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Wear 271 (2011) 2438– 2447

Contents lists available at ScienceDirect

Wear

j o ur nal ho me p age: www.elsev ier .com/ locate /wear

hort communication

ail corrugation development in high speed lines

. Correa, O. Oyarzabal ∗, E.G. Vadillo, J. Santamaria, J. Gomezepartment of Mechanical Engineering, University of the Basque Country UPV-EHU, Alameda de Urquijo s/n, 48013 Bilbao, Spain

r t i c l e i n f o

rticle history:eceived 1 September 2010eceived in revised form1 December 2010

a b s t r a c t

Rail corrugation wear is one of the most important types of track wear in the railroad industry. The mostcommon cases of rail corrugation that have been documented in the literature were classified by Grassie[1] in six categories, according to the damage and wavelength fixing mechanisms. Except for heavyhaul railroads corrugation and for light rail corrugation, in all the other four types of rail corrugation the

ccepted 22 December 2010

eywords:ail undulatory wearail corrugation

damage mechanism is wear. This paper analyses the possible existence and degree of rail corrugation wearon four types of high speed tracks (RHEDA 2000, AFTRAV, STEDEF and high performance ballasted track),examining different vehicle velocities and track radii, and taking into account the dynamic behaviour ofthe high speed wheelset rolling on the rails. A numerical method that takes into account the dynamicsof the track and the wheelset as well as the wear mechanism has been used. The four high speed tracks

ail co

igh speedheelset

are ranked according to r

. Introduction

Rail corrugation is an undulatory wear which can be occasionallybserved on the rail rolling surface [2]. As soon as the corrugationegins the wear development grows exponentially. It is generallyccepted that there are six types of rail corrugation, which can belassified according to the damage and wavelength mechanism,nd that wear is the damage mechanism in four of them [1].

Rail corrugation has been thoroughly studied for the lastecades. It is worth mentioning the work of the Berlin Group,

ncluding Hempelmann [3,4], Hempelmann and Knothe [5], Müller6,7], Igeland and Ilias [8], and Knothe and Ripke [9].

Up to the present time the Chalmers Group has significantlyontributed to the rail corrugation knowledge, including Anderssonnd Johansson [10], where railway vehicles running at speeds of0 and 130 km/h were studied, and Johansson and Nielsen [11],here the authors studied in the time domain rail corrugations

enerated by the Swedish high-speed train X2 running at speeds ofp to 200 km/h.

The European Commission has been concerned with rail corru-ations research, for all types of rail vehicles, since the beginningf ORE-ERRI D185 Committee, with the support of the Universitiesf Berlin and Cambridge [12].

Some of the models developed so far are linear models workingn the frequency domain [3–7,9], while some others as [8,10,11]

ork in the time domain. To study specific situations sophisticatedodels have been developed that consider self-excited vibrations

∗ Corresponding author. Tel.: +34 946014223; fax: +34 94 6014215.E-mail address: olatz.oyarzabal@ehu.es (O. Oyarzabal).

043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.wear.2010.12.028

rrugation wear development.© 2011 Elsevier B.V. All rights reserved.

[13] and stick-slip [14], multiple wheelsets interaction [15], etc. Tocarry out the present study, the authors have developed a modelin the frequency domain, the track being modelled by means ofthe Finite Strip Method and the Periodic Structure Theory. This hasthe advantage that the track is not modelled by beam elements butrather with finite elements, and even the deformation of the railcross-section is being taken into account. Moreover, by using thefinite strip method only the rail section has to be meshed using 2-Dfinite elements instead of generating a 3-D mesh for a finite section.In the cases studied in this paper each vertical rail cross-sectionhas been meshed with 69 nodes. The results have been validatedwith MSC/NASTRAN [16]. The discrete supports have been takeninto account using the theory of periodic structures, which allowsconsidering an infinite length of track. The benefit of this model isthat it increases the accuracy of the track behaviour, saving compu-tation time and avoiding inaccuracies due to a finite track length.The basic assumptions of the model are described in [17,18].In themodel used in this paper, corrugation wear is calculated as a feed-back process between the existing irregularities on the rail surface,characterised by a random wavelength, and the dynamic struc-ture of the vehicle and track. The wear is increased as a result ofexisting forces and creepages in the contact between wheel andrail, which are calculated using DINATREN a railway dynamic sim-ulation tool developed by the authors [19]. The contact law andwear rate law used are explained in Section 4. Models that workin the time domain predict the worn pattern of the rail surface

after a number of thousands of wheelset passages, as a result ofthe dynamics of the system and the initial conditions, and one canobserve the position of troughs and peaks as well as the domi-nant undulatory wear wavelength. On the contrary, in this model,being a frequency domain model, wear is predicted by means of the

N. Correa et al. / Wear 271 (2011) 2438– 2447 2439

Fig. 1. Type of rail corrugation searched for, on ballasted track (a) and on slab track (b).

Table 1Characteristics of the 4 studied tracks.

Span length Upper stage: vertical stiffness Intermediate plate’s mass Sleeper mass Lower stage: vertical stiffness

4.4 kg–

––

gpiwwtgaa

RHEDA 2000 0.65 m 4.5e−8 N/m

AFTRAV 0.65 m 4e−7 N/m

STEDEF 0.6 m 1.5e−8 N/m

Ballasted 0.6 m 1e−8 N/m

rowth function concept. These growth functions show the predis-osition to the appearance of corrugation as a function of frequency

n Hz. Resonance of the wheelset at a certain frequency togetherith the track receptance at that same frequency determine the

ear growth at that precise frequency, and the dominant undula-

ory wear frequencies and wavelengths are obtained. In this modelrowth functions can be computed at any distance of the track,nd for this work they have been computed both at midspan andbove a sleeper, the aim being to predict whether corrugation will

Fig. 2. (a) Wheelset modelled with finite elements; (b) radial re

– 2.6e−7 N/m– –221.7 kg 2.5e−7 N/m320 kg 5e−7 N/m

develop or not in those sections, and if it does at what frequency andwavelength.

Fig. 1(a) and (b) shows the type of rail corrugation searched for,on ballasted track and on slab track. They aroused in conventional

railway lines with conventional wheelsets, and have been used tocalibrate the model used in this paper. The shiny areas correspondto trough zones, where the corrugation wear is manifest. The dullareas correspond to the areas where the rail remains unworn. Thecorrugation wear wavelength � is shown in Fig. 1(b). Small vari-

ceptance; (c) axial receptance; (d) tangential receptance.

2440 N. Correa et al. / Wear 271 (2011) 2438– 2447

F modem 85 Hz;

aw

rl

ig. 3. (a) Torsion mode at 79 Hz; (b) first bending mode at 89 Hz; (c) umbrella type

ode of the wheelset at 426 Hz; (g) torsion mode at 440 Hz; (h) bending mode at 8

tions in track or vehicle configuration can make rail corrugationear develop or not, as for example is shown in [20–22].

This paper shows part of the results of a study carried out at theequest of CEDEX (Centre for Studies and Experimentation in Pub-ic Works—Spanish Ministry of Public Works and Infrastructures)

at 258 Hz; (d) umbrella type mode at 331 Hz; (e) wheel mode at 381 Hz; (f) bending (i) wheel mode at 1010 Hz.

due to an expected increase in the number of kilometres of highspeed lines during the next decade. This study analyses the pos-sible existence and degree of corrugation on 4 types of high speedtracks (high performance ballasted track, RHEDA 2000, STEDEF andAFTRAV).

N. Correa et al. / Wear 271 (2011) 2438– 2447 2441

rhtgaor

fiaeo

2

cJ[dr

Fig. 4. Vertical and lateral receptances of RHEDA 2000 track.

This work has examined different vehicle velocities and trackadii, and the results have taken into account the four wheels of aigh-speed bogie. Vertical, lateral and longitudinal receptances forrack and vehicle have been obtained, as well as the corrugationrowth functions. The rail corrugation wear results obtained for

high speed wheelset show considerable differences from thosebtained for a conventional wheelset. In the paper the tracks areanked according to corrugation development.

The characteristics of the 4 tracks analysed in this study can beound in Table 1. All of them are standard track gauge. The AFTRAVs a track which has only one elastic stage and therefore has neither

sleeper nor lower stage. The RHEDA 2000 does not have sleepersither, but instead has intermediate plates with two elastic pads,ne above and the other below each intermediate plate.

. Wheelset

In the past wheelset receptances or mobilities have been cal-

ulated for several types of railway vehicles, among others, byohnson’s group at Cambridge University [23] and by Thompson24,25], where an NS Intercity wheel and a UIC 920 mm stan-ard freight wheel receptances were calculated, and the measuredesponse of a BR ‘Commonwealth’ 1.06 m diameter wheel is shown.

Fig. 5. Vertical and lateral receptances of AFTRAV track.

In this work the wheelset of a high speed commercial rail vehi-cle, which is named ‘A-Wheelset’, has been used. Its mass is 1343 kgtaking into account the three brake disks. The inertia moments ofthe wheelset are 106.1 kg m2 in the axle direction (Y axis in Fig. 2(a))and 549.2 kg m2 in the direction perpendicular to the axle (X and Zaxes). The mass of each braking disk is 130 kg, and their diameter is640 mm, with 430 mm being the distance between two brake discs.The wheel diameter is 920 mm and the total length of the wheelsetis 2180 mm.

This wheelset has a very low mass, in an attempt to reducethe vehicle unsprung mass as much as possible. In this workthe wheelset receptances and modes have been calculated usingfinite elements with MSC/NASTRAN [16]. The wheelset geometryand properties have been considered with great detail in orderto achieve accurate results. The results obtained are consistentwith those of similar (although not identical) high speed wheelsets[26,27].

The radial, axial and tangential receptances obtained for this

wheelset are shown in Fig. 2. These receptances are necessary toobtain the undulatory wear growth functions.

Some important vibrating modes of this wheelset are shown inFig. 3. In this figure the distortion of the grid makes it possible toascertain the mode shape. Fig. 3(a) shows the first torsional mode of

2442 N. Correa et al. / Wear 271 (2011) 2438– 2447

ttiafiFmiot3tiItmfFiTao(

Fig. 6. Vertical and lateral receptances of STEDEF track.

he wheelset which appears at 79 Hz. The first peak of the tangen-ial receptance (Fig. 2(d)) occurs at this frequency. The second modellustrated is the first bending mode of the wheelset, which occurst 89 Hz. In the radial and axial receptances (Fig. 2(b) and (c)) therst peak appears at this frequency. The third mode that appears inig. 3 is the umbrella type mode with the wheels in antiphase. Thisode occurs at 258 Hz, as can be observed in the axial receptance

n Fig. 2(c) (the fourth peak of this receptance, next to the thirdne). The mode which is depicted in Fig. 3(d) is also the umbrellaype mode, but with the wheels in phase. This mode appears at31 Hz, and the peak related to it can be found in the axial recep-ance (the fifth peak of this receptance). The fifth mode illustrateds at 381 Hz and is related to a wheel with two nodal diameters.ts corresponding peak can be observed in the axial receptance,he sixth peak. The next mode shown (Fig. 3(f)) is another bending

ode of the wheelset, which appears at 426 Hz and a peak can beound at this frequency mainly in the radial wheelset receptance. Inig. 3(g) the mode illustrated is a further torsional mode (440 Hz and

ts corresponding peak is depicted in the tangential receptance).he deformation of this mode can be noted in the figure by lookingt the distorted mesh. The next mode shown is a bending modef the wheelset that appears at 885 Hz. The last mode illustratedFig. 3(i)) is the mode related to a wheel with three nodal diame-

Fig. 7. Vertical and lateral receptances of high performance ballasted track.

ters. It appears at 1010 Hz and can be clearly distinguished in theaxial receptance.

The modes in combination with the receptances are needed totake into account the wheelset dynamic behaviour, and finally tocalculate the rail wear. Likewise they are needed to interpret theresults of rail wear and the causes of each wear wavelength.

3. Track receptances

In this section, the receptances of the four types of track areshown. These receptances have been calculated by the mathemat-ical tool RACING, which has been developed by the authors, andusing MSC/NASTRAN [16].

In Fig. 4 the vertical and lateral receptances of the RHEDA 2000track are depicted, both at midspan and over sleeper. In the verticalreceptance three peaks can be observed, the first one correspondingto the vertical vibration of the rail and the intermediate plate abovethe lower stage, at 122 Hz; the second one, at 840 Hz, is related to a

mode that is characterised by having one node at midspan and max-imum displacement above a sleeper; and the last one, at 944 Hz,is the first vertical pinned–pinned of the track, whose behaviouris the opposite to the previous mode. In the lateral receptance(Fig. 4(b)), the first peak observed is at 136 Hz and is due to the

N. Correa et al. / Wear 271 (2011) 2438– 2447 2443

r the

rl

ccrl

aaa(8p

sttFodt

4

“

Fig. 8. Rail corrugation wear growth tendencies fo

otation of the rail and the plate above the lower stage. The firstateral pinned–pinned occurs at 450 Hz.

The AFTRAV track receptances are shown in Fig. 5. In thisase, the vertical pad mode is produced at 160 Hz and the verti-al pinned–pinned at 946 Hz. In the lateral direction (Fig. 5(b)) theotation mode of the rail above the pad occurs at 90 Hz and theateral pinned–pinned at 442 Hz.

In the STEDEF track case, the vertical resonances (Fig. 6(a)) aret: 66 Hz corresponding to the vibration of the rail and sleeperbove the boot; at 350 Hz the mode related to the pad; andt 1076 Hz the vertical pinned–pinned. In the lateral receptanceFig. 6(b)) it can be observed: the rotation mode of the rail at0 Hz; the peak related to the pad at 178 Hz and the first lateralinned–pinned at 510 Hz.

The vertical and lateral receptances of the ballasted track arehown in Fig. 7. The peaks of the vertical receptance (Fig. 7(a)) are:he first corresponding to the ballast at 80 Hz; the one related tohe pad at 282 Hz and the vertical pinned–pinned at 1076 Hz. Inig. 7(b), one can observe the lateral receptance’s peaks, the firstne being related to the ballast in lateral (32 Hz), the second oneue to the rotation of the rail above the pad (106 Hz) and at 510 Hzhe lateral pinned–pinned.

. Rail corrugation wear tendencies

There have been proposed several empirical wear models orwear indices”. One of the most extensively used for wheel–rail

Rheda 2000 track in a curve with a 3550 m radius.

contact wear estimations is the Archard’s [28] model, which quan-tifies the volume of removed material due to wear Vwear [m3] as:

Vwear = k1Fzs

H(1)

where Fz is the normal force in the wheel–rail contact in N, s isthe sliding distance in the wheel–rail contact patch in m, H is thehardness of the softer material (wheel or rail) in N/m2 and k1 is anon-dimensional wear coefficient.

Alternatively, the other most usual approach to estimatewheel–rail contact wear is based on the frictional power [29], bothlateral and longitudinal, which is the product of the tangentialforces and the slip in the contact area. This frictional power is con-sidered to consist of two parts: one of constant value, which is thecause of the uniform wear on the rail surface, and another one offluctuating value, which will amplify or attenuate the initial irregu-larities on the rail surface, leading to undulatory wear developmentor removal.

As the wheelsets pass, the development of the periodical irreg-ularity with amplitude �z and wavelength � = v/f, can be describedthrough this Eq. (2) [3]:

∂�z(x, n) k0

∂n= −

2�bv�PfrictFH (2)

in which v is the train speed in m/s, f is the frequency of the periodicirregularity in Hz, x is the longitudinal coordinate, n is the numberof axles that pass above the studied point, k0 a wear coefficient [3],

2444 N. Correa et al. / Wear 271 (2011) 2438– 2447

due to

wa(fdaar

ipfG

ia2aso

oal

Fig. 9. Rail corrugation wear growth tendencies for the Rheda 2000 track

hich will vary according to the type of steel used in the wheelsnd rails, � is the steel density, b the wheel–rail contact semiaxeslateral or longitudinal, as required), �Pfrict the fluctuations of therictional power (lateral or longitudinal) and FH the filter due to theimensions of the contact between wheel and rail, which takes intoccount the effectivity associated with each wavelength. This is thepproach used in this paper, in view of its general acceptance forail corrugation wear predictions [3,5–10,30].

Eq. (2) can also be expressed as:

∂�x(x, n)∂n

= R �z (3)

n which the real part R represents the wear rate developed with theass-by of each wheelset [17] given that it is a frequency dependentunction and is designated as corrugation wear growth function(f).

In this article the tendency to corrugation development is stud-ed both at midspan and over a sleeper, for four types of track,nd for the following combinations of speeds and curve radii:50 km/h and 3550 m; 140 km/h and 1000 m; 45 km/h and 320 m;nd 35 km/h and 150 m. The two first situations correspond topeeds and radii common in high speed lines, whereas the two last

nes can be found in crossings and switches, respectively.

Furthermore, the corrugation wear growth functions due to eachf the wheels of one bogie are calculated separately, and wheelsre numbered in the following way: wheel 1, outside wheel of theeading axle; wheel 2, inside wheel of the leading axle; wheel 3, out-

wheel number 2, (a) 3550 m radius, (b) 1000 m, (c) 320 m and (d) 150 m.

side wheel of the trailing axle; wheel 4, inside wheel of the trailingaxle.

The number of studied cases totalled 128 and only some of thosewear growth functions are shown due to space limitations. As anexample, in Fig. 8 the values of the corrugation growth functionsof the RHEDA 2000 track are shown for a curve radius of 3550 mand a train velocity of 250 km/h, due to the pass of each of the fourwheels of the bogie. These values are non-dimensional. The positivevalues imply a tendency to corrugation growth, whereas the nega-tive values signify that any undulatory wear at that frequency willtend to disappear. It is known [5] that positive values above 1e−2correspond to situations where rail corrugation wear will certainlyappear.

The highest peak is produced at 900 Hz (Fig. 8(d)) over thesleeper, due to wheel 4. It is a peak whose magnitude is 3.59e−7.This magnitude is very low compared to the corrugation growthfunctions that are found in real tracks that developed corrugation,which have been used to calibrate this model [21]. Therefore, suchcorrugation development is not foreseen. Another peak can also beobserved over sleeper at 920 Hz (Fig. 8(b)) corresponding to wheel2. It has a value very similar to the previous one, 3.05e−7, andconsequently the development of undulatory wear is not foreseen

either.

Fig. 9 shows the corrugation growth functions that have beencalculated for different curve radii and rail vehicle speeds forthe RHEDA 2000 track, due to the passage of wheel 2. It can benoticed that the tendency for the development of undulatory wear

N. Correa et al. / Wear 271 (2011) 2438– 2447 2445

to wh

iv4

totdb

gt4ftw

TS

Fig. 10. Rail corrugation wear growth tendencies due

ncreases when decreasing the curve radius. In fact, the maximumalue for 3550 m is 3.05e−7; for 1000 m is 9.58e−7; for 320 m is.78e−4, and for 150 m is 1.08e−3.

Fig. 10 shows the undulatory wear growth functions for the fourypes of tracks due to wheel 4. In this particular case, it can bebserved that although the maximum values of the growth func-ions are not very different for the different tracks, small differenceso exist between them, and the track with the lowest value is theallasted track, followed by the AFTRAV track.

The remaining results are shown summarized in Tables 2–5. Ineneral we can see that the maximum values of the growth func-ions are very low for radii of 3550 m and 1000 m, being up to

, 5 or 6 orders of magnitude lower than the values that can beound in real tracks which developed corrugation wear. Therefore,he tendency to develop undulatory wear would be very small asell. For the radii of 320 m and specially 150 m, the values of the

able 2ummary of the results of the growth functions for R = 3550 m and V = 250 km/h.

Track At midspan

Maximum Frequency (Hz) Wh

RHEDA 2000 1.17e−7 440 2

AFTRAV 1.36e−7 960 4

STEDEF 1.60e−7 1110 4

Ballast 8.85e−8 440 2

eel 4 in a curve with a 3550 m radius, for each track.

corrugation growth functions become significant, and corrugationcould develop. However, it should be taken into account that forthese radii the highest peaks occur at very high frequencies, above900 Hz, and that the train speed is very low, thus the wavelength ofthe undulatory wear would be very small, becoming smaller thanthe size of the contact patch. It can also be seen that the wheels thatproduce the greatest values of the growth functions are the innerwheels, of both the leading and trailing axles.

Comparing the four types of track, it was found that at highspeeds the ones least prone to corrugation wear formation arethe ballasted track, followed by the AFTRAV track. Although differ-ent track parameters may lead to different results, the favourable

behaviour of the ballasted track was also obtained by Tassily andVincent, who developed a numerical model for rail corrugationwhich they applied to compare two ballasted tracks and a concretetrack [30].

Over sleeper

eel Maximum Frequency (Hz) Wheel

3.59e−7 900 41.08e−7 440 26.74e−8 250 28.86e−8 50 4

2446 N. Correa et al. / Wear 271 (2011) 2438– 2447

Table 3Summary of the results of the growth functions for R = 1000 m and V = 140 km/h.

Track At midspan Over sleeper

Maximum Frequency (Hz) Wheel Maximum Frequency (Hz) Wheel

RHEDA 2000 8.05e−7 440 2 9.58e−7 910 2AFTRAV 7.31e−7 440 2 7.31e−7 440 2STEDEF 1.48e−6 180 2 1.67e−6 250 2Ballast 1.80e−6 50 2 1.80e−6 50 2

Table 4Summary of the results of the growth functions for R = 320 m and V = 45 km/h.

Track At midspan Over sleeper

Maximum Frequency (Hz) Wheel Maximum Frequency (Hz) Wheel

RHEDA 2000 1.39e−4 810 2 4.78e−4 910 2AFTRAV 1.68e−4 1030 2 1.19e−4 1030 2STEDEF 4.26e−4 1130 2 2.13e−4 1030 2Ballast 1.43e−4 1130 2 2.06e−4 1030 2

Table 5Summary of the results of the growth functions for R = 150 m and V = 35 km/h.

Track At midspan Over sleeper

Maximum Frequency (Hz) Wheel Maximum Frequency (Hz) Wheel

44

4

4

5

l(t1riiopte

rolr1itoottssattff

A

P

[

[

[

[

[

[

[

RHEDA 2000 1.58e−3 830AFTRAV 1.48e−3 970

STEDEF 3.90e−3 1130

Ballast 7.76e−4 1160

. Conclusions

Rail corrugation wear growth tendency in high speed railroadines has been studied. Four types of track have been consideredRHEDA 2000, AFTRAV, STEDEF and a high performance ballastedrack), assuming several train velocities and track radii. A total of28 cases have been evaluated, representing the most importanteal situations. The wear tendencies have been estimated tak-ng into account the fluctuations of creep forces and creepagesn wheel–rail contact, which lead to fluctuations in the wear raten the rail surface. The dynamic properties of track and vehiclerovoke such fluctuations, and it has been envisaged that the recep-ances of the high speed wheelset have a crucial influence on theventual corrugation wear appearance.

As expected, the larger the track radius the lower the rail cor-ugation wear will be. For radii of 1000 m and above, the valuesf the corrugation growth function are of the order of 1e−6 andower for all types of track studied, well below the values that cor-espond to real corrugation development, which are of the order ofe−3. For radii of 320 m and 150 m, typical of switches and cross-

ngs and of shunting yards, the corrugation growth functions reachhe order of 1e−3, partially as a consequence of the dynamic modef the wheelset at 1010 Hz that appears at the end of Fig. 3 andf the pinned–pinned antiresonance of the vertical track recep-ances shown in Figs. 6 and 7. However, even for these radii, withhese types of track and with the new type of vehicle that has justtarted operation, it will take several years for the corrugation totart developing for the first time. It has also been found that, forll tracks, radii and speeds, the two wheels of the bogie that facehe center of the curve (wheels 2 and 4) provoke a higher corruga-ion than the other two. Comparing the four types of track, it wasound that at high speeds the ones least prone to corrugation wearormation are the ballasted track, followed by the AFTRAV track.

cknowledgements

The authors thank CEDEX for their funding through contractT2006-024-11CCPM, MICINN for TRA2010-18386 and the Basque

[

[

8.87e−3 920 41.42e−3 940 41.30e−3 1070 41.51e−3 1070 4

Government for its financial assistance through IT-453-10 as wellas for Research Grant BFI08.172.

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