High-SpeedTrain-Track-BridgeDynamicInteractionconsidering ...downloads.hindawi.com/journals/sv/2019/5874678.pdf · model of high-speed train-track-bridge interaction is for-mulated.ismodellingisbasedonthetrain-track-bridge

Research ArticleHigh-Speed Train-Track-BridgeDynamic Interaction consideringWheel-Rail Contact Nonlinearity due to Wheel Hollow Wear

Chao Chang Liang Ling Zhaoling Han Kaiyun Wang and Wanming Zhai

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

Correspondence should be addressed to Liang Ling lianglingswjtueducn

Received 2 August 2019 Accepted 28 September 2019 Published 31 October 2019

Academic Editor Sakdirat Kaewunruen

Copyright copy 2019 Chao Chang et al (is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Wheel hollow wear is a common form of wheel-surface damage in high-speed trains which is of great concern and a potential threatto the service performance and safety of the high-speed railway system At the same time rail corridors in high-speed railways areextensively straightened through the addition of bridges However only few studies paid attention to the influence of wheel-profilewear on the train-track-bridge dynamic interaction (is paper reports a study of the high-speed train-track-bridge dynamicinteractions under new and hollow worn wheel profiles A nonlinear rigid-flexible coupled model of a Chinese high-speed traintravelling on nonballasted tracks supported by a long-span continuous girder bridge is formulated (is modelling is based on thetrain-track-bridge interaction theory the wheel-rail nonelliptical multipoint contact theory and themodified CraigndashBamptonmodalsynthesis method(e effects of wheel-rail nonlinearity caused by the wheel hollow wear are fully considered(e proposed model isapplied to predict the vertical and lateral dynamic responses of the high-speed train-track-bridge system under new and worn wheelprofiles in which a high-speed train passing through a long-span continuous girder bridge at a speed of 350 kmh is considered (enumerical results show that the wheel hollow wear changes the geometric parameters of the wheel-rail contact and then deterioratesthe train-track-bridge interactions (e worn wheels can increase the vibration response of the high-speed railway bridges

1 Introduction

Over the last decade China has constructed the largest high-speed railway network around the world(emileage of high-speed railway with train running speed from 200 kmh to350 kmh in China exceeds 29000 kmMoreover China plansto construct 38000 km of passenger dedicated high-speedrailway lines by 2025 However a series of severe challengesincluding the wear problems of the high-speed wheelrailsystems have to be faced during the operation stage of Chinesehigh-speed railways (e wear problems of the Chinese high-speed railway include the wheel polygons rail corrugationwheel hollow wear wheel flange wear rail side wear anduneven welds among which the wheel uneven wear is of greatconcern [1] With the aggravation of wheel hollow wear thewheel-rail contact characteristics inevitably change whichthen intensifies the high-speed wheel-rail interaction

Railway corridors in high-speed railways are extensivelystraightened through the addition of bridges So the train-track-bridge dynamic interaction is of great interest in

research field of high-speed railways In fact the train thetrack and the bridge are an integrated dynamic system inwhich the train and the track are coupled by the wheel-railcontact relationship and the track and the bridge are linkedthrough the track-bridge interaction As a link connectingthe train and the railway infrastructure the wheel-railcontact relationship plays a crucial role in the high-speedtrain-track-bridge dynamic interaction (erefore thewheel-rail uneven wear not only affects the quality of trainoperation but also influences the vibration characteristics oftracks and bridges Herein we present a study of the high-speed train-track-bridge dynamic interaction due to thewheel hollow wear where the wheel-rail contact non-linearities caused by wheel uneven wear are fully considered

ldquoUsing bridge instead of subgraderdquo has been widely usedin the construction of Chinese high-speed railway Bridgesplay a vital role in high-speed railway infrastructure ac-counting for more than 50 of total high-speed railwaymileage in China because the use of bridges can avoid theinterruption of existing lines and occupy land With the

HindawiShock and VibrationVolume 2019 Article ID 5874678 18 pageshttpsdoiorg10115520195874678

increase of speed of passenger trains and because of the factthat taller and longer bridges are being built the consid-eration of train-track-bridge interaction becomes moresignificant [2] Growing attentions have been paid to thestudy of train-track-bridge coupled vibration for the last fewyears [3ndash10] For example Zhai et al [2] proposed an ef-ficient and practical theoretical model for the analysis of thetrain-track-bridge interaction which takes into account avariety of nonlinear factors aiming to provide a method foranalyzing and assessing the running safety and the comfortof high-speed trains passing through bridges [2ndash4] Zhanget al [5 6] reported a new intersystem iteration method fordynamic analysis of the coupled train-bridge system In thismethod the dynamic responses of train subsystem andbridge subsystem are solved separately the iteration withintime-step is avoided the computation memory is saved andit is convenient to use the commercial structural analysissoftware for bridge subsystem Li et al [8] put forward theinteractive method by using the commercial finite-element(FE) software ANSYS and multibody dynamics (MBD)software SIMPACK to simulate the vehicle-bridge coupledvibration It is shown that the interactive method has highcomputational efficiency and good convergence rate forvarious bridge and the vehicle-bridge coupled vibrationanalysis can be conducted well and followed conveniently byother researchers Melo et al [9] developed a numericalvibration prediction scheme for train-bridge systems withFE software ABAQUS and numerical software MATLABAnd the experimental response obtained from a dynamictest under railway traffic revealed a good agreement with thenumerical response Antolın et al [10] compared four dif-ferent wheel-rail contact models (nonlinear linear rigidand virtual path) in vehicle-bridge coupling vibration (enumerical investigation found that the forces obtained bynon-linear wheel-rail contact model are generally larger thanthose of other three models mainly because frictional slipexist in the real wheel-rail contact conditions Arvidssonet al [11] established a 2D train-track-bridge interactionmodel that allows for wheel-rail contact loss to analyze thedynamic performance of high-speed trains running onnonballasted bridges in Europe

More and more research focus on train-track-bridgesafety performance Dhanasekar et al [12 13] studied theimpact coefficient and local deformation of long-span sus-pension bridges and other bridges under actual train loadsZhang et al [14] carried out a detailed study on the safety oftrain operation due to the settlement of high-speed railwaybridges and put forward the corresponding safety limit ofpier settlement Zeng et al [15ndash18] applied the actualrecorded seismic wave data or pseudo-excitation method(PEM) to analyze the responses of train-track-bridge systemunder the excitation of seismic waves Accordingly somepeople have studied how to reduce bridge vibration such astuned mass damper (TMD) [19 20] install fluid viscousdampers [21 22] and magnetorheological damper equip-ment on bridge structure [23] Ling et al [24 25] predictedthe post-derailment behavior of a freight train composed ofone locomotive and several wagons on bridge caused bytrack irregularity based on a coupled finite-element-

multibody dynamics (FE-MBD) theory Rocha et al [26 27]assessed the train running safety passing through bridgesbased on the probability density evolution method Otherstudies include train-bridge coupled simulation of a com-posite structure bridge [28] train-bridge coupled vibrationanalysis considering environmental wind loads [29 30] andthe interaction between the train-bridge system and thefoundation-soil system by the substructure method [31]

Besides numerous scholars have done a lot of work onthe wheel wear and its influence on railway vehicle dy-namics Polach and Nicklisch [32] presented a new standardto identify wheel-rail contact geometry parameters related tovehicle behavior (e new parameter called contact con-centration index makes up for the shortcomings of tradi-tional equivalent conicity and assess new proposals for wheeland rail profiles regarding their wear in service Shi et al [33]demonstrated the wheel wear evolution and related vehicledynamics of Chinese high-speed trains with an operatingdistance of around two million kilometers by a long-termexperimental test Ren [34] proposed a three-dimensionalwheel flat model considering the length width and depth ofthe flat spot (us it is more in line with the real wheeldamage state (e results indicated that the width the lengthof the wheel flat and the widthlength ratio have an obviousinfluence on the wheelrail impact dynamics

However few scholars pay attention to the influence ofwheel uneven wear on the dynamic response of high-speedtrain-track-bridge system In the traditional studies of train-track-bridge interaction the wheel and rail profiles wereconsidered as new profiles (is is because the wheel-railrolling contact algorithms adopted in the traditional train-track-bridge interaction models are difficult to consider thenonlinear contact characteristics of uneven worn wheel andrail profiles (erefore a nonlinear rigid-flexible coupledmodel of high-speed train-track-bridge interaction is for-mulated (is modelling is based on the train-track-bridgeinteraction theory the wheel-rail nonelliptical multipointcontact theory and the modified CraigndashBampton modalsynthesis method (e effects of wheel-rail multipoint andconformal contact behaviors caused by the wheel hollowwear are fully considered (e proposed model is thenapplied to predict the vertical and lateral responses of thehigh-speed train-track-bridge system under new and wornwheel profiles in which a high-speed train passing through along-span continuous girder bridge at speed of 350 kmh isconsidered Based on the measured high-speed train wornwheel profiles the wheel-rail contact geometry of wheelprofiles at different mileage was analyzed (e influences ofwheel hollow wear on vibration responses of the high-speedtrain-track-bridge system are reported

2 Numerical Model

A numerical model of high-speed train-track-bridge non-linear interaction (see Figure 1) is formulated based on thetrain-track-bridge dynamic interaction theory [35] (emodel consists of four sub models (1) the train dynamicsmodel (2) the track dynamics model (3) the bridge dy-namics model and (4) the contact models for wheel-rail

2 Shock and Vibration

interaction and track-bridge interaction [24] It fully con-siders the nonlinear characteristics of the wheel-rail contactthe suspension components of the train the nonballastedtrack and complex structure of super-large bridge

21 High-Speed Train Model A high-speed train funda-mentally consists of car bodies bogies and wheel sets ewheel sets are connected with the bogie frame by springs anddampers of the primary suspension system and the bogie isconnected to the car body by a joint through the secondarysuspension system including air springs lateral and verticaldampers antihunting dampers and lateral stop Figure 2depicts the dimension of wheelbase bogie center distanceand adjacent wheelbase of CRH2C high-speed train used inthis paper

In this study a high-speed train consisting of eightvehicles (T +M+M+M+M+M+M+TMmotor vehicleT trailer vehicle) is assumed as a multibody system (MBS)in which the rigid body vibration is categorized into thelongitudinal lateral vertical yaw pitch and roll motionsFor each vehicle model 15 rigid bodies are considered

Among them the car body the bogie frame and the wheelset each have 6 degrees of freedom (DOFs) and the axle boxhas one rotational DOF relative to the wheel set us eachvehicle model has a total of 50 DOFse degrees of freedomof each vehicle are listed in Table 1 A schematic model of avehicle is shown in Figure 3 e symbols Z and β representthe DOFs of the vertical and pitch motions of a componentM and I denote the mass and inertia of a rigid body thesubscripts c t and w represent successively the car bodybogie frame and wheel set v stands for the running speed ofthe vehicle Ksz and Csz are the vertical stiness and dampingof the secondary suspension respectivelyKpz andCpz are thevertical stiness and damping of the primary suspension Yand Ψ denote the DOFs of the lateral and yaw motions of acomponent Ksy and Csy are the lateral stiness and dampingof the secondary suspension Ksx and Csx are the longitudinalstiness and damping of the secondary suspension Kpy andCpy are the lateral stiness and damping of the primarysuspension Kpx and Cpx are the longitudinal stiness anddamping of the primary suspension Φ denotes the DOF ofthe roll motion of a component Krx and Kmy representantirolling stiness and lateral stop stiness respectively

Train

Rail

v

Subgrade

Slab

SubgradePier PierBridge

(a)

Bridge

Cph

Cpv

Kph

Kpv

KshCsh

Rail

Track slab

Subgrade

Pier

(b)

Figure 1 High-speed train-track-bridge coupled dynamic model (a) side view and (b) end view

Shock and Vibration 3

Hcb is the distance from vehicle body center to frame centerof mass andHbw is the distance from frame center of mass towheel set center of mass

(e trainmodel fully considers the nonlinear elements inthe wheel-rail contact geometry relationship wheel-railcontact forces and vehicle suspension systems(e dampingforces of the vehicle suspension systems are solved by theMaxwellmodels which consider the stiffness of the joint andthe nonlinear behavior of the anti-yaw dampers (e airsprings are simulated by the linear spring and damper el-ements (e rubber bushes and bearings are simulated withspecial spring and damper elements (e general form of thedynamic equilibrium equations for the train can beexpressed as

Mtv euroutv + Ctv _utv + Ktvutv fwr (1)

whereMtv is the mass matrix of the train Ctv and Ktv are thedamping and stiffness matrices respectively utv is the dis-placement vector of train components fwr is the vector of thenonlinear wheel-rail contact forces (e detailed formationof the M C and K matrices and their derivation process canbe found in [36]

22 Track Model (e nonballasted track model consists ofrails slabs and subgrade as shown in the lower part ofFigure 1 (e nonballasted track model consists of twoTimoshenko beams for the rails 3D solid FE model for the

Table 1 Degrees of freedom of the vehicle

ComponentType of motion

Longitudinal Lateral Vertical Roll Pitch YawCar body Xc Yc Zc ϕc βc ΨcBogie frame (i 1sim2) Xti Yti Zti ϕti βti ΨtiAxle box (i 1sim8) mdash mdash mdash mdash βai mdashWheel set (i 1sim4) Xwi Ywi Zwi ϕwi βwi Ψwi

250 250 250 250 250370 1750 350 450 1750 450 450

2501750

Figure 2 Composition and main dimensions of the considered CRH2C train (unit cm)

Mc

Ksz

Mc

MtKmy

Kmy

Cpx

ψcψw1ψt1ψw2

Kpx2dsk2dscXw2

Yw2

Cpy

KsxYt1

Xt1Xw1

Yw1

CsdxCsxKpy

Yc

Xc

Ksy

Ksy

Ksz

KpyMw YwZt

IwxZw

2dwk

2dwc

ϕw

KrxItxMtCsy

Cpy

Primary suspension system

Secondary suspension system

Kpz

HBtZt1

HtwZw1Zw2Zw3

CpzKpz Zt2

Zw42lt2lc

Ity

Csz

Cpz

Kmy

vβc

βt2 βt1

Icy

Icx

ZcZc

CszHcB

Ycϕc

ϕtYt

Figure 3 A schematic diagram of the vehicle model


concrete slabs periodic discrete viscoelastic elements rep-resenting the rail fasteners that connect the rails and theslabs uniformly viscoelastic elements for the cement asphaltlayer beneath the slabs e lateral and vertical bendingdeformations and torsion of the rails are considered Eachnode in the FE track slab model has six DOFs

e general form of the dynamic equilibrium equationsfor the track system can be expressed as

Mtt euroutt + Ctt _utt + Kttutt fwr + f tb (2)

whereMtt is the mass matrix of the track Ctt and Ktt are thedamping and stiness matrices respectively utt is the trackdisplacement vector ftb is the vector of the interaction forceswith the bridge e detailed description of the nonballastedtrack model is given in [3]

23 Bridge Model e bridge structures are modelled withthe FE method e exible displacements are supposed tobe small in the body-xed frame of reference and could bedescribed in terms of linear FE analysis Introducing exiblebodies into amodel of mechanical system is used for creatingthe more detailed models and obtaining more accurateresults of simulation As shown in Figure 4 taking the elasticdeformation of a simply supported rail bridge as an examplekinematics of bridge is described with the help of the so-called oating frame of reference Ob-XbYbZb Kinematicalformulas are noted in this oating frame of reference Po-sition of certain point K of the bridge in the global O-XYZ isdened by

rk r0 + Tobdk r0 + Tob ub + ρk( ) (3)

where r0 is radius vector of the origin of Ob-XbYbZb in O-XYZ Tob is transformation matrix ρk is radius vector ofpoint K of undistorted exible body in Ob-XbYbZb vector ubpresents elastic displacements of the point

Small elastic displacements of bridge points in Ob-XbYbZb are the product of the modal matrix and the matrix-column of modal coordinates

ub(x y z t) ubx

uby

ubz

sumS

i1ϕix(x y z)qi(t)

sumS

i1ϕiy(x y z)qi(t)

sumS

i1ϕiz(x y z)qi(t)

sumS

i1Φiqi

Φbqb(4)

where Φi is the i-th mode of the bridge qi is the modalcoordinate that describes exible displacements correspondto mode i S is referred as the number of used modes Φ iscalled modal matrix which is solved by the CraigndashBamptonmodal synthesis method [37]

As shown in Figure 5 the CraigndashBampton xed interfacecomponent mode synthesis method divides the globalstructure into serval substructures ese substructures areconnected with a xed interface at the interface boundary Γ

(Figure 5(c)) Using the CraigndashBampton method the actualDOFs of bridge are expressed by modal matrix and modalcoordinates

ub Φbqb ubBubI

[ ] Ib 0

ϕIC ϕIN[ ]

qCqN

(5)

in which the subscripts I B N and C in the equation are theindexes to indicate the internal interfacial dominant modesand constrained modes respectively ϕIC is constrainedmodal set ϕIC is dominant modal set (after truncatinghigher-order modes) ubB and ubI are the interface and in-ternal displacement vectors

e generalized stiness matrix and mass matrix inCraig-Bampton method are obtained by modaltransformation

Kb ΦTbΚbΦb

Ib 0

ϕIC ϕIN

T KBB KBI

KIB KBB

Ib 0

ϕIC ϕIN

KCC 0

0 KNN

Mb ΦTbMbΦb

Ib 0

ϕIC ϕIN

T MBB MBI

MIB MBB

Ib 0

ϕIC ϕIN

MCC MNC

MCN MNN

(6)

By abstracting the motion of a single elastic body into alinear combination of modal elements (rst coordinatetransformation) the dynamic equation of the substructure isestablished and the dynamic simulation of the elastic bodyconsidering the characteristics of the interface is realizeden the modal coordinates of all substructures are trans-formed into generalized coordinates (second coordinatetransformation) by using the interface connection conditionand the dynamic equation of the system is obtained and thedynamic characteristics and motion of the whole system aresolved Because there are six rigid body degrees of freedomembedded in the constraint modal set (which must be

OX Y

Z

Ob

Xb Yb

Zb

ρkub

rk r0

Kprime

K

dk

Figure 4 Floating reference frame for the long-span continuousbridge structure


removed before assembly with the multibody system sincethe rigid body displacement of components has been definedin the multibody system) and the essence of the constraintmodal is static modal (ese modes cannot correspond tofrequencies so the CraigndashBampton method needs to bemodified so that the elastic substructures can be coupled withthemultibody dynamicmodel and dynamically analyzed [38]

(e final step of the preparing set of modes is theorthonormalization of columns of the modal matrix basedon eigenvalue problem solution with generalized mass andstiffness matrix (e obtained orthogonal eigenvectors canform transformation matrices N and perform orthogonaltransformation

Kbqb λMbqb

qb Nqb(7)

(e diagonal form of transformed generalized matricesleads to minimal CPU efforts during the integration ofequations of motion It is the basic advantage of such anapproach Another aim of such transformations is the ex-clusion of modes that correspond to movement of theflexible subsystem as a rigid body (e original modal co-ordinates are represented by a new CraigndashBampton modalcoordinate So the physical coordinates can be approxi-mately expressed as

ub 1113944S

i1Φiqi Φbqb asymp Φbqb (8)

After assembly and transformation into the global sys-tem the dynamic equilibrium equation for the bridge systemcan be written as

Mb euroub + Cb _ub + Kbub f tb (9)

(e bridge damping matrix includes the materialdamping of the bridge itself and the element damping of thetrack model can be given by

Cb αMb + βKb + 1113944

Ne

j1Cj (10)

where α and β are the Rayleigh damping coefficients Ne isthe number of damping elements Cj is the damping matrixof the jth track damper element

α 2ξbωiωj

ωi + ωj

β 2ξb

ωi + ωj

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(11)

where ωi and ωj are the natural frequencies of the two se-lected flexible modes ξb is the material dependent dampingratio of the bridge a value of 2 is selected for the concretebridge

24 Contact Models

241 Wheel-Rail Contact Model A wheel-rail nonellipticalmultipoint contact model proposed by Kik-Piotrowski[39 40] is applied to connect the vehicle subsystem and thetrack subsystem (e Kik-Piotrowski method is a non-Hertzian wheel-rail contact approach based on the virtualpenetration theory It is assumed that the shape of the wheel-rail contact patch can be directly determined by the wheeland rail profiles and the amount of interpenetration (ismethod can deal with the complex contact situations such asthe multipoints and conformal contact conditions caused bywheel-rail profile wear It is assumed that the normal contactstress pz is the semielliptical in the rolling direction of thewheel set

pz(x y) p0

xi(0)

xi(y)2 minus x21113969

(12)

wherep0 is the maximum normal pressure xl(y) is the halflongitudinal length of the contact patch at the lateral co-ordinate y According to the basic assumption of this al-gorithm the penetration area is regarded as the contact area(e approximate edges of contact patch consist of inter-secting lines of contact surfaces

xl(y)

2Rg(y)

1113969

(13)

(e normal contact force can be obtained by integratingnormal contact stress in the whole contact patch

N p0

xl(0)1113946

yl

yr

1113946xl(y)

minus xl(y)

xl(y)2 minus x21113969

dx dy (14)

Ω

(a)

Ω1Ω2

Γ

(b)

Ω2

Ω1

(c)

Figure 5 Global and partitioned structural models and interface handling in the CraigndashBampton method (a) Global (nonpartitioned)structure Ω (b) substructures Ωi (i 1 2 S) and interface boundary Γ (c) interface boundary treatment


where yl and yr are the left and right boundary of the wheel-rail contact patch in the y direction respectivelye normaldeformation of the initial contact point (00) is

w0 1 minus μ2

πEp0xl(0)

intyl

yrintxl(y)

minus xl(y)

xl(y)

2 minus x2

x2 + y2

radic

dx dy (15)

e penetration volume of the contact point isδ0 2w(0 0) 2w0 which is based on the above equation

N πEδ0

2 1 minus μ2( )intylyrintxl(y)minus xl(y)

xl(y)

2 minus x2radic

dx dy

intylyr intxl(y)minus xl(y)

xl(y)

2 minus x2( ) x2 + y2( )radic

dx dy

p0 N

2Rδ0radic

intylyrintxl(y)minus xl(y)

xl(y)

2 minus x2radic

dx dy

(16)

After obtaining the clearance and normal contact forceof the wheel-rail contact the calculation of tangential creepforces is carried out based on the FASTSIM algorithm byKalker [41] e use of FASTSIM is not only limited toelliptical contact patch but also can obtain good results inmultipoint contact conditions

242 Track-Bridge Contact Model For a nonballasted trackthe bridge supports the track structure via the cement as-phalt layers under the track slabs In this study the cementasphalt layers were represented by uniformly distributednonlinear spring and damper elements (refer to Figure 1(b))erefore the track-bridge contact force ftb can be calculatedby

f tb Ksh uts minus ub( ) + Csh _uts minus _ub( ) (17)

In the above equation Ksh is the nonlinear stinessmatrix of the cement asphalt layer Csh is the nonlinearviscous damping matrix and uts is the track slab displace-ment vector e detailed derivation process has been givenin reference [2]

25 Validation of the Model To verify the accuracy of theproposed train-track-bridge model the simulation dataobtained with the current model is compared with the ledmeasured data as shown in Figures 6ndash8 e eld tests werecarried out on the Tianjin-Qinhuangdao passenger high-speed railway in China A total of 13 trains have beenmeasured e rail displacement and acceleration weremeasured at the middle span of the 32m double-tracksimply supported PC girders with box sections e trainsare reorganized and the speed range is 200ndash350 kmh Be-cause the track irregularities of the tested lines were notobtained the German low-disturbance track spectrum wasapplied in the simulations Considering the dierence be-tween track irregularity samples used in simulation and theactual track irregularities the accelerations of axle box andbogie frame are processed by low-pass ltering and the cut-o frequency is 300Hz From the comparison of simulationand test results of the bogie frame acceleration and axle box

acceleration (Figures 6 and 7) the simulation results are ingood agreement with the test results Figure 8 is the com-parison of the measured and calculated displacement andacceleration of the rails e simulation results are close tothe measured data Overall the errors between the resultsobtained by eld test and simulation are negligible andhence the proposed model can be reliable and reasonable

3 Variation of Wheel-Rail ContactGeometry due to Wheel Hollow Wear

31 Evolution of the Hollow Wear e evolution of wheelproles of a Chinese high-speed train is rst investigatedbased on the data from a long-term tracking tests con-centrating on the natural wear process of high-speed trainwheels [42] Figure 9 compares several typical worn wheelproles with dierent travelling distances From the changesof the proles at the nominal rolling circle radius it can beclearly observed that the wheel hollow wear depth graduallyincreases with an increase in train operating mileage e

Measured resultCalculated result

ndash30

ndash20

ndash10

0

10

20

30

Vert

ical

acce

lera

tion

(ms

2 )

0 4 6 8 102Time (s)

(a)

ndash20

ndash10

0

10

20

Late

ral a

ccel

erat

ion

(ms

2 )

0 4 6 8 102


Time (s)

(b)

Figure 6 Comparison of measured and calculated result of bogieframe acceleration at a train speed of 350 kmh (a) time history ofvertical acceleration (b) lateral acceleration


section of the worn wheel tread around nominal rollingcircle is consistent with the new wheel tread

Figure 10 shows the wear distribution along the wheelwidth for dierent travelling distances It indicates that themain wear region on the wheel tread concentrates on thearea ranging from minus 20 to 20mm around the nominal rollingcircle and the wear in the ange area is relatively light isregion is the main contact region between the wheel and therail With the train travelling distance increase the wheelwear depth in this region aggravates gradually According tothe eld measurement results the maximum wheel weardepth of the train with travelling distances of 83000 km132000 km 169000 km and 192000 km attain 034mm052mm 064mm and 072mm respectively as shown in

Figure 10 e region of the worn wheel proles near thenominal rolling circle presents an obvious concave shapewhich substantially aects the wheel-rail contact geometrye location of the maximum wheel hollow wear depthappears at about +3mm from the nominal rolling circleradius of the wheel prole

It should be noted that the wheel hollow wear hasreached the limit regulated by Railway Electric MultipleUnits Operation and Maintaining Regulation [43] aftertravelling about 210000 km and the wheel tread of the testedhigh-speed train is required to be reproled at that time

32 Variation of Wheel-Rail Contact Geometry e wheel-rail contact geometric analysis for the measured wheel worn

ndash200

ndash100

0

100

200

Vert

ical

acce

lera

tion

(ms

2 )

5 7 8 9 106


Time (s)

(a)

ndash30

ndash20

ndash10

0

10

20

30

Late

ral a

ccel

erat

ion

(ms

2 )

6 7 8 9 105


Time (s)

(b)

Figure 7 Comparison of measured and calculated result of axle box acceleration at a speed of 350 kmh (a) time history of verticalacceleration (b) lateral acceleration

220 240 260 280 300 32000

02

04

06

08

Vert

ical

disp

lace

men

t (m

m)

Speed (kmh)

Fitting result


(a)

220 240 260 280 300 3200

30

60

90

120

150

180Ve

rtic

al ac

cele

ratio

n (m

s2 )

Speed (kmh)

Fitting result


(b)

Figure 8 Comparison of measured and calculated result of rail displacement and acceleration (a) vertical displacement (b) verticalacceleration


and new profiles were carried out respectively (e newCHN60 profile was applied in these analyses Figure 11shows the location and layout of contact points of newand worn wheel profiles under different travel mileage Inactual operation of high-speed trains the wheel set lateraldisplacement is generally within the range of 10mm so thelateral displacement in Figure 11 was set at minus 10sim10mm

It is easy to see that the distribution of wheel-rail contactpoints is concentrated when the new wheel profile matcheswith the new CHN60 profile In this case the distribution ofwheel-rail contact points near the wheel flange side is sparseand uniform which is an ideal one-point contact situationBut when the wheel travel distance is increased to 83000 kmthe wheel-rail contact status evolved from the one-pointcontact to the multipoint contact and the distribution ofwheel-rail contact points appears in a larger area (e wornwheel-rail contact situations of the wheel travel distanceincreased to 132000 and 169000 km are similar to that of83000 km Compared with the new wheel-rail contact sit-uation the worn wheel-rail contact points are more dis-persed and nonuniform (e contact points at the wheelflange area increase which also slightly shift to the insidecorner of the railsWhen the wheel travel distance is increasedto 192000 km the worn wheel-rail system has an obvioustwo-point contact trend Two concentrated wheel-rail contact

point areas appear in the center and inside corner of the rails(is means the wheel hollow wear greatly changes the wheel-rail contact status resulting in a very dispersed and non-uniform distribution of wheel-rail contact points Under sucha severe condition the wheel-rail two-point contact behaviorwill occurr frequently It should be noted that the wheel-railtwo-point contact or multipoint contact behavior will in-tensify wheel-rail interaction and then increase the wear anddamage of wheel and rail profiles

(e rolling radius difference equivalent conicity contactangle and contact angle parameters are other four importantwheel-rail rolling contact geometric parameters It can beseen from Figure 12(a) that when the new wheel-rail profileis matched the rolling radius difference increases slowlywith wheel set lateral displacement less than 7mm Whenthe wheel set displacement is greater than 7mm the rollingradius difference increases sharply At this time the wheel-rail contact point approaches the wheel flange and the curveof rolling circle radius difference presents a nonlinear changelaw But for the worn wheels the fluctuation of rolling radiusdifference increases obviously when the lateral wheel setdisplacement is in the range of 1ndash9mm (e variationtendency of the rolling radius difference of the wheels withtravel distances of 83000 and 169000 km are similar andthe fluctuation of the case with travel distances of192000 km is the most intense

For the new profile the equivalent conicity Figure 12(b))keeps within 01 and changes smoothly when the wheel setdisplacement is less than 8mm But the equivalent conicityof the worn wheel profiles are obviously larger than that ofthe new profile when the wheel set displacement is largerthan 1mm(e equivalent conicity of the worn wheel profilewith travel distances of 192000 km is larger than that ofother cases when the wheel set displacement is in the rangeof 1ndash9mm (e equivalent conicity with a wheel set dis-placement of 15mm is equal to 028 According to theKlingel principle when lateral span and rolling radius of awheel set are kept constant an increasing equivalent conicitywill increase the bogie hunting motion frequency and finallydecrease the vehicle running stability

(e variation of contact angle and contact angle pa-rameter are shown in Figures 12(c) and 12(d) (e contactangle parameter ε is used for linear approximation of thefunction E(y) on the interval of the lateral shift of the wheelset

E(y) βl(y) minus βl(y)

2S

2asymp εy (18)

(e designation βl(y) βr(y) are introduced for thecontact angles of the left and right wheels depending on thewheel set shift If the left and right pairs of profiles are equalthe value βl(0) βr(0) β0 corresponds to the contact anglefor symmetric position of the wheel set (e dependence onthe lateral shift is used for definition of the contact angleparameter Here S is the distance between the wheel setrolling radius

Figure 12 shows that the change of contact angle is gentlefor the new wheels when the lateral displacement is in therange of minus 7ndash8mm But for the worn wheels the fluctuation

ndash20 ndash10 0 10 20

ndash2

0

2

New profile83000 km132000 km

169000 km192000 km

Nominal rolling circle positionndash10

0

10

20

30

Whe

el pr

ofile

hei

ght (

mm

)

ndash40 ndash20 0 20 40 60ndash60Wheel width (mm)

Figure 9 Comparison of measured wheel profiles with differenttravelling distances

83000 km132000 km

169000 km192000 km

Main wear area

Nominal rolling circle position

00

02

04

06

08

10

Whe

el w

ear d

epth

(mm

)


Figure 10 Comparison of measured wheel hollow wear depth fordifferent travelling distances


ndash080 ndash076 ndash072 ndash068ndash084Y coordinates (m)

ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(a)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(b)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(c)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(d)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(e)

Figure 11 Distribution of wheel-rail contact points of new and worn proles (a) new prole (b) 830000 km (c)132000 km (d)169000 km (e) 192000 km


169000 km192000 km

2 4 6 80Wheel displacement (mm)

0

1

2

3

4

Rolli

ng ra

dius

diff

eren

ce (m

m)

(a)


169000 km192000 km


000

005

010

015

020

025

030

035

Equi

vale

nt co

nici

ty

(b)

Figure 12 Continued


range of contact angle becomes larger and there are manysudden changes when the lateral wheel set displacement isnegative With the increasing train travel mileage thecontact characteristics between wheel and rail deterioratewhich led to the increase in the wheel-rail contact angle evariation trend of wheel-rail contact angle parameters issimilar to that of the contact angle

e above results show that the wheel hollow wear has agreat inuence on the geometric parameters of the wheel-railcontact which can aggravate the wheel-rail interaction andnally aect the train-track-bridge interactions

4 Results and Discussions

e proposed model shown in Section 2 was applied topredict the vertical and lateral responses of the high-speedtrain-track-bridge system under new and worn wheel pro-les in which a Chinese high-speed train passing through along-span continuous girder bridge (see Figure 13) at thespeed of 350 kmh was considered Based on the measuredhigh-speed train worn wheel proles shown in Section 3 andnumerical simulations the inuences of wheel hollow wearon vibration responses of the high-speed train-track-bridgesystem are discussed

41 Illustration of the Bridge e Chengjiang bridge locatedin Hechi City of China was selected as example It is a super-large continuous concrete girder bridge on the Nanning-Guizhou high-speed railway in which the bridge span is(915 + 180 + 915) m and the approach bridge is a 24-mprestressed concrete simply supported bridge A double-track railway is positioned on the bridge and the transversedistance between the railway lines is 50m e bridge bodyis mainly made of C55 concrete and the arch ribs are madeof composite materials and steel cables e overall size ofthe bridge is shown in Figure 13e second span box girderof the bridge contains transverse webs which can enhance

the stiness of the whole bridge structure e cross sectionand the main dimensions of the girder are shown inFigure 14

42 FE Model of the Chengjiang Bridge In the FE modellingof the Chengjiang bridge several types of elements wereapplied to simulate the distinct parts of the bridge Specif-ically 3D two-node EulerndashBernoulli beam elements(BEAM188) were used to simulate the arch ribs transversestructures and diagonal structures based on the actual shapeand geometric dimensions of the cross-section propertiesTwo-node uniaxial link (LINKl0) elements were used tomodel the bridge cables with three translational DOFs (pernode x y and z) Elastic four-node axisymmetric quadri-lateral shell elements (SHELL63) with both membrane andbending capabilities were used to simulate the bridge webdeck and other structures Shell element is not suitable forthe middle and two ends because of their large thickness Sosolid element (SOLID185) is used to simulate these partsConnection between dierent types of cells is accomplishedby coupling nodes with CERIGmethod which can eliminatethe calculation error caused by dierent types of elementsDOFs inconsistency

According to the constraints prescribed in the bridgebearing arrangement (see Figure 15) the girder body and pierare connected by the node coupled method e arrow rep-resents the release direction of the DOFs whereas the DOF inthe arrow direction is not constrained For example a singleldquordquo represents that both horizontal and vertical DOFs areconstrained and xed e overall layout of the bridge FEmodel is shown in Figure 16 e model consists of 98118elements and 99938 nodes which meets the requirement ofcalculation accuracy through the numerical testse two endsof the bridge were connected to the 24 m-length simplesupported beam bridges ree-span simple supported beambridges were arranged on each side which can be simulated asconventional beam elements and coupled with the nodes at


169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)

ndash4 0 4 8ndash8Wheel displacement (mm)

(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)

Figure 12 Wheel-rail rolling contact parameters (a) Rolling circle radius dierence (b) equivalent conicity (c) contact angle (d) contactangle parameters


both ends of Chengjiang bridge (e bridge FE model wasimported into train-track-bridge dynamic interaction calcu-lation program by Craig-Bampton method

43 Results Discussion and Comparisons Based on theproposed high-speed train-track-bridgemodel the influenceof wheel hollow wear on the vibration characteristics of thetrain-track-bridge system is investigated and presented inthis section Here the new profile and the worn profile withtravel distance of 192000 km were taken as the input wheelprofiles Since the highest operational speed of high-speedtrains in China is 350 kmh at present the train speed in thesimulations was also set to this value (e time domainsample of track irregularity obtained from the spectraltransformation of low-disturbance track of German high-speed railway was applied

Figures 17ndash19 show the wheel-rail forces of high-speedtrains with new and worn profiles in time and frequencydomains Figure 17(a) shows that wheel wear has a certaineffect on wheel-rail force After severe wheel wear it willincrease the impact between wheel and rail leading to asharp increase in some peak values of wheel-rail forceFigure 17(b) shows that wheel wear has a greater impact onthe lateral force of wheel and rail than the vertical force ofwheel and rail (e amplitude of the lateral force of wheeland rail wearing wheel increases obviously (e maximumwheel-rail vertical force before and after wheel wear changedfrom 22158 kN to 23490 kN which increased by 601(emaximum wheel-rail lateral force before and after wheelwear increased from 984 kN to 1438 kN which increased by461

In the frequency domain wheel wear results in a slightincrease in the high frequency of wheel-rail vertical force as

915 180 915 240

125215

385

Figure 13 (e overall size of the Chengjiang bridge (unit m)

1600

40

20 20 20 20

165 times 55165 times 55165 times 55 165 times 55

30 times 3030 times 30

680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085

Figure 14 Cross-section of the Chengjiang bridge (unit cm)

575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction

Figure 15 Bridge bearing layout (unit cm)


Bridge direction

O

Z

Y

X

Arch rib

Transverse structures

Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63

Figure 16 3D FE model of the Chengjiang bridge

0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)

New profileWorn profile

(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)

Figure 17 Wheel-rail force (a) vertical (b) lateral

10ndash710ndash610ndash510ndash410ndash310ndash210ndash1100101102

PSD

(kN

2 Hz)

1 10 10001Frequency (Hz)


(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)

Figure 18 Power spectral density of vertical wheel-rail force (a) overall (b) enlarged diagram of 100sim500Hz


shown in Figure 18 In the meanwhile the increase in wheel-rail lateral force is mainly reflected in the middle and highfrequencies from Figure 19 (is shows that the wear ofwheel material mainly affects the wheel-rail force in themiddle and high frequencies domain but has little effect onthe low frequency wheel-rail force

(e dynamic responses of the bridge with initial (new)wheel profile and worn profile at 350 kmh speed are plottedin Figures 20ndash25 (e vertical and lateral displacements ofthe midsection of the main span are shown in Figure 20 Itreveals that wheel wear has little effect on the bridge dis-placement as the bridge displacement of the cases with wornand new profiles are basically the same (e vertical dis-placement curves are basically the same before and after thewheel profile changes and the maximum values maintain atabout 36mm (e lateral displacement curves fluctuateslightly but the amplitudes are quite small the maximumvalues are stable around 011mm

Figures 21 and 22 depict the time histories of bridgevertical and lateral displacement of the left and right-sidespans Similar to the dynamic response of the main spanwheel wear has no obvious effect on the vertical displace-ment of the bridge while small difference is found in thelateral displacements (e vertical displacement peak valuesof left and right span attain about 2mm and the lateraldisplacement peak values fluctuates around 006mm

Figures 23 and 24 display the time domain diagram ofbridge vertical and lateral acceleration of the main span Itis not difficult to observe that the wheel wear has obviouseffects on the vibration acceleration of the bridge (emaximum vertical accelerations of the cases with new andworn profiles were 00525ms2 and 00643ms2 re-spectively which increased by 231 (e maximumvalues of lateral accelerations of the cases with new andworn profiles are 00138ms2 and 00222ms2 re-spectively with an increase of 609(e results show thatthe responses of bridge accelerations obtained with themodels considering the wheel worn profiles are higherthan those obtained by the models without consideringwheel wear

Figure 25 shows the PSD diagram of the bridge verticaland lateral accelerations presented in Figures 23 and 24 Forthe vertical acceleration the main frequencies appeararound 053Hz 759Hz 229Hz and 269Hz But there isno obvious difference between the PSDs of the cases withnew and worn profiles (is means that the wheel hollow

01 1 10 10010ndash910ndash810ndash710ndash610ndash510ndash410ndash310ndash210ndash1100

PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)

Figure 19 Power spectral density of lateral wheel-rail force (a) overall (b) enlarged diagram of 100sim500Hz

1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)

Figure 20 Time histories of displacement at the midsection of themain span (speed v 350 kmh) (a) vertical (b) lateral


wear has little effect on frequency domain curves of bridgevertical acceleration in the range of 0sim30Hz For the lateralacceleration the PSD changes obviously After the wheelprofile wear occurring the peak frequency appearing at153Hz decreases significantly while the peak frequencynear 396Hz increases obviously It is noted that the peakfrequencies of 153Hz and 396Hz are corresponded to thelateral modal shapes of the bridge girders It indicates that

the wheel hollow wear may cause the amplitude of bridgevibration acceleration to change or shift in frequencydomain

Figures 26 and Table 2 show the peak values of bridgeaccelerations and displacements of the main span left-sidespan and right-side span (e abscissa represents differentoperating mileage and corresponds to different worn wheeltreads From these results the dynamic characteristics of the

ndash25ndash20ndash15ndash10ndash05

000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)

Figure 21 Time histories of displacement at the midsection of the left side span (speed v 350 kmh) (a) vertical (b) lateral


ndash20ndash15ndash10ndash05

000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)

Figure 22 Time histories of displacement at the midsection of the right-side span (speed v 350 kmh) (a) vertical (b) lateral


1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )

Figure 23 Time histories of vertical acceleration at the midsectionof the main span (speed v 350 kmh)


ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)

Figure 24 Time histories of lateral acceleration at the midsectionof the main span (speed v 350 kmh)


269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)

Figure 25 PSD analysis of bridge accelerations of the main span (a) vertical (b) lateral

Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )

Figure 26 Peak values of bridge accelerations (a) vertical acceleration of midspan (b) lateral acceleration of midspan (c) vertical accelerationof left-side span (d) lateral acceleration of left-side span (e) vertical acceleration of right-side span (f) lateral acceleration of right-side span

Table 2 (e peak values of bridge displacement

Operating mileage (times104 km)Midspan Left-side span Right-side span

Vertical Lateral Vertical Lateral Vertical Lateral0 36364 01022 19590 00606 19838 0067283 36353 01037 19593 00563 19840 00608132 36357 01028 19593 00558 19840 00606169 36357 01011 19593 00558 19839 00603192 36357 01037 19593 00558 19836 00625


bridge under different wheel worn profiles can be sum-marized as follows

(1) (e wheel hollow wear has little effect on the dy-namic displacement of the long-span bridge (ereason should be that the bridge main girder has alarge overall stiffness as it is made of high-strengthconcrete material thus the displacement of thebridge is mainly related to the axle load and dis-tribution characteristics of the train

(2) (e maximum bridge accelerations increase fast inlateral and vertical directions with the wheel weardepth increase It shows that both vertical and lateralbridge accelerations are greatly affected by thechange of wheel profile

5 Conclusions

(is paper reported a study of the high-speed train-track-bridge dynamic interactions considering the wheel-railcontact nonlinearity due to hollow worn wheel profiles Anonlinear rigid-flexible coupled model of a high-speed traintravelling on a long-span continuous girder bridge wasestablished (e accuracy of the model is validated bycomparing with the measured data (e vertical and lateraldynamic responses of the high-speed train-track-bridgesystem under new and worn wheel profiles were discussed

(e simulation results have shown that the wheel hollowwear of high-speed trains has a great influence on thegeometric parameters of the wheel-rail contact which canaggravate the wheel-rail interaction and finally deterioratesthe train-track-bridge interactions (e wheel wear has littleeffect on the bridge dynamic displacement However thebridge vertical and lateral accelerations increase with theaccumulation of the wheel hollow wear It is suggested thatthe influence of worn wheel-rail profiles should be con-sidered in the dynamic analysis of train-track-bridge in-teraction during the stage of bridge structure design andsafety assessment

Data Availability

(e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

(e authors declare that they have no conflicts of interest

Acknowledgments

(e authors would like to thank all the students involved inthe on-track test from State Key Laboratory of TractionPower at Chengdu China (is work was supported by theNational Natural Science Foundation of China (grant nos51735012 11790283 and 51805452) the Application BasicResearch Project of Sichuan Province (grant no2019YJ0232) the Open Project of State Key Laboratory ofTraction Power (grant no 2018TPL_T09) and the

Fundamental Research Funds for the Central Universities(grant no 2682018CX67)

References

[1] WM Zhai X S Jin Z FWen and X Zhao ldquoWear problemsof high-speed wheelrail systems in china observationscauses and counter measuresrdquo in Proceedings of the 11thInternational Conference on Contact Mechanics and Wear ofRailwheel Systems Delft Netherland September 2018

[2] X He T Wu Y Zou Y F Chen H Guo and Z Yu ldquoRecentdevelopments of high-speed railway bridges in ChinardquoStructure and Infrastructure Engineering vol 13 no 12pp 1584ndash1595 2017

[3] W Zhai Z Han Z Chen L Ling and S Zhu ldquoTrainndashtrackndashbridge dynamic interaction a state-of-the-art reviewrdquoVehicle System Dynamics vol 57 no 7 pp 984ndash1027 2019

[4] W M Zhai H Xia and C B Cai ldquoHigh-speed trainndashtrackndashbridge dynamic interactionsndashpart I theoretical modeland numerical simulationrdquo International Journal of RailTransportation vol 1 no 1-2 pp 3ndash24 2013

[5] W M Zhai S Wang N Zhang et al ldquoHigh-speed trainndashtrackndashbridge dynamic interactionsndashpart II experimentalvalidation and engineering applicationrdquo International Journalof Rail Transportation vol 1 no 1-2 pp 25ndash41 2013

[6] N Zhang and H Xia ldquoDynamic analysis of coupledvehiclendashbridge system based on inter-system iterationmethodrdquo Computers amp Structures vol 114-115 pp 26ndash342013

[7] V N Dinh K D Kim and P Warnitchai ldquoDynamic analysisof three-dimensional bridgendashhigh-speed train interactionsusing a wheelndashrail contact modelrdquo Engineering Structuresvol 31 no 12 pp 3090ndash3106 2009

[8] Y Li X Xu Y Zhou C Cai and J Qin ldquoAn interactivemethod for the analysis of the simulation of vehiclendashbridgecoupling vibration using ANSYS and SIMPACKrdquo Proceedingsof the Institution of Mechanical Engineers Part F Journal ofRail and Rapid Transit vol 232 no 3 pp 663ndash679 2018

[9] L R T Melo T N Bittencourt D Ribeiro and R CalccediladaldquoDynamic response of a railway bridge to heavy axle-loadtrains considering vehiclendashbridge interactionrdquo InternationalJournal of Structural Stability and Dynamics vol 18 no 1Article ID 1850010 pp 1ndash27 2018

[10] P Antolın N Zhang J M Goicolea H Xia M A Astiz andJ Oliva ldquoConsideration of nonlinear wheelndashrail contact forcesfor dynamic vehiclendashbridge interaction in high-speed rail-waysrdquo Journal of Sound and Vibration vol 332 no 5pp 1231ndash1251 2013

[11] T Arvidsson A Andersson and R Karoumi ldquoTrain runningsafety on non-ballasted bridgesrdquo International Journal of RailTransportation vol 7 no 1 pp 1ndash22 2019

[12] M Dhanasekar P Prasad J Dorji and T Zahra ldquoService-ability assessment of masonry arch bridges using digital imagecorrelationrdquo Journal of Bridge Engineering vol 24 no 2Article ID 04018120 pp 1ndash16 2019

[13] Y L Li S F Dong Y L Bao K J Chen and S Z QiangldquoImpact coefficient analysis of long-span railway cable-stayedbridge based on coupled vehicle-bridge vibrationrdquo Shock andVibration vol 2015 Article ID 641731 9 pages 2015

[14] X H Zhang Y Shan and X W Yang ldquoEffect of bridge-pierdifferential settlement on the dynamic response of a high-speed railway train-track-bridge systemrdquo MathematicalProblems in Engineering vol 2017 Article ID 896062813 pages 2017


[15] Z-P Zeng Y-G Zhao W-T Xu Z-W Yu L-K Chen andP Lou ldquoRandom vibration analysis of trainndashbridge undertrack irregularities and traveling seismic waves using trainndashslab trackndashbridge interaction modelrdquo Journal of Sound andVibration vol 342 pp 22ndash43 2015

[16] Z P Zeng Z W Yu Y G Yang W-T Xu L-K Chen andP Lou ldquoNumerical simulation of vertical random vibration oftrain-slab track-bridge interaction system by PEMrdquo Shockand Vibration vol 2014 Article ID 304219 21 pages 2014

[17] X Kang L Jiang Y Bai and C C Caprani ldquoSeismic damageevaluation of high-speed railway bridge components underdifferent intensities of earthquake excitationsrdquo EngineeringStructures vol 152 pp 116ndash128 2017

[18] X Yang H H Wang and X L Jin ldquoNumerical analysis of atrain-bridge system subjected to earthquake and runningsafety evaluation of moving trainrdquo Shock and Vibrationvol 2016 Article ID 9027054 15 pages 2016

[19] Z Chen H Fang Z Han and S Sun ldquoInfluence of bridge-based designed TMD on running trainsrdquo Journal of Vibrationand Control vol 25 no 1 pp 182ndash193 2019

[20] M Luu V Zabel and C Konke ldquoAn optimization method ofmulti-resonant response of high-speed train bridges usingTMDsrdquo Finite Elements in Analysis and Design vol 53pp 13ndash23 2012

[21] J Lavado A Domenech and M D Martınez-RodrigoldquoDynamic performance of existing high-speed railway bridgesunder resonant conditions following a retrofit with fluidviscous dampers supported on clamped auxiliary beamsrdquoEngineering Structures vol 59 pp 355ndash374 2014

[22] S Radestrom M Ulker-Kaustell A Andersson V Tell andR Karoumi ldquoApplication of fluid viscous dampers to mitigatevibrations of high-speed railway bridgesrdquo InternationalJournal of Rail Transportation vol 5 no 1 pp 47ndash62 2017

[23] M Luu M D Martinez-Rodrigo V Zabel and C KonkeldquoSemi-active magnetorheological dampers for reducing re-sponse of high-speed railway bridgesrdquo Control EngineeringPractice vol 32 pp 147ndash160 2014

[24] L Ling M Dhanasekar and D P (ambiratnam ldquoDynamicresponse of the trainndashtrackndashbridge system subjected to de-railment impactsrdquo Vehicle System Dynamics vol 56 no 4pp 638ndash657 2018

[25] L Ling M Dhanasekar K Wang W Zhai and B WestonldquoCollision derailments on bridges containing ballastless slabtracksrdquo Engineering Failure Analysis vol 105 pp 869ndash8822019

[26] J M Rocha A A Henriques and R Calccedilada ldquoProbabilisticassessment of the train running safety on a short-span high-speed railway bridgerdquo Structure and Infrastructure Engi-neering vol 12 no 1 pp 78ndash92 2016

[27] Z-W Yu J-F Mao F-Q Guo andW Guo ldquoNon-stationaryrandom vibration analysis of a 3D trainndashbridge system usingthe probability density evolution methodrdquo Journal of Soundand Vibration vol 366 pp 173ndash189 2016

[28] K Matsuoka A Collina and M Sogabe ldquoDynamic simula-tion and critical assessment of a composite bridge in high-speed railwayrdquo Procedia Engineering vol 199 pp 3027ndash30322017

[29] X He Y Gai and T Wu ldquoSimulation of trainndashbridge in-teraction under wind loads a rigid-flexible coupling ap-proachrdquo International Journal of Rail Transportation vol 6no 3 pp 163ndash182 2018

[30] J M Olmos andM A Astiz ldquoNon-linear vehicle-bridge-windinteractionmodel for running safety assessment of high-speed

trains over a high-pier viaductrdquo Journal of Sound and Vi-bration vol 419 pp 63ndash89 2018

[31] H Qiao H Xia and X Du ldquoDynamic analysis of an in-tegrated trainndashbridgendashfoundationndashsoil system by the sub-structure methodrdquo International Journal of StructuralStability and Dynamics vol 18 no 5 Article ID 1850069 pp1ndash25 2018

[32] O Polach and D Nicklisch ldquoWheelrail contact geometryparameters in regard to vehicle behaviour and their alterationwith wearrdquo Wear vol 366-367 pp 200ndash208 2016

[33] H Shi J Wang P Wu C Song and W Teng ldquoFieldmeasurements of the evolution of wheel wear and vehicledynamics for high-speed trainsrdquo Vehicle System Dynamicsvol 56 no 8 pp 1187ndash1206 2018

[34] Z S Ren ldquoAn investigation on wheelrail impact dynamicswith a three-dimensional flat modelrdquo Vehicle System Dy-namics vol 57 no 3 pp 369ndash388 2019

[35] W M Zhai and H Xia Train-Track-Bridge Dynamic In-teraction Meory and Engineering Application Science PressBeijing China 2011

[36] L Ling X-B Xiao J-Y Xiong L Zhou Z-F Wen andX-S Jin ldquoA 3Dmodel for coupling dynamics analysis of high-speed traintrack systemrdquo Chinarsquos High-Speed Rail Technol-ogy vol 15 no 12 pp 309ndash339 2018

[37] R R Craig andM C C Bampton ldquoCoupling of substructuresfor dynamic analysesrdquo AIAA Journal vol 6 no 7pp 1313ndash1319 1968

[38] J-G Kim and P-S Lee ldquoAn enhanced CraigndashBamptonmethodrdquo International Journal for Numerical Methods inEngineering vol 103 no 2 pp 79ndash93 2015

[39] J Piotrowski and W Kik ldquoA simplified model of wheelrailcontact mechanics for non-Hertzian problems and its ap-plication in rail vehicle dynamic simulationsrdquo Vehicle SystemDynamics vol 46 no 1-2 pp 27ndash48 2008

[40] Y Sun Y Guo and W Zhai ldquoPrediction of rail non-uniformwearmdashinfluence of track random irregularityrdquo Wearvol 420-421 pp 235ndash244 2019

[41] J J Kalker ldquoA fast algorithm for the simplified theory ofrolling contactrdquo Vehicle System Dynamics vol 11 no 1pp 1ndash13 1982

[42] W Zhai P Liu J Lin and K Wang ldquoExperimental in-vestigation on vibration behaviour of a CRH train at speed of350 kmhrdquo International Journal of Rail Transportation vol 3no 1 pp 1ndash16 2015

[43] TGCL 127-2013 Railway Electric Multiple Units Operationand Maintaining Regulation China Railway CorporationBeijing China 2013


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

increase of speed of passenger trains and because of the factthat taller and longer bridges are being built the consid-eration of train-track-bridge interaction becomes moresignificant [2] Growing attentions have been paid to thestudy of train-track-bridge coupled vibration for the last fewyears [3ndash10] For example Zhai et al [2] proposed an ef-ficient and practical theoretical model for the analysis of thetrain-track-bridge interaction which takes into account avariety of nonlinear factors aiming to provide a method foranalyzing and assessing the running safety and the comfortof high-speed trains passing through bridges [2ndash4] Zhanget al [5 6] reported a new intersystem iteration method fordynamic analysis of the coupled train-bridge system In thismethod the dynamic responses of train subsystem andbridge subsystem are solved separately the iteration withintime-step is avoided the computation memory is saved andit is convenient to use the commercial structural analysissoftware for bridge subsystem Li et al [8] put forward theinteractive method by using the commercial finite-element(FE) software ANSYS and multibody dynamics (MBD)software SIMPACK to simulate the vehicle-bridge coupledvibration It is shown that the interactive method has highcomputational efficiency and good convergence rate forvarious bridge and the vehicle-bridge coupled vibrationanalysis can be conducted well and followed conveniently byother researchers Melo et al [9] developed a numericalvibration prediction scheme for train-bridge systems withFE software ABAQUS and numerical software MATLABAnd the experimental response obtained from a dynamictest under railway traffic revealed a good agreement with thenumerical response Antolın et al [10] compared four dif-ferent wheel-rail contact models (nonlinear linear rigidand virtual path) in vehicle-bridge coupling vibration (enumerical investigation found that the forces obtained bynon-linear wheel-rail contact model are generally larger thanthose of other three models mainly because frictional slipexist in the real wheel-rail contact conditions Arvidssonet al [11] established a 2D train-track-bridge interactionmodel that allows for wheel-rail contact loss to analyze thedynamic performance of high-speed trains running onnonballasted bridges in Europe

More and more research focus on train-track-bridgesafety performance Dhanasekar et al [12 13] studied theimpact coefficient and local deformation of long-span sus-pension bridges and other bridges under actual train loadsZhang et al [14] carried out a detailed study on the safety oftrain operation due to the settlement of high-speed railwaybridges and put forward the corresponding safety limit ofpier settlement Zeng et al [15ndash18] applied the actualrecorded seismic wave data or pseudo-excitation method(PEM) to analyze the responses of train-track-bridge systemunder the excitation of seismic waves Accordingly somepeople have studied how to reduce bridge vibration such astuned mass damper (TMD) [19 20] install fluid viscousdampers [21 22] and magnetorheological damper equip-ment on bridge structure [23] Ling et al [24 25] predictedthe post-derailment behavior of a freight train composed ofone locomotive and several wagons on bridge caused bytrack irregularity based on a coupled finite-element-

multibody dynamics (FE-MBD) theory Rocha et al [26 27]assessed the train running safety passing through bridgesbased on the probability density evolution method Otherstudies include train-bridge coupled simulation of a com-posite structure bridge [28] train-bridge coupled vibrationanalysis considering environmental wind loads [29 30] andthe interaction between the train-bridge system and thefoundation-soil system by the substructure method [31]

Besides numerous scholars have done a lot of work onthe wheel wear and its influence on railway vehicle dy-namics Polach and Nicklisch [32] presented a new standardto identify wheel-rail contact geometry parameters related tovehicle behavior (e new parameter called contact con-centration index makes up for the shortcomings of tradi-tional equivalent conicity and assess new proposals for wheeland rail profiles regarding their wear in service Shi et al [33]demonstrated the wheel wear evolution and related vehicledynamics of Chinese high-speed trains with an operatingdistance of around two million kilometers by a long-termexperimental test Ren [34] proposed a three-dimensionalwheel flat model considering the length width and depth ofthe flat spot (us it is more in line with the real wheeldamage state (e results indicated that the width the lengthof the wheel flat and the widthlength ratio have an obviousinfluence on the wheelrail impact dynamics

However few scholars pay attention to the influence ofwheel uneven wear on the dynamic response of high-speedtrain-track-bridge system In the traditional studies of train-track-bridge interaction the wheel and rail profiles wereconsidered as new profiles (is is because the wheel-railrolling contact algorithms adopted in the traditional train-track-bridge interaction models are difficult to consider thenonlinear contact characteristics of uneven worn wheel andrail profiles (erefore a nonlinear rigid-flexible coupledmodel of high-speed train-track-bridge interaction is for-mulated (is modelling is based on the train-track-bridgeinteraction theory the wheel-rail nonelliptical multipointcontact theory and the modified CraigndashBampton modalsynthesis method (e effects of wheel-rail multipoint andconformal contact behaviors caused by the wheel hollowwear are fully considered (e proposed model is thenapplied to predict the vertical and lateral responses of thehigh-speed train-track-bridge system under new and wornwheel profiles in which a high-speed train passing through along-span continuous girder bridge at speed of 350 kmh isconsidered Based on the measured high-speed train wornwheel profiles the wheel-rail contact geometry of wheelprofiles at different mileage was analyzed (e influences ofwheel hollow wear on vibration responses of the high-speedtrain-track-bridge system are reported

2 Numerical Model

A numerical model of high-speed train-track-bridge non-linear interaction (see Figure 1) is formulated based on thetrain-track-bridge dynamic interaction theory [35] (emodel consists of four sub models (1) the train dynamicsmodel (2) the track dynamics model (3) the bridge dy-namics model and (4) the contact models for wheel-rail






Train

Rail

v

Subgrade

Slab


(a)

Bridge

Cph

Cpv

Kph

Kpv

KshCsh

Rail

Track slab

Subgrade

Pier

(b)











250 250 250 250 250370 1750 350 450 1750 450 450

2501750


Mc

Ksz

Mc

MtKmy

Kmy

Cpx

ψcψw1ψt1ψw2

Kpx2dsk2dscXw2

Yw2

Cpy

KsxYt1

Xt1Xw1

Yw1

CsdxCsxKpy

Yc

Xc

Ksy

Ksy

Ksz

KpyMw YwZt

IwxZw

2dwk

2dwc

ϕw

KrxItxMtCsy

Cpy



Kpz

HBtZt1

HtwZw1Zw2Zw3

CpzKpz Zt2

Zw42lt2lc

Ity

Csz

Cpz

Kmy

vβc

βt2 βt1

Icy

Icx

ZcZc

CszHcB

Ycϕc

ϕtYt











ub(x y z t) ubx

uby

ubz

sumS

i1ϕix(x y z)qi(t)

sumS

i1ϕiy(x y z)qi(t)

sumS

i1ϕiz(x y z)qi(t)

sumS

i1Φiqi

Φbqb(4)




ub Φbqb ubBubI

[ ] Ib 0

ϕIC ϕIN[ ]

qCqN

(5)



Kb ΦTbΚbΦb

Ib 0

ϕIC ϕIN

T KBB KBI

KIB KBB

Ib 0

ϕIC ϕIN

KCC 0

0 KNN

Mb ΦTbMbΦb

Ib 0

ϕIC ϕIN

T MBB MBI

MIB MBB

Ib 0

ϕIC ϕIN

MCC MNC

MCN MNN

(6)


OX Y

Z

Ob

Xb Yb

Zb

ρkub

rk r0

Kprime

K

dk





Kbqb λMbqb

qb Nqb(7)


ub 1113944S





Cb αMb + βKb + 1113944

Ne

j1Cj (10)


α 2ξbωiωj

ωi + ωj

β 2ξb

ωi + ωj

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(11)


24 Contact Models


pz(x y) p0

xi(0)


(12)


xl(y)

2Rg(y)

1113969

(13)


N p0

xl(0)1113946

yl

yr

1113946xl(y)

minus xl(y)


dx dy (14)

Ω

(a)

Ω1Ω2

Γ

(b)

Ω2

Ω1

(c)




w0 1 minus μ2

πEp0xl(0)

intyl

yrintxl(y)

minus xl(y)

xl(y)

2 minus x2

x2 + y2

radic

dx dy (15)


N πEδ0


xl(y)

2 minus x2radic

dx dy


xl(y)


dx dy

p0 N

2Rδ0radic


xl(y)

2 minus x2radic

dx dy

(16)










ndash30

ndash20

ndash10

0

10

20

30

Vert

ical

acce

lera

tion

(ms

2 )

0 4 6 8 102Time (s)

(a)

ndash20

ndash10

0

10

20

Late

ral a

ccel

erat

ion

(ms

2 )

0 4 6 8 102


Time (s)

(b)








ndash200

ndash100

0

100

200

Vert

ical

acce

lera

tion

(ms

2 )

5 7 8 9 106


Time (s)

(a)

ndash30

ndash20

ndash10

0

10

20

30

Late

ral a

ccel

erat

ion

(ms

2 )

6 7 8 9 105


Time (s)

(b)


220 240 260 280 300 32000

02

04

06

08

Vert

ical

disp

lace

men

t (m

m)

Speed (kmh)

Fitting result


(a)

220 240 260 280 300 3200

30

60

90

120

150

180Ve

rtic

al ac

cele

ratio

n (m

s2 )

Speed (kmh)

Fitting result


(b)










2S

2asymp εy (18)




ndash2

0

2


169000 km192000 km


0

10

20

30

Whe

el pr

ofile

hei

ght (

mm

)



83000 km132000 km

169000 km192000 km

Main wear area


00

02

04

06

08

10

Whe

el w

ear d

epth

(mm

)





ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(a)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(b)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(c)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(d)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(e)



169000 km192000 km


0

1

2

3

4

Rolli

ng ra

dius

diff

eren

ce (m

m)

(a)


169000 km192000 km


000

005

010

015

020

025

030

035

Equi

vale

nt co

nici

ty

(b)

Figure 12 Continued











169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)


(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)







915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Train

Rail

v

Subgrade

Slab


(a)

Bridge

Cph

Cpv

Kph

Kpv

KshCsh

Rail

Track slab

Subgrade

Pier

(b)











250 250 250 250 250370 1750 350 450 1750 450 450

2501750


Mc

Ksz

Mc

MtKmy

Kmy

Cpx

ψcψw1ψt1ψw2

Kpx2dsk2dscXw2

Yw2

Cpy

KsxYt1

Xt1Xw1

Yw1

CsdxCsxKpy

Yc

Xc

Ksy

Ksy

Ksz

KpyMw YwZt

IwxZw

2dwk

2dwc

ϕw

KrxItxMtCsy

Cpy



Kpz

HBtZt1

HtwZw1Zw2Zw3

CpzKpz Zt2

Zw42lt2lc

Ity

Csz

Cpz

Kmy

vβc

βt2 βt1

Icy

Icx

ZcZc

CszHcB

Ycϕc

ϕtYt











ub(x y z t) ubx

uby

ubz

sumS

i1ϕix(x y z)qi(t)

sumS

i1ϕiy(x y z)qi(t)

sumS

i1ϕiz(x y z)qi(t)

sumS

i1Φiqi

Φbqb(4)




ub Φbqb ubBubI

[ ] Ib 0

ϕIC ϕIN[ ]

qCqN

(5)



Kb ΦTbΚbΦb

Ib 0

ϕIC ϕIN

T KBB KBI

KIB KBB

Ib 0

ϕIC ϕIN

KCC 0

0 KNN

Mb ΦTbMbΦb

Ib 0

ϕIC ϕIN

T MBB MBI

MIB MBB

Ib 0

ϕIC ϕIN

MCC MNC

MCN MNN

(6)


OX Y

Z

Ob

Xb Yb

Zb

ρkub

rk r0

Kprime

K

dk





Kbqb λMbqb

qb Nqb(7)


ub 1113944S





Cb αMb + βKb + 1113944

Ne

j1Cj (10)


α 2ξbωiωj

ωi + ωj

β 2ξb

ωi + ωj

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(11)


24 Contact Models


pz(x y) p0

xi(0)


(12)


xl(y)

2Rg(y)

1113969

(13)


N p0

xl(0)1113946

yl

yr

1113946xl(y)

minus xl(y)


dx dy (14)

Ω

(a)

Ω1Ω2

Γ

(b)

Ω2

Ω1

(c)




w0 1 minus μ2

πEp0xl(0)

intyl

yrintxl(y)

minus xl(y)

xl(y)

2 minus x2

x2 + y2

radic

dx dy (15)


N πEδ0


xl(y)

2 minus x2radic

dx dy


xl(y)


dx dy

p0 N

2Rδ0radic


xl(y)

2 minus x2radic

dx dy

(16)










ndash30

ndash20

ndash10

0

10

20

30

Vert

ical

acce

lera

tion

(ms

2 )

0 4 6 8 102Time (s)

(a)

ndash20

ndash10

0

10

20

Late

ral a

ccel

erat

ion

(ms

2 )

0 4 6 8 102


Time (s)

(b)








ndash200

ndash100

0

100

200

Vert

ical

acce

lera

tion

(ms

2 )

5 7 8 9 106


Time (s)

(a)

ndash30

ndash20

ndash10

0

10

20

30

Late

ral a

ccel

erat

ion

(ms

2 )

6 7 8 9 105


Time (s)

(b)


220 240 260 280 300 32000

02

04

06

08

Vert

ical

disp

lace

men

t (m

m)

Speed (kmh)

Fitting result


(a)

220 240 260 280 300 3200

30

60

90

120

150

180Ve

rtic

al ac

cele

ratio

n (m

s2 )

Speed (kmh)

Fitting result


(b)










2S

2asymp εy (18)




ndash2

0

2


169000 km192000 km


0

10

20

30

Whe

el pr

ofile

hei

ght (

mm

)



83000 km132000 km

169000 km192000 km

Main wear area


00

02

04

06

08

10

Whe

el w

ear d

epth

(mm

)





ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(a)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(b)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(c)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(d)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(e)



169000 km192000 km


0

1

2

3

4

Rolli

ng ra

dius

diff

eren

ce (m

m)

(a)


169000 km192000 km


000

005

010

015

020

025

030

035

Equi

vale

nt co

nici

ty

(b)

Figure 12 Continued











169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)


(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)







915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










250 250 250 250 250370 1750 350 450 1750 450 450

2501750


Mc

Ksz

Mc

MtKmy

Kmy

Cpx

ψcψw1ψt1ψw2

Kpx2dsk2dscXw2

Yw2

Cpy

KsxYt1

Xt1Xw1

Yw1

CsdxCsxKpy

Yc

Xc

Ksy

Ksy

Ksz

KpyMw YwZt

IwxZw

2dwk

2dwc

ϕw

KrxItxMtCsy

Cpy



Kpz

HBtZt1

HtwZw1Zw2Zw3

CpzKpz Zt2

Zw42lt2lc

Ity

Csz

Cpz

Kmy

vβc

βt2 βt1

Icy

Icx

ZcZc

CszHcB

Ycϕc

ϕtYt











ub(x y z t) ubx

uby

ubz

sumS

i1ϕix(x y z)qi(t)

sumS

i1ϕiy(x y z)qi(t)

sumS

i1ϕiz(x y z)qi(t)

sumS

i1Φiqi

Φbqb(4)




ub Φbqb ubBubI

[ ] Ib 0

ϕIC ϕIN[ ]

qCqN

(5)



Kb ΦTbΚbΦb

Ib 0

ϕIC ϕIN

T KBB KBI

KIB KBB

Ib 0

ϕIC ϕIN

KCC 0

0 KNN

Mb ΦTbMbΦb

Ib 0

ϕIC ϕIN

T MBB MBI

MIB MBB

Ib 0

ϕIC ϕIN

MCC MNC

MCN MNN

(6)


OX Y

Z

Ob

Xb Yb

Zb

ρkub

rk r0

Kprime

K

dk





Kbqb λMbqb

qb Nqb(7)


ub 1113944S





Cb αMb + βKb + 1113944

Ne

j1Cj (10)


α 2ξbωiωj

ωi + ωj

β 2ξb

ωi + ωj

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(11)


24 Contact Models


pz(x y) p0

xi(0)


(12)


xl(y)

2Rg(y)

1113969

(13)


N p0

xl(0)1113946

yl

yr

1113946xl(y)

minus xl(y)


dx dy (14)

Ω

(a)

Ω1Ω2

Γ

(b)

Ω2

Ω1

(c)




w0 1 minus μ2

πEp0xl(0)

intyl

yrintxl(y)

minus xl(y)

xl(y)

2 minus x2

x2 + y2

radic

dx dy (15)


N πEδ0


xl(y)

2 minus x2radic

dx dy


xl(y)


dx dy

p0 N

2Rδ0radic


xl(y)

2 minus x2radic

dx dy

(16)










ndash30

ndash20

ndash10

0

10

20

30

Vert

ical

acce

lera

tion

(ms

2 )

0 4 6 8 102Time (s)

(a)

ndash20

ndash10

0

10

20

Late

ral a

ccel

erat

ion

(ms

2 )

0 4 6 8 102


Time (s)

(b)








ndash200

ndash100

0

100

200

Vert

ical

acce

lera

tion

(ms

2 )

5 7 8 9 106


Time (s)

(a)

ndash30

ndash20

ndash10

0

10

20

30

Late

ral a

ccel

erat

ion

(ms

2 )

6 7 8 9 105


Time (s)

(b)


220 240 260 280 300 32000

02

04

06

08

Vert

ical

disp

lace

men

t (m

m)

Speed (kmh)

Fitting result


(a)

220 240 260 280 300 3200

30

60

90

120

150

180Ve

rtic

al ac

cele

ratio

n (m

s2 )

Speed (kmh)

Fitting result


(b)










2S

2asymp εy (18)




ndash2

0

2


169000 km192000 km


0

10

20

30

Whe

el pr

ofile

hei

ght (

mm

)



83000 km132000 km

169000 km192000 km

Main wear area


00

02

04

06

08

10

Whe

el w

ear d

epth

(mm

)





ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(a)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(b)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(c)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(d)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(e)



169000 km192000 km


0

1

2

3

4

Rolli

ng ra

dius

diff

eren

ce (m

m)

(a)


169000 km192000 km


000

005

010

015

020

025

030

035

Equi

vale

nt co

nici

ty

(b)

Figure 12 Continued











169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)


(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)







915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










ub(x y z t) ubx

uby

ubz

sumS

i1ϕix(x y z)qi(t)

sumS

i1ϕiy(x y z)qi(t)

sumS

i1ϕiz(x y z)qi(t)

sumS

i1Φiqi

Φbqb(4)




ub Φbqb ubBubI

[ ] Ib 0

ϕIC ϕIN[ ]

qCqN

(5)



Kb ΦTbΚbΦb

Ib 0

ϕIC ϕIN

T KBB KBI

KIB KBB

Ib 0

ϕIC ϕIN

KCC 0

0 KNN

Mb ΦTbMbΦb

Ib 0

ϕIC ϕIN

T MBB MBI

MIB MBB

Ib 0

ϕIC ϕIN

MCC MNC

MCN MNN

(6)


OX Y

Z

Ob

Xb Yb

Zb

ρkub

rk r0

Kprime

K

dk





Kbqb λMbqb

qb Nqb(7)


ub 1113944S





Cb αMb + βKb + 1113944

Ne

j1Cj (10)


α 2ξbωiωj

ωi + ωj

β 2ξb

ωi + ωj

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(11)


24 Contact Models


pz(x y) p0

xi(0)


(12)


xl(y)

2Rg(y)

1113969

(13)


N p0

xl(0)1113946

yl

yr

1113946xl(y)

minus xl(y)


dx dy (14)

Ω

(a)

Ω1Ω2

Γ

(b)

Ω2

Ω1

(c)




w0 1 minus μ2

πEp0xl(0)

intyl

yrintxl(y)

minus xl(y)

xl(y)

2 minus x2

x2 + y2

radic

dx dy (15)


N πEδ0


xl(y)

2 minus x2radic

dx dy


xl(y)


dx dy

p0 N

2Rδ0radic


xl(y)

2 minus x2radic

dx dy

(16)










ndash30

ndash20

ndash10

0

10

20

30

Vert

ical

acce

lera

tion

(ms

2 )

0 4 6 8 102Time (s)

(a)

ndash20

ndash10

0

10

20

Late

ral a

ccel

erat

ion

(ms

2 )

0 4 6 8 102


Time (s)

(b)








ndash200

ndash100

0

100

200

Vert

ical

acce

lera

tion

(ms

2 )

5 7 8 9 106


Time (s)

(a)

ndash30

ndash20

ndash10

0

10

20

30

Late

ral a

ccel

erat

ion

(ms

2 )

6 7 8 9 105


Time (s)

(b)


220 240 260 280 300 32000

02

04

06

08

Vert

ical

disp

lace

men

t (m

m)

Speed (kmh)

Fitting result


(a)

220 240 260 280 300 3200

30

60

90

120

150

180Ve

rtic

al ac

cele

ratio

n (m

s2 )

Speed (kmh)

Fitting result


(b)










2S

2asymp εy (18)




ndash2

0

2


169000 km192000 km


0

10

20

30

Whe

el pr

ofile

hei

ght (

mm

)



83000 km132000 km

169000 km192000 km

Main wear area


00

02

04

06

08

10

Whe

el w

ear d

epth

(mm

)





ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(a)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(b)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(c)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(d)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(e)



169000 km192000 km


0

1

2

3

4

Rolli

ng ra

dius

diff

eren

ce (m

m)

(a)


169000 km192000 km


000

005

010

015

020

025

030

035

Equi

vale

nt co

nici

ty

(b)

Figure 12 Continued











169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)


(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)







915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Kbqb λMbqb

qb Nqb(7)


ub 1113944S





Cb αMb + βKb + 1113944

Ne

j1Cj (10)


α 2ξbωiωj

ωi + ωj

β 2ξb

ωi + ωj

⎧⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎩

(11)


24 Contact Models


pz(x y) p0

xi(0)


(12)


xl(y)

2Rg(y)

1113969

(13)


N p0

xl(0)1113946

yl

yr

1113946xl(y)

minus xl(y)


dx dy (14)

Ω

(a)

Ω1Ω2

Γ

(b)

Ω2

Ω1

(c)




w0 1 minus μ2

πEp0xl(0)

intyl

yrintxl(y)

minus xl(y)

xl(y)

2 minus x2

x2 + y2

radic

dx dy (15)


N πEδ0


xl(y)

2 minus x2radic

dx dy


xl(y)


dx dy

p0 N

2Rδ0radic


xl(y)

2 minus x2radic

dx dy

(16)










ndash30

ndash20

ndash10

0

10

20

30

Vert

ical

acce

lera

tion

(ms

2 )

0 4 6 8 102Time (s)

(a)

ndash20

ndash10

0

10

20

Late

ral a

ccel

erat

ion

(ms

2 )

0 4 6 8 102


Time (s)

(b)








ndash200

ndash100

0

100

200

Vert

ical

acce

lera

tion

(ms

2 )

5 7 8 9 106


Time (s)

(a)

ndash30

ndash20

ndash10

0

10

20

30

Late

ral a

ccel

erat

ion

(ms

2 )

6 7 8 9 105


Time (s)

(b)


220 240 260 280 300 32000

02

04

06

08

Vert

ical

disp

lace

men

t (m

m)

Speed (kmh)

Fitting result


(a)

220 240 260 280 300 3200

30

60

90

120

150

180Ve

rtic

al ac

cele

ratio

n (m

s2 )

Speed (kmh)

Fitting result


(b)










2S

2asymp εy (18)




ndash2

0

2


169000 km192000 km


0

10

20

30

Whe

el pr

ofile

hei

ght (

mm

)



83000 km132000 km

169000 km192000 km

Main wear area


00

02

04

06

08

10

Whe

el w

ear d

epth

(mm

)





ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(a)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(b)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(c)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(d)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(e)



169000 km192000 km


0

1

2

3

4

Rolli

ng ra

dius

diff

eren

ce (m

m)

(a)


169000 km192000 km


000

005

010

015

020

025

030

035

Equi

vale

nt co

nici

ty

(b)

Figure 12 Continued











169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)


(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)







915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



w0 1 minus μ2

πEp0xl(0)

intyl

yrintxl(y)

minus xl(y)

xl(y)

2 minus x2

x2 + y2

radic

dx dy (15)


N πEδ0


xl(y)

2 minus x2radic

dx dy


xl(y)


dx dy

p0 N

2Rδ0radic


xl(y)

2 minus x2radic

dx dy

(16)










ndash30

ndash20

ndash10

0

10

20

30

Vert

ical

acce

lera

tion

(ms

2 )

0 4 6 8 102Time (s)

(a)

ndash20

ndash10

0

10

20

Late

ral a

ccel

erat

ion

(ms

2 )

0 4 6 8 102


Time (s)

(b)








ndash200

ndash100

0

100

200

Vert

ical

acce

lera

tion

(ms

2 )

5 7 8 9 106


Time (s)

(a)

ndash30

ndash20

ndash10

0

10

20

30

Late

ral a

ccel

erat

ion

(ms

2 )

6 7 8 9 105


Time (s)

(b)


220 240 260 280 300 32000

02

04

06

08

Vert

ical

disp

lace

men

t (m

m)

Speed (kmh)

Fitting result


(a)

220 240 260 280 300 3200

30

60

90

120

150

180Ve

rtic

al ac

cele

ratio

n (m

s2 )

Speed (kmh)

Fitting result


(b)










2S

2asymp εy (18)




ndash2

0

2


169000 km192000 km


0

10

20

30

Whe

el pr

ofile

hei

ght (

mm

)



83000 km132000 km

169000 km192000 km

Main wear area


00

02

04

06

08

10

Whe

el w

ear d

epth

(mm

)





ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(a)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(b)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(c)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(d)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(e)



169000 km192000 km


0

1

2

3

4

Rolli

ng ra

dius

diff

eren

ce (m

m)

(a)


169000 km192000 km


000

005

010

015

020

025

030

035

Equi

vale

nt co

nici

ty

(b)

Figure 12 Continued











169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)


(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)







915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







ndash200

ndash100

0

100

200

Vert

ical

acce

lera

tion

(ms

2 )

5 7 8 9 106


Time (s)

(a)

ndash30

ndash20

ndash10

0

10

20

30

Late

ral a

ccel

erat

ion

(ms

2 )

6 7 8 9 105


Time (s)

(b)


220 240 260 280 300 32000

02

04

06

08

Vert

ical

disp

lace

men

t (m

m)

Speed (kmh)

Fitting result


(a)

220 240 260 280 300 3200

30

60

90

120

150

180Ve

rtic

al ac

cele

ratio

n (m

s2 )

Speed (kmh)

Fitting result


(b)










2S

2asymp εy (18)




ndash2

0

2


169000 km192000 km


0

10

20

30

Whe

el pr

ofile

hei

ght (

mm

)



83000 km132000 km

169000 km192000 km

Main wear area


00

02

04

06

08

10

Whe

el w

ear d

epth

(mm

)





ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(a)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(b)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(c)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(d)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(e)



169000 km192000 km


0

1

2

3

4

Rolli

ng ra

dius

diff

eren

ce (m

m)

(a)


169000 km192000 km


000

005

010

015

020

025

030

035

Equi

vale

nt co

nici

ty

(b)

Figure 12 Continued











169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)


(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)







915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









2S

2asymp εy (18)




ndash2

0

2


169000 km192000 km


0

10

20

30

Whe

el pr

ofile

hei

ght (

mm

)



83000 km132000 km

169000 km192000 km

Main wear area


00

02

04

06

08

10

Whe

el w

ear d

epth

(mm

)





ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(a)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(b)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(c)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(d)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(e)



169000 km192000 km


0

1

2

3

4

Rolli

ng ra

dius

diff

eren

ce (m

m)

(a)


169000 km192000 km


000

005

010

015

020

025

030

035

Equi

vale

nt co

nici

ty

(b)

Figure 12 Continued











169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)


(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)







915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(a)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(b)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(c)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(d)


ndash04

ndash02

00

02

04

06

Z co

ordi

nate

s (m

)

(e)



169000 km192000 km


0

1

2

3

4

Rolli

ng ra

dius

diff

eren

ce (m

m)

(a)


169000 km192000 km


000

005

010

015

020

025

030

035

Equi

vale

nt co

nici

ty

(b)

Figure 12 Continued











169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)


(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)







915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











169000 km192000 km

ndash20

ndash15

ndash10

ndash5

0

Con

tact

angl

e (deg)


(c)


169000 km192000 km

ndash100

ndash50

0

50

100

Con

tact

angl

e par

amet

er E

(y)


(d)







915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






915 180 915 240

125215

385


1600

40

20 20 20 20



680

40


120680

1360

40R10

40

3575

340

450 620 40 620 40

120

R10

7534

045

035

12555 55

120 85 80 25 200 250 250 200 25 80 120 4085


575

575

620

620

620

620

575

575

0 1 2 3

85 180009130 9130 85

Bridge direction



Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Bridge direction

O

Z

Y

X

Arch rib


Diagonal structures

Main span

Le side span

Right-side span

Cable

Solid185

Beam188

Link10

Shell63


0

50

100

150

200

Whe

el-r

ail v

ertic

al fo

rce (

kN)

25 30 35 40 45 5020Time (s)


(a)

25 30 35 40 45 5020Time (s)

ndash12

ndash8

ndash4

0

4

8

12

Whe

el-r

ail l

ater

al fo

rce (

kN)


(b)



PSD

(kN

2 Hz)



(a)

10ndash6

10ndash5

10ndash4

10ndash3

10ndash2

10ndash1

100

PSD

(kN

2 Hz)

200 300 400 500100Frequency (Hz)


(b)









PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








PSD

(kN

2 Hz)

Frequency (Hz)


(a)

10ndash9

10ndash8

10ndash7

10ndash6

10ndash5

10ndash4

10ndash3

100 200 300 400 500

PSD

(kN

2 Hz)

Frequency (Hz)


(b)


1 2 3 4 5 6 70Time (s)

ndash5

ndash4

ndash3

ndash2

ndash1

0

1

Vert

ical

disp

lace

men

t (m

m)


(a)

1 2 3 4 5 6 70Time (s)

ndash005

000

005

010

015

Late

ral d

ispla

cem

ent (

mm

)


(b)







000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






000510

Vert

ical

disp

lace

men

t (m

m)


2 3 4 5 6 70 1Time (s)

(a)

ndash002

000

002

004

006

Late

ral d

ispla

cem

ent (

mm

)


2 3 4 5 6 70 1Time (s)

(b)




000510

Vert

ical

disp

lace

men

t (m

m)

2 3 4 5 6 7 81Time (s)

(a)


ndash002

000

002

004

006

008

Late

ral d

ispla

cem

ent (

mm

)

2 3 4 5 6 7 81Time (s)

(b)



1 2 3 4 5 6 70Time (s)

ndash008

ndash004

000

004

008

Vert

ical

acce

lera

tion

(ms

2 )



ndash002

ndash001

000

001

002

Late

ral a

ccel

erat

ion

(ms

2 )

1 2 3 4 5 6 70Time (s)



269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


269 Hz

229 Hz759 Hz

PSD

((m

s2 )2 H

z)


053 Hz

00

50 times 10ndash6

10 times 10ndash5

15 times 10ndash5

20 times 10ndash5

25 times 10ndash5

30 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(a)

PSD

((m

s2 )2 H

z)


117 Hz769 Hz

396 Hz

153Hz

00

20 times 10ndash6

40 times 10ndash6

60 times 10ndash6

80 times 10ndash6

10 times 10ndash5

12 times 10ndash5

5 10 15 20 25 300Frequency (Hz)

(b)


Vertical

00520054005600580060006200640066

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(a)

Lateral

0014

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(b)

Vertical

008

009

010

011

012

013

Peak

val

ues (

ms

2 )5 10 15 200

Mileage (104km)

(c)

Lateral

0016

0018

0020

0022

0024

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(d)

Vertical

009010011012013014015016

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(e)

Lateral

00180019002000210022002300240025

Peak

val

ues (

ms

2 )

5 10 15 200Mileage (104km)

(f )









5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





5 Conclusions



Data Availability




Acknowledgments



References

















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

High-SpeedTrain-Track-BridgeDynamicInteractionconsidering ...downloads.hindawi.com/journals/sv/2019/5874678.pdf · model of high-speed train-track-bridge interaction is for-mulated.ismodellingisbasedonthetrain-track-bridge