InfluenceofFull-LifeCycleWheelProfileontheContact ... · sides, a vehicle/turnout system dynamic...

Research ArticleInfluence of Full-Life Cycle Wheel Profile on the ContactPerformance of Wheel and Standard Fixed Frog in HeavyHaul Railway

He Ma Jinming Zhang Jun Zhang Tao Tao Jin and Chun Yu Song

School of Mechanical-Electronic and Automobile Engineering Beijing University of Civil Engineering and ArchitectureBeijing 100044 China

Correspondence should be addressed to Jun Zhang zhangjun611buceaeducn

Received 5 September 2020 Revised 28 October 2020 Accepted 13 November 2020 Published 26 November 2020

Academic Editor Nicolo Zampieri

Copyright copy 2020 HeMa et al -is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Wheel wear is unavoidable which affects the contact performance of the wheel and rail -is article explores the effects of wheelprofile wear on the static contact and dynamic interaction between wheel and standard fixed frog in heavy haul railway -ecoupling dynamic models of the vehicle-fixed frog system are established to calculate the change regulation of displacementcontact force and acceleration when a vehicle passes through the standard fixed frog at a speed of 50 kmh in the facing move inthe diverging line Besides the finite element models of wheel and standard fixed frog at key positions are developed to simulatethe contact patch and distribution of von Mises stress in the regions of the wheel-fixed frog Compared with the standard profilethe maximum lateral displacement of the worn profile can be reduced by up to 9mm -e vertical contact force can be reducedfrom 750 kN to 320 kN and the decrease is 573 -e von Mises stress could decrease up to 34 compared with the standardAnd the results show that the wheel profile wear changes the positions of the wheel-rail contact points along the longitudinaldirection and affects the dynamic interaction of vehicle and standard fixed frog For the measured worn wheel profiles in thisarticle profile wear relieves the dynamic responses and it is good for the nose rail

1 Introduction

Turnout (switch and crossing) is a crucial part of the railwaysystem which enables the train to run from one track toanother Many types of turnouts are available while thesingle turnout is the most common Single turnout consistsof a switch panel and crossing panel which are connected bya closure panel-e fixed andmovable turnout are two kindsof turnout-e structure of the fixed turnout is simple whilethe simplicity of its structure results in the inevitableldquoharmful spacerdquo problem -e gap between the narrowestpoint of the two wing rails and the tip of the nose rail is calledthe ldquoharmful spacerdquo as shown in Figure 1 Although themovable turnout could avoid the ldquoharmful spacerdquo it requiresmore maintenance and entails higher cost because of itscomplex structure [1] Moreover the movable turnout is notsuitable for the transportation mode of heavy haul railways

those are large axle weight high density and large freightvolume -us the fixed turnout accounts for more than 90percent of turnouts which are used in heavy haul railways[2ndash4]

In the crossing panel of single fixed turnout thecrossing rail is composed of fixed frog (nose rail and wingrail) and check rail When the train passes through thecrossing panel in the facing move (the wheel runs on thewing rail to the nose rail) it is possible that the wheel mightgo wrong and cause the train to derail -is is the purposeof setting the check rail which is to force the direction ofthe wheels

In the process of the wheel passing through the turnoutin the facing move the wheel has an impact on the nose railWhile in the trailing move (the wheel runs on the nose railto the wing rail) the wheel has an impact on the wing railDue to the inevitable ldquoharmful spacerdquo and the inherent

HindawiShock and VibrationVolume 2020 Article ID 8866692 12 pageshttpsdoiorg10115520208866692

structural irregularity of the fixed frog severe vibration willoccur affecting the safety of train operation and the speed

Wheel-rail contact behavior in the crossing has beenstudied with a number of laboratory experiments and nu-merical procedures Lateral and vertical dynamic force andwheel contact angle with different speed were studied in theturnout aera [5 6] -e characteristics of the wheel-railcontact geometry relationship of the turnout zone are studiedby Ren and Sun [7] -en they investigated the influence ofthe nose rails height on the wheel-rail contact characteristicsby the high-speed vehicleturnout dynamic model [8] Be-sides a vehicleturnout system dynamic model was estab-lished to analyze the dynamics capability while passingthrough the turnout [9] A model on the basis of the vehicle-track coupling dynamic theory was established by Zhai andWang to study on the safety of trains when the locomotivepasses through the branch line of turnout In addition theyinvestigated the influence of running speed [10]

Based on No 42 high-speed turnout a wheelrail contactmodel with different point hiding tip structures and wheelprofiles was established to analyze the characteristics of ir-regularity in the crossing zone [11] Li et al [12] established awheel-crossing finite element contact model to study thecontact trails characteristics and Mises stress Wiest et al [13]assessed four methods based on calculating contact stresscontact patch size and penetration depth in wheel-rail or switchcontact-e fourmodels are as followsHertz and non-Hertzianmethod implemented in the computer program CONTACTand elastic and elastic-plastic finite element contact modelsinvestigated with the commercial code ABAQUS -e findingsshowed that the contact pressure distributions calculated inHertz and CONTACT are consistent with the results acquiredfrom the finite element method as long as there is no plasti-fication of the material And the literature [14] presented adynamic finite elementmodel for the process of a wheel passingthe frog -is model accounts for the dynamic process theelastic deformations of the wheel and the elastic-plastic de-formations of the crossing In order to simulate the situation inwhich the wheel passes through the frog the finite elementmodels have been developed by Pletz et al [15] -e dynamicresponse of the wheel passing through the frog and the variationlaws of the contact stress and contact status were concluded

-e above experts ignore the influence of wheel wear onthe wheel-rail relationship -e wheels wear leads to wheelprofile change and thus strongly affects the dynamic per-formance of vehicles and the static contact performance-e

calculation of dynamic and static contact performancemakes it possible to properly design the profile of the fixedfrog Xu et al [16] studied the contact analysis and dynamicresponse of worn rail in the switch rail area of high-speedtrain turnout Chen et al [17] studied the influence of wheelprofile evolution on the dynamic interaction between thewheel of high-speed railway and the switch rail in theturnout While in heavy haul railway the fixed frog isutilized And the dynamic response is different from themovable frog used in the high-speed railway

In this paper the contact between the wheel whichconcluded the full-life cycle profile and the standard fixedfrog is studied in the simulation software Simpack andABAQUS-e influences of wheel profile wear on the wheelstandard fixed frog contact performance are accounted for inthe simulation Nominal and measured worn wheel profilesare used as boundary conditions of wheel-standard fixedfrog contact -e effects of full-life cycle wheel profile on thewheel-rail static contact status and dynamic interaction ofvehicle and standard fixed frog in heavy haul railway areresearched In practice the frog will also be worn with theincrease of service time-erefore future work will study thecontact between wheel profile and wear frog

2 Wheel and Fixed Frog Profiles

With the increase of trains the profiles of wheel and fixedfrog change with cumulative abrasion A series of work hasbeen conducted to track and test the evolution of wheelprofiles in heavy haul railway as is shown in Figure 2 Wornwheel profiles are measured using the instrument namedCALIPRI a wheel-rail profile measuring instrument Use theCALIPRI to measure the worn profile of the wheelsets in thefield And then import the profile wireframe scanned by theinfrared ray of the CALIPRI into the HYPERMESH -eprofile of the wheel is discretized -e discrete point data isgenerated into prr files and imported into the Simpack tobecome a usable worn profile Nominal profile represents theLM Profiles I II III and IV are all measured worn profileswhose vertical wear loss in the radius of the rolling circle isrespectively 1318mm 2622mm 3861mm and 5759mm-e figure shows that the abrasion on the tread is moresevere compared with that on the flange Moreover with thewear of the wheel its conicity on the tread decreasesgradually Hence the tread flattens out Profile I and profileII are called initial worn profiles and profile III and profile IVare called late worn profiles based on the wear loss

-e nominal geometry of the studied turnout is astandard design CN75-350-112 (curve radius 350m turn-out angle 1 12) According to the change of nose rail widthand the location of frog injury researched in field the keysections of the theoretical nose of crossing (Section A) and10mm (Section B) 20mm (Section C) 30mm (Section D)40mm (Section E) and 50mm (Section F) mm width ofnose rail respectively are analyzed -e variation of railprofiles along the turnout is accounted for by sampling therail cross sections at several key positions as shown inFigure 3 -e spline interpolation method is used to stretch

Switch rail

Nose railWing rail

Check railHarmful space

Switch panel Closure panel Crossing panel

Figure 1 Single turnout

2 Shock and Vibration

the key sections to form the required frog in dynamicsoftware SIMPACK

3 Calculation of Wheel-Fixed FrogContact Geometry

When the vehicle passes through the turnout the wheel-railcontact positions could be predicted at the crossing panel Itmay be the wheel flange or tread contacts with the nose railor the outside of the wheel tread contacts with the wing rail

-e minimum distance method is used to determine thecontact point pairs between wheels and frogs as shown inFigure 4-e wheel-rail contact point pairs between differentwheel profiles and fixed frog at Sections D and E calculatedthrough the principle are indicated in Figure 5 At Section Ethe wheels with different worn profiles all contact with thenose rail at different lateral displacements And at Section Dthe wheel with nominal profile profile I or profile II contactswith the nose rail With the wear of the wheel the wheeltread wears more seriously than the outside of the wheeltread -erefore the wheel with profile III or profile IVcontacts with the wing rail when the wheel-rail lateraldisplacement ranges from minus3 to 15mm at Section D

4 Dynamic Interaction of Vehicle andFixed Frog

41 Vehicle-Turnout Dynamic Model -e vehicle-turnoutdynamic model is simulated in the commercial softwareSIMPACK -e calculation model (see Figure 6) includestwo parts the vehicle model of the Chinese C80 wagon inDatong-Qinhuangdao heavy haul railway and the turnoutrailway which are connected by a wheel-rail contact model

-e calculation model of the vehicle includes carbodyprimary and secondary suspension elements frames andwheelsets In the three-dimensional multibody dynamicmodel of the vehicle carbody frames and wheelsets areimplemented as rigid bodies and the parameters of thevehicle are listed in Table 1-e rotary K6 bogies used in C80trucks are three-piece truck bogies of cast steel -e rotaryK6 bogie adopts the axle box elastic shear pad as the primarysuspension and the central pillow spring suspension systemwith variable friction damping device as the second sus-pension in which the second stage stiffness adopts the pillowspring and equipped with JC double-acting often contactselastic side bearing A lower cross support device with sideframe elasticity is arranged along the horizontal plane be-tween the two sides of the frame which can effectivelyhinder the rhombic deformation between the two sides of

the frame and then improve the rhombic stiffness of thebogie-is would help to improve the stability of the bogie inoperation

-e track is described by the discrete track and sleepermodel and the trackpad follows the single support model Inconsidering the sleeper mass the track and sleeper areconsidered part of the route -e spring-damping models inthe lateral and vertical directions are employed to connectwith the ground -e variations in rail cross section andwheel wear are considered in the calculation dynamic model-e vehicle is switching into the turnout track in facingmove in the simulation

-e wheel-rail relationship is very complex in theturnout railway because of the variation of rail profiles -ewheel-rail geometry has been calculated in advance -eprecalculated contact points between wheel and rail havebeen saved in tables and would be utilized in dynamicanalysis -e contact points and contact angle determine thelocations and directions of contact force respectively Multi-Hertzian contact theory is used to solve the normal contactproblem and the FASTSIM algorithm is applied for calcu-lation of the tangential contact force

-e dynamic calculation could predict the motion of allparts of the vehicle and forces between different parts -edynamic responses such as wheel-rail contact force andrelative displacement between wheel and rail could be usedas inputs in the following finite element models

To simplify the calculation the model will make thefollowing assumptions -e plastic deformation of thecontact zone and the elastic deformation of the rail are notconsidered Although there will be wear and tear in theservice of the train the frog profile used in this paper isstandard Likewise the ballast under the track is notconsidered

42 Dynamic Responses When the vehicle reverse passesthrough the fixed frog in the facing move the wheel firstenters the throat area (minus3736mmsimminus7334mm from thetheoretical nose of crossing) of the frog then passes throughthe theoretical nose of crossing and finally transitions fromthe wing rail to the nose rail (transition zone) until it is in fullcontact with the nose rail

-e effects of wheel profiles wear on the dynamic in-teraction between vehicle and fixed frog in heavy haulrailway are researched and the simulation is carried out atthe speed of 50 kmh for the vehicle-e results conclude thelateral and vertical displacement of wheelset the verticalcontact force at the side of the crossing panel and thevertical acceleration of carbody (the mass center of carbody)shown in Figure 7 -e x-axis represents the positions alongthe longitudinal direction of the crossing panel and number0m in the x-axis represents the theoretical point of the frog

As can be seen from Figure 7(a) the lateral displacementof all profiles reaches a maximum in front of the theoreticalnose of crossing and in the transition zone -e standardprofile reaches the maxima before the theoretical nose thevalue is 9mm Profile II reaches the maxima in the transitionzone and the value is 7mm Overall the lateral displacement

Standard profile Profile I Profile II

Profile III Profile IV

Figure 2 Wheel profiles at different abrasion stages

Shock and Vibration 3

Section ASection B

Section CSection D

Section ESection F

Sect

ion

A

Sect

ion

B

Sect

ion

C

Sect

ion

D

Sect

ion

E

Sect

ion

F

Wing rail

Nose rail

Figure 3 Cross sections of the fixed frog

yw Φw

Z

Y

Figure 4 Determination of wheel-rail contact points

100

80

60

40

20

0

ndash20

Y (m

m)

100

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900

15 12 9 6 3 0 ndash3 ndash6 ndash9ndash12ndash15 15 12 9 6 3 0 ndash3ndash6 ndash9ndash12ndash15

Section D Section E

(a)

100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900

Section D Section E

1512 9 6 3 0 ndash3 ndash6 ndash9 ndash12ndash1515 12 9 6 3 0 ndash3 ndash6ndash9ndash12ndash15

(b)

Figure 5 Continued


100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900

Section D Section E

15 12 9 6 3 0 ndash3 ndash6 ndash9ndash12ndash1515 12 9 6 3 0 ndash3 ndash6 ndash9ndash12ndash15

(c)

100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900Section D Section E

15 12 9 6 3 0 ndash3 ndash6 ndash9ndash12 ndash1515 12 9 6 3 0 ndash3 ndash6 ndash9ndash12 ndash15

(d)

100

80

60

40

20

0

ndash20

Y (m

m)

100

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900

1512 9 6 3 0 ndash3ndash6 ndash9ndash12ndash1515 12 9 6 3 0 ndash3 ndash6 ndash9ndash12 ndash15

Section D Section E

(e)

Figure 5 Distribution of wheel-rail contact pairs (a) Wheel nominal profile (b) Wheel profile I (c) Wheel profile II (d) Wheel profile III(e) Wheel profile IV

Figure 6 -e vehicle-turnout system dynamic model


of the wear wheel is lower than that of the standard wheelCompared with other worn profiles the lateral displacementof profile II before the theoretical nose is the smallest closeto 0mm but the lateral displacement in the transition area islarger -e lateral displacement of the profile IV in thetransition region is the smallest and the value is 4mm andthe lateral displacement before the theoretical nose is 2mmIt could be inferred that the worn profile could effectivelyreduce the lateral displacement of the wheel when it passesthrough the frog

From Figure 7(b) it can be seen that the vertical dis-placement of all profiles reaches the maximum value in thethroat area and the variation amplitude of the verticaldisplacement in the theoretical nose and transition area isrelatively small which is stable near a fixed value -emaximum vertical displacement of the standard profile is8mm In the worn profiles the maximum vertical dis-placement of profile IV is the largest the value is 12mm-emaximum vertical displacement of profile I is the smallestand the value is 9mm It could be concluded that the wornprofile might aggravate the vertical displacement of thewheel through the frog to a certain degree

From Figure 7(c) it can be concluded that the verticalcontact force of each profile after the tip of the theory (throatarea) reaches the maximum and gradually decreased at both

ends -e maximum vertical contact force of the standardprofile is the largest reaching 750 kN A maximum verticalcontact force of profile IV is the smallest with a value of320 kN On the whole the vertical contact force of the wornprofile is less than that of the standard profile

As can be seen from Figure 7(d) the vibration acceler-ation of all profiles entering the frog and leaving the frog isrelatively large In the whole process of passing the frog thevibration acceleration of the worn profile is less than that ofthe standard profile -e maximum vibration acceleration ofthe carbody is 33ms2 for the standard profile and it is 11ms2 for the worn profile reduced by 667-is characteristic isobvious in the throat area and transition area Of all the wornprofiles profile IV performs best and its vibration acceler-ation is basically the smallest in the whole process

It is inferred that wheel profile abrasion has a greatinfluence on the dynamic interaction between vehicle andfixed frog In the crossing panel the dynamic responsesare the local maximum when the wheel transfers from thewing rail to the nose rail which is the possible reason forthe serious wear of the nose rail For the worn wheelprofiles measured in this study wheel profile wear re-lieves the lateral and vertical dynamic responses It couldbe explained by changes of wheel-rail contact pointsbetween the wheel with different profiles and fixed frog

Table 1 -e parameters of the vehicle

Parameters Values Units-e mass of carbody 100000 kg-e rolling moment of inertia of carbody 48000 kgmiddotm2

-e nodding moment of inertia of carbody 440000 kgmiddotm2

-e yawing moment of inertia of carbody 445000 kgmiddotm2

-e mass of bolster 800 kg-e rolling moment of inertia of bolster 240 kgmiddotm2

-e nodding moment of inertia of bolster 20 kgmiddotm2

-e yawing moment of inertia of bolster 240 kgmiddotm2

-e mass of side frame 500 kg-e rolling moment of inertia of side frame 20 kgmiddotm2

-e nodding moment of inertia of side frame 200 kgmiddotm2

-e yawing moment of inertia of side frame 200 kgmiddotm2

-e mass of carrying-saddle 27 kg-e rolling moment of inertia of carrying-saddle 04 kgmiddotm2

-e nodding moment of inertia of carrying-saddle 02 kgmiddotm2

-e yawing moment of inertia of carrying-saddle 04 kgmiddotm2

-e mass of wedge 10 kg-e rolling moment of inertia of wedge 006 kgmiddotm2

-e nodding moment of inertia of wedge 006 kgmiddotm2

-e yawing moment of inertia of wedge 008 kgmiddotm2

-e mass of wheelset 1200 kg-e rolling moment of inertia of wheelset 800 kgmiddotm2

-e nodding moment of inertia of wheelset 110 kgmiddotm2

-e yawing moment of inertia of wheelset 800 kgmiddotm2

-e longitudinal stiffness of the secondary suspension 18 MNm-e lateral stiffness of the secondary suspension 18 MNm-e vertical stiffness of the secondary suspension 261 MNm-e longitudinal stiffness of the primary suspension 14 MNm-e lateral stiffness of the primary suspension 10 MNm-e vertical stiffness of the primary suspension 170 MNm


-e dynamic interaction between the wheel and the fixedfrog is reduced due to the sudden changes of the contactpoints in the vertical direction

5 Analysis of Wheel-Rail Contact Patch andDistribution of Equivalent Stresses

51 Finite Element Model -e fixed frog profiles have beendesigned to be changed along the crossing panel and the plasticcharacteristics of wheel and fixed frog have been considered inthe finite element model So it is applied to determine thecontact patches and calculate the equivalent stresses

-e ABAQUS software is utilized to establish the finiteelement models of the wheel-fixed frog contact in which thewheel profiles at different wear stages are considered -ewheelset stock rail and fixed frog are divided into a finitenumber of elements shown in Figure 8-e rail bottom is fullyconstrained -e lateral displacement and contact force cal-culated in Simpack software are used as inputs of the finiteelement model

-e accuracy of calculation mainly depends on the sizesof elements but it is often a trade-off between accuracy andcalculative efficiency To overcome this problem the

wheelset and rails are meshed into elements with the size of1mm in the potential contact areas However those ele-ments that are far away from the contact area are meshedwith bigger element sizes see Figure 9

In the finite element model a bilinear kinetic intensifymodel is used to represent the elastoplastic characteristics of thewheel-rail materials which conforms to von Mises yield cri-terion and kinetic hardening rule-e vonMises yield criterionis expressed by

σe

12

σ1 minus σ2( 11138572

+ σ2 minus σ3( 11138572

+ σ3 minus σ1( 11138572

1113960 1113961

1113970

ge σs (1)

where σe is the equivalent stress σ1 σ2 and σ3 are theprincipal stresses and σs is the yield stress of the material

When the equivalent stress σe satisfies equation (1) thematerial begins to deform plastically -e kinetic hardeningrule is expressed by

σ Eeε εle εs

σs + Ep ε minus εs( 1113857 εgt εs

⎧⎨

⎩ (2)

where Ee is Youngrsquos modulus Ep is the strain hardeningmodulus and εs is the total strain at yield point Ee Ep and

ndash10

ndash5

0

5

10

15La

tera

l disp

lace

men

t (m

m)

Nominal profileProfile IProfile II

Profile IIIProfile IV

ndash5 0 5 10ndash10Positions (m)

(a)



ndash10

ndash5

0

5

10

15

Ver

tical

disp

lace

men

t (m

m)


(b)



0100200300400500600700800

Ver

tical

cont

act f

orce

(kN

)


(c)



ndash6

ndash4

ndash2

0

2

4

6

Vib

ratio

n ac

cele

ratio

n (m

s2 )


(d)

Figure 7 -e comparison of the dynamic interaction of vehicle and fixed frog (a) Lateral displacement of wheelset (b) Vertical dis-placement of wheelset (c) Vertical contact force (d) Vibration acceleration of carbody


σs of wheel and rail are listed in Table 2 and the equivalentstressndashstrain curve of wheel-rail material is shown inFigure 10

52 Calculation Results -e dynamic responses of the ve-hicle and fixed frog such as normal contact force and lateraldisplacement of wheelset are utilized as inputs for the finiteelement model -e finite element method could simulatethe internal stresses of wheel and fixed frog and the cal-culations of von Mises stresses for the selected profiles atSections D and E are shown in Figure 11

At Section D the wheels with nominal profile profiles Iand II contact with the nose rail of the fixed frog With thewheel profiles wearing the wheel tread wears more seriouslythan the outer side of the wheel so the wheels with profilesIII and IV contact with the wing rail of the fixed frog -ewheels with nominal profile and all worn profiles contactwith nose rail at Section E It means that the wheels havealready transferred onto the nose rail from the wing rail Andthe above kinetic results show that the wheels have an impacton the nose rail at the instantaneous transition from wingrail to nose rail And that makes the nose rail wear seriously

-e maximum von Mises stresses of wheel and railexceed the material yield limit which is located in the regionof 23ndash35mm right under the surface -e material of wheel

and fixed frog in this region forms a plastic deformationWhen the plastic deformation accumulates to limit value theinternal cracks would occur -e wheel profile wear cannotalways decrease the von Mises stress At Section E the wheelprofiles wear worsens the wheel-rail conditions which leadsto increasing the von Mises stress

It can be seen from the above figure that the maximumvon Mises stress decreases with the increase of wear atSection D from 1336MPa of standard profile to 8813MPaof profile IV with a reduction of 34

From the finite element calculation for the wheel withprofile III or IV it is known that the wheels contact with thewing rail at Section D and at Section E the wheels contactwith the nose rail It could be concluded that the wheelstransfer to the nose rail at the range of Section D and SectionE while for the wheel with the nominal profile profile I or IIat Section D and Section E the wheels contact with nose railAnd the wheels contact with the wing rail at Section C Sothe wheels transfer from wing rail to nose rail at the range ofSection C and Section D -e profile wear makes thetransition position backwards which is good for the nose railbecause the top head of nose rail is wider

As shown in Table 3 with the increase of wheel wear thecontact spot area increased from 73mm2 to 152mm2 inSection D -e contact position of the standard profileprofile I and profile II is in the nose rail and the contact

y

z x

Figure 8 -e wheel-rail finite element model

Figure 9 -e two-dimensional finite elements of wheel-rail contact


Table 2 -e values of wheel-rail Youngrsquos modulus kinetic hardening modulus and yield stress

Wheel Fixed frog Stock railYoungrsquos modulus (Ee) (GPa) 206 210 206Strain hardening modulus (Ep) (GPa) 206 21 206Yield stress (σs) (MPa) 540 400 460

WheelCrossing railStock rail

σ (M

Pa)

0

200

400

600

800

1000

1200

0 0005 001 0015 002ε

Figure 10 Equivalent stress-strain curve of wheel-rail materials

+1336e + 03+1225e + 03+1114e + 03+1002e + 03+8910e + 02+7797e + 02+6684e + 02+5572e + 02+4459e + 02+3346e + 02+2234e + 02+1121e + 02+8395e ndash 01


(a)



(b)

Figure 11 Continued


position of the other worn profile is in the wing rail Whenthe position of the contact spot changes from the nose rail tothe wing rail the contact area decreases slightly from110mm2 to 105mm2 -e contact spot area fluctuates upand down in the range of 80mm2 as the wheel wear deepensin Section E-e contact spot size of profile IV at Section E is104mm2 which is 30 more than that of the standard

profile And the location of the contact spot is always on thenose rail

In the transition process there are two-point contactbetween wheel and fixed frog and the contact shapes areshown in Figure 12 -e contact status is long and narrow-e length of the contact status is about 21mm to 28mmand its width is about 2mm to 5mm-e contact area is very



(c)


+2438e + 03+2235e + 03+2032e + 03+1828e + 03+1625e + 03+1422e + 03+1219e + 03+1016e + 03+8127e + 02+6096e + 02+4065e + 02+2034 + 02+2376e ndash 01

(d)



(e)

Figure 11 von Mises stresses of wheel-rail contact (the above for Section D and the below for Section E) (a) Wheel nominal profile(b) Wheel profile I (c) Wheel profile II (d) Wheel profile III (e) Wheel profile IV


small so that the wheel and frog damage is more serious thanthe common rail In addition the centers of the contactstatus on the wing and nose rails are not found in the samelongitudinal position -us a relative slip occurs betweenthe wheel and frog thereby causing both to wear

6 Conclusions

-e influences of wheel profile wear on the static and dynamiccontact performance of the vehicle and fixed frog in heavy haulrailway are simulated in this article Both wheel profiles atdifferent wear stages and the changing cross sections of fixedfrog are as inputs for the simulation According to the simu-lation it could be summarized that

(1) Compared with the standard profile the maximumlateral displacement of the worn profile can be reducedby up to 9mm but the vertical displacement increasesby up to 4mm -e vertical contact force can be re-duced from 750kN to 320kN and the decrease is ashigh as 573 In addition the vibration acceleration isalso reduced-e wheel profile wear strongly affects thedynamic interaction of the vehicle and fixed frog

(2) -e vertical contact force reaches a maximum of750 kN after passing through the theoretical nose ofcrossing at the range of 20mmndash40mm nose railwidth For the wheels with different wear stagesprofiles they transit from the wing rail to the noserail at the width range of 20mm and 40mm when

passing through the fixed frog in the facing move-ere are impacts on the nose rail which make thenose rail wear seriously

(3) -e wheel profile wear affects strongly the distri-bution of the wheel-rail von Mises stress and thecontact patches -e area of the contact spot in-creases with the increase of the profile wear whichmakes the vonMises stress decrease accordingly-evon Mises stress of profile IV decreases by 34compared with the standard profile at 30mm of noserail width-e larger the contact area of the nose railthe larger the loading area and the lighter the wearthe wider the top surface of the nose rail which isgood for the nose rail

-is research could provide fundamental guidance forthe profiles design and optimization of fixed frog and wheeland grinding of the fixed frog

Data Availability

-e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

-e authors declare no conflicts of interest with respect tothe research authorship andor publication of thisarticle

Acknowledgments

-is study was financially supported by National NaturalScience Foundation of China (51775031) and BeijingPostdoctoral Research Foundation

References

[1] H Zhao ldquoDiscussion on technical indicators of turnout onDaqin heavy haul railwayrdquo Railway Engineering vol 4pp 89ndash91 2010

[2] J Yan and M Fu Vehicle Engineering China Railway Pub-lishing House Beijing China 2009

[3] C Li ldquoResearch onmovable frog reconstruction scheme of no18 turnout with 75 kgm rail used in Datong-Qinhuangdaorailwayrdquo Railway Engineering vol 8 pp 117ndash120 2012

Table 3 -e contact spot size and contact position of each type of profile at Section D and Section E

Section D Section EArea(mm2)

Longitudinal length(mm)

Lateral length(mm) Positions Area

(mm2)Longitudinal length

(mm)Lateral length

(mm) Positions

Standardprofile 73 23 3 Nose rail 80 16 7 Nose rail

Profile I 98 21 5 Nose rail 85 16 5 Nose railProfile II 110 20 6 Nose rail 60 17 6 Nose railProfile III 105 22 5 Wing rail 58 21 3 Nose railProfile IV 152 26 8 Wing rail 104 19 6 Nose rail

Figure 12 Contact status on the nose and wing rail


[4] T Zhao Y Luo and Y Xu ldquoResearch on no 18 unmovablefrog with 75 kgm rail used in Datong-Qinhuangdao heavyhaul railwayrdquo Railway Standard Design vol 2 pp 7ndash11 2012

[5] R F Lagos A Alonso J Vinolas and X Perez ldquoRail vehiclepassing through a turnout analysis of different turnout de-signs and wheel profilesrdquo Proceedings of the Institution ofMechanical Engineers Part F Journal of Rail and RapidTransit vol 226 no 6 pp 587ndash602 2012

[6] Y Q Sun C Cole and M McClanachan ldquo-e calculation ofwheel impact force due to the interaction between vehicle anda turnoutrdquo Proceedings of the Institution of Mechanical En-gineers Part F Journal of Rail and Rapid Transit vol 224no 5 pp 391ndash403 2010

[7] Z Ren and S Sun ldquoResearch on the wheelrail contact ge-ometry relationship in the turnout zonerdquo Engineering Me-chanics vol 25 no 11 pp 223ndash230 2008

[8] K Gao and Z Ren ldquoDynamic performance analysis of wagonwith 25 t axle load through turnoutrdquo Journal of BeijingJiaotong University vol 30 no 4 pp 105ndash108 2006

[9] Z Ren Z Liu and X Jin ldquoStudy on the influence of the topsurface lower value of nose rail on the wheelturnout dynamicinteractionrdquo Journal of the China Railway Society vol 31no 2 pp 79ndash83 2009

[10] W Zhai and K Wang ldquo-e operation safety assessment oflocomotive and vehicle passing through the branch of turn-outrdquo Journal of Tongji University (Nature Science) vol 32no 3 pp 382ndash386 2004

[11] X Cai and C Li ldquo-e wheel-rail contact irregularity in high-speed frogrdquo Journal of Southwest Jiaotong University vol 43no 1 pp 86ndash90 2008

[12] J Li J Zhang J Zhang et al ldquo-e elastic-plastic contactanalysis of locomotive wheel and fixed frogrdquo Railway Loco-motive and Motor Car vol 9 pp 23ndash26 2014

[13] M Wiest E Kassa W Daves et al ldquoAssessment of methodsfor calculating contact pressure in wheel-railswitch contactrdquoWear vol 265 no 9-10 pp 1439ndash1445 2008

[14] P Martin D Werner and O Heinz ldquoA wheel passing acrossing nose dynamic analysis under high axle loads usingfinite element modelingrdquo Proceedings of the Institution ofMechanical Engineers Part F Journal of Rail and RapidTransit vol 226 no 6 pp 603ndash611 2008

[15] M Pletz W Daves and H Ossberger ldquoA wheel setcrossingmodel regarding impact sliding and deformationmdashexplicitfinite element approachrdquo Wear vol 294-295 pp 446ndash4562012

[16] J Xu P Wang L Wang et al ldquoEffects of profile wear onwheelndashrail contact conditions and dynamic interaction ofvehicle and turnoutrdquo Advances in Mechanical Engineeringvol 8 no 1 pp 1ndash14 2016

[17] R Chen J Chen P Wang et al ldquoImpact of wheel profileevolution on wheel-rail dynamic interaction and surfaceinitiated rolling contact fatigue in turnoutsrdquo Wear vol 438-439 Article ID 203109 2019


structural irregularity of the fixed frog severe vibration willoccur affecting the safety of train operation and the speed

Wheel-rail contact behavior in the crossing has beenstudied with a number of laboratory experiments and nu-merical procedures Lateral and vertical dynamic force andwheel contact angle with different speed were studied in theturnout aera [5 6] -e characteristics of the wheel-railcontact geometry relationship of the turnout zone are studiedby Ren and Sun [7] -en they investigated the influence ofthe nose rails height on the wheel-rail contact characteristicsby the high-speed vehicleturnout dynamic model [8] Be-sides a vehicleturnout system dynamic model was estab-lished to analyze the dynamics capability while passingthrough the turnout [9] A model on the basis of the vehicle-track coupling dynamic theory was established by Zhai andWang to study on the safety of trains when the locomotivepasses through the branch line of turnout In addition theyinvestigated the influence of running speed [10]

Based on No 42 high-speed turnout a wheelrail contactmodel with different point hiding tip structures and wheelprofiles was established to analyze the characteristics of ir-regularity in the crossing zone [11] Li et al [12] established awheel-crossing finite element contact model to study thecontact trails characteristics and Mises stress Wiest et al [13]assessed four methods based on calculating contact stresscontact patch size and penetration depth in wheel-rail or switchcontact-e fourmodels are as followsHertz and non-Hertzianmethod implemented in the computer program CONTACTand elastic and elastic-plastic finite element contact modelsinvestigated with the commercial code ABAQUS -e findingsshowed that the contact pressure distributions calculated inHertz and CONTACT are consistent with the results acquiredfrom the finite element method as long as there is no plasti-fication of the material And the literature [14] presented adynamic finite elementmodel for the process of a wheel passingthe frog -is model accounts for the dynamic process theelastic deformations of the wheel and the elastic-plastic de-formations of the crossing In order to simulate the situation inwhich the wheel passes through the frog the finite elementmodels have been developed by Pletz et al [15] -e dynamicresponse of the wheel passing through the frog and the variationlaws of the contact stress and contact status were concluded

-e above experts ignore the influence of wheel wear onthe wheel-rail relationship -e wheels wear leads to wheelprofile change and thus strongly affects the dynamic per-formance of vehicles and the static contact performance-e

calculation of dynamic and static contact performancemakes it possible to properly design the profile of the fixedfrog Xu et al [16] studied the contact analysis and dynamicresponse of worn rail in the switch rail area of high-speedtrain turnout Chen et al [17] studied the influence of wheelprofile evolution on the dynamic interaction between thewheel of high-speed railway and the switch rail in theturnout While in heavy haul railway the fixed frog isutilized And the dynamic response is different from themovable frog used in the high-speed railway

In this paper the contact between the wheel whichconcluded the full-life cycle profile and the standard fixedfrog is studied in the simulation software Simpack andABAQUS-e influences of wheel profile wear on the wheelstandard fixed frog contact performance are accounted for inthe simulation Nominal and measured worn wheel profilesare used as boundary conditions of wheel-standard fixedfrog contact -e effects of full-life cycle wheel profile on thewheel-rail static contact status and dynamic interaction ofvehicle and standard fixed frog in heavy haul railway areresearched In practice the frog will also be worn with theincrease of service time-erefore future work will study thecontact between wheel profile and wear frog

2 Wheel and Fixed Frog Profiles

With the increase of trains the profiles of wheel and fixedfrog change with cumulative abrasion A series of work hasbeen conducted to track and test the evolution of wheelprofiles in heavy haul railway as is shown in Figure 2 Wornwheel profiles are measured using the instrument namedCALIPRI a wheel-rail profile measuring instrument Use theCALIPRI to measure the worn profile of the wheelsets in thefield And then import the profile wireframe scanned by theinfrared ray of the CALIPRI into the HYPERMESH -eprofile of the wheel is discretized -e discrete point data isgenerated into prr files and imported into the Simpack tobecome a usable worn profile Nominal profile represents theLM Profiles I II III and IV are all measured worn profileswhose vertical wear loss in the radius of the rolling circle isrespectively 1318mm 2622mm 3861mm and 5759mm-e figure shows that the abrasion on the tread is moresevere compared with that on the flange Moreover with thewear of the wheel its conicity on the tread decreasesgradually Hence the tread flattens out Profile I and profileII are called initial worn profiles and profile III and profile IVare called late worn profiles based on the wear loss

-e nominal geometry of the studied turnout is astandard design CN75-350-112 (curve radius 350m turn-out angle 1 12) According to the change of nose rail widthand the location of frog injury researched in field the keysections of the theoretical nose of crossing (Section A) and10mm (Section B) 20mm (Section C) 30mm (Section D)40mm (Section E) and 50mm (Section F) mm width ofnose rail respectively are analyzed -e variation of railprofiles along the turnout is accounted for by sampling therail cross sections at several key positions as shown inFigure 3 -e spline interpolation method is used to stretch

Switch rail

Nose railWing rail

Check railHarmful space

Switch panel Closure panel Crossing panel

Figure 1 Single turnout





















Section ASection B

Section CSection D

Section ESection F

Sect

ion

A

Sect

ion

B

Sect

ion

C

Sect

ion

D

Sect

ion

E

Sect

ion

F

Wing rail

Nose rail


yw Φw

Z

Y


100

80

60

40

20

0

ndash20

Y (m

m)

100

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900


Section D Section E

(a)

100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900

Section D Section E


(b)

Figure 5 Continued


100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900

Section D Section E


(c)

100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)



(d)

100

80

60

40

20

0

ndash20

Y (m

m)

100

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900


Section D Section E

(e)






































σe

12

σ1 minus σ2( 11138572

+ σ2 minus σ3( 11138572

+ σ3 minus σ1( 11138572

1113960 1113961

1113970

ge σs (1)



σ Eeε εle εs


⎧⎨

⎩ (2)


ndash10

ndash5

0

5

10

15La

tera

l disp

lace

men

t (m

m)




(a)



ndash10

ndash5

0

5

10

15

Ver

tical

disp

lace

men

t (m

m)


(b)



0100200300400500600700800

Ver

tical

cont

act f

orce

(kN

)


(c)



ndash6

ndash4

ndash2

0

2

4

6

Vib

ratio

n ac

cele

ratio

n (m

s2 )


(d)











y

z x







σ (M

Pa)

0

200

400

600

800

1000

1200

0 0005 001 0015 002ε




(a)



(b)

Figure 11 Continued







(c)



(d)



(e)




6 Conclusions







Data Availability




Acknowledgments


References









(mm)Lateral length

(mm) Positions







































Section ASection B

Section CSection D

Section ESection F

Sect

ion

A

Sect

ion

B

Sect

ion

C

Sect

ion

D

Sect

ion

E

Sect

ion

F

Wing rail

Nose rail


yw Φw

Z

Y


100

80

60

40

20

0

ndash20

Y (m

m)

100

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900


Section D Section E

(a)

100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900

Section D Section E


(b)

Figure 5 Continued


100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900

Section D Section E


(c)

100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)



(d)

100

80

60

40

20

0

ndash20

Y (m

m)

100

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900


Section D Section E

(e)






































σe

12

σ1 minus σ2( 11138572

+ σ2 minus σ3( 11138572

+ σ3 minus σ1( 11138572

1113960 1113961

1113970

ge σs (1)



σ Eeε εle εs


⎧⎨

⎩ (2)


ndash10

ndash5

0

5

10

15La

tera

l disp

lace

men

t (m

m)




(a)



ndash10

ndash5

0

5

10

15

Ver

tical

disp

lace

men

t (m

m)


(b)



0100200300400500600700800

Ver

tical

cont

act f

orce

(kN

)


(c)



ndash6

ndash4

ndash2

0

2

4

6

Vib

ratio

n ac

cele

ratio

n (m

s2 )


(d)











y

z x







σ (M

Pa)

0

200

400

600

800

1000

1200

0 0005 001 0015 002ε




(a)



(b)

Figure 11 Continued







(c)



(d)



(e)




6 Conclusions







Data Availability




Acknowledgments


References









(mm)Lateral length

(mm) Positions




















100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900

Section D Section E


(c)

100

120

80

60

40

20

0

ndash20

Y (m

m)

100

120

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)



(d)

100

80

60

40

20

0

ndash20

Y (m

m)

100

80

60

40

20

0

ndash20

Y (m

m)

600 650 700 750X (mm)

800 850 900 600 650 700 750X (mm)

800 850 900


Section D Section E

(e)






































σe

12

σ1 minus σ2( 11138572

+ σ2 minus σ3( 11138572

+ σ3 minus σ1( 11138572

1113960 1113961

1113970

ge σs (1)



σ Eeε εle εs


⎧⎨

⎩ (2)


ndash10

ndash5

0

5

10

15La

tera

l disp

lace

men

t (m

m)




(a)



ndash10

ndash5

0

5

10

15

Ver

tical

disp

lace

men

t (m

m)


(b)



0100200300400500600700800

Ver

tical

cont

act f

orce

(kN

)


(c)



ndash6

ndash4

ndash2

0

2

4

6

Vib

ratio

n ac

cele

ratio

n (m

s2 )


(d)











y

z x







σ (M

Pa)

0

200

400

600

800

1000

1200

0 0005 001 0015 002ε




(a)



(b)

Figure 11 Continued







(c)



(d)



(e)




6 Conclusions







Data Availability




Acknowledgments


References









(mm)Lateral length

(mm) Positions






















































σe

12

σ1 minus σ2( 11138572

+ σ2 minus σ3( 11138572

+ σ3 minus σ1( 11138572

1113960 1113961

1113970

ge σs (1)



σ Eeε εle εs


⎧⎨

⎩ (2)


ndash10

ndash5

0

5

10

15La

tera

l disp

lace

men

t (m

m)




(a)



ndash10

ndash5

0

5

10

15

Ver

tical

disp

lace

men

t (m

m)


(b)



0100200300400500600700800

Ver

tical

cont

act f

orce

(kN

)


(c)



ndash6

ndash4

ndash2

0

2

4

6

Vib

ratio

n ac

cele

ratio

n (m

s2 )


(d)











y

z x







σ (M

Pa)

0

200

400

600

800

1000

1200

0 0005 001 0015 002ε




(a)



(b)

Figure 11 Continued







(c)



(d)



(e)




6 Conclusions







Data Availability




Acknowledgments


References









(mm)Lateral length

(mm) Positions




























y

z x







σ (M

Pa)

0

200

400

600

800

1000

1200

0 0005 001 0015 002ε




(a)



(b)

Figure 11 Continued







(c)



(d)



(e)




6 Conclusions







Data Availability




Acknowledgments


References









(mm)Lateral length

(mm) Positions























σ (M

Pa)

0

200

400

600

800

1000

1200

0 0005 001 0015 002ε




(a)



(b)

Figure 11 Continued







(c)



(d)



(e)




6 Conclusions







Data Availability




Acknowledgments


References









(mm)Lateral length

(mm) Positions

























(c)



(d)



(e)




6 Conclusions







Data Availability




Acknowledgments


References









(mm)Lateral length

(mm) Positions





















6 Conclusions







Data Availability




Acknowledgments


References









(mm)Lateral length

(mm) Positions




















InfluenceofFull-LifeCycleWheelProfileontheContact ... · sides, a vehicle/turnout system dynamic...

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Transcript of InfluenceofFull-LifeCycleWheelProfileontheContact ... · sides, a vehicle/turnout system dynamic...