a railway vehicle of the lateral and

longitudinal stiffness of the primary suspension and

the longitudinal damping of the secondary suspension.

Wickens[2] studied the relationship between the

damping and the critical hunting speed of a truck.

He[3] also illustrated the boundaries of the hunting

stability as functions of the suspension stiffness for

trucks with linkage steered wheelsets. Lee et al.[4]

investigated the influences of the parameters of the

primary suspension on critical hunting speed. Mehdi

and Shaopu[5] stated the influences of suspension

parameters on the critical hunting speed of a vehicle

considering nonlinear damping forces. Zhang[6]

investigated the effect of the suspension parameters

and equivalent conicity of wheel tread on the critical

speed. Horak and Wormley[7] illustrated the effect of

equivalent conicity of wheel tread on the critical

hunting speed of a passenger car running on

irregularly aligned rails. Haque and Lieh[8]

employed the Floquet theory to examine the

parametric hunting stabilities of a passenger car and a

freight car running on tangent tracks for harmonic

variations in the equivalent conicity of the wheel

tread.

The critical speed of vehicle is the one of the main

target when designing EMU bogie, while the

performance of curve negotiation is usually neglected.

Most of the high-speed line is tangent line and curve

line with big radius; however, these are lots of sharp

curves near the railway stations. When the train

passing the sharp curve, the wheel flange could

contact and press the rail which cause the rail gauge

corner wear seriously. Based on the field investigated

recently, the rail on one sharp curve was replaced

frequently, which disturbed the normal railway

operation.

In reality the wheel flange wear and rail gauge corner

wear are not new problems. Cantera [9] investigated

the excessive wheel flange wear on FEVE rail.

Zakharov et.al [10] studied the modeling of the wear

process between wheel flange and side face of rail

head. Descartes et al. [11] investigated the wheel

flange and rail gauge corner contact lubrication. Jin

et.al [12] simulated the wheel flange wear and rail

gauge corner wear by experiment. Choi et.al [13]

designed a new wheel profile to reduce wheel flange

wear and fatigue.

With more and more rail be replaced on sharp curves,

the ability of curve negotiation of bogie attracts

attention gradually. In order to investigate the effects

of key parameters of bogie on rail gauge corner wear,

a vehicle dynamic model was built based on the

reality vehicle parameters and the vehicle dynamic

behaviors were simulated. The parallel inverse design

method [14] was improved to design a new profile

which can reduce the rail gauge corner wear.

2. FIELD TEST

There is one sharp curve which radius is 300m near a

station. When the train passing the sharp curve, the

wheel flange could contact and press the rail which

cause the rail gauge corner wear seriously as shown

in figure 1. This lead to the rail on the sharp curve

has to be replaced every five months, which disturbed

the normal railway operation.

Fig.1 Rail gauge corner wear

In order to solve this problem, rails wear shapes and

the lateral force on rail were measured in the sharp

curve. Figure 2 shows the worn rail profiles in

different position in the curve. The number in figure

2 is the distance between measured position and the

start point of the curve. It is can be seen that the rail

gauge corner wear at the middle of the curve is

bigger than that near the start point of the curve. The

value of the rail gauge corner wear in the middle of

the curve is 12.69mm.

-40 -30 -20 -10 0 10 20 30 40

-40

-30

-20

-10

0

z(m

m)

y(mm)

0m

6m

12m

18m

24m

30m

Fig.2 Worn rail profiles

Correspondingly, the wheel profiles have flange wear

significantly, as shown in figure 3. The wheel re-

profiling is the primary method of wheel maintenance.

During the enquiry it is found that the new profile is

obtained by translation the standard profile to the

flange side in order to reduce the cutting output. As

the wheel flange wear and the action of re-profiling,

the flange thickness will be lost with the re-profiling

times increased. Figure 4 shows the amount of flange

thickness loss in different wheel re-profiling period.

In this figure we can see that the amount of flange

thickness loss is nonlinear growth with the re-

profiling period increased. The flange thickness loss

owing to re-profiling in different re-profiling period

is similar, so it can be seen that the amount of flange

wear is bigger and bigger with the re-profiling period

increase.

Figure 5 shows the wheel-rail lateral force when the

train passing the sharp curve with different speeds. It

is can be seen that the lateral force at high rail is

much bigger than that at the low rail. Although the

trains are different in the test, the influence of the

speed on the wheel-rail lateral force is little. The big

lateral force in the high rail is the primary cause of

the rail gauge corner wear.

-60 -40 -20 0 20 40 60

-30

-25

-20

-15

-10

-5

0

5

z (

mm

)

y (mm)

New profile

70 kilometers

140 kilometers

200 kilometers

Fig.3 Worn wheel profiles

New profile First re-profiling Second re-profiling Third re-profiling

0.0

0.5

1.0

1.5

2.0

Am

ou

nt o

f fla

nge

thic

kn

ess loss (

mm

)

Re-profiling period

Fig.4 Amount of flange thickness loss

5 10 15 20 25 30 35 40 4510

20

30

40

50

60

Wh

eel

rail

la

tera

l fo

rce(

kN

)

Speed(km/h)

Low rail

High rial

Fig.5 Wheel rail lateral force vs. running speed

3 ANALYSIS OF THE KEY PARAMETERS OF

BOGIE

The previous studies on EMU bogie are aim to

increasing the vehicle behaviors on tangent line less

considering the curving negotiation performance.

With more and more rail be replaced on sharp curves,

the ability of curve negotiation of bogie attracts

attention gradually. In order to investigate the effects

of key parameters of bogie on rail gauge corner wear,

a vehicle dynamic model was built [15,16] based on

the reality vehicle parameters and the vehicle

dynamic behaviors were simulated. The key

parameters of bogie, such as axle-box positioning

stiffness, axle base, rim inside distance, et al., affect

the vehicle behavior directly[6], which has been

investigated below.

3.1 Numerical Modeling

In order to make the analysis easier and clearer, a

relatively simple model was used. Parameters of the

model were set to be appropriate for a high-speed

train. In this model the series stiffness of the

hydraulic shock absorbers were considered in detail.

Shen–Vermeulen– Johnson theory [17] which is an

improved version of the Vermeulen–Johnson theory

has been previously shown to be able to calculate

results that closely match test results was applied to

calculate the wheel/rail contact force. This model [16]

includes 15 bodies which has 50 freedoms. Figure 6

shows the schematic drawing of the vehicle system

model used in the study.

The minimum distance searching method [18] is

improved to calculate the position of wheel-rail

contact points as shown in figure 7. When wheelset

has lateral displacement yG and attack angle , the

wheel-rail contact points in the wheel tread could

meet

[ ( , ) ] [ ( , ) ]WL yG RL WR yG RR (1)

Where WL and WR are functions of wheel tread

profile for the left and right side. RL and RR are the

functions of rail profile for the left and right side.

is the rolling angle. is the value of acceptable

deviation.

After the contact point solved, the contact state of

wheel flange and rail gauge corner should be judged.

if 1 1

y yWR RR , the yG should be adjust and the

wheel-rail contact points in the wheel tread should be

calculated again until the parameters meet inequality

(2). 1 1( , )y yWR yG RR (2)

1

yWR is the inverse function of wheel flange for right

side, 1

yRR is the inverse function of rail gauge corner

profile in right side. is the value of acceptable

deviation.

In current study the distribution of normal force in

different contact points cannot be solved when multi-

contact occurred in wheel and rail. The multi-contact

is only emerged when vehicle passing the sharp curve.

Under this condition the running speed is low and the

contact angle on wheel flange approaching to 90

degree. In this paper the hypothesis that the contact

point in wheel tread support the whole vertical force

and the contact point in wheel flange only support the

lateral force is adopted. A program was written to

calculate the vehicle dynamic behavior.

The critical hunting speed is the index used to

analyse the running stability of the vehicle, and

UIC518[19] introduces methods to calculate the

critical hunting speed. In this study, the limit value of

R.M.S wheelset acceleration is 5 m/s2. The R.M.S

value is analysed as a continuous average value over

100 m distance calculated with steps of 10m.

(a) Elevation

(b) Planform

Fig.6 Vehicle system model

Y

Z

RL(yG) RR(yG)

WR(yG)WL(yG)

yG

φ

Fig.7 Diagram of solving the wheel-rail contact point positions

3.2 Curving Negotiation Performance

Most of the high-speed track is tangent line and curve

line with big radius more than 6000 m; however,

there are lots of sharp curves near the railway stations.

Figure 8 and figure 9 show the wheel-rail attack

angle and lateral force when vehicle passing different

radiuses of curves. It can be seen that wheel-rail

attack angle and lateral force increase with the curve

radius reducing. When the curve radius is less than

800 m, the attack angle and lateral force will be

promoted rapidly with the radius decreasing, and the

lateral force will be 37 kN when the curve radius is

300 m, this is similar to the test data in figure 5.

0 1000 2000 3000 4000 5000 6000 7000 8000-0.002

0.000

0.002

0.004

0.006

0.008

Wh

ee

l-ra

il a

tta

ck a

ng

le(r

ad

)

Curve radius(m)

Fig.8 Wheel-rail attack angle vs. curve radius

0 1000 2000 3000 4000 5000 6000 7000 80000

5

10

15

20

25

30

35

40

Wheel-ra

il la

tera

l fo

rce(k

N)

Curve radius(m)

Fig.9 Wheel-rail lateral force vs. curve radius

0 20 40 60 80 100 120

-8

-6

-4

-2

0

La

tera

l d

isp

lace

me

nt

of

wh

ee

lse

t (m

m)

Time (s)

Figure.10 Wheelset displacement when vehicle passing the 300 m

radius curve

0 20 40 60 80 100 120

-0.008

-0.006

-0.004

-0.002

0.000

0.002

Time (s)

Wh

ee

l-ra

il a

tta

ck a

ng

le (

rad

)

Figure.11 Wheel-rail attack angle when vehicle passing the 300 m

radius curve

In order to illuminated the vehicle dynamic

performance when vehicle passing the sharp curve,

the displacement of wheelset and attack angle are

given in figure 10 and figure 11. When vehicle passes

the sharp curve, the wheel-rail creepforce is not

sufficient to lead the bogie to run along the track, so

the wheelset should move to the side of high rail and

the attack angle will be increased. In this condition,

the wheel-rail contact state is show in figure 12. The

contact point A mainly sustains the wheel-rail

vertical force, and the contact point B sustains the

lateral force of wheelset. When vehicle running at a

very low speed, the wheel-rail lateral force can be

written as

sinlateral flange N creepF F con F F (3)

Where lateralF is wheel-rail lateral force, flangeF is

the normal force at contact point B, NF is the normal

force at contact point A, creepF is creep force at

contact point A. is the flange angle which equal to

70 degree here, is the wheel-rail contact angle.

In an instant of wheel-rail rolling contact, the point B

slides surrounding point A. The length b in figure 12

is the sliding arm. Under the same conditions, the

flange wear depend on the flange force flangeF and

the sliding arm b [20]. Based on the wheel-rail

geometrical relationship as shown in figure 11, the

sliding arm b can be written as 2 2 2 2( sin )b d h l h (4)

Where d is the distance between A and B in

longitudinal direction, h is the distance between A

and B in vertical direction, l is the distance between

A and B in lateral direction and is wheel-rail attack

angle.

The wheel profile in the study has very low conicity

and the contact angle has little influence when wheel-

rail relationship varied. Base on the equation (3) and

(4), it is can be seen that the wheel rail lateral force

and the attack angel are the key factors for the rail

gauge corner wear and flange wear. In simulation the

wheel-rail lateral force is shown in figure 13 which

tally with test data.

Fig .12 Schematic diagram of whee-rail contact state

0 20 40 60 80 100 120

0

5

10

15

20

25

30

35

40

Whe

el-

rail

late

ral fo

rce (

kN

)

Time (s)

Fig.13 Wheel-rail lateral when vehicle passing the 300 m radius

curve

3.3 Suspension Parameters Analysis

The critical speed of vehicle is the main target when

designing EMU bogie, and some key parameters are

set to increase the vehicle behaviors on tangent line.

However, the requirement of critical speed and

curving negotiation is contradictious. In this chapter

the key parameters which include axle-box

d

A

NF flangeF B

V

l

h

b

positioning stiffness, coefficient of anti-hunting

damper and axle base are discussed through analysis

the critical speed in straight line and wheel-rail lateral

force and attack angle in sharp curve(radius is 300 m,

passing speed is 10 km/h).

The two wheelsets of one bogie have two kinds of

motion models as shown in figure 14, one is bending

model and the other is shear model[21]. The studies

in the last three decades illustrate that hunting

stability shall be given as a function of the bending

and shear stiffness relative to two wheelsets. At

rocker type journal box positioning device, the lateral

and longitudinal stiffness can be regarded as shear

and bending stiffness respectively.

(a) Bending mode (b) Shear model

Fig. 14. Motion model of wheelset [21]

Figure 15 shows the influence of axle-box

positioning stiffness on critical hunting speed. It is

noted that the critical hunting speed increases with

the lateral stiffness decreasing and with the

longitudinal stiffness increasing. The bending motion

is restrained with increasing longitudinal stiffness, so

it can keep wheelset hunting down. Projection curves

of the contour in the curved surface present linear

characteristic as shown in figure. 15. In other words,

when the ratio of longitudinal stiffness to lateral

stiffness is determined, the critical hunting speed

should be similar. The critical hunting speed

enhances with the ratio increasing.

24

6

8

10

1012

1416

1820

400

500

600

700

800

Longitudinal position stiffness (MN/m)Late

ral p

osition st

iffness

(MN/m

) Cri

tica

l h

un

tin

g s

pe

ed

(km

/h)

Current value

Fig.15 Critical hunting speed vs. axle-box positioning stiffness

A high bending stiffness implies that both of the

wheelsets remain essentially parallel to one another

and hence may not attain a radial position in a curve.

Thus, there is a limit on the ability of the bogie to

negotiate sharp curves. Figure 16 and figure 17 show

the wheel-rail lateral force and attack angel when

vehicle passing the sharp curve with radius of 300m.

It is can be seen from this figure that the lateral

stiffness has little influence on the wheel-rail lateral

force and attack angle, while, the longitudinal

stiffness has significant effect on them. Considering

the curving negotiation performance and critical

speed, the lateral and longitudinal stiffness should be

cut down and kept the ratio of longitudinal stiffness

to lateral stiffness same to the current value. In this

way, wheel-rail lateral force and attack angle should

be decreased significantly and the critical speed

would not loss.

24

68

1012

1416

1820

10

15

20

25

30

35

109

87

65

43

2

Longitudinal position stiffness (MN/m)

Wh

ee

l-ra

il la

tera

l fo

rce

(kN

)

Latera

l posit

ion s

tiffn

ess (M

N/m)

Current value

Fig.16 Wheel-rail lateral force vs. axle-box positioning stiffness

24

68

1012

1416

1820

0.002

0.004

0.006

0.008

109

87

65

43

2

Lateral position stiffn

ess (MN/m)

Longitudinal position stiffness (MN/m)

Attack

angle

(ra

d)

Current value

Fig.17 Wheel-rail attack angle vs. axle-box positioning stiffness

The anti-hunting motion damper is an absolutely

necessary component on high-speed railway vehicle.

The property of the anti-hunting motion damper

depends on three parameters, first damping

coefficient, unloading force and series stiffness. The

influence of unloading velocity and unloading force

on critical hunting speed is investigated as shown in

figure 18. The figure illustrates that the critical speed

enhances with the unloading force increasing or the

unloading velocity reducing. According to figure 18,

the ratio of unloading force to unloading velocity is

the first damping coefficient which determines the

critical hunting speed.

6

8

10

12

0.004

0.008

0.012

0.016

200

300

400

500

600

700

800

Unloading velocity (m/s)

Critical h

unting s

peed

(km

/h)

Unloading forc

e (kN)

Fig.18 Critical hunting speed vs. unloading force and velocity

When vehicle runs at a high speed, the anti-hunting

motion damper can reduce the hunting motion by

restraining the yaw motion of bogie. Thus, the

curving negotiation performance can be decreased.

But when vehicle passing the sharp curve at a very

low speed, the vibration of the system is small and

the anti-hunting motion damper will not work. Figure

19 and figure 20 give the wheel-rail lateral force and

attack angle when vehicle passing the sharp curve at

10 km/h. From figure 19 and figure 20 it is can be

seen that dropping the first damping coefficient can

reduce the wheel-rail lateral force and attack angle,

but the amplitude is very small. Based on an overall

analysis of critical hunting speed, wheel-rail lateral

force and attack angle, the parameters of anti-hunting

motion damper do not be suggested to adjust.

5

6

7

8

9

0.002

0.0040.006

0.0080.010

0.0120.014

0.016 30.0

30.5

31.0

31.5

32.0

32.5

Unloading velocity (m

/s) Unloading fo

rce (kN)

Whe

el-

rail

late

ral fo

rce (

kN

)

Fig.19 Wheel-rail lateral force vs. unloading force and velocity

5

6

7

8

9

0.002

0.0040.006

0.0080.010

0.0120.014

0.016

0.00765

0.00768

0.00771

0.00774

Unloading velocity (m

/s) Unloading fo

rce (kN)

Attack a

ngle

(ra

d)

Fig.20 Wheel-rail attack angle vs. unloading force and velocity

The wheelbase is a primary parameter which

influences the dynamic behavior[22]. Figure 21

indicates that the critical speed will decrease when

the wheelbase reduced. The wheel-rail lateral force

affected by wheelbase is less as shown in figure 22,

while, the wheel-rail attack angle will decrease

linearly along with reducing the wheelbase as shown

in figure 23. Under the condition of meeting the

vehicle running speed, reducing the wheelbase could

slow down the rail gauge corner wear and flange

wear.

2.4 2.5 2.6 2.7 2.8

580

590

600

610

620

630

Critical speed

(km

/h)

Wheelbase (m) Fig.21 Critical speed vs. wheelbase

2.2 2.3 2.4 2.5 2.6 2.7 2.828

29

30

31

32

Whe

el-

rail late

ral fo

rce

(kN

)

Wheelbase (m) Fig.22 Wheel-rail lateral force vs. wheelbase

2.2 2.3 2.4 2.5 2.6 2.7 2.8

0.0070

0.0075

0.0080

0.0085

0.0090

Att

ack a

ng

le (

rad

)

Wheelbase (m) Fig.23 Wheel-rail attack angle vs. wheelbase

The other suspensions such as the primary suspension

spring, the secondary lateral damper and air spring

have little influence on the sharp curve negotiation

according to the calculation. So the results of these

parameters were not given in this article for brief.

4 WHEEL PROFILE OPTIMIZATION

4.1 optimization schemes

The wheel and rail rolling radii difference is a main

parameter which influences the critical speed and

curve negotiation performance. Low rolling radii

difference can provide high critical speed but cannot

provide enough guiding force for vehicle negotiating

the sharp curve which lead to the rail gauge corner

contacts the wheel flange.

0 2 4 6 8 10 12 14 16

0

5

10

15

20

25

30

32 mm

30 mm

28 mm

Rolli

ng r

adii

diffe

rence (

mm

)

Lateral displacement of wheelset (mm)

wheel flange thickness:

Fig.24 Rolling radii difference of different re-profiling wheels

Based on current wheel re-profiling method, when

wheel has flange wear as shown in figure 3, the new

profile is obtained by translation the standard profile

to the flange side in order to reduce the cutting output.

Figure 24 gives the rolling radii differences of three

re-profiling wheels with different wheel flange

thickness. Figure 24 indicates that rolling radii

difference will be decreased with the wheel flange

thickness cutting down. Reducing rolling radii

difference could worsen the sharp curve negotiation

performance of vehicle. So the wheel flange wear

will enhance with the re-profiling period increases as

shown in figure 4.

In order to improve the sharp curve negotiation

performance of vehicle, the rolling radii difference of

the wheel was enhanced and the new profile was

obtained by parallel inverse design method[14].

However, the target function of rolling radii

difference cannot be given directly and should be

solved by another optimization program.

The function of rolling radii difference was

controlled by 4 points on regular wheelset

displacement spacing of 3 mm as shown in figure 25,

and cubic spline curve connected end to end was used

to generate the target function of rolling radii

difference. In the course of the optimization

procedure, the point 2 and point 3 were adjusted to

obtained different function of rolling radii difference.

Then different wheel profiles could be solved by

employ the parallel inverse design method. When a

new wheel profile is solved, the critical speed of the

vehicle with it will be calculated. If the critical speed

does not meet the vehicle operation in reality, the

control point should be lower.

Considering the curve negotiation performance and

the critical speed, the target function can be written

as

0 2 0 2

1 1 1 2 2 2( ) ( ) max1000

vw z z z z w (5)

The new profile must meet the requirement of vehicle

running at high speed in tangent line as reads:

0v v (6)

In order to ensure that the value of rolling radii

difference increase with the wheelset displacement

added, the vertical ordinate of the control points

should subject to

0 2 1 1 3 22 , 2z z z z z z (7)

Where ( 1,2)iz i is the vertical ordinate of the

control point of rolling radii difference for ith new

profile. 0( 1,2)iz i is the original value of point i .

( 1,2)iw i is the weight of i part, in this paper

1 0.7w and 2 0.3w . v is the vehicle critical speed

and 0v is the practical speed of the vehicle, in this

paper 0v =300 km/h. is coefficient of safety which

be set though the vehicle dynamic modal, in this

paper 1.3 .

0 3 6 9

0

5 point 3

point 2

point 1

Ro

llin

g r

ad

ii d

iffe

ren

c (

mm

)

Wheelset displacement (mm)

point 0

Fig.25 The control points of rolling radii difference

4.2 Optimization result and discussion

The Neldes-Mead method[23] is employed to solve

this optimization problem and the new wheel profile

is achieved as shown in figure 26. From this figure

we can see that the slope of the new profile is larger

than that of initial profile in wheel tread and the two

profiles have the same flange size. The large slope of

profile can increase the rolling radii difference and

contact angle. Increasing the rolling radii difference

can achieve better curving. When wheel flange

contacts rail gauge corner unavoidably, the big

contact angle can provide big wheel-rail lateral force,

then the normal force on wheel flange will be

reduced.

-60 -40 -20 0 20 40 60

-30

-25

-20

-15

-10

-5

0

5

z (

mm

)

y (mm)

Initial profile

New profile

Fig.26 Initial and optimized wheel profiles

Figure 27 indicates that rolling radii differences of

new profile and target are evidently larger than that

of initial profile. Rolling radii difference of new

profile is approach to the target value but not the

same, which may be associated with the number of

design variables and the convergence of the

algorithm. The new profile has small rolling radii

difference for small lateral displacement of wheelset,

which can provide a good stability of vehicle on

straight track. When vehicle passing the sharp curve,

the lateral displacement of wheelset will be large and

the new profile has a large rolling radii difference to

achieve better curving and less wear.

0 2 4 6 8 10-1

0

1

2

3

4

5

Target

Initial proflie

New proflie

Ro

llin

g r

ad

ii d

iffe

ren

ce

(m

m)

Lateral displacement of wheelset (mm)

Fig.27 Rolling radii difference of initial profile, target and new

profile

In figure 28 the distributions of wheel-rail contact

points versus lateral displacement of wheelset is

shown. It is can be seen that with the same lateral

displacement of wheelset to flange the contact points

of new profile is close to flange, which will provide

larger rolling radii difference and creepforce when

passing sharp curve. The smoothly transition from

tread to flange will reduce flange wear.

(a) Initial profile

(b) New profile

Fig.28 The distribution of the wheel-rail contact points with of

intial profile and new profile

700 720 740 760 780

-20

-10

0

10

20

30

Y /mm

Z /

mm

0246810 -4 -8 -10

LMa-CHN60

700 720 740 760 780

-20

-10

0

10

20

30

Y/mm

Z/m

m

04812 -4 -8 -12

OPT73-CHN60

In order to investigate wheel-rail matching

performance in detail, Kalker’s theory [24,25] of

three-dimensional elastic bodies in rolling contact

with non-Hertzian is utilized to analyze the normal

pressure and tangential traction in the contact surface

of wheels and rails in static state. Max normal

pressure distribution is given in figure 29. From this

figure we can see that when lateral displacement of

wheelset is smaller than 6 mm the normal pressure of

two profiles have the close value. The normal

pressure of new profile is higher than that of initial

profile when lateral displacement of wheelset range

from 6 mm to 9 mm. The higher normal pressure in

this bound will cause more wear in root of flange

when vehicle passing sharp curve. However, the

existing problem is the serious flange wear and rail

gauge corner wear but not the wear in root of flange.

0 2 4 6 8 10 120

1000

2000

3000

4000

5000

6000

Ma

x n

orm

al p

ressu

re d

istr

ibu

tio

n (

MP

a)

Lateral displacement of wheelset (mm)

Initial profile

New profile

Fig.29 Max normal pressure distributions of initial profile and

new profile vs. lateral displacement of wheelset

In figure 30 and figure 31 the creep force distribution

were shown. These figures illustrate that the new

profile has higher longitudinal and lateral creep force,

especially when the lateral displacement of wheelset

range from 6 mm to 9 mm, which is due to the higher

rolling radii difference. The high longitudinal creep

force can provide large turning force when vehicle

passing the sharp curve and the high lateral creep

force can reduce the flange force.

The dynamic behavior of the EMU vehicle with the

new wheel profile has been simulated on the same

curved track (radius 300m) and with the same

conditions as for the initial profile. The lateral

displacement of first wheelset is presented in figure

32 and the attack angle is presented in figure 33.

Figure 32 shows that the lateral displacements of

wheelset with two profiles are in close proximity

when vehicle passing the sharp curve, which is owing

to the flange contact with the corner of rail. The

wheel-rail attack angel with new profile is smaller

than that with initial one as shown in figure 32, which

can reduce the wear of rail gauge.

0 2 4 6 8 10 12

0

300

600

900

1200

1500

1800

Initial profile

New profile

Max longitudin

al cre

ep forc

e d

istr

ibution (

MP

a)

Lateral displacement of wheelset (mm)

Fig.30 Max longitudinal creep force distributions of initial profile

and new profile vs. lateral displacement of wheelset

0 2 4 6 8 10 120

50

100

150

200

250

300

350

Initial profile

New profile

Ma

x la

tera

l cre

ep

fo

rce

dis

trib

utio

n (

MP

a)

Lateral displacement of wheelset (mm)

Figure.31 Max lateral creep force distributions of initial profile

and new profile vs. lateral displacement of wheelset

0 20 40 60 80 100 120-10

-8

-6

-4

-2

0

2 Initial profile

New profile

La

tera

l d

isp

lace

me

nt o

f w

he

els

et (m

m)

Time (s)

Fig.32 Lateral displacement of wheelset with initial profile and

new profile

0 20 40 60 80 100 120

-0.008

-0.006

-0.004

-0.002

0.000

0.002

Initial profile

New profile

Time (s)

Wheel-ra

il attack a

ngle

(ra

d)

Fig.33 Wheel-rail attack angle with initial and new profile

The dynamic behavior of vehicle with the two

profiles on trunk railway has also been calculated in

recent study. The critical speed of vehicle with the

new profile on straight track is 470 km/h which is

slower than that with the initial one (574km/h).

However, that speed mentioned above still can meet

the requirement of vehicle practical server. In figure

34 the lateral displacement of wheelset is shown

when vehicle passing the curve on trunk railway. The

curved track consists of 100 m straight track

continuing into 670 m transition curve, then

switching into the 1880 m curve with R 7000 m and

670 m transition curve and ending with 500 m

straight track. The vehicle travels with the speed of

300 km/h. Figure 34 illustrates that vehicle with new

profile has smaller lateral displacement of wheelset

than that with initial one when no flange and rail

gauge corner contacts. According to the calculation,

the two-point contact of wheel and rail can occur

when passing the radius 800 m curve with initial

profile and radius 600 m curve with new profile. So

the new profile can reduce the chance of wheel flange

and rail gauge corner contact and decrease the rail

gauge corner wear.

0 500 1000 1500 2000 2500 3000 3500 4000

-4

-3

-2

-1

0

1 Initial profile

New profile

Late

ral dis

pla

cem

ent of w

heels

et (m

m)

Running distance (m) Fig.34 Lateral displacement of wheelset

5 CONCLUSIONS

The wheel flange/rail gauge corner wear was

measured on sharp curve. We can find that on sharp

curve, the high pressure between wheel flange and

rail gauge corner would cause violent rail gauge

corner wear and more serious flange wear would

happen with smaller rolling radii difference of re-

profiling wheelset.

A vehicle dynamic model was established based on

the true vehicle structure and effects of key

parameters were studied. The results show that under

the condition of great yaw stiffness of wheelset, the

yaw angles of wheelset is not enough to pass the

sharp curve, which increases attack angle between

wheel and rail. Then wheel-rail two-point contact

would occur and cause serious wheel flange/rail

gauge corner wear. The rail gauge corner wear can be

reduced by adjusting the axle-box positioning

stiffness and wheelbase.

Satisfying the requirement of high speed on tangent

track and curve passing behavior, a improved parallel

inverse design method is introduced for a new

profile. The simulation results show that the new

profile can provide high lateral and longitudinal creep

force , as well as reduce the chance of wheel flange

and rail gauge corner contact and attack angle, which

can promote the curve negotiation performance and

decrease the rail gauge corner wear

6 ACKNOWLEDGEMENTS

The present work has been supported by the National

Natural Science Foundation of China (U1134202,

51275427, 51275430), the China Postdoctoral

Science Foundation(2015M572492),the Fundamental

research Funds for the central Universities

(2682014CX018EM) and the Construction Fund for

High-level Researcher of Emei Campus of Southwest

Jiaotong University(RC2013-13)

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