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Wear 261 (2006) 1253–1264

A mathematical model to predict railway wheelprofile evolution due to wear

F. Braghin a,∗, R. Lewis b, R.S. Dwyer-Joyce b, S. Bruni a

a Politecnico di Milano, Mechanical Engineering Department, Italyb University of Sheffield, Department of Mechanical Engineering, UK

Received 20 April 2005; received in revised form 28 February 2006; accepted 10 March 2006Available online 18 April 2006

bstract

Wheel and rail wear is a fundamental problem in the railway field: the change of profile shape deeply affects the dynamic characteristics ofailway vehicles such as stability or passenger comfort and, in the worst cases, can cause derailment. It is therefore of great economic relevance toevelop a software able to predict the wheel profile evolution due to the wear process since it could be used to effectively evaluate maintenancentervals, to optimise wheel and rail profiles with respect to wear and to optimise the railway vehicle’s suspensions with new and worn wheelrofiles.

A wheel wear prediction model is a rather complex mathematical tool since it couples several tasks: simulation of vehicle dynamics, localheel–rail contact model, local wear model, each one bearing its own uncertainties. Moreover, each single task may be solved by different

pproaches that may be more or less accurate and, correspondingly, may require a higher or lower computational effort. This paper presents aast and reliable wear prediction model that has been validated through comparison with full-scale experimental tests carried out on a single

ounted wheelset under laboratory conditions. As described later in this paper, the wear prediction model can also be used to determine the

est re-profiling interval (to minimise total life cycle costs) and to determine those vehicle design parameters that determine less wheel (and rail)ear.2006 Elsevier B.V. All rights reserved.

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eywords: Railway wheel wear; Numerical model; Wear coefficients; Twin dis

. Introduction

The life of railway wheels is usually limited by wear. Theheel surface is subjected to high normal and tangential con-

act stress. Contact forces change magnitude and orientations the wheel travels over the rail curves, crossings, and localurface perturbations. This constantly changing contact patchoves over the wheel tread and to a certain extent the flange.he contact is nominally rolling but a small amount of local slid-

ng takes place at the interface. The amount of sliding dependsn the contact patch geometry, normal force, lateral force, and

riction coefficient.

The removal of material from the surface by wear is a functionf the sliding and contact stresses. These quantities depend on

∗ Corresponding author. Tel.: +39 02 2399 8306; fax: +39 02 2399 8492.E-mail address: francesco.braghin@polimi.it (F. Braghin).

varAted

043-1648/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.wear.2006.03.025

ing

he railway vehicle dynamics that is affected by the change ofheel profile shape: both stability and passenger comfort dependn wheel and rail wear.

There are several advantages to be gained by the availabilityf a reliable predictive model of wheel wear. Primarily, it wouldllow operators to effectively define maintenance schedules forheel re-profiling. But it would also facilitate the design of vehi-

les and wheelsets that cause reduced wear to both wheel andail surfaces.

The requirements for modelling wheel profile evolution dueo wear are threefold. First, it is necessary to determine theariation of wheel contact forces as the wheelset passes overpre-defined rail track route. Secondly, these forces must be

elated to the contact patch position and local traction and slip.

nd finally, the local contact patch conditions must be related

o the material removal by wear. The calculation process is nec-ssarily iterative, because wheel profile changes will alter theynamic behaviour of the wheelset and therefore the contact

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254 F. Braghin et al. / We

orces. Each of these tasks can be carried out using a differentpproach with various degrees of accuracy and computationalffort. As yet, there is no general consensus to the best approach.

This paper covers all three aspects of the modelling proce-ure; a multi-body simulation package is used to predict contactorces, an advanced contact model is used to deduce local contactonditions, and experimental data is used to relate these condi-ions to wear rates. This procedure has been used to simulatehe performance of a full-scale axle roller test rig. The predictedear rates are then compared with measurements from the testedheels.

. Background

One of the first attempts to simulate wear of railway wheelsas made by Pearce and Sherratt [1]. Their model is very sim-le in order to achieve a reasonable simulation time: after thealculation of the global contact forces and creepages actingn the contact patch the amount of material removed is calcu-ated through a wear index (later called the “Derby wear index”).he considered track is made of a straight line plus an S curve.maximum kilometres updating strategy is used. The optimal

oute length for the updating is found to be equal to 1100 km.Zobory [2] used Hertz theory to solve the wheel–rail normal

ontact problem and FASTSIM to solve the tangential contactroblem. The multi-body vehicle model used is ELDACW. Dif-erent wear modelling approaches are discussed, mainly basedn the proportionality of wear with the energy dissipated at theontact. Due to the very different wear regimes on wheel treadnd wheel flange, Zobory introduced two proportionality con-tants, one for the “mild” regime on the tread and one for thesevere” regime on the flange. The transition between the twoegimes depends on wheel and rail material properties. Simu-ation results are compared with various on-line measurementselated to a vehicle running on the Gotthard line for a maxi-um mileage of 27,000 km. Wheel profiles are updated every

000 km. To be able to compare experimental data and numeri-al results, a smoothing procedure (based on a smoothing spline)as applied to the updated wheel profile.Jendel and Berg [3] developed a similar model using the

ulti-body code Gensys for the dynamic railway vehicle simu-ations. Again, the local contact analysis was solved by applyingertz theory and FASTSIM. The contact model used within theulti-body simulation was able to find at most two contact points

t the same time on a given wheel–rail pair. For the wear predic-ion, Archards wear model was applied locally. The wheel profileas updated every time a maximum wear depth of 0.1 mm was

eached or a maximum distance of 1500 km was run. A cubicpline was applied both on wear distribution and the updatedheel profile for smoothing purposes. The simulation resultsere compared with measurements of serviced wheels on the

ommuter railway network in Stockholm.Braghin et al. [4] developed a wheel wear prediction model

ased on a multi-body code for the railway dynamic simula-ions, on CONTACT93 algorithm by Kalker [5] to solve bothhe non-Hertzian normal contact problem as well as the tangen-ial problem and on a local wear model that assumes a direct

3

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1 (2006) 1253–1264

roportionality between material removed and work done athe wheel–rail interface (the proportionality constant was deter-

ined from full-scale experimental tests). Since simulation timeas excessive, wheel profiles were updated only twice over aileage of 10,500 km. The use of the contact model proposed

y Kik and Piotrokswi [6] was also investigated, showing thathis algorithm can be used as a valid alternative to CONTACT93o speed up simulations.

A number of different techniques have been used for study-ng wear rates of railway wheel steels to generate data for usen wear modelling procedures. Field measurements have beensed in the past to study the causes of wear as in Dearden [7].

large amount of data has also been gathered from simulatedeld experiments carried out on specially built test tracks [8].aboratory methods used range from full-scale laboratory exper-

ments [9] and scaled-down tests [10] to bench tests using a twinisc set-up [11–15]. The twin disc approach has been used morehan most because it offers greater control over experimentalariables as well as the ability to test a wide range of materialst lower cost.

The Derby wear index used by Pearce and Sherratt [1] adoptsn energy approach in the analysis of the relationship betweenear rate and contact conditions. It is assumed that wear rate

�g/m rolled/mm2 contact area) is related to work done at theheel–rail contact (wear rate = KTγ/A, where T is tractive force

ndγ slip at the wheel–rail interface, K a wear coefficient and A ishe contact area). Various researchers have reported wheel–railear results using twin disc test machines of varying geome-

ries as well as full-scale test results that support this approach12,10,13,9,16]. While it has been found to break down at highlip and contact stress conditions [12], it still provides the mostuitable basis for a wear model and has a number of advan-ages over the other models mentioned above. It was apparent,owever, that improvements could be made to this modellingpproach, especially with regard to the wear regime at higherlips and contact stresses. Tread and flange wear fall with differ-nt wear regimes and it may therefore be better to use differentear constants for each. An improved definition of the wear

egimes was also required.In this work it was decided to adapt the Derby wear index

pproach to take account of the point made above and to generatehe wear coefficient using a series of twin disc tests varying Tnd γ , as will be explained in the next section.

. Twin disc wear tests

In order to characterise the wear of the wheel material, wearests were carried out using a twin disc test machine. These wereesigned to establish the wear mechanisms, identify the wearegimes of the wheel material and determine the wear constantsecessary for the wear index analysis to be carried out in theear modelling procedure described later.

.1. Apparatus

The twin disc test machine was used to carry out the testingshown in Fig. 1). The original development of this machine, and

F. Braghin et al. / Wear 261 (2006) 1253–1264 1255

of the twin disc test machine.

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vrslip. Table 1 shows the test conditions and corresponding valuesof Tγ/A. Typical wheel–rail Tγ/A values occur up to 10 N/mm2

for tread contacts and greater than 20 N/mm2 for flange contacts.

Table 1Twin disc test conditions and values of the wear index Tγ/A

Contact pressure (N/m2) Slip (%) Tγ/A (N/mm2)

1500 0.2 0.211500 0.3 0.641500 0.5 1.471500 0.7 2.471200 1.0 3.581500 1.0 4.121800 1.0 4.811500 1.5 7.071500 2.0 10.371500 3.0 16.611500 5.0 28.27

Fig. 1. Schematic diagram

ore recent work carried out to add a feedback control system,ave been described previously [17,18].

The test discs are hydraulically loaded together and driven atontrolled rotational speed by independent electric motors. Shaftncoders monitor the speeds continuously. A torque transducers assembled on one of the drive shafts and a load cell is mountedeneath the hydraulic jack. The slip ratio required is achievedy adjustment of the rotational speeds. All data is acquired on aC which is also used for load and speed control. Repeatability

n wear and fatigue testing on the test rig has been shown to beery good and wear results are consistently within ±0.1 �g [18].

.2. Specimens

Discs to be used during the testing were cut from R8T wheelims and UIC60 900A rail sections and machined to a diameterf 47 mm with a contact track width of 10 mm. Wheel specimensere drawn from the wheel rim parallel and as close as possible

o the outer surface.

.3. Experimental procedure

Wear tests were carried out using the wheel disc as the drivingisc and rail disc as the braking disc, as shown in Fig. 2. All testsere done in dry conditions without lubrication (resulting in a

riction coefficient of 0.45–0.50).A nominal disc rotational speed of 400 rpm was used in the

ests. An environment chamber enclosed the discs and air coolingas provided to both. Suction was provided to remove wearebris for analysis. Wear measurement was determined by massoss of the discs, measured before and after tests and at intervalsuring initial tests to determine the number of cycles requiredo reach steady state wear. Weighing scales with an accuracy of

0.00001 g were used for the measurements. Contact stressesnd slip were changed in order to vary the Tγ/A parameter forhe wear index analysis (see Section 4.2), T being the contactorce in the contact plane, A being the contact area and γ beinghe relative slip defined as

= sv

= 2v1 − v2

v1 + v2(1)

here v1 and v2 are the tangential velocities of the two discpecimen, v the reference speed equal to the mean value ofhe tangential velocities of the two disc specimen and s is theimposed) slip equal to the difference between the tangential

1111

Fig. 2. Schematic diagram of the disc environment chamber.

elocities of the two disc specimens. Tests were performed at aange of Tγ/A values achieved by varying both the load and the

500 7.5 40.64500 10.0 53.01500 15.0 79.52500 20.0 117.81

1256 F. Braghin et al. / Wear 261 (2006) 1253–1264

Tγ/A values and (b) over the full range of Tγ/A values.

At

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Fig. 3. R8T wheel material wear rates at: (a) low

steady state wear rate is achieved after 20,000 cycles. Eachest lasted 30,000 cycles.

Tests were carried out under dry conditions so that resultsf the modelling to be carried out could be compared realisti-ally with those from the full-scale tests, which were also runry. Clearly in field conditions environmental conditions such asain and varying humidity and friction modifiers applied at someurves will mean that the wheel–rail contact will be partiallyubricated at times. However, determining wear coefficients forhese conditions and then incorporating this into a wear mod-lling procedure would be extremely complex, but would be theext step in this type of work.

.4. Wear test results

Fig. 3 shows the wear rate against the wear index Tγ/A. Atow values of Tγ/A, wear rate is proportional to Tγ/A. It cane seen that varying contact pressure to change Tγ/A still givesesults that fit on the same line of proportionality.

As Tγ/A was increased, however, the wear rate levelled andhen increased again quite rapidly indicating that as the severityf the contact is increased different wear regimes are apparentsee Fig. 3).

At low Tγ/A oxidative wear was seen to occur on both wheelnd rail discs. The disc surfaces turned a rusty brown colour.

similar effect has been observed on wheel treads in full-scale

esting, as observed by McEwen and Harvey [9] and after tests onfull-scale roller-rig, as shown in Fig. 4. Closer examination of

he wear surface of the wheel disc revealed abrasive score marksnd evidence of the oxide layer breaking away from the surface

pwmt

Fig. 5. R8T wheel material di

Fig. 4. Wheel rolling surface on the full-scale roller rig after 2000 km.

see Fig. 5a). Fig. 5b also shows the subsurface morphologyf the wheel disc. At the surface the oxide layer is just visible.here is a very small amount of deformation just below the wearurface of the disc.

As Tγ/A was increased, the wear mechanism altered. Theheel material appeared to wearing by a delamination process.loser examination of the wheel disc surfaces revealed that thisas the case (see Fig. 6a). Observation of the subsurface mor-

hologies revealed that a larger amount of plastic deformationas occurring below the wheel disc wear surface and crack for-ation just below the surface was visible which was leading

o thin slivers of material breaking away from the surface (see

sc surface at low Tγ/A.

F. Braghin et al. / Wear 261 (2006) 1253–1264 1257

Fig. 6. R8T wheel material disc surface at higher Tγ/A.

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Table 2Wear regimes and coefficients for R8T wheel and UIC60 900A rail materials

Regime Tγ/A (N/mm2) Wear rate (�g/m/mm2)

KKK

ttwtWrt

4

mu

1234

Starting from the vehicle characteristics and initial wheel and

Fig. 7. Wear rate for different values of the wear index Tγ/A.

ig. 6b). As Tγ/A was increased further these cracks were seen tolter direction from running parallel to the wear surface and turn-ng up to turning down into the material causing larger chunksf material to break away. The wear features and mechanismsre discussed in greater detail in Lewis and Dwyer-Joyce [15].

With wear testing such as the twin disc methodology usedere, there is always an issue of scaling the results to the full-cale application. The Tγ/A approach used here provided theest way to accomplish this. Comparisons of wheel and railaterial wear rates determined during small scale testing have

een compared with those from full-scale tests for given valuesf Tγ/A and have been shown to compare well [9,19,15].

In order to provide wear coefficients for use in the wheel

ear modelling procedure the wear rate data was split into three

egions (see Fig. 7). A wear coefficient was defined for each ofhese regions (see Table 2).

rrd

Fig. 8. Scheme of the wheel wear

1 Tγ/A < 10.4 5.3Tγ/A2 10.4 < Tγ/A < 77.2 55.03 77.2 < Tγ/A 61.9Tγ/A

Clearly, with the lack of data generated in the third regimehere is a possibility of less accurate wear predictions for con-acts at these conditions. It would be anticipated, however, thatheel–rail contact is in K1 and K2 regions most if not all of

he time and only reaches K3 region in the most severe curves.ork carried out to compare wear regimes with predicted tread-

ail head and flange-gauge corner contacts has shown this to behe case [19].

. Wheel profile wear prediction model

A schematic representation of the wheel wear predictionodel ProfCon (Profile Control) is shown in Fig. 8, and is made

p of four main tasks:

. multi-body simulation of railway vehicle dynamics;

. local analysis of wheel–rail contact;

. wear calculation;

. smoothing and updating of the wheel profile.

ail profiles, a sequence of service conditions (e.g. tangent trackunning at different speeds, curve negotiation at specified canteficiencies, etc.) called the vehicle “mission track” is simulated

prediction model ProfCon.

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258 F. Braghin et al. / We

sing a multi-body vehicle model (task 1). At each integrationtep of the multi-body simulation, global contact parametersposition and dimensions of the various active contacts, resultingontact forces and creepages) are downloaded and used to per-orm the local contact analysis which provides as an output theistribution of slip and tractions over the contact patch (task 2).

Then, the wear model described in Section 3.4 is used to cal-ulate the distribution of removed material in each contact patchnd the wear caused by a single mission track is determinedtask 3). Since the variation of wheel profiles produced by oneingle mission track is so small that it produces negligible vari-tions on the results of the multi-body dynamic simulations andf the local contact analysis, in order to speed up the wheel pro-le wear prediction, the amount of wear is multiplied by n. The

nteger n is chosen in order to obtain a total wear amount belowprescribed threshold. This threshold has to be small enough inrder to produce small variations on the results of the dynamicimulation and of the local contact analysis. Then, wheel pro-les are updated and eventually smoothed and the correspondingistance run, equal to n times the length of the mission track,s added to the total vehicle mileage (task 4). The worn pro-les obtained by this procedure are fed back into the multi-bodyodel of the railway vehicle.The described procedure is repeated several times until the

hole wear life of the profiles (i.e. the mileage after which re-rofiling is necessary) is reached. At the end of each iteration,he worn wheel profiles are stored together with wear controlarameters Qr, Sh and Sd used for maintenance purposes (seeection 5.2). Another output of the model is the amount of weart each iteration associated with the three wear regions identifiedhrough twin disc tests (mild, intermediate and severe wear) asescribed in Section 3.4.

Besides the modelling problems associated with the aboveescribed tasks, the choice of the mission track is critical withespect to the comparison between numerical results and exper-mental wear data. In principle, the set of running conditionso be simulated should include all the different conditions theheelset will encounter during its lifetime. At the same time

hese running conditions should be kept as small as possible inrder to reduce the computational effort.

Also the criterion adopted for wheel profile updating is criti-al: increasing n leads to a smaller computational effort but theccuracy of the results will be poorer. If n is too big, the wheelrofile wear prediction algorithm may also diverge.

.1. Multi-body model of the railway vehicle

Vehicle dynamic simulations of the specified mission trackre performed using a mathematical model of train–track inter-ction previously developed at the Mechanical Engineeringepartment of Politecnico di Milano [20,21]. Carbodies andogies are schematised through rigid bodies while the wheelsetsre represented as flexible bodies by means of the modal super-

osition approach. Primary and secondary suspensions are rep-esented through linear and non-linear viscoelastic elements,hile track deformability may be accounted for either by meansf a detailed finite element model or by means of a simpli-

[mas

1 (2006) 1253–1264

ed lumped parameter scheme. The equations of motion of theehicle are linearised (only with respect to kinematic non-linearffects) assuming the motion of the vehicle to be a small per-urbation around that of a moving reference travelling along therack centreline with constant speed and having longitudinal axisangent to the track centreline.

The inputs of the multi-body code are the vehicle parame-ers and speed, the wheel and rail profiles, the track flexibility,he ideal geometry of the line (in particular, for curved tracks,he curve radius, the cant and the length of transition curves)nd wheel and rail irregularities. Wheel and rail profiles areescribed by discrete points making it possible to update therofile by the procedure described above.

The procedure adopted to compute wheel–rail contact forcesakes into account that contact between a single wheel and rail

ay occur simultaneously at more than one location (multipleontact condition). Due to the fact that the two contacting bodiesave the same elastic properties (Young’s modulus and Poisson’satio) the problem of finding the normal contact force componentnormal problem) can be considered de-coupled from that ofetermining the tangential contact force component (tangentialroblem). Therefore, these two problems are solved separatelynd sequentially.

In order to solve the normal contact problem, a multi-Hertzianpproach is applied. This approach allows to approximate theenerally non-Hertzian contact area through multiple ellipses.he number of considered ellipses directly influences the accu-

acy of the methodology: by increasing this number, the approx-mate solution converges to the exact one. Thus, a best compro-

ise between accuracy and computational cost can be found.he tangential contact problem, a function of the normal forcend of the creepage components, is then solved through theeuristic formulae by Shen at al. [22]. More details on theheel–rail contact model used in the multi-body simulations

an be found in Braghin et al. [23]. It should be pointed outhat the Hertzian approach is used to solve the normal contactroblem both inside the multi-body code and in the local contactnalysis. The formulae used to solve the tangential contact prob-em, instead, are very fast and reliable, but do not provide theistribution of stresses and slippages inside the contact patch.hus, the local contact analysis is necessary.

.2. Local contact analysis

The local contact analysis is carried out to compute slip-age and traction distributions inside the contact patch oncehe “global” contact quantities, i.e. the contact area dimensionssemi-axes of the elliptical patch), the normal contact force, theongitudinal and lateral creepages, the friction coefficient and thepeed of the train, are given. To this end, different algorithmsre available, like the approximate solution for elliptic contactatches called FASTSIM by Kalker [5,24], the approximateolution for non-Hertzian contact patches by Kik and Piotrokswi

6] or the “exact” solution (within the elastic half-space approxi-ation for the contacting bodies) implemented in CONTACT93

lgorithm by Kalker [5]. In the present work a simplified ver-ion of FASTSIM algorithm neglecting the effect of spin was

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F. Braghin et al. / We

pplied to each Hertzian ellipse forming the multi-Hertzian con-act patch. The choice was driven by the fact that, among allther possible choices, this method requires the smallest com-utational effort but, despite its simplicity, provides results ofcceptable accuracy when compared to the “reference” methodONTACT93. On the other hand, the direct use of CONTACT93lgorithm for performing the local contact analysis has beenroven to be too slow in a previous work [4]. In any event,ONTACT93 algorithm has been used as a “reference” model

o check, for some particular cases, the approximations intro-uced by FASTSIM.

FASTSIM algorithm is based on the hypothesis that the localangential surface deformations u are linearly related to the tan-ential surface tractions p by a constant coefficient L calledexibility:

(x, y) = Lp(x, y) (2)

being the longitudinal direction and y being the transversalirection in the contact plane. For more details on the propor-ionality constant L see Kalker [24].

The elliptical contact patch is discretised using a rectangularrid having cell dimensions �x and �y. It should be noted that,hile �y is constant over the whole elliptical contact path, �x

s a function of the width of the contact ellipse in longitudinalirection (a strip). This non-uniformity in longitudinal directions due to the fact that the width of the contact ellipse alonghis direction is always divided into an equal number of cells.he result of this approach is that, with a minimum increase inomputational time, much more accurate results are achieved ifompared to a fully uniform grid in both x- and y-directions.

The slip s that occurs in each cell is a function of the tangentialurface deformations u and of the rigid slip w that is equal tohe creepage vector (w = {ξ, η}T):

(x, y)�x

v= u(x, y) − u(x − �x, y) + w�x (3)

here x − �x is the position of the preceding cell (at a givenateral position y) and v the speed of the train. Substituting Eq.2) into Eq. (3) we obtain

(x, y)�x

v= Lp(x, y) − Lp(x − �x, y) + w�x (4)

et us assume that the considered cell is inside the adhesionegion of the contact patch. In this case the slip s is equal to zerond

A(x, y) = p(x − �x, y) − w�x

Land sA(x, y) = 0 (5)

o verify the assumed adhesion, the obtained pA value has toe compared with the traction bound pL that is equal, apply-ng Hertz theory to determine the normal pressure value andoulombs friction law locally, to√ ( ) ( )

L(x, y) = μ

3

2

Q

πab1 − x

a

2 − y

b

2(6)

here μ is the (static) friction coefficient and Q the appliedormal load. If |pA| is smaller than pL value, adhesion occurs.

hmdw

1 (2006) 1253–1264 1259

therwise, slippage occurs and p is equal to

S(x, y) = pL(x, y)pA(x, y)

|pA(x, y)| and

sS(x, y) = Lv

�x[pS(x, y) − pA(x, y)] (7)

ear occurs only in the slip region of the contact patch and, ashown in Section 3, it is a function of the non-dimensional slipthat is equal to

(x, y) = sS(x, y)

v= L

�x[pS(x, y) − pA(x, y)] (8)

hus, the wear index Tγ/A for the considered cell is equal to thecalar product of the traction times the non-dimensional slip:

Tγ

A= p(x, y) · γ(x, y) (9)

he wear index, together with the information concerning theosition of the contact point along the wheel profile, representshe input of the wear model.

.3. Wear model

The wear model is based on the wear tests described inection 3. For each cell in the contact patch, the material loss pro-uced by wear is determined according to the wear law depictedn Fig. 7. Since the model is intended to simulate only the forma-ion of “regular wear” (i.e. the variation of the transverse profilend not the formation of wear patterns along the circumferen-ial direction), the wear that occurs at a given time instant andt a particular wheel transversal position may be spread overhe whole circumference of the wheel according to the ratioetween the real travelled distance v�t and the length of theircumference 2πR, �t being the time interval between subse-uent integration steps and R the rolling radius of the wheel thatorresponds to the considered contact patch. Accordingly, theear depth δ for each cell is equal to

(x, y) = K

(Tγ

A

)v�t

ρ

v�t

2πR(10)

being the wear rate, a function of the wear index (Fig. 7 andable 2) and ρ being the density of the wheel material. The wearepth values δ are then summed over the longitudinal directionnd added to the cumulative wear depth vector.

.4. Smoothing and updating of the wheel profile

The updating strategy is a key point of the profile wear pre-iction model. Its purpose is to determine the mileage afterhich wheel profiles should be updated and a new calculationf contact forces, tractions and slips should be performed. A tooconservative” strategy, requiring too frequent profile updates,ould result in unnecessary computational effort. On the other

and, increasing the mileage between two calculations too muchay lead to inaccuracies in the final worn wheel profile (or even

ivergence in the numerical procedure) due to the non-updatedheel profiles in the multi-body code.

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260 F. Braghin et al. / We

Different wheel profile updating strategies were compared25] and it was found that the most efficient one is based on theaximum wear depth, i.e. the profile is updated when a given

hreshold of the maximum value of cumulative wear depth iseached. A sensitivity analysis showed that a threshold of 0.1 mms low enough to guarantee a good accuracy and at the same timeoes not lead to excessive computational effort.

The worn wheel profile is then smoothed in order to avoidhort wavelength concavities along the wheel profiles that haveo physical meaning. In fact, due to the continuous variationf the worn wheel profile that occurs in reality, wheel–rail con-act is not stationary in position even if the running conditionsf the wheel are maintained constant thus leading to a smoothrofile. For computational reasons, the wheel profile is updatedt discrete steps. Therefore, the smoothing process is necessarynd allows to better approximating the continuous wear processith a discrete sequence of profile updates.Different smoothing strategies were compared [25] in terms

f computational cost and stability and accuracy of the results.he best smoothing strategy was found to be a combination of aoving average applied to the cumulative wear depth before pro-le update and a cubic smoothing spline applied to the updatedrofiles before starting a new iteration of the wear predictionodel.

. Validation of the wheel profile wear prediction model

The profile wear prediction model described in Section 4 wasalidated by means of comparison with experimental data. The

alidation work was performed using the results of wear testserformed on a full-scale roller rig for mounted wheelsets. These of data coming from these laboratory tests allows to preciselyvaluate the model’s accuracy since test variables and working

noon

Fig. 9. Schematic diagram of the BU300 full

1 (2006) 1253–1264

onditions (such as rail profiles, track gauge, operating speednd loads and friction conditions) are precisely measured andept under control (tests were carried out at ambient temper-ture, i.e. at 23 ◦C, and at relative humidity of approximately5%). Service data, as the one used by Jendel and Berg [3],nstead, are generally affected by a high dispersion of work-ng conditions and test variables. Therefore, the evaluation ofhe accuracy of the wear prediction model may be, in this case,ffected by unknown contact loads, vehicle speed, rail profiles,emperature, humidity and friction coefficient values encoun-ered by the wheelset during service. It could be questioned thataboratory tests are not fully representative of real working con-itions. However, the test stand used is specifically designed toeproduce as close as possible the real behaviour of the wheelsetn a wide variety of operating conditions. Therefore, collectedear data are closely representative of real service conditions.

.1. Full-scale wear tests

Wear tests were carried out on the BU300 roller rig, ownedy Lucchini Sidermeccanica and schematically shown in Fig. 9.he rig is composed by two discs driven by a DC motor andearing rail profiled steel rings. The wheelset is placed on theseiscs and is connected, by the primary suspension, to a transverseeam representing the half-bogie. Two hydraulic actuators arelaced vertically over the transversal beam, one for each side,nd are used to apply different vertical loads on each wheel, thuseproducing the vertical load acting on the wheelset as well as theoad transfer from one wheel to the other occurring during curve

egotiation. A third hydraulic actuator applies a lateral forcen the transversal beam to reproduce the lateral force actingn the wheelset in different service conditions such as curveegotiation. At each side of the transversal beam two electric

-scale roller rig for mounted wheelsets.

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ervomotors are placed longitudinally at two different heights.hese actuators are used to control the yaw movement of the

ransversal beam and therefore the wheelset’s angle of attack.The test rig has been interfaced with a multi-body model of

he railway vehicle so that the reference signals for the actuatorsan be derived from the results of the simulation of a particularervice condition taking into account the effect of railway vehiclearameters (static loads, geometry, properties of the primarynd secondary suspensions), track layout and irregularities, trainpeed, etc. More details on the test rig and on the generation ofhe references for the actuators can be found in Bruni et al. [26].

For the experimental investigation of railway wheel wear aew wheelset equipped with R8T wheels of an ETR500 Italianigh speed train with ORES 1002 profiles was used. The rails,nstead, are UIC60 900A. The wear track, that was repeated sev-ral times in order to achieve a total mileage of 10,500 km, isade up of a mix of tangent track running and curve nego-

iations. Since the percentage of curves in the wear track isuch higher than in reality, the wear phenomenon is signifi-

antly accelerated. Thus, the obtained wear amount correspondso a mileage of approximately 50,000–80,000 km of normal ser-ice. Traction and braking conditions were not included in theear track. Profile changes due to wear are measured after every000 km using a MiniProf device. The procedure followed toefine the wear track and the results obtained in the tests areescribed in Braghin et al. [4]. In this work, the same resultsill be used to validate the wheel profile wear prediction modelescribed in Section 4.

.2. Experimental–numerical comparison

Wear tests were simulated by the wheel profile wear predic-ion model. To this end, a mathematical model of the test rigas used in order to correctly take into account the dynamicehaviour of the wheelset on the roller rig. The test rig model isescribed in Bruni et al. [26] and includes the same wheel–railontact model as the one used by the vehicle’s multi-body

odel described in Section 4.1 as well as the models of the

ydraulic and electric actuators together with their control log-cs. This model replaces the multi-body vehicle model in Prof-on algorithm (see Fig. 8). Therefore, the calculated global

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ig. 10. Comparison between (a) experimental and (b) numerical transversal profile wircle in Fig. 11).

1 (2006) 1253–1264 1261

ontact parameters (contact dimensions and locations, resultingorces and creepages) correspond to the tests performed on theoller rig.

In Fig. 10 the wear depths measured on the right wheel forifferent mileages are compared to the results of numerical simu-ation performed using the wheel profile wear prediction model.t can be observed in Fig. 10a that, at approximately 7500 km,ear occurred at a lateral position of about −45 mm. This

ocalised damage, not visible in the numerical model results,s due to a failure in the control system and not to regular wear.ortunately, this localised damage is located outside the regionhere contact normally takes place and therefore does not affect

he numerical–experimental validation.Two separate wear regions are visible in Fig. 10a, one on

he wheel flange (from −40 to −30 mm) and one on the wheelread (from 0 to 30 mm). Flange wear occurs when the wheel isushed against the rail by the lateral actuator, reproducing theondition of flanging contact typical of the outer wheel of theeading wheelset during curve negotiation. Tread wear insteads mainly due to the longitudinal creep forces that are generatedhen the opposite wheel is flanging. Fig. 10a also shows thatange wear mainly occurred during the initial 2500 km. During

he following part of the wear test, the flange wear rate of growthas smaller. This is due to the fact that, for a new profile, smallerange contact patches with higher values of local pressures,nd therefore of frictional work, take place. Tread wear insteadvolves more uniformly with mileage.

The results of the numerical simulations performed using theheel profile wear prediction model (Fig. 10b) are in very good

greement with the measurements: the model is able to correctlyeproduce the position as well as the amount of flange and treadear regions. In fact, the estimated total tread wear amount aftermileage of 10,500 km is 5% smaller than the experimental

ne that is indeed a very good result considering that the wearndexes used in the wheel wear prediction model come fromwin disc wear tests and no adjustment nor calibration of eitheromponent of the wheel wear prediction model was done. Con-

erning flange wear, the wheel wear prediction model is ableo correctly foresee that about 60% of the total wear occurs inhe first 2500 km. However, comparing the experimental and theumerical total flange wear amount, an overestimation of about

ear depths at different milages (the X-axis reference corresponds to the rolling

1262 F. Braghin et al. / Wear 26

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0% is obtained by the prediction model. Several reasons can beound for this error: the Hertzian approximation of flange con-act (where contact patches are non-elliptic), the neglecting ofhe spin creepage (that is particularly significant for the flangeontact) and the use of a single friction coefficient value foroth tread and flange contacts (the friction coefficient value waseasured on the wheel tread on BU300 test rig but no measure-ent facility was available to determine the friction coefficient

alue on the flange). Also the inaccuracy of the profilometersed to measure the wheel transversal profile should be takennto account: the declared accuracy is equal to ±0.1 mm but, due

o the size factor of the tracer, higher errors could occur in casef steep profile changes like those of a worn flange.

ig. 12. Comparison between experimental and numerical evolution of flangehickness control parameter Sd with mileage.

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able 3ear track geometry used to simulate vehicle service on the “Direttissima” line

urve radius (m) Cant (mm) Length of full curve (m) Length of tran

900 125 720 230000 125 620 230700 105 1086 260000 105 856 260800 80 570 155

1 (2006) 1253–1264

In railway maintenance practice three indexes, called wearontrol parameters and denoted by the symbols Sd, Sh and Qr,re used to quantify the degree or severity of profile wear. Thed index measures the flange thickness, the Sh index the flangeeight and the Qr index the flange steepness (Fig. 11).

Fig. 12 shows the experimental and numerical evolution of Sdndex with mileage. Experimental and numerical results are wellverlapped. In particular, the initial flange thickness decreasef 0.6–0.7 mm (occurring in the first 2000 km) is clearly vis-ble. This thickness remains almost constant in the following000 km (both experimentally and numerically) and then startso decrease again but of a lower rate than in the early running.s discussed in Section 6, this behaviour is related to the occur-

ence of different wear regimes (mild, intermediate and severeear) that took place during the tests.

. Prediction of wheel wear in standard service

In this section the wheel wear profile prediction model ispplied to predict the evolution of the wheel profile during stan-ard service thus allowing to set-up an optimised maintenancere-profiling) strategy and/or to design a railway vehicle that isess aggressive from a wheel wear point of view. To this end, anTR500 Italian high speed passenger vehicle initially equipped

ith ORES 1002 wheel profiles is taken as reference. The vehi-

le is designed to be continuously operated on a high speed line.In order to define a wear track (see Section 5.1), the geome-

ry of the high speed “Direttissima” line, connecting Rome with

ig. 13. Numerical evolution of flange thickness control parameter Sd withileage (lower) and amount of abraded material for each wear regime withileage (upper).

sitions (m) % of occurrence Non-compensated acceleration (m/s2)

33 0.8528 0.7916 0.6217 0.526 0.31

F. Braghin et al. / Wear 261 (2006) 1253–1264 1263

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ig. 14. Numerical evolution of flange thickness control parameter Sd with mileongitudinal stiffness (b).

lorence, was considered. Fot this line, curves fall into threeain groups that have mean curve radius of about 3000, 4000

nd 5800 m. Thus, in order to correctly represent the curve dis-ribution along the “Direttissima” line, five typical curves wereelected as representative of the whole line. Their length wasetermined taking into account the total length of similar curvesnd then re-scaled in order to maintain the correct percentagef occurrence. For each of these curves, cant, gauge and lengthf the cubic transitions were determined as the average valuesf these parameters for the curves with equal curve radii alonghe line. Also the vehicle speed (i.e. the non-compensated lateralcceleration) was chosen as the mean value of the nominal pre-cribed speeds along the corresponding curves. The wear tracksed for wheel wear prediction is summarised in Table 3. As inhe validation process, the effect of braking was not taken intoccount. It should be observed that this does not mean that theheel wear prediction model cannot reproduce braking condi-

ions. If enough precise data about the braking transients werevailable, also braking manoeuvres could be included in the wearrack.

.1. Optimisation of wheel re-profiling strategy

Based on the wear track described in Table 3, the service lifef a wheelset was simulated. Fig. 13 shows, in the upper part, themount of abraded material (in grams) on the whole wheel pro-le that corresponds to the three identified wear regimes (mild,

ntermediate and severe wear) for every 25,000 km of mileagend, in the lower part, the continuous evolution of the flangehickness parameter Sd with mileage. As already observed, theate of material removal is rather high in the first 25,000 kmf service (significant intermediate wear occurs) leading to aather steep decrease of the flange thickness. From 50,000 to25,000 km the wear rate is much lower and the flange thick-ess remains almost unchanged. In the final part of the serviceife, the wear rate increases again and severe wear is observed.or a mileage higher than 200,000 km the wear rate becomes

ery high, thus leading again to a steep decrease of the flangehickness. After 310,000 km the minimum allowed value of Sdear control parameter is reached and the wheel has to be

e-profiled.hb

n the case of reduced bogie wheelbase (a) and of increased primary suspension

The results of the simulation suggest that a different main-enance strategy could lead to a longer wheel life. In fact, re-rofiling the wheel after about 200,000 km would reduce thehickness of the removed material layer to less than a half, thuseading to a doubling of the wheel service life. However, theumber of re-profilings would be greater with higher associ-ted tooling costs. In any event, this application shows how therofCon algorithm could be used, together with an estimationf the costs associated with production and maintenance of theheelset, to define an optimal re-profiling strategy and thus min-

mising total life cycle costs.

.2. Optimisation of railway vehicle’s design parametersrom a wear point of view

Another possible application of the wheel wear predictionodel is the determination of the effects of a railway vehicle’s

esign parameters on wheel wear. As an example, Fig. 14a showshe evolution of Sd wear control parameter for the referenceTR500 vehicle. The two cases show a vehicle having the samearameters except that the bogie wheelbase is equal to 2.7 mnstead of 3 m. Fig. 14b shows a similar result but for the caseshere the longitudinal stiffness of the primary suspension is

ncreased by 50% with respect to the nominal value. In the casef the decrease of the bogie wheelbase service life before re-rofiling is increased by about 20,000 km. While in the casef the increase in the primary suspension stiffness service lifeefore re-profiling is decreased by about 50,000 km.

Of course, the choice of these design parameters also affectsther critical issues such as vehicle stability and safety. There-ore, the advantage/disadvantage of modifying the values ofhese parameters should be judged considering all involved prob-ems. Nevertheless, these examples show the potentialities of theheel wear prediction model that can be used as a design tool

s well as for the optimisation of the maintenance process.

. Conclusions

In this paper a fast and reliable wheel wear prediction modelas been described. The model is based on a vehicle’s multi-ody code, a local contact analysis model and a local wear

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odel based on experimental twin disc tests. Comparing exper-mentally measured wear profiles coming from full-scale wearests carried out under precisely measured working conditionsith numerically simulated ones, it can be seen that the vari-us sub-programs and their interactions are correct. However,n overestimation of flange wear can be observed. This may beue to a too approximate description of K3 region, i.e. of theevere wear regime.

The problem of defining the mission track, in terms of repre-entativness especially when the track is not a priori known, is,owever, still to be solved. Moreover, the model’s accuracy inhe case of unknown or disperse parameters (such as rail profiles,riction coefficient, etc.) has to be verified.

Simulations of wheelset life showed that a re-profiling of theheel after about 200,000 km would nearly double the wheel

ervice life thus minimising total life cycle costs. Moreover, its shown that the proposed tool could be advantageously used toesign railway vehicle less aggressive from a wheel wear pointf view.

eferences

[1] T.G. Pearce, N.D. Sherratt, Prediction of wheel profile wear, Wear 144(1991) 343–351.

[2] I. Zobory, Prediction of wheel/rail profile wear, Vehicle Syst. Dynam. 28(1997) 221–259.

[3] T. Jendel, M. Berg, Prediction of wheel profile wear, Suppl. Vehicle Syst.Dynam. 37 (2002) 502–513.

[4] F. Braghin, S. Bruni, F. Resta, Wear of railway wheel profiles: a comparisonbetween experimental results and a mathematical model, Suppl. VehicleSyst. Dynam. 37 (2002) 478–489.

[5] J.J. Kalker, Three-Dimensional Elastic Bodies in Rolling Contact, KluwerAcademic Publisher, Dordrecht, 1990.

[6] W. Kik, J. Piotrowsky, A fast, approximate method to calculate normalload at contact between wheel and rail and creep forces during rolling, in:Proceedings of the Second Mini Conference on Contact Mechanics andWear of Rail–Wheel Systems, 1996.

[7] J. Dearden, The wear of steel rails and tyres in railway service, Wear 3(1960) 43–49.

[8] R.K. Steele, Observations of in-service wear of railroad wheels and railsunder conditions of widely varying lubrication, ASLE Trans. 25 (1982)400–409.

[

[

1 (2006) 1253–1264

[9] I.J. McEwen, R.F. Harvey, Full-scale wheel-on-rail testing: comparisonswith service wear and a developing theoretical predictive model, Lubric.Eng. 41 (1985) 80–88.

10] S. Kumar, D.L.P. Rao, Wheel–rail contact wear, work, and lateral force forzero angle of attack—a laboratory study, Trans. ASME J. Dynam. Syst.Meas. Control 106 (1984) 319–326.

11] T.M. Beagley, Severe wear of rolling/sliding contacts, Wear 36 (1976)317–335.

12] P.J. Bolton, P. Clayton, I.J. McEwen, Wear of rail and tyre steels underrolling/sliding conditions, ASLE Trans. 25 (1982) 17–24.

13] P.J. Bolton, P. Clayton, Rolling–sliding wear damage in rail and tyre steels,Wear 93 (1984) 145–165.

14] H. Krause, G. Poll, Wear of wheel–rail surfaces, Wear 113 (1986) 103–122.

15] R. Lewis, R.S. Dwyer-Joyce, Wear mechanisms and transitions in railwaywheel steels, in: Proceedings of the IMechE Part J, J. Eng. Tribol. 218(2004) 467–478.

16] S.M. Zakharov, I.A. Zharov, Simulation of mutual wheel/rail wear, in: Pro-ceedings of the Fifth International Conference on Contact Mechanics andWear of Rail/Wheel Systems, 2000.

17] J.E. Garnham, J.H. Beynon, The early detection of rolling–sliding contactfatigue cracks, Wear 144 (1991) 103–116.

18] D.I. Fletcher, J.H. Beynon, Development of a machine for closely con-trolled rolling contact fatigue and wear testing, J. Test. Eval. 28 (2000) 267–275.

19] R. Lewis, U. Olofsson, Mapping rail wear regimes and transitions, Wear257 (2004) 721–729.

20] S. Bruni, A. Collina, G. Diana, P. Vanolo, Lateral dynamics of a railwayvehicle in tangent track and curve: tests and simulation, Suppl. VehicleSyst. Dynam. 33 (2000) 464–477.

21] S. Bruni, A. Collina, R. Corradi, Numerical modelling of railway runnabil-ity and ballast settlement in railroad bridges, in: Proceedings of the EURO-DYN International Conference, 2002.

22] Z.Y. Shen, J.K. Hedrick, J.A. Elkins, A comparison of alternative creep-force models for rail vehicle dynamic analysis, Suppl. Vehicle Syst. Dynam.12 (1983) 79–82.

23] F. Braghin, S. Bruni, G. Diana, Experimental and numerical investiga-tion on the derailment of a railway wheelset with solid axle, Vehicle Syst.Dynam. 44 (2006) 305–325.

24] J.J. Kalker, A fast algorithm for the simplified theory of rolling contact,Vehicle Syst. Dynam. 11 (1982) 1–13.

25] G. Barbarino, A fast and reliable mathematical model for the prediction ofrailway wheel wear, Master Thesis at Politecnico di Milano, 2004.

26] S. Bruni, F. Cheli, F. Resta, A model of an actively controlled roller rig fortests on full size wheelsets, Proceedings of IMechE. Part F. Rail and RapidTransit, vol. 215 (2001) 277–288.