rail temperature rise characteristics caused by … · rail temperature rise characteristics caused...
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Journal of Traffic and Transportation Engineering ( English Edition)
2014,1(6) :448-456
Rail temperature rise characteristics caused by linear eddy current brake of high-speed train
Xiaoshan Lu', Yunfeng Li2 , Mengling Wu', Jianyong Zuo1' • , Wei Hu'
1 /nstitute of Railway Transit, Tongji University, Shanghai, China 2 CSR Qingdao Sifang LDcomotive Co. , Ltd. , Qingdao, Shandong, China
3 Ecole Nationale Supirieure d'Arts et Mitiers, Angers, Pays de la Loire, France
Abstract: The rail temperarure rises when the linear eddy current hrake of high-speed train is working, which may lead to a change of rail physical characteristics or an effect on train operations. Therefore , a study concerning the characteristics of rail temperarure rise caused by eddy current has its practical necessity. In the research , the working principle of a linear eddy current brake is introduced and its FEA model is established. According to the generation mechanism of eddy current, the theoretical formula of the internal energy which is produced by the eddy current is deduced and the thennalload on the rail is obtained. ANSYS is used to simulate the rail temperarure changes under different conditions of thermal loads. The research result shows the main factors which contribute to the rising of rail temperarure are the train speed, brake gap and exciting current. The rail temperarure rises non-linearly with the increase of train speed. The rail temperarure rise curve is more sensitive to the exciting current than the air gap. Moreover, the difference stimulated by temperarure rising between rails of 60 kg/m and 75 kg/m is presented as well.
Key words: high-speed train; linear eddy current brake; thennal load; rail temperarure rise
1 Introduction
The traction and the braking are two main issues for a high -speed train ( Zhu and Zhang 1996 ) . As the dras
tic increasing in operation velocity of trains during
recent years, the adhesion coefficient between the
wheel and the rail at high speed decreases greatly as
well as the coefficient of friction between the brake shoe and wheeL Therefore, it is necessary to use a
• Corresponding author: Jianyong Zuo , PhD , Associate Professor.
E-maD: zuojy@tongji. edu. en.
non-adhesive braking system for a supplementary bra
king force (Chen 2008; Yan eta!. 2010). The linear eddy current brake is such a non-adhesive form of
non-contact brake system which has been already put
into application on ICE3 (Chen 2001 ; Graber 2003 ;
Kunz 2005 ; Treib 2013) , shown in Fig. 1. The linear eddy current brake has distinguished advantages in
cluding no wear, no pollution, low maintenance , quick response and so on (Ding et a!. 2012; Dong
Journal of Traffic and Transportation Engineering( English Edition) 449
2007 ; Xu 2011 ) . Thus , its application will greatly enhance the safety of train operation.
Fig. 1 LECB installed on ICE3
However, due to the energy conversion principle of
train braking, the kinetic energy of the train is con
verted to other forms of energy and dissipated ( Zhi
et al. 1983; Zhu 1994; Zhang et al. 2011). The lin
ear eddy current brake ( LECB ) achieves this by
using eddy current effect converting the kinetic energy
of the train into thermal energy of the rail. Based on
the fact that the thermal energy on the rail caused by
the eddy current effect can not be dissipated instanta
neously, it will have a significant impact on the me
chanical and electromagnetic performances of the rail
and the effect of eddy current brake ( Li et al. 2011) .
Therefore , a research on the rail temperature rise is
necessary.
In fact, LECB is still in the experimental stage ,
which means it is not be widely commercially applied
and there exist several problems itself. As to research
on the rail temperature rise caused by LECB , some
results have been obtained by German researchers and
Japanese researchers respectively and lead the world
in this domain ( Hendrichs 1986 ; Kashiwagi et al.
2009) . Both of them are based on the experiment.
Other papers usually focus on the thermal characteris
tics on a magnet pole ( Jung 2003 ) . Nevertheless, a
systematic research on thermal characteristics of rail
affected by LECB is deficient, which is the main fo
cus in the paper.
The study is set out based on simulation and a 3D
FEM model of LECB and rail is established. Accord
ing to electromagnetic theory , the heat load on the
rail is calculated before simulation so that the complex
electrical-thermal coupling calculation can be avoi
ded. The main factors of LECB that affect the rail
temperature rise are studied.
2 Modeling for thermal simulation
Figure 2 (SchOpf 2008) illustrates the working princi
ple of LECB in which F represents magnetic force,
Fa represents braking force and FA is attractive force.
A LECB consists of the yoke, pole cores and coils.
The magnetized directions of pole cores change alter
natively. The LECB and the rail maintain a certain air
gap ( called brake gap ) . When the train is running ,
there is a relative movement between the LECB and
the rail , which generates an unsteady magnetic field
on the head of rail. According to Faraday's law of
electromagnetic induction, eddy currents are genera
ted on the head of rail, shown in Fig. 3. The eddy
currents generated on the rail interfere in the original
magnetic field and distort it. The electromagnetic
force between the rail and LECB has a horizontal
component along the direction of the train speed ( di
rection Y) in addition to a vertical component ( direc-
450
tion Z) . The horizontal component is just the train
braking force F 8 • Meanwhile the kinetic energy of the
Relative velocity vis 0
-""' --- r-- - - --
1
0
Xiaoshan Lu et al.
train is converted to the eddy current loss which cau
ses the rise of rail temperature.
v>O ~
r---
~
I FA
-
• ~
Fl
F.
I
--Air gap
~~-Rail
(a) Non-operating state (b) Operating state (c) Structure ofLECB
Fig. 2 Schematic of LECB
Magnetic pole
N
~-f-:,.<·•:::·:.::::·::.:::::::·:::z":· ··=·· l::=--..f-7'
...•..•. ······,.: ....... ·················: ... ::::::··:::.·.·:.-.:· ··········:.::-:::··
s
... ··· ,·.·.·.··· ··· ... ·· .... ........ ····•··•· ~ .• .
·. ··············· .. ·.·.·.:.:>"'''/ -~ ··················· ....... ··
··························
Surface of rail
Fig. 3 Schematic of eddy current
The simplified model for illustrating the LECB is
shown in Fig. 4. The load applied on the rail in this
magnetic-thermal coupled system can be the thermal
load only . Therefore, the simulation can be further
simplified to an individual thermal simulation with its
value deduced in advance.
2.1 Determination of thermal load
In order to further the simulation of the rail tempera
ture rise trend under the thermal load of linear eddy
current brake ( Liu and Liu 2008 ) , the derivation of
the formula for simulation is required. The relative
magnetic permeability is denoted by J.L, permeability
of vacuum by J.Lo , the magnetic path length of the core
by l, the brake gap by X0 , magnetic induction inten
sity by B, the magnetic flux by <Ps , the magnetomo
tive force ( MMF) by g., the magnetomotive force
caused by coils by g m , the equivalent magnetomotive
force caused by eddy currents by g e , the induced elec
tromotive force (EMF) by g, the excitation current in
coils by / 0 , the effective transient eddy current by i,
the magnetic reluctance in the core by r m, the mag
netic reluctance of the airgap by Rm , the yoke area of
the magnetic pole by S, the number of coil turns of a
Journal of Traffic and Transportation Engineering( English Edition) 451
pair of magnetic poles by N, the diameter of an eddy
current area by D, the spacing of the adjacent mag
netic poles of the same polarity by d, the relative
movement speed between the rail and LECB by v, the
penetration depth of eddy currents on the head of rail
by 8 and the conductivity of the rail by 7J , the radius
of eddy current area by r, time by t , the period time
by T. The magnetic flux in the circular area of the top
surface of the rail corresponding to the poles changes
continuously according to a law as "B7rr2 -O-B7rr2 -0"
(Long et al. 2007). According to the cosine law,
the period is d/ v and the magnetic flux <P is ( Rodger
et al. 1989; Tsuchimoto et al. 1992; Wang and Chi
ueh 1998; Xie 2001 )
Fig. 4 Simplified model of LECB and rail
2 -cP = B7rr cos(27rvt/d) (1)
Therefore , the EMF on the rail surface is
~ 2 - -g = - dt =- B7rr (- 27rv/d)sin(27rvt/d) =
(2)
The circular area above is deemed as an area consti
tuted by several metal rings with the parameters
shown in Fig. 5. The resistance of a ring is
dR = 27rr dr ( 3) 7]8
In Eq. ( 3 ) , the penetration depth of eddy currents
8 is
8 = J d/ 7rV7JJ.l.I.Lo (4)
The instantaneous power in the circular area of
diameter D is D IT 2 3 2 - 2 2 - 3
P = 0
(2B 7r 7]8V /d )sin (27rvtld)r dr (5)
The effective power in the whole area of diameter
D within on circle T is
- 1 Jr 2 3 2 4 - 2 p = T /dt = B 'IT 7]8V D /64d (6)
Fig. 5 Eddy current computing model
The effective transient eddy current in the circular
area of diameter D is ( Kunckel et al. 2003)
i = l__ B7r!J8vD2 ( 7 )
fi 4d
Since the eddy current on the surface of rail is rela
tively strong, the eddy current magnetic field has a
weakening effect on excitation field. Therefore the
magnetomotive force of the magnetic circuit is
452
(8)
In Eq. ( 8) , k. is a conversion coefficient usually at
a value 1. 5 ( He et al. 2004) . According to loop the
orem , there are
rm = l!J.1.1.L0 S
Rm = 2X0 IJL0 S Substituting Eqs. ( 7) , ( 8) , ( 10)
Eq. ( 9 ) , it can be concluded
(9)
( 10)
(11)
and ( 11 ) into
16Nl0 JLod B = ( 12)
/ik. 'ITTJ8vD2JL0 + 16X0d According to the device dimension of LECB , the
value of Dis 0.175 m, dis 0. 35m. Then it can be
concluded
1. 4074/0 B = --------~--0. 455V + 5. 6X0
(13)
where / 0 represents the excitation current, whose unit
is A; X0 represents the brake gap, unit mm; V repre
sents the train velocity, unit km/h.
Equation ( 6 ) can also be rewritten by the device
dimension, shown as follow
P = 23. 7B2 V2 (14)
Then the thermal flux is
q = 4P = 76. 03B2 V2 (15) 'ITDz
Equation ( 15) is the formula that can be used to
calculate the thermal flux on the rail when the LECB
is working. When braking parameters /0 , X0 and V
are given, the thermal power per unit area on the rail
surface when LECB is working can be deduced.
2.2 FEA model of rail for thennal simulation
According to what has been concluded, there is no
need to keep LECB model for simulation analysis. The
thermal load can be applied to the top of rail directly.
The rail of model type 60 kg/m ( GB 2585-2007
hot-rolled steel rails for railway) with the length of
350 mm is adopted as simulation model and the pro
ftle of the rail is not simplified for keeping high simu
lation accuracy. The material of the rail is set to
U71Mn and the initial temperature is set to 20 't. The rail FEA model and its meshing result are shown
in Fig. 6. The total number of elements after meshing
is 14565 .
Xiaoshan Lu et al.
Fig. 6 Rail model and meshing result
Because the operation speed of the train is high and
the relative short action length of LECB is only
1. 05 m (including three pairs of magnetic poles and
each of them is 0. 35 m long) , the period change is
so quick that the time in which a pair of magnetic
poles passing over the corresponding region of the rail
where the eddy current is generated is merely
0. 0033 s to 0. 2520 s. Therefore, the thermal effects
generated by adjacent pole pairs passing over the same
position on the rail can be superimposed. Here as
sumes that the load of thermal flux is generated by
one pair of magnetic poles. The rail temperature rise
affected by the whole LECB can be superposed by
several pairs of magnetic poles. Consequently when
effects of the whole brake device are researched, the
result of temperature rise can be directly obtained by
superposing the simulation results.
3 Simulation result analysis
In order to study trends of rail temperature rise under
different brake gaps, excitation currents and train
speeds, the simulation analysis is done according to
conditions listed in Tab. 1.
The conditions sum up to 45 , so that not all the re
sults are listed in the paper. Fig. 7 shows the simula
tion result in the condition where the brake gap is
Journal of Traffic and Transportation Engineering( English Edition) 453
7 mm, excitation current is 50 A and the train speed
is 200 km/h. The result shows that the maximum rail
temperature rise is 25. 94 'C and the penetration depth
is about 2 mm.
Tab. 1 List of parameters required for simulation
Brake gap
(mm)
6
7
8
Excitation
current (A) Train speed ( km/h)
30 50, 100, 200, 300, 380
50 50, 100, 200, 300, 380
70 50, 100, 200, 300, 380
30 50, 100, 200, 300, 380
50 50 , 100 , 200, 300, 380
70 50, 100, 200, 300, 380
30 50, 100, 200, 300, 380
50 50, 100, 200, 300, 380
70 50, 100 , 200 , 300 , 380
20.000
20.660
21.321
21.981
22.641
23 .302
23 .962
24 .622
25 .283
25 .943
(a) Temperature distribution along the rail surface
20.000
20.660
21.321
The effects of train speed, brake gap and excitation 21.981
current on rail temperature rise are shown as follows. 22.641
3 .1 Effects of train ~eeds on rail temperature lire
When the brake gap is 6 mm and excitation current is
70 A ( the condition where the rail temperature rea
ches its maximum of all ) , the rail temperature rise
trend caused by eddy current brake is shown in Fig.
8 . The lower curve represents the maximum rail tem
perature trend under an pair of magnetic poles and the
upper curve represents the maximum rail temperature
trend when the LECB (including three pairs of mag
netic poles) is passing over. As the figure indicates,
the rail temperature increases non-linearly with the in
crease of train speed. According to Faraday's law of
electromagnetic induction , with the train speed in
creasing, the amount of change of magnetic flux per
unit time at some point of the rail is increased and the
eddy current generated is correspondingly increased.
The increase of eddy current will lead to an increase
of rail temperature rise inevitably which is relatively
sensitive to the speed of the train at low speed while
tending to ease at high speed according to Fig. 8. The
result can be confirmed by theoretical arithmetic ( Guo
et al. 2012).
23.302
23.962
24.622
25 .283
25 .943
(b) Temperature distribution on the cross section of rail
Fig. 7 Simulation results of one condition
Besides, Fig. 8 also indicates that the maximum rail
temperature in all conditions reaches 111. 28 'C.
3.2 Effects of bra!E gaps on rail temperature lire
When the excitation current is selected at 50 A con
stantly , the maximum rail temperature curves by taking
different brake gaps ( 6, 7, 8 mm) are shown in Fig. 9.
Comparing the three curves illustrated in Fig. 9 , a
conclusion can be drawn that as the brake gap increa
ses , the maximum rail temperature will be slightly re
duced though the level of the reduction limited by 1%
to 3% per 1 mm change of brake gap. According to
magnetic circuit theory , the total magnetic circuit re
luctance increases in pace with the brake gap increas-
454
ing, which leads to the decrease of magnetic field in
tensity and eddy currents generated. In short, with an
equivalent input of the excitation currents, the influ
ence of the brake gap on the rail temperature rise
trend is minimized.
120 111.28
'"'"'100 2-" ~ 80 ... " "" 8 -WholeLECB .B 8 60 "
--+-- One pair of magnetic poles
.§ ><I
"' :::E 40 33.12 35.94 37.09
20~------~--------~------~------~
0 100 200 300 400
Train speed (km/h)
Fig. 8 Curves of rail maximum temperature trend
90
-+- 6mm ---- 7mm ......._ 8mm
65
60~------~--------~------~------~
0 100 200 300 400
Train speed (km/h)
Fig. 9 Maximum temperature curves under different brake gaps
3.3 Effects of excitation currents on rail tempera
ture rise
When the brake air gap is selected at 7 mm constant
ly, for example, the maximum rail temperature
curves by taking different excitation currents ( 30 , 50 ,
70 A) are shown in Fig. 10.
It is manifested in Fig. 10 that the effects of excita
tion currents on the rail temperature are more explicit
compared with brake gaps. Having a great impact on
Xiaoshan Lu et al.
the entire magnetic field intensity, the excitation cur
rent has greater influence on the eddy current effects ,
which leads to a greater effect on braking torque and
temperature. The analysis data demonstrate that at the
speed of 50 km/h, the maximum temperature in
creased by 3% to 7% per 20 A increase in the excita
tion current while the maximum temperature increased
by 22% to 27% for each 20 A increase in the excita
tion current with the train speed up to 380 km/h.
Therefore , it can be obtained that the excitation current
has a greater effect on temperature rise under high train
speed; otherwise, the influence is relatively small un
der the low-speed case.
110
'"'"' 100 2-" ... ~
90 ... " "" 8 .B 8 80 s
·>< "' :::E
70
60 0
Fig. 10
-+- 30 A ----50 A ......._ 70 A
100 200 300
Train speed (km/h)
Maximum temperature curves under different
excitation currents
400
3.4 Effects of types of rail on rail temperature rise
Holding steady values of all other parameters , the rail
temperature rises on different types of rail are studied
as well. The mode type 60 kg/m is usually used in
high-speed lines while the mode type 75 kg/misused
in heavy-haul railways. The maximum rail tempera
ture curves by taking different types of rail are shown
in Fig. 11. Obviously, the maximum temperatures of rail types
of 75 kg/m and 60 kg/m have little difference.
Although there are many different dimensional param
eters of these two types of rail , the penetration depth
is about 2 mm on the top surface of the rail where the
contour shapes of them have few differences in term
of the whole rails.
Journal of Traffic and Transportation Engineering( English Edition) 455
115 ----60km/m 111.28
110 -+-75km/m
~ 105
"' .... 100 .a .. ....
"' 95 1'1. s 2
90 ~ .§ 85
><I .. ::E 80
75
70 0 100 200 300 400
Train speed (km!h)
Fig. 11 Maximum temperature curves under different types of rail
4 Conclusions
By theoretical derivation and simulation analysis, the
effects of eddy current brake on the rail temperature
rise are studied. The results show that there are three
main aspects of LECB that affect the rail temperature
rise: the train speed, brake gap and excitation cur
rent. The influence of these three aspects on rail tem
perature rise is quantitatively analyzed by simulation.
Because the simulation of rail temperature rise of
LECB is an electrical-thermal coupling problem, the
heat load on the rail is calculated by electromagnetic
theory before simulation in order to avoid the complex
electrical-thermal coupling calculation. Therefore, the
simulation process has been greatly simplified.
If the brake gap and excitation current keep con
stant, the rail temperature rises non-linearly with the
increase of train speed. The rail temperature rise
curve is relatively sensitive to the speed of the train at
low speed while tending to ease at high speed.
Under the specific circumstances with the same
train speed and excitation current , rail temperature
rise would decrease with a gain of brake gap which
has a light effect on the temperature rise. And if keep
brake gap and train speed as constant , the increasing
excitation current will lead to the increase of rail tem
perature rise. What's more, the excitation current has
greater influence on temperature rise with higher train
speed.
There is no significant difference of rail temperature
rise trends between the rail types of 60 kg/ m and
75 kg/m.
The maximum rail temperature in all conditions rea
ches 111. 28 't: .
Acknowledgments
This project is supported by the Fundamental Research
Funds for the Central Universities (No. 2860219030)
and Foundation of State Key Laboratory of Traction
Power, Southwest Jiaotong University ( No.
TPL1308).
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