6th International Conference on Contact Mechanics and Wear of Rail/Wheel Systems(CM2003) in Gothenburg, Sweden June 10–13, 2003

INTEGRATING DYNAMICS AND WEAR MODELLING TOPREDICT RAILWAY WHEEL PROFILE EVOLUTION

R Lewis1, F. Braghin2, A.Ward1, S. Bruni2, R.S. Dwyer-Joyce1, K. Bel Knani3 and P. Bologna3

1The University of Sheffield,Dept. of Mech. Eng.,

Mappin Street, Sheffield, S1 3JD,UK

2Dept. of Mech. Eng.,Politecnico di Milano,

Via La Masa 34,20158, Milano,

ITALY

3Fiat Research Centre,Strada Torino 50,

10043, Orbassano (TO),ITALY

roger.lewis@sheffield.ac.uk, francesco.braghin@mecc.polimi.it

AbstractThe aim of the work described was to predict wheelprofile evolution by integrating multi-body dynamicssimulations of a wheelset with a wear model.

The wear modelling approach is based on a wearindex commonly used in rail wear predictions. Thisassumes wear is proportional to Tγ, where T is tractiveforce and γ is slip at the wheel/rail interface. Twin disctesting of rail and wheel materials was carried out togenerate wear coefficients for use in the model.

The modelling code is interfaced withADAMS/Rail, which produces multi-body dynamicssimulations of a railway wheelset and contact conditionsat the wheel/rail interface. Simplified theory of rollingcontact is used to discretise the contact patchesproduced by ADAMS/Rail and calculate traction andslip within each.

The wear model combines the simplified theory ofrolling contact, ADAMS/Rail output and the wearcoefficients to predict the wear and hence the change ofwheel profile for given track layouts.

INTRODUCTIONNew specifications are being imposed on railway wheelwear and reliability to increase the time between wheelreprofiling operations, improve safety and reduce totalwheelset lifecycle costs. In parallel with theserequirements, railway vehicle missions are changingdue to: the need to operate rolling stock on track withlow radius curves as well as the high radius curves onhigh speed lines; increasing speeds and the decrease oftrack quality due to a reduction in maintenance.

These are leading to an increase in the severity ofthe wheel/rail contact conditions [1] which will increasethe likelihood of wear occurring. Excessive wear canaffect the dynamic behaviour of the railway vehicle andreduce ride comfort; impact upon the potential forderailment and reduce the integrity of the wheelmaterial [2].

In order to deal with these demands new designmethodologies are required that integrate advancednumerical tools for modelling of railway vehicledynamics and suitable models to predict damagesustained by wheels under typical operating conditions.

The aim of the work described was to developsuch a procedure, integrating multi-body dynamicssimulations of a railway wheelset with a wear model topredict wheel profile evolution. This will help inscheduling wheel maintenance and regrinding;optimising railway vehicle suspensions and wheelprofiles and in evaluating new wheel materials.

The main drawback in existing analysis tools, thatincorporate dynamic and wear modelling for predictingthe evolution of wheel profiles [3, 4, 5], is in theapproach to wear modelling used in each. Previouslydeveloped wear models are taken and used with wearcoefficients taken from the literature. No properinvestigations have been conducted to investigate thewheel material wear mechanisms or regimes andvalidate the wear models being used. The aims in thiswork were therefore to assess wear modellingapproaches used for wheel/rail wear prediction andselect the most appropriate for this application and tofully investigate the wear properties of the wheelmaterial and generate suitable data to use in the wearmodel developed.

This work was carried out as part of the EuropeanCommunity funded project HIPERWheel. One of theaspects of this project was to develop an integrated CAEprocedure for assessing wheelset durability taking intoaccount damage mechanisms such as metal fatigue,rolling contact fatigue, wear and fretting.

BACKGROUND

Wheel Motion on a RailThe dynamic behaviour of a rail vehicle running intangent track or curve is strictly related to wearphenomena occurring on wheel profiles. In fact, wheel

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wear occurs as a consequence of the contact conditions(contact forces and slips) induced by the wheelsetservice. Conversely, the modification of wheel surfacesproduced by wear has a large impact on vehicleperformances and running behaviour.

Two main wear effects are commonly present inrailway wheels: a change in the transversal profile,sometimes called regular wear, and the formation ofperiodic wear patterns in circumferential direction,called wheel out-of-roundness or irregular wear.Regular wear, upon which this work focuses, isproduced by slowly varying values of contact forces andslips associated with the longitudinal and lateral motionof the wheelset on the track.

Particularly relevant to the formation of regularwear is the wheel motion during curve negotiation. Thewheelset experiences a lateral motion with respect to therail, together with a yaw rotation which leads to theformation of an angle of attack between the local radialdirection of the curve and wheelset axle. The lateralwheel motion leads to a change in the position of wheel-rail contact patch along the profiles and to a variation ofthe rolling radius; whilst, the presence of a non-zeroangle of attack produces a lateral creepage component.

As a consequence of this rather complex wheel-rail contact regime, two distinct wear regions appear onthe wheel profile: one on the flange and the other thetread. Flange wear typically takes place for each bogieon the outer wheel of the leading axle, which issubjected to a high flange force under large longitudinaland lateral creepages, while tread wear occurs on theinner wheel due to creep forces [6]. Wear rates in thesetwo regions depend on a large variety of parametersincluding vehicle type (dimensions, axle loads, vehiclesuspensions), vehicle mission profile (service speed,geometry of the line) and the wheel and rail materials.

Appropriate models of the wear phenomena andtheir interaction with vehicle dynamics are thereforeneeded in order to optimise wheelset resistance to wearand to minimise total life cycle costs.

Mathematical Modelling of Wheel/RailContactIn order to investigate wear effects at wheel/railinterface, it is necessary to reproduce the variableposition of the contact patch along the profiles, togetherwith the values of longitudinal and lateral creepages andthe corresponding contact force components. Themathematical description of these phenomena is furthercomplicated by the fact that all contact parametersstrongly depend on the geometry of wheel and railprofiles, and that, under some circumstances, multiplecontacts can take place between the same wheel/railpair.

The study of wheel/rail contact can be divided intoa normal problem, involving the computation of the

number, position and size of wheel/rail contact patchestogether with the distribution of normal pressures insidethe contact, and a tangential problem, consisting of thecalculation of the tangential stresses in each contactpatch [7]. Owing to the quasi-identity assumption, thesetwo problems are assumed to be decoupled and solvedseparately.

Available methods for solving the normal problemrange from the analytical solution by Hertz to thenumerical procedure implemented in the CONTACTsoftware [7]. This latter method requires a very highcomputational effort, and therefore is not well suited forrepeated applications as is required in the simulation ofwear formation processes. A reasonable compromise isrepresented by approximate numerical techniques, likethe method of rigid interpenetration [8] or by a multi-elliptic approximation [9]. Several different approachesare available also to solve the tangential problem.Nevertheless, a reasonable compromise betweenaccuracy and numerical efficiency can be achievedusing the FASTSIM procedure [10].

The CONTACT algorithm has been used in thepast with the output of vehicle dynamics simulations topredict wear and good qualitative agreement noted [11].In the work described here, the procedure is improvedby incorporating a faster contact simulation and animproved wear process.

Wheel Wear PhenomenaAs mentioned above, wheel wear is related to conditionsof force and slip in the wheel/rail contact. Two wearregimes for wheel materials have been defined [12],mild (low force, low slip) and severe (high force, highslip). The regimes were described in terms of wearmechanism as well as wear rate.

At the very lowest conditions of contact stress andslip typical of those seen in a tread contact (mildregime), a nearly continuous oxide film was observedon the material surfaces. As contact conditions becamemore arduous (towards those experienced in a flangecontact) in severe wear, the material exhibited partiallyoxidised surfaces together with metal flakes. The oxideparticles were less than 2µm across while the metalflakes were 100-200µm across. These elongated metalflakes resulted from cracks running back from thesurface following the flow lines of the deformedmaterial. The severe wear mode generated wear debrisconsisting only of metal flakes up to 50µm thick.

Wheel Wear Modelling ApproachesMost wear indices developed for predicting wear ofrails/wheels [13, 14, 15, 16, 17] are either linear orquadratic functions of angle of attack, θ, implying thatwear tends to zero as θ tends to zero. It has been shown,however, that these indices were not fully valid as wear

was apparent in tests run with an attack angle of zero[18].

A wear index approach has been proposed forpredicting wear of rails that adopts an energy approachin the analysis of the relationship between wear rate andcontact conditions [19]. It is assumed that wear rate(µg/m rolled/mm2 contact area) is related to work doneat the wheel/rail contact (wear rate = KTγ/Α, where T istractive force and γ is slip at the wheel/rail interface, Kis a wear coefficient and A is the contact area). Variousresearchers have reported wheel/rail wear results usingtwin disc test machines of varying geometries as well asfull scale test results that support this approach [12, 18,20, 21, 22]. This approach, however, has limitations. Itwas found to break down at high slip and contact stressconditions [12].

The most suitable basis for a wear model wasclearly the wear index based on the proportionality ofwear with work done at the wheel/rail contact. It wasapparent, however, that improvements could be made tothis modelling approach, especially with regard to thewear regime at higher slips and contact stresses. Treadand flange wear fall with different wear regimes and itmay therefore be better to use different wear constantsfor each. An improved definition of the wear regimeswas also required.

WEAR TESTINGIn order to characterise the wear of the wheel material,wear tests were carried out using a twin disc testmachine. These were designed to establish mechanisms,identify wear regimes of the wheel material anddetermine constants necessary for the wear indexanalysis to be carried out in the modelling proceduredescribed later.

ApparatusA twin disc test machine was used to carry out thetesting (shown in figure 1). The original development of

this machine and more recent work carried out to add acomputer control system have been describedpreviously [23, 24].

The test discs are hydraulically loaded togetherand driven at controlled rotational speed by independentelectric motors. Shaft encoders monitor the speedscontinuously. A torque transducer is assembled on oneof the drive shafts and a load cell is mounted beneaththe hydraulic jack. The slip ratio required is achieved byadjustment of the rotational speeds. All data is acquiredon a PC which is also used for load and speed control.

SpecimensDiscs to be used during the testing were cut from R8Twheel rims and UIC60 900A rail sections and machinedto a diameter of 47mm with a contact track width of10mm. Wheel specimens were drawn from the wheelrim parallel and as close as possible to the outer surface.

Experimental ProcedureWear tests were carried out using the wheel disc as thedriving disc and rail disc as the braking disc. A nominaldisc rotational speed of 400rpm was used in the tests.An environment chamber enclosed the discs and air-cooling was provided to both. Suction was provided toremove wear debris for analysis. Wear measurementwas determined by mass loss from the discs, measuredbefore and after tests and at intervals during initial teststo determine the number of cycles required to reachsteady state wear. Contact stresses and slip werechanged in order to vary the Tγ/A parameter for thewear index analysis.

ResultsAs shown in figure 2, at low values of Tγ/A, wear rate isproportional to Tγ/A. It can be seen that varying contactpressure to change Tγ/A still gives results that fit on thesame line of proportionality.

Solid DriveShaft

FixedBearing

TorqueTransducer

Test Discs

Pivoted DriveShaft

PivotedBearing

PC

Motor

MotorController

Hydraulic Pistonand Load Cell

ShaftEncoder

ShaftEncoder

Motor

figure1 Schematic diagram of the twin disc test machine

0

10

20

30

40

50

60

70

80

0 5 10 15 20

Tγ/A (N/mm2)

Wea

r R

ate

( µg/

m/m

m2 )

figure 2 R8T wheel steel wear rates at low Tγ/Αvalues

As Tγ/A was increased, however, the wear ratelevelled and then increased again quite rapidlyindicating that as the severity of the contact is increaseddifferent wear regimes are apparent (see figure 3). Inorder to provide wear coefficients for use in the wheelwear modelling procedure the wear rate data was splitinto three regions (see figure 3). A wear coefficient wasdefined for each of these regions.

At low Tγ/Α oxidative wear was seen to occur onboth wheel and rail discs. The disc surfaces turned arusty brown colour. Closer examination of the wearsurface of the wheel disc revealed abrasive score marksand evidence of the oxide layer breaking away from thesurface. Figure 4a shows the subsurface morphology ofthe wheel disc. At the surface the oxide layer is justvisible. There is a very small amount of deformationjust below the wear surface of the disc.

As Tγ/Α was increased, the wear mechanismaltered. The wheel material appeared to be wearing by adelamination process. Closer examination of the wheeldisc surfaces revealed that this was the case (see figure4b). It could be seen that a larger amount of plasticdeformation was occurring below the wheel disc wearsurface and crack formation just below the surface wasvisible which was leading to thin slivers of materialbreaking away from the surface. As Τγ/Α was increasedfurther these cracks were seen to alter direction fromrunning parallel to the wear surface and turning up toturning down into the material causing larger chunks ofmaterial to break away. These observations tie in withthose of previous work [12].

0

500

1000

1500

2000

2500

3000

0 20 40 60 80 100 120

Tγ/A (N/mm2)

Wea

r R

ate

(g/

m/m

m2 )

K1K2

K3

Regime Tγ/A (N/mm2) Wear Rate (µg/m/mm2)K1 Tγ/A < 10.4 5.3Tγ/AK2 10.4 < Tγ/A < 77.2 55K3 77.2 < Tγ/A 61.9Tγ/A

figure 3 Wear regimes and coefficients

figure 4 R8T wheel material disc sub-surfacemorphology: (a) Tγ/A = 0.2 N/mm2; (b)Tγ/A = 16 N/mm2; (c) Tγ/A = 28 N/mm2

MODELLING METHODOLOGYThe modelling methodology for the estimation of wheelprofile evolution wear is made up of three mainelements:

1. a multi-body model of the railway vehicle, used toevaluate as function of time the number andposition of wheel/rail contact points and the

resulting global contact force and creepagecomponents.

2. a contact model to derive the local pressure,traction and creepage distributions within thecontact area using inputs from the multi-bodymodelling.

3. wheel profile evolution calculation based on thewear model developed from twin disc wear testingand using inputs from the local contact analysis.

The complete procedure is schematicallyrepresented in figure 5. Starting from the vehiclecharacteristics and initial wheel and rail profiles, a wearsequence reproducing the vehicle mission profile issimulated using the multi-body vehicle model. For eachtime step of the simulation, the results in terms of globalcontact parameters (position of contacts, resultingcontact forces and creepages) are used to perform alocal contact analysis which provides as output thedistribution of frictional work inside the contact patch.Finally, the modification to wheel profiles produced bythe wear sequence is computed using the wear modelbased on the experimental results obtained from twindisc wear tests. By subtracting this modification to theinitial wheel profile, the worn wheel profile isdetermined. This wear loop can be repeated severaltimes to predict wear progress on wheel surface.

MULTI-BODY VEHICLE MODELThe railway vehicle model used to evaluate wheel/railcontact forces as function of wheelset service wasdeveloped in the ADAMS/Rail environment. The modelincludes a mathematical description of the full vehiclewhere car body, bolsters, bogie frames and wheelsetsare treated as rigid bodies, while primary and secondarysuspensions are represented by means of linear and nonlinear elastic and damping elements (figures 6 and 7).

Vehicle Data

VehicleMission Profile

Rail Profile

Wheel Profile

MULTI-BODYMODEL OFRAILWAYVEHICLE

Contact PatchGeometry

Position ofContacts

Global ContactForces

Global Slip

LOCALCONTACTANALYSIS

Distributionof force andslip in thecontact

WHEELPROFILE

EVOLUTIONCALCULATION

Wear Coefficientsfrom Twin Disc

Testing

figure 5 Modelling methodology

(a)

(b)

(c)

figure 6 Railway vehicle model

figure 7 Bogie model

Vehicle parameters were defined with reference toan ETR470 Pendolino railway vehicle. This kind ofvehicle is particularly interesting for wheel wearanalysis because it can be operated at high levels of cantdeficiency, which leads to high values of lateral contactforces and creepages and therefore to accelerated wheelwear [6]. More details about the vehicle model arereported in [1].

The dynamic analysis method is used withinADAMS/Rail to calculate, as a function of time, allquantities related to the dynamic behaviour of thevehicle and the wheel/rail contact. In order to integratethe wheel wear calculation and dynamic analysis resultsthese have been enhanced to include quantities such ascontact patch dimensions and actual rolling radius,necessary for wear evaluation.

LOCAL CONTACT ANALYSISADAMS/Rail provides information about the load andtractions applied to the whole wheel/rail contact patchand its location. In this model it is assumed that thecontact between the wheel and rail can be approximatedby an elliptical contact patch. This allows the use of afaster solution method to determine the traction and slipdistribution within the contact.

ADAMS/Rail provides the total normal force, thetraction applied and the semi-axes a and b for each

elliptical contact patch and it is from these values thatlocal contact analysis is performed. Each ellipticalcontact patch is discretised into strips. Each strip is thendivided into equal sized cells. The contact analysiscalculates traction, T, pressure, p, and slip, γ, for eachcell (see figure 8) from the leading edge of the contact,sequentially to the rear. The forces determined for eachcell are compared to slip/adhesion criteria enabling slipand adhesion regions to be identified and the slipmagnitude and direction to be determined. Thisapproach is similar to the method employed in theFASTSIM algorithm [10].

LateralCreepage

LongitudinalCreepage

SpinCreepage

(a)

Cell

Ty, γy

Tx, γx

x (rolling direction)

y

(b)

figure 8 Output from: (a) ADAMS/Rail and (b) localcontact analysis

WHEEL PROFILE EVOLUTIONTo determine the evolution of the wheel profile as itwears, the wheel profile was discretised intocircumferential strips. This enabled the elliptical contactpatches to be located on the wheel circumference. Thediscretisation of the contact patches could then be madeto coincide exactly with the strips of the wheel (see

figure 9). By aligning the discretisation strips in thisway, wear calculated for each strip could be summed tocalculate the wear depth for that region of the wheelprofile.

The positioning of the wheel strips was achievedby setting a co-ordinate system for the wheel anddeciding on an interval width for discretisation. Thestrip width can be reduced to improve resolution orincreased to reduce computing time. For subsequentpressure, traction and slip calculations the contact isnormalised giving the relationship between the wheeland ellipse co-ordinate systems as:

b

Cyy

pwwe

−= (1)

where ye is the y value in the ellipse co-ordinate system,yw is the y value in the wheel co-ordinate system, Cpw isthe contact point on the wheel and b is the ellipse semi-axis.

Cpw

xw

yw

RollingDirection

Contact

2a

2b

DiscretisedWheel

ye

xe

figure 9 Discretised wheel and elliptical contact co-ordinate systems

A value for Tγ/A was calculated for each cell inthe local contact analysis and compared to the wearregimes identified from wear test data (as shown infigure 3). The corresponding wear coefficient, K, foreach wear regime was used to calculate the wearvolume per cell, WDcell. The depth of wear per cell isthen given by:

ργ tV

KA

TWDcell

∆= (2)

where V is the rolling velocity, ρ is the density of thewheel steel and ∆t is the duration of the contact timestep.

Each cell in the contact ellipse has an associatedwear depth. The wear on each strip (in the rollingdirection) is summed and that depth removed from the

corresponding circumferential strip on the wheel. Thecontact time interval, ∆t, in the output data fromADAMS/Rail is not necessarily equal to one revolutionof the wheel. It is generally observed that wear occursuniformly over a wheel circumference. Therefore it isreasonable to proportion the wear caused by a givenpatch location over the time, ∆t, equally over the wholecircumference of the wheel according to the ratioV∆t/2πR, where R is the wheel radius. This is carriedout for each strip in the contact patch to determine thewear caused by that contact over the time, ∆t. Eachcontact patch obtained from the ADAMS/Railsimulation is treated in the same way to obtain the wornwheel profile. This procedure is shown schematically infigure 10.

Cpw

0 - t

2t - 3t

t - 2t3t - 4t

4t -5t

AccumulatedWear Depth

WheelPosition

figure 10 Summation of the wear per strip to givetotal wear depth

SAMPLE RUNSThe wear prediction algorithm has been introduced asbuilt-in tool in ADAMS/Rail. Runs have been carriedout for an ETR470 Pendolino vehicle running on sampleright hand curves of varying radius as detailed in table1. The wear predictions for each length of track areshown in Figures 11 to 13. Wear is shown forindividual contact patches. Within ADAMS/Rail theseare totalled and then used to update the wheel profile.

Curve Radius(m)

Vehicle Speed(km/h)

Gauge(m)

Cant(m)

370 120 1.438 0.15600 160 1.438 0.15960 160 1.438 0.15

table 1 Track parameters for sample runs carriedout using ADAMS/Rail

As expected the greatest wear occurs on theoutside (left) wheel of the leading axle as this is wherethe contact conditions are at their most severe. As theradius of curvature increases the magnitude of weardecreases and the position where the wear is occurringalters. For example, the wear on the leading outside(left) wheel moves from the flange to the tread.

Simple validation has been carried out for thewear algorithm [24]. This involved running a sample ofADAMS/Rail data consisting of a vehicle running on alength of track made up of a straight section, curve andthen straight again. After 33000 wheel revolutions,where the vehicle has been repeatedly running over theabove sample of track, the wear depth for the tread onthe inside wheel on the leading axle was 3µm. It hasbeen observed that for a wheel rolling along a straighttrack for 33000 cycles, approximately 1µm of wearoccurs [25]. Whilst this data is for a different vehicleand track configuration, the amount of wear is of asimilar order. Especially considering that for theADAMS/Rail result the contact patch position does notvary over a large region. The result of this is toconcentrate the wear to a small region of the wheel.

DISCUSSIONWhile the integrated multi-body dynamics and wearprediction procedure outlined provides a powerful toolfor railway wheel wear assessment, further work isrequired to improve a number of areas.

As yet only a simple validation has been carriedout. A full validation procedure is being undertaken aspart of the HIPERWheel project. Demonstrators arecurrently being manufactured for this purpose and full-scale tests will be carried out.

The contact patch is assumed to be ellipticalwithin ADAMS/Rail to facilitate quicker solution timesby using FASTSIM for the local contact analysis.Clearly real wheel/rail contacts will not be elliptical inshape. Improvements could be made by using non-elliptical contacts from ADAMS/Rail combined withlocal contact analysis using CONTACT to provide amore realistic representation of the contact. Theadvantages, however, have to weighed up against thesubstantial increase in computing time that will result.

At present wheel profile up-dates are carried outwithin ADAMS/Rail after a block of wheel cycles,rather than after each cycle, to speed up calculations.Evolution of the wheel profile has a large impact onvehicle dynamics so continual updating may give moreaccurate results. Although this again would have to beweighed up against increase in computing time.

CONCLUSIONSA model has been developed to predict the wear of

railway wheels. This assumes wear is related to Tγ/A,where T is tractive force, γ is slip at the wheel/railinterface and A is contact area. Twin disc testing of railand wheel materials was carried out to generate wearcoefficients for use in the model.

Left Wheel – Axle 1 Right Wheel – Axle 1

Left Wheel – Axle 2 Right Wheel – Axle 2

figure 11 Sample ADAMS/Rail output for a 370m radius curve

CP1

CP2

CP1

CP2

CP1

CP1

FlangeFlange Tread

Tread

Left Wheel – Axle 1 Right Wheel – Axle 1

Left Wheel – Axle 2 Right Wheel – Axle 2

figure 12 Sample ADAMS/Rail output for a 600m radius curve

Left Wheel – Axle 1 Right Wheel – Axle 1

Left Wheel – Axle 2 Right Wheel – Axle 2

figure 13 Sample ADAMS/Rail output for a 960m radius curve

The model has been incorporated intoADAMS/Rail, which produces multi-body dynamicssimulation of a railway wheelset. The methodology forpredicting the evolution of a railway wheel profile ismade up of three stages: ADAMS/Rail outputs contactconditions at the wheel/rail interface; simplified theoryof rolling contact is then used to discretise the contactpatches and calculate traction and slip within each;finally the wear coefficients are used with the tractions

and slips to predict the wear and hence the change ofwheel profile.

This simulation routine will be used as part of aCAE package for assessing wheelset durability for thedesign of new wheelsets.

The model has been applied to multi-bodysimulation of a passage around sample track lengths.For a simple validation case the worn profile isquantitatively similar to published data.

CP1

CP2

CP1

CP2

CP1

CP2

CP1

Flange Tread Flange Tread

CP1

CP2

CP1

CP2

CP1

CP2

CP1

Flange Tread Flange Tread

AcknowledgmentsThe work reported in this paper was carried out as partof the European Community funded projectHIPERWheel (contract number: G3RD-CT2000-00244).

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