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A new criterion for assessment of train derailment risk

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DynamicsEngineers, Part K: Journal of Multi-body Proceedings of the Institution of Mechanical
http://pik.sagepub.com/content/224/1/83The online version of this article can be found at: DOI: 10.1243/14644193JMBD203 2010 224: 83
Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics
M Durali and M M Jalili
A new criterion for assessment of train derailment risk
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83
Anewcriterionforassessmentoftrainderailmentrisk
MDurali
and
MMJalili
∗
Mechanical Engineering Department, Center of Excellence in Design, Robotics and Automation,Sharif University ofTechnology,Tehran, Iran
The manuscript was received on 26 December 2008 and was accepted after revision for publication on 20 July 2009.
DOI: 10.1243/14644193JMBD203
Abstract:
A new criterion for prediction of train derailment is presented in this article. A three-degrees-of-freedom(3DOF)wheelsetmodelisusedtoidentifythemaindynamicparametersthataffect wheelset derailment. Using these parameters and conventional deﬁnition of derailmentcoefﬁcient, a new criterion for prediction of wheelset derailment is introduced. The proposedcriterion, in addition to providing the required precision in prediction of wheel set derailment,requires measurements that are easy to perform. To evaluate the capability of the new criterionin prediction of derailment, a full wagon model with 48 DOF moving on a track with differentrandomirregularitieswasused.Thetrackisassumedtobemountedonaviscoelasticfoundation.The wagon model is a three-dimensional, non-linear model of a train passenger car. The modelincludes non-linear elements for primary and secondary suspension systems. Friction and slack betweenelements,thecentrepivotwithkinematicsconstraints,forcesbetweenpads,andbolsterare also included in this model.The motion of the wagon on tangent and curved tracks is simulated for different travelspeeds. Derailment coefﬁcient and a new derailment criterion are used to investigate the pos-sibility of wheelset derailment in each case. The study shows that the new criterion can very well predict wheelset derailment and can duplicate the predictions by conventional derailmentcoefﬁcient
(
Y
/
Q
)
.
Keywords:
railroad dynamics, vehicle–track interaction, derailment coefﬁcient, track randomirregularities, train safety
1 INTRODUCTION
Since the early development of railroad in England,train derailment has been a challenge for the railroadsystem. Safety in transportation is a prime concernespecially for public transportation. Derailment hasalwaysbeenoneofthemajorsourcesoftrainaccidentsin the world. For this reason, it has been a point of attention to railway engineers and researchers.Different criteria based on operating experienceare offered for predicting derailment of wheelset.Limits of derailment parameters differ in differentstandards and are affected by track quality, trafﬁc vol-ume, and axle loads. As high trafﬁc volume and axleloads decrease rail quality in the long run, the risk of wheelset derailment increases.
∗
Corresponding author: Department of Mechanical Engineering,Sharif University of Technology,PO Box 11365-9567,Tehran,Iran.email:mmjalili@mehr.sharif.edu
Based on derailment criteria, different wagon mod-els are developed to simulate wheelset motion andpredict derailment. For instance, Zhia
et al.
[
1
] useda37degreesoffreedommodel(37DOF)toinvestigate wagonderailmentmovingonatrackwithlateralirreg-ularities. A typical complete wagon model in derail-mentstudieswasdevelopedbyDuraliandShadmehri[
2
]. Their model is a non-linear, three-dimensional(3D) model with 42 DOF per wagon in which all non-linearities of springs, dampers, gaps, and clearances,the effect of dry friction, mechanical stops in sus-pension system, and the links between wagons areconsidered. Using this model, the derailment coefﬁ-cient is determined for several train conﬁgurationsand the tendency of the wheelsets to derailment isinvestigated. In addition, Durali and Jalili [
3
] havesimulated train derailment in curves using a 43 DOFmodelforeachwagon.Thelatterworkhasstudiedtheeffects of axial tensile and compressive forces along the train on initiation of train derailment, especially when the train is passing through a curve.
JMBD203 Proc. IMechE Vol. 224 Part K: J. Multi-body Dynamics
84 MDuraliandMMJalili
Accurate determination of contact points betweenthe wheel and rail, and the contact force betweenthem play an important role in derailment studies.To do this, various methods, such as solving alge-braic equations or nodal search, are employed. Forexample, Shabana
et al.
[
4
] developed an algorithmfor solving differential and algebraic equations of thecontact problem. In this method, the constraints putagainst axle motion by the rail are used to calculatethenormalforcesatthewheel–railcontactpoint.Also,Shabana
etal.
[
5
]developedanelasticforcemethodforsolving wheel–rail contact problems. In this method, which is based on the relative position of the wheeland rail, Hertz contact theory or other theories basedon wheel–rail stiffness and damping coefﬁcients areusedtoﬁndthenormalcontactforces.Alsoaformula-tionforonlinedeterminationofthewheel–railcontactpoint in general 3D contact was developed by Pombo
et al.
[
6
] and Pombo and Ambrósio [
7
]. This formula-tion allows for the study of lead and lag ﬂange contactscenarios both in usual derailment situations as wellas cases involving switches.In the present work, a 3D non-linear model of a wagon is presented. Using a simple wheelset model,a new parameter for the investigation of wheelsetderailment is deﬁned. The wagon model is run ondifferent types of track with irregularities, and thenew parameter is determined for each simulatedcase. Validation of the new parameter is checked by comparing derailment predictions by the new param-eter with the results based on determination of thederailment coefﬁcient.
2 BRIEFREVIEWONTHEDERAILMENTCRITERIA
One of the criteria for prediction of train derailment isderailment coefﬁcient, which is deﬁned as the ratio of lateral to vertical load at the wheel–rail contact point.In 1908, Nadal put forward the ﬁrst equation to cal-culate the critical derailment coefﬁcient [
8
]. Figure 1showsthesystemofforcesactingontheﬂangecontactpoint. In this ﬁgure
T
is the tangential force across theﬂange,
N
isthenormalforceontheﬂange,and
α
istheﬂangeangleatthewheel–railcontactpoint.Usingthisﬁgure, it can be written
Y Q
=
tan
α
−
(
T
/
N
)
1
+
(
T
/
N
)
tan
α
(1)inwhich
Y
and
Q
arethelateralandverticalwheel–railcontact forces, respectively. As the tangential force
T
cannot exceed the valueof normal force multiplied by the coefﬁcient of fric-tion at the wheel–rail contact point, the lower limit of the derailment coefﬁcient proposed by Nadal can be
Fig.1
Forces acting on the wheel in the wheel–railcontact point
written as
Y Q
=
tan
α
−
µ
1
+
µ
tan
α
(2)In equation (2)
µ
is the coefﬁcient of friction at the wheel–rail contact point. Although the derailment coefﬁcient proposed by Nadalisratherconservative,butbecauseofitssimplic-ity, it is still widely used. This coefﬁcient determinesthe minimum value of
Y
/
Q
at which a ﬂange may climb the rail, causing derailment. Other criteria likeequations proposed by Chartet [
9
] andWeinstock [
10
] were also developed to investigate derailment theo-retically. Weinstock proposed a criterion for setting alimit on the sum of the absolute values of derailmentcoefﬁcientsoftwowheelsonacommonaxle[
10
].Thiscriterion is deﬁned as follows when the coefﬁcient of friction between wheels and rail
µ
is considered to beequal for both wheels
Y Q
=
tan
α(
1
+
µ
2
)
1
+
µ
tan
α
(3) Although there are a number of relations for deter-miningthederailmentcoefﬁcient,inmanystandards,thetwoquantities,
Y
and
Q
,aremeasuredexperimen-tally or calculated by simulations. To obtain
Y
and
Q
from simulation, an accurate dynamic model of thetrain is essential.The reduction of wheel normal force is also takenas a measure of potential towards derailment in somestandards[
11
].Thelimitingvaluesoftheseparametersdiffer in different standards. According to the BritishStandard [
12
], the value of
Y
/
Q
must not exceed 1.2for more than 0.05s. In addition, wheel vertical loadshould never be
<
60 per cent of its static value. Thiscondition is expressed as
QQ
0
<
0.6
QQ
0
=
(
Q
−
Q
0
)
Q
0
(4)in which
Q
0
is the static wheel load and
Q
is thereduction in the wheel load compared to
Q
0
.
Proc. IMechE Vol. 224 Part K: J. Multi-body Dynamics JMBD203
Anewcriterionforassessmentoftrainderailmentrisk 85
In Japanese Standard [
13
], the maximum value of the derailment coefﬁcient is deﬁned as
Y Q
=
0.8
t
>
0.05 s
Y Q
=
0.04
t
t
<
0.05 s(5)in which
t
denotes the time interval for maximumvalue of derailment coefﬁcient.In China, the limiting value of
Y
/
Q
is 1 [
11
]. InNorth America, Elkins and Carter [
14
] used a vehicleequipped with load measuring wheelsets and othernecessaryinstrumentationtomeasurelateralandver-ticalwheelforces.Acceptableperformanceduringtherail cross-level variation test is that the axle sum
Y
/
Q
neverexceed1.5,themaximumvehiclebodyrollangledoes not exceed 6
◦
peak to peak, and the minimumvertical wheel load is never
<
10 per cent of the static wheel load. In addition, acceptable performance forthe variation of the track alignment test requires thatbogie-side
Y
/
Q
does not exceed 0.6 and the axle sum
Y
/
Q
never exceed 1.5 [
14
].British Railway Group Standard number GM/RT2141 prescribes design requirements for tractionand rolling stock and for the on-track plant, toensure acceptable resistance against ﬂange climbing derailment [
15
]. In this reference, three ﬂowchartsare presented for determination of the resistance of adeveloped vehicle against ﬂange climbing derailment(Fig.2).Thevehiclesarecategorizedintothreegroups,namely vehicles with neither a novel suspension norrunning gear nor a multi bogie/axle conﬁguration(usingchart(a)),vehiclesthathaveamulti-bogie/axleconﬁguration but not a novel suspension or run-ning gear (using chart (b)), and vehicles with a novelsuspension or running gear (using chart (c)).Theothercriterionforpredictionoftrainderailmenthas been proposed by Jun and Qingyuan [
13
] and Jun
et al.
[
16
]. This criterion, named energy increment, isexpressed as
σ
c
< σ
p
No derailment (6)
σ
c
> σ
p
In derailment (7)
σ
c
=
σ
p
In critical state of derailment (8)Intheaboveequations
σ
c
istheworkdonebythesys-tem when it is resisting against transverse vibrationsand
σ
p
is the energy input to the transverse vibrationsof the system.Two new criteria were developed by Braghin
et al.
[
17
] on the basis of the test results. In this referencethe effect of different parameters such as wheelsetangle of attack and the ratio between the vertical
Fig.2
GM/RT ﬂow diagram for vehicle acceptance against climbing derailment: (a) vehicles withneither a multi-bogie/axle conﬁguration nor a novel suspension or running gear; (b) vehi-cles with a multi-bogie/axle conﬁguration but not a novel suspension or running gear; and(c) vehicles with a novel suspension or running gear
JMBD203 Proc. IMechE Vol. 224 Part K: J. Multi-body Dynamics
86 MDuraliandMMJalili
Fig.3
Wheel standard proﬁle [
18
]
loads acting on the ﬂanging and non-ﬂanging wheels was investigated. Another parameter used as the derailment crite-rionisthewheelsetlateralandverticaldisplacements.Larger values of lateral and vertical displacements of wheelsets increase the risk of derailment. Figure 3illustrates a sample of wheel proﬁle (S1002) that isused in Iran railroad [
18
]. According to this ﬁgure, theﬂange has a larger diameter than the tread and limitsthe lateral wheelset motion. Wheelset lateral motion will bring the ﬂange in contact with the rail and lim-its the wheelset further motion. If the ﬂange fails tolimit lateral wheelset motions, derailment may occur.For instance, in the wheel proﬁle presented in Fig. 3if the wheelset maximum lateral displacement equals
y
max
=
55mm andthewheelsetmaximumverticaldis-placement equals
z
max
=
28mm, the ﬂange climbs therail head and will run over the rail and derailmentmay occur.Depending on wheel proﬁle and line quality, differ-entstandardshavedeviseddifferentlimitingvaluesforallowable lateral and vertical wheelset displacements.For example, according to the Chinese Standard,the limiting values of these parameters are deﬁnedas [
19
]
y
max
=
54mm
z
max
=
25mm(9)In reference [
19
], the maximum allowable values of lateral and vertical wheelset displacements are
y
max
=
70mm
z
max
=
30mm(10)The wheelset lateral positions for these standardsareillustratedinFig.4.Asshowninthisﬁgure,inbothcases the ﬂange climbs the rail head, and as a resultrails cannot limit wheelset lateral movement. In suchcases, derailment has occurred.
Fig.4
Wheel–rail relative position in derailment
Based on the above review, one will conclude thatthe maxima of lateral and vertical wheel displace-ments can determine the fact of derailment whilethe derailment coefﬁcient predicts the probability of derailment. However, the determination of thederailment coefﬁcient by measurement of wheel–railcontact forces is not always practical and thereforethis parameter cannot easily be used as a means forcontrolling derailment.
3 WHEELSETCO-ORDINATESYSTEM
In Fig. 5 the co-ordinate systems used in this analysisareshown.Theﬁxedco-ordinatesystem
x
′′′
y
′′′
z
′′′
hasitssrcin at the track centre-line.The co-ordinate system
x
′′
y
′′
z
′′
is an intermediate frame that is obtained fromrotation of
x
′′′
y
′′′
z
′′′
about the
z
′′′
axis through an angle
ψ
. The local co-ordinate system
x
′
y
′
z
′
has its srcinat the centre of mass of the wheelset and it is gen-erated from rotation of
x
′′′
y
′′′
z
′′′
about the
x
′′
axis by
Proc. IMechE Vol. 224 Part K: J. Multi-body Dynamics JMBD203

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