effects of key parameters of emu bogie on rail gauge
TRANSCRIPT
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: [email protected]
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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