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Wear 262 (2007) 1296–1307

Rail corrugation growth—Influence of poweredwheelsets with wheel tread irregularities

Anders Johansson a,b,∗, Jens C.O. Nielsen a,b

a CHARMEC, Department of Applied Mechanics, Chalmers University of Technology, SE-412 96 Goteborg, Swedenb Epsilon HighTech AB, Lindholmspiren 9, SE-417 56 Goteborg, Sweden

Received 11 November 2005; received in revised form 1 November 2006; accepted 5 January 2007Available online 16 February 2007

bstract

A multibody system model for simulation of general three-dimensional train-track interaction (accounting for frequencies up to several kHz) issed to investigate the hypothesis that rail corrugation is generated by powered wheelsets on the Swedish high-speed train X2. Part of the brakingffort on the powered wheelsets is accomplished by tread braking with cast iron brake blocks. In particular, the influence of wheel corrugation,hich is present because of such braking, on rail corrugation growth is studied. The numerical model uses an iteration scheme including simulationf dynamic train-track interaction in the time domain coupled with a long-term wear model. Measured wheel–rail contact forces and measured rail

oughness are compared to the simulated results. Wheel–rail contact forces are considerably higher when wheel irregularities are present. However,he averaging effect from several passing wheelsets with different sets of wheel irregularities is found to give a rate of rail corrugation growthimilar to the one obtained if the wheels had been completely round. The rail corrugation wavelengths are found to be explained by irregular wearue to high wheel–rail contact forces and slip caused by local rail bending modes between the two wheelsets in a bogie.

2007 Elsevier B.V. All rights reserved.

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eywords: Rail corrugation; Wheel corrugation; Dynamic train-track interactio

. Introduction

Discrete or periodic irregularities on wheel and rail sur-aces exist in a number of different forms. Examples of wheelrregularities are flats causing severe repeated impact loads,orrugation with wavelengths in the order of 3–10 cm, andolygonalization with wavelengths between about 20 cm andne wheel circumference (i.e. about 3.5 m). Rail corrugation,ith wavelengths between 25 mm and 1.5 m, has been catego-

ized into six different types by Grassie and Kalousek [1]. Thisategorization is based on different damage and wavelength-xing mechanisms. The wheel and rail irregularities lead to

ncreased rolling noise levels and increased magnitudes of

heel–rail contact forces. Consequences are difficulties in meet-

ng noise legislation, and increasing safety hazards due toeduced life of different track and vehicle components, such as

∗ Corresponding author at: Chalmers University of Technology, Departmentf Applied Mechanics, Division of Dynamics, SE-412 96 Goteborg, Sweden.el.: +46 31 7721500; fax: +46 31 7723827.

E-mail address: anders.johansson@epsilon.nu (A. Johansson).

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043-1648/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.wear.2007.01.004

ear; Measurements

heels, axles and rails, see e.g. [2]. Causes and consequences ofifferent types of wheel out-of-roundness (OOR) and rail corru-ation are surveyed by Nielsen and Johansson [3] and Nielsent al. [4].

Most reported models for simulation of development of rail-ay wheel OOR or rail corrugation use an iteration modelhich combines simulations of dynamic train-track interaction

nd long-term wear. In the dynamics model, wheel–rail contactorces, creepages (i.e. ratio of rigid slip at contact point centreo rolling speed) and sizes and positions of the contact patch arealculated. These variables are used as input to the wear model.he rail and wheel profiles are then updated and kept constanturing the next simulation of train-track interaction. Using thisterative procedure, the development of wheel OOR or rail corru-ation is investigated. The same concept is adopted in the presenttudy. An overview of numerical simulation models is given byielsen et al. [4].Out-of-roundness measurements on different types of railway

heels in Sweden were performed in the autumn of 2002 [5].ome of the wheels were powered and trailer (non-powered)heels of the high-speed train X2. The ØDS (Ødegaard) &anneskiold-Samsøe wheel roughness measurement system

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A. Johansson, J.C.O. Nielse

as used. The wheel radius in three bands around the wheel cir-umference was measured with a sampling distance of 0.5 mmnd an amplitude resolution of 0.06 μm. Measurements of hard-ess using the EquoTip equipment and transverse wheel profilesing the MiniProf measuring device were also performed. Highevels of roughness (up to 20 dB re 1 μm, evaluated in one-thirdctave bands) in the wavelength interval 3–8 cm were foundn the powered X2 wheels, whereas the corresponding trailerheels were smooth. It was concluded that the corrugation on

hese railway wheels was caused by tread braking with cast ironrake blocks. In addition to the wheel out-of-roundness measure-ents, rail roughness was measured (by the Swedish Nationalail Administration, Banverket) on several sites in Sweden [6].easurements were performed both on severely corrugated rails

nd on smooth recently ground rails. Finally, wheel–rail contactorces have been measured using an X2 test train with wheelsnstrumented with strain gauges on the wheel discs.

Corrugation with wavelengths of the order of 3–8 cm wasetected on both the powered X2 wheelsets and on several rails.he wavelength-fixing mechanism on wheels with cast ironrake blocks is the generation of so-called hot spots [7]. Duringread braking, some regions on the wheel tread become warmerhan neighbouring regions (formation of hot spots) owing to ahermoelastic instability (TEI). Material is then transferred fromhe brake blocks to the tread surface, creating a corrugation crestcorrugation peak) on the wheel tread at the position of a hot spot4]. The wavelengths of the generated corrugation seem to bendependent of train speed. The wavelength-fixing mechanismf the observed short-pitch rail corrugation (denoted “roaringails” in [1]) will be determined here.

A mathematical model for simulation of general three-imensional train-track interaction and prediction of irregularear on wheel treads and rail heads is used in this paper. In

ts most general form, the model simultaneously accounts forow-frequency (<20 Hz) vehicle dynamics and high-frequencyrain-track interaction including the deformation of discretelyupported rail cross-sections (several kHz) [8,9]. To calculatehe wear, Kalker’s simplified theory (FASTSIM) [10] is usedogether with Archard’s wear model [11]. The mathematicalodel used in the present investigation is thoroughly described

n [8] and [12].Using an initial broad-band spectrum of roughness wave-

engths to obtain simultaneous wheel–rail excitation at severalrequencies is an efficient approach for simulation of short-pitchail corrugation in the time domain [9,13,14]. This approach willlso be adopted in the present study. Measured OOR from pow-red X2 wheelsets are used as input for the radial irregularitiesn the wheels. The rails are initially considered to be relativelymooth assuming an initial irregularity (roughness) based on theSO3095 limit curve [15]. For the long-term wear process, it isssumed that the roughness amplitudes decrease for some wave-engths, whereas the amplitudes increase for others due to theynamics of the coupled train-track system. In the previous mod-

ls, wear prediction based on frictional work in the wheel–railontact has been used. The Archard wear model chosen here haseen used to study wear of the transverse wheel profile [16] andevelopment of polygonal wheels [12].

Anm

ear 262 (2007) 1296–1307 1297

In summary, the objective of this study is to apply a generalool for prediction of irregular wheel/rail wear, and to explain thebserved rail corrugation growth. In particular, the influence ofheel OOR on formation of rail corrugation will be investigated.he present investigation is limited in the sense that neither plas-

ic deformation within the wheel–rail contact, nor any variationf material properties along the rails, is considered. The wearoefficient is thus assumed to be independent of hardening of theaterial in the rail head and the positions of the contact patch.

. Measurements

.1. Wheel–rail contact forces

Vertical wheel–rail contact forces have been measured onn X2 train running on the line Stockholm–Goteborg. A trailerheelset was instrumented with strain gauges on the wheel discs

17]. Four strain gauges with an equidistant separation of 90◦ere mounted in a bridge on each side of the disc. The mea-

urements were performed in order to identify track sectionsith severe rail irregularities. The train speed and the sampling

requency were 200 km/h and 9.6 kHz, respectively. Before theest, the wheelset was calibrated using static (vertical and lat-ral) loads on the wheels. However, the wheelset has severaligenmodes in the frequency range excited by short-pitch railorrugation. Since the dynamics of the wheelset is not consid-red in the data processing, this leads to measurement errors inertain frequency intervals. From an experimental modal anal-sis, it was concluded that the most significant source of errors the radial wheel mode with two nodal diameters at 1712 Hz.t this frequency the true load is magnified by a factor of 100.he error contributions from other wheelset eigenmodes (withr without axle bending) seem to be smaller and restricted toarrow frequency bands. The wheelset was turned before theest, although trailer wheelsets have been confirmed to havemooth wheel treads with roughness levels that are well belowhe ISO3095 spectrum, see Fig. 1(b). Results from measure-ents of wheel–rail contact forces are presented and compared

o numerical results in Section 6.

.2. Rail and wheel irregularities

From the measurements described in the previous subsection,everal sites along the railway line generating exceptionally highertical wheel–rail contact forces were identified. In general, therigin to the increased forces is vertical irregularities on the run-ing surface of the rail, such as short-pitch corrugation, welds,nsulating joints or crossings. To determine the irregularities athese locations, the accelerometer-based measurement systemAT (Corrugation Analysis Trolley) [18] was used. Four of the

nvestigated sites (Vretstorp, Sodertalje, Gardsjo and Toreboda)re discussed in the present study. A survey of roughness mea-urement is presented by Verheijen [19].

The conditions at the selected sites are similar in many ways.ll sites are on tangent track with UIC60 900A rails, nomi-al sleeper distance 0.65 m, Pandrol fastenings and concreteonobloc sleepers (250 kg) on ballast. The operating speed

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298 A. Johansson, J.C.O. Nielse

f the one-way traffic X2 trains is 200 km/h. Roughness levelpectra evaluated in one-third octave bands, based on CAT mea-urements performed along track lengths ranging from 210 m to00 m, are shown in Fig. 1(a). The roughness level is defined by

kr = 20 log10

(rk

rref

)(1)

here rk (m) is the root mean square value of the roughnessrofile r(x) (m), evaluated in one-third octave band k with centreavelength λk (m),

k = 0.01 × 10k/10 (2)

ith k = −10, −9, . . ., 14, 15. Details concerning the mathemat-cal analyses of similar measured data are given in [5].

It is observed that the spectra from three of the four sites havesignificant local maximum in the wavelength interval 4–8 cm

ndicating severe short-pitch rail corrugation. These three railsere installed in 1993 or 1994 and have not been ground since

hen. At the sites Vretstorp and Sodertalje, the track has a positiveupward) slope of 10‰. No recording of traction effort of the X2owered units has been performed. However, for such large pos-tive slopes, the maximum traction effort (available at the currentpeed) is needed to maintain the speed 200 km/h. This means aotal distributed traction force of 55 kN for one power unit hav-ng four powered wheelsets. At Gardsjo, the track instead has aegative slope of 10‰. This rail was ground in September 2001.owever, after 18 months of traffic, there were no signs of rail

orrugation. Possibly this can be explained by the lower tractionffort required in a negative slope. Thus, the hypothesis adoptedn the present study is that high roughness levels are generatedy powered X2 units on track sections where they exert a highraction force at uniform train speed. The Toreboda site with a

egative slope of 3–4‰ could be an exception to the hypothesis.owever, in this case the high roughness levels could possiblye explained by that the train is braking when approaching aection of the track with speed limit 160 km/h (Fig. 1).

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ig. 1. (a) Roughness level spectra based on CAT measurements on selected secterformed in March 2003. The years when the rails, according to available databaseheel roughness spectra for powered and trailer X2 wheels are compared to disc/trea

ear 262 (2007) 1296–1307

As mentioned previously, out-of-roundness measurementsave been performed on several different types of railway wheels5]. The measured X2 wheels were randomly selected but allf them had travelled a distance exceeding 100,000 km. Theeasurements were conducted when the train coaches had been

aken out of traffic for maintenance for other reasons than wheelOR. In total, 10 powered X2 wheels and 5 trailer X2 wheelsere measured. For the powered X2 wheelsets, most of theraking is generated using disc brakes and electric braking byhe traction motor. A so-called scrubber brake was designedo keep the wheel tread clean and thereby increase the avail-ble wheel–rail friction. However, it was found that the scrubberrake is also used as a service brake, which was not the inten-ion in the original design. Thus, due to the frequent use of theast iron brake blocks, wheel corrugation is developed in theame way as on tread braked freight wheels, as explained byernersson [20].

Measured wheel roughness spectra (energy mean values) areiven in Fig. 1(b). Results from a Dutch investigation [21] onassenger train wheels with combined disc and tread brakingre also shown. The prEN ISO 3095 spectrum [15] that is usedo define a limit roughness level for rails in connection withcoustic type testing of trains is included for comparison. Notehat roughness levels on the powered X2 wheels are comparableo the results from [21]. The trailer X2 wheels (disc brakes only)ere found to be smooth.By comparing the measured rail and wheel irregularities in

ig. 1(a) and (b), it is observed that both roughness levels andominating wavelengths are similar. This raised the question ofhe influence of wheel corrugation on rail corrugation growth.

. Train-track interaction model

In the following subsections, the models of track, vehicle andheel–rail contact are described. The surface geometries of theheel tread and the rail head are also explained. More detailedescriptions are given in [8] and [12].

ions of the line between Stockholm and Goteborg. The measurements wereinformation, were installed or ground are reported in the legend, (b) measuredd braked passenger train wheels [21].

A. Johansson, J.C.O. Nielsen / W

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ig. 2. Illustration of the track model. The rail support consists of rigid sleeperasses (ms) and two layers of springs and dampers, (kp, cp) and (kb, cb),

epresenting the pads and the ballast/subgrade, respectively.

.1. The track and the vehicle

A principal sketch of the adopted model of a straight tracks shown in Fig. 2. The model is calibrated using experimentalata from a test campaign carried out in 2000 by Banverket andHARMEC, see [22]. The track model is three-dimensional in

he sense that it allows for simultaneous deflections and forcesn all three directions at the wheel–rail contacts. However, lon-itudinal and lateral track displacements are constrained to zeron the present application (see Section 6) to reduce the num-er of degrees of freedom in the model and thus the simulationime. The track model allows for asymmetric train motion sinceoth rails are included in the model. The track model is of finiteength, here 70 sleeper bays. The length of the model is cho-en to ensure that the rail boundary conditions have a negligiblenfluence on the dynamics when the wheelsets pass the studied

id-section of the track. The influence of lateral track dynamicsn rail corrugation growth on tangent track is studied in [9].

The track is divided into two main parts: the rails and theirupports. The rails are modelled using Rayleigh-Timoshenko-aint-Venant finite beam elements, accounting for transversehear deformation and rotatory inertia, see [23]. There are eighteam elements within each sleeper bay. Data for the present railodel are given in Table A.1 in Appendix A. Each support model

for one rail) describes the subsystem under the rail consistingf one railpad, one rail fastening, one half sleeper, the ballastnd the subgrade. It is here described as the discretized systemndicated in Fig. 2. The track model is taken as repetitive so thatll support models along the rail have the same property values,ee Table A.2 in Appendix A.

The properties of the track model were calibrated by compar-ng simulated wheel–rail contact forces from impacts of a wheelat to the corresponding loads measured in a wheel impact load

etector. The calibration procedure is further described in [24],hile the measurements are reported in [22]. In the calculatedertical track receptance, three resonances can be identified forrequencies below 2.5 kHz. The first resonance is obtained at

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ear 262 (2007) 1296–1307 1299

10 Hz. Here the complete track structure is vibrating in phasen the ballast. A second resonance, with a large relative motion ofail and sleepers, is obtained at around 300 Hz. The fundamentalinned-pinned rail resonance is found at 940 Hz.

The vehicle model is a three-dimensional bogie model con-isting of two wheelsets, a bogie frame and primary suspension.

multibody dynamics method, which allows for bodies thatndergo small elastic deformations but large rotations is used.he wheel axles may be treated as rigid, or as flexible according

o Euler-Bernoulli-Saint-Venant beam theory.

.2. The surface geometry of rail head and wheel tread

General wheel and rail profiles are used in the simulations.or the rail, the UIC60 profile is used with an inclination anglef 1:30, see Table A.1 in Appendix A. For the wheel, the nominal1002 profile is adopted.

An initial (low) level of roughness, including a wide spectrumf wavelengths, is present also on new rails. The adopted simula-ion strategy is to account for such an initial irregularity spectrumith wavelengths in the interval 2.0–31.6 cm. The wheels are

ssumed to be corrugated with an irregularity obtained fromhe measurements performed in 2002 [5]. Filtering of the initialrregularity profiles to account for the finite size of the wheel–railontact patch is performed prior to the simulation. The contactlter is applied by a successive averaging of the irregularityith a distance corresponding to the longitudinal length of theertzian contact patch for the current axle load. The ISO3095

pectrum before and after contact filtering is shown in Fig. 3(a).he algorithm for generation of the initial rail irregularity from

he ISO3095 spectrum, is described by Hiensch et al. [14].An example of a measured wheel OOR is given in Fig. 3(b),

here also the nominal radius of the wheel is indicated. Theeasured wheel OOR and the generated rail irregularities are

pplied to the elements defining the geometry of the wheel andail surface, respectively. For simplicity, it is assumed that thehapes of the initial irregularities are independent of the lateralosition on the wheel and rail profiles.

.3. The wheel–rail contact

In each time step of the simulation, the wheel–rail contactosition is computed by the contact search algorithm describedn [8], using the current positions of the wheel and the rail,ogether with the surface geometries of wheel tread and railead. The magnitude and the orientation of the contact loadre calculated by considering the normal and tangential contactroblems separately: the bodies in contact are assumed to beuasi-identical. Hertz theory was chosen for the normal contactroblem [25], while the model by Shen et al. was selected forhe tangential contact [26].

. Wear prediction

As discussed previously, the hypothesis adopted in the presentnvestigation is that rail corrugation is generated by pow-red high-speed train X2 wheels due to irregular wear in the

1300 A. Johansson, J.C.O. Nielsen / Wear 262 (2007) 1296–1307

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ig. 3. (a) Initial rail roughness level spectrum based on the ISO3095 spectrumeasurements. The dashed line represents the mean radius of the worn wheel.

heel–rail interface. Other damage mechanisms, such as plasticeformation in the wheel–rail contact, are not considered. Therchard wear model is defined by

wear = kwNd

H(3)

ith the parameters: Vwear is the volume of worn material (m3),the sliding distance (m), N the normal contact force (N), H

he hardness of the material (N/m2) and kw the wear coefficient.ased on Eq. (3), the formula for the wear depth distributionithin the contact patch, �z(x, y), is (with local coordinates (x,

))

z(x, y) = 3N kw

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(x

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y

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here a and b are the semi-axes of the contact ellipse, sx (m/s)nd sy (m/s) are the slips in longitudinal and lateral directions, υcs the speed by which a material point moves through the contactatch, and �x is the longitudinal length of one grid element ofhe FASTSIM discretization. For a more detailed derivation ofq. (4), see [27]. Note that the Archard wear model is valid only

n the slip region of the contact patch. The stick and slip regionsre determined from calculations in FASTSIM. The value ofhe parameter kw depends on the current combination of normalontact pressure and slip velocity.

Using the FASTSIM algorithm, the contact patch is dividednto ny strips in the lateral direction and each strip is divided lon-itudinally into nx elements. The coordinates x and y are chosens the midpoints of the elements in the grid of the contact patch.he wear depth is evaluated assuming that the slip s is piecewiseonstant in time. To obtain only one wear depth value in the lon-itudinal direction of the contact ellipse, all the contributions inne longitudinal strip are summed. In this way, a lateral distri-ution of wear depth is obtained for each contact ellipse. Thesealculated wear data form the basis of the wear interpolation onhe rail mesh using the algorithm described in [12].

. Coupling of train-track interaction and wear

The multibody system model for the train-track dynamicsnd the model for long-term wear prediction are coupled in an

H(c

e and after contact filtering, (b) wheel irregularity (exaggerated) based on OOR

teration process. A flow chart of the iteration scheme is givenn Fig. 4. First, a measured wheel OOR is applied on each wheelnd an initial rail irregularity is generated for each rail usinghe method described in [14]. A simulation of dynamic train-rack interaction along a selected number of sleeper bays (here5 sleeper bays) is performed where time histories of wheel–railontact forces, creepages, spins, etc. are calculated. The time his-ories in the beginning of the simulation that are influenced by theoundary conditions of the track model (e.g. the first 10 sleeperays) are excluded. In order to rapidly attenuate the effects of thenitial conditions, artificial damping in the vehicle primary sus-ension is added when the vehicle model is travelling along therst part of the track (here the first eight sleeper bays). The wear

s calculated using the truncated time histories as input to therchard wear model coupled to the FASTSIM algorithm. The

alculated wear depth is scaled with a factor to simulate a largeumber of wheelset passages (of the order of 104). The rail pro-les are updated, according to the mapping algorithm described

n [12]. A new simulation of dynamic train-track interaction ishen performed based on the updated irregularity for each rail,nd the obtained time histories are used to calculate wear thatpdates the rail surfaces once again. The solution of the dynam-cs of the coupled train-track system is achieved by using theime-stepping algorithm presented by Andersson [28].

. Results and discussion

In the following subsections, amplitude Fourier spectra ofifferent variables (e.g. contact forces and wear depths) wille presented. The spectrum N(fp) (N) for a discretized timeistory of a wheel–rail contact force N(tk) (N) with length T (s) isalculated for the (P + l)/2 (where P is an odd number) discreterequencies fp = p/T (Hz), p = 0,1, 2, 3, . . ., (P−l)/2, using theiscrete Fourier transform (DFT) as

ˆ (fp) = 2

P

P−1∑e−2πipk/PN

(kT

P

)(5)

k=0

ere the time history is given for P discrete times, tk = kT/Ps) k = 0,1, 2, 3, . . ., P−1. Only the magnitude |N(fp)| of theomplex spectrum is presented. Since the DFT is symmetric

A. Johansson, J.C.O. Nielsen / Wear 262 (2007) 1296–1307 1301

tions

wf(a

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ith respect to the mid (discrete) frequency, it is evaluated onlyor the first (P + l)/2 points. In Fig. 5, the power spectral densityPSD) spectrum is used. The PSD SN(fp) (N2/Hz) is calculateds

P 2

ˆN (fp) =

2fs

|N(fp)| (6)

ith fs (Hz) being the sampling frequency of the wheel–railontact force time history.

ig. 5. PSD of measured and simulated vertical wheel–rail contact forces. Trainpeed 200 km/h. Track properties and roughness level spectrum based on mea-urements at Vretstorp.

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of dynamic train-track interaction and calculations of wear.

.1. Validation of train-track interaction model

Vertical contact forces measured at test site Vretstorp are usedor a validation of the simulation model. Track receptances mea-ured with impact load excitation (no static preload) were usedo tune the track model at frequencies above 300 Hz. Ballast andail pad properties that have a large influence on track dynamicst lower frequencies were selected from another validation exer-ise that accounted for the vehicle load [24]. The measured trackontains UIC60 rails, Pandrol fastenings with resilient rail padsnd concrete monobloc sleepers on ballast. The roughness levelpectrum from Vretstorp in Fig. 1(a) was used to derive a samplef a rail roughness profile, using the method described by Hien-ch et al. [14]. Note that the measured roughness spectrum onlyontains information for wavelengths in one-third octave bandsith centre wavelengths up to 16 cm, corresponding to excita-

ion frequencies above f = 340 Hz at train speed υX = 200 km/husing f = υX/�, where λ is the wavelength). However, wave-engths in the interval 2–250 cm (22–2780 Hz) were accountedor in the simulations by using the ISO3095 spectrum to deter-ine roughness levels for one-third octave bands with centreavelengths longer than 16 cm.The PSD:s of the measured and simulated contact force for

he leading wheelset are compared in Fig. 5. Further, the trainodel containing two rigid wheelset masses of 1390 kg each and

xle distance 2.9 m is compared to a single rigid wheelset model.

he simulated PSD spectrum was derived from a response calcu-

ated along a distance of 19.3 m (30 sleeper bays, sleeper distance.645 m), while the recorded measurement distance was 800 m.oth spectra were derived after low-pass filtering of the signals

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302 A. Johansson, J.C.O. Nielse

sing the cut-off frequency 1500 Hz. To obtain an accurate PSDpectrum, a windowing technique (Tukey, cosine-tapered win-ow) was used together with averaging a number of overlappingSD:s of the same signal. The number of PSD:s was chosen toorrespond to a distance of about 2 m in each PSD calculationnd an overlap of 50% was used. The local maximum at 55 Hz,ommon for the measured and simulated results, is the so-called2 resonance, which is the resonance of the coupled wheelset-

rack system where wheelset, rails and sleepers vibrate in phasen the ballast/subground. The wide peak in the frequency range00–1400 Hz is due to the local maximum in the roughness levelpectrum for wavelengths 4–8 cm, see Fig. 1(a). For frequenciesbove 1500 Hz (not shown here), the measured PSD exceeds thealculated one because the measurement technology fails aroundhe wheel resonance at 1712 Hz. In general, the agreementetween calculated and measured contact forces is acceptable.

In Fig. 5, the difference between results from the two sim-lation models at frequencies around 570 Hz, 830 Hz, 1100 Hznd 1410 Hz should be noted. At these frequencies, local railending modes occur with boundaries constrained by the twoheelsets. It is observed that the magnitudes of the simulatedSD from the model with one rigid wheelset agree better with

he measured PSD. However, the model with one wheelset can-ot capture the effects of the local rail bending modes, which areisible in the measured PSD. It is believed that such modes aremportant for the development of rail corrugation, cf. [13,29].hus, the model with two wheelsets is selected even if the localaxima in the simulated PSD exceed the measured values. A

etter agreement is foreseen if the two wheelsets are modelled asexible using so called Craig-Bampton modes, see [2], but suchmodel would increase simulation times considerably. A fur-

her validation of the train-track interaction model is presentedn [30].

.2. Prediction of rail corrugation growth

.2.1. Modelling aspects and numerical input dataIn the model, an external driving torque is applied on each of

he powered wheelsets. A “braking force”, equal to the sum of thealculated longitudinal friction forces, is applied as a horizontalomponent of an external force acting on the bogie to maintainconstant vehicle speed.

The wear coefficient kw is chosen to have the constant value.0 × 10−4 since only train-track interaction on straight tracks simulated and all calculated combinations of contact pressurend sliding velocity are assumed to be located within one sectionf the wear map presented by Lewis et al. [31]. The adopted wearata were measured for the interaction of a UIC 900A rail and an8T wheel. However, the B92 material in powered X2 wheels

s similar to R8T. The hardness of the rail material H = 2.65 GPas based on investigations performed by Olofsson and Telliskivi32], while the coefficient of friction is set to μ = 0.4. In theimulations, only powered wheelsets on X2 trains are included

nd thus the influence of X2 trailer wheelsets, other passengerrain wheelsets and freight wheelsets on rail wear is neglected.he number of bogie passages in 1 year is based on the trainchedule for the line Stockholm–Goteborg during 2005.

fpa

ear 262 (2007) 1296–1307

Two initial rail irregularity profiles (one for each rail) areenerated based on the ISO3095 spectrum, see Fig. 3(a). Atrain speed υX = 200 km/h, the surface irregularities excite fre-uencies in the interval 176–2780 Hz. When wheel OOR is alsoncluded, the lower limit for the excitation frequency intervals decreased to 16 Hz corresponding to the wavelength of oneheel circumference (3.46 m). Using the model, it is possible topdate both wheel and rail irregularities in the same simulation.owever, in order to decrease simulation time, the wheel sur-

aces are not updated in the present investigation. According toernersson [7], the corrugation of cast-iron tread braked railwayheels is formed and stabilized only after a few braking cycles.urther, in [33], it was found that wheel roughness levels onast-iron tread braked wheels do not increase significantly withileage.

.2.2. ResultsTo study the effects of wheel OOR on rail corrugation growth,

n identical (measured) irregularity was first applied on all theheels of the bogie. This resulted in a sharp, high-magnitudeeak for the one-third octave band with centre wavelength.0 cm. Using different irregularities on the different wheelsenerated a broader spectrum. Finally, rotating the out-of-roundheels before the dynamics simulation in each iteration in Fig. 4ielded a decreased growth rate and thus a lower final rail cor-ugation level. The wheel rotations were performed to resembleeal conditions by assuring that the same point on the rail did noteet the same points on the wheels in each iteration. The cho-

en rotation angles were 20◦ and 40◦ for the leading and trailingnon-leading) wheelset of the bogie, respectively. Note that theheel rotations lead to a distribution (an averaging effect) of

rregular wear along the rail.Normal wheel–rail contact forces from simulations using

ound wheels (i.e. perfectly round, without irregularities) andnitial rail irregularities based on the ISO3095 spectrum arehown in Fig. 6. For comparison, wheel–rail contact forces dueo rail roughness developed after 4 years of train traffic areresented in Fig. 7. The sleeper passing frequency is seen atfrequency of approximately 85 Hz, but the force magnitude

t this frequency is not altered much after 4 years of X2 trainraffic (44,000 bogie passages). Comparing the initial wheel–railontact forces to the ones obtained after 4 years of roughnessrowth, it is seen that the force components increase in magni-ude around the frequencies 570 Hz, 830 Hz, 1100 Hz, 1410 Hz,750 Hz and 2200 Hz. These frequencies correspond to local railending modes between the wheelsets in the bogie. The pres-nce of such resonances have been reported by Igeland [13] andy Wu and Thompson [29]. Comparisons with a beam modelf the rail, with length corresponding to the wheelbase of theogie and pinned-pinned boundary conditions, confirm that theifferent modes correspond to three (570 Hz), four (830 Hz), five1100 Hz), six (1410 Hz), seven (1750 Hz) and eight (2200 Hz)alf wavelengths between the wheels of the bogie.

Fig. 8 shows that accounting for measured roughness on theour wheels leads to significantly higher contact forces com-ared to when the wheels are round. Some additional peaksre observed for frequencies below the sleeper passing fre-

A. Johansson, J.C.O. Nielsen / Wear 262 (2007) 1296–1307 1303

Fwr

qθ

HtoniarbOba(t

Fwr

Fwr

fi

lepatmdlengths and vice versa. However, changing the wheelbase willshift the frequencies of the modes (e.g. a longer wheel-base

ig. 6. Calculated (truncated) time history and Fourier spectrum of the normalheel–rail contact force for a wheel in the leading wheelset of the bogie. Initial

ail roughness and round wheels.

uency. These correspond to the low OOR orders (f = 16 Hz × θ,= 1, 2, 3, 4), possibly in combination with the P2 resonance.owever, these low frequencies (long wavelengths) do not con-

ribute to the roughness growth within the wavelength intervalf interest here (2.0–31.6 cm). Note that large force compo-ents corresponding to the local rail bending modes are foundn the results for both round (after 4 years of train traffic)nd out-of-round wheels (see Figs. 7 and 8). However, foround wheels, there is a smoother envelope around the contri-utions from the local rail bending modes than for wheels withOR present. This is probably due to additional large contri-

utions from high OOR orders. The peaks in the DFT spectrare separated by frequencies corresponding to the wheelbasef = υX/λ = 19.1 Hz) and the wheel circumference (16.1 Hz) inhe results for round and out-of-round wheels, respectively. The

ig. 7. Calculated (truncated) time history and Fourier spectrum of the normalheel–rail contact force for a wheel in the leading wheelset of the bogie. Rail

oughness developed after 4 years of train traffic and round wheels.

ya

Fpfi

ig. 8. Calculated (truncated) time history and Fourier spectrum of the normalheel–rail contact force for a wheel in the leading wheelset of the bogie. Initial

ail roughness and wheel OOR based on measurements.

requency resolution for the DFT spectra presented in Figs. 6–8s 2.1 Hz.

Fig. 9 shows the wear depth spectrum evaluated for a trackength of 25 sleeper bays when wheel OOR is neglected. Theffects of the local rail bending modes are also visible here. Theeaks around 4 cm, 5 cm and 6.7 cm correspond to the peaksround 1410 Hz, 1100 Hz and 830 Hz in Fig. 7. It should be notedhat the wavelength-fixing mechanism of the local rail bending

odes is frequency constant rather than wavelength constant, i.e.ecreasing train speed will cause corrugation at shorter wave-

ields lower resonance frequencies), see [9,13]. From Fig. 7nd Fig. 8, it is seen that the modes with frequencies close to

ig. 9. Calculated wear depth developed during the fifth year of train trafficresented as narrow band spectrum for left (upper figure) and right rail (lowergure). Round wheels.

1304 A. Johansson, J.C.O. Nielsen / W

Fig. 10. Calculated wear depth after one bogie passage for left (upper figure) andrrl

th

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sfbrtwr

ight rail (lower figure) evaluated in one-third octave bands. Comparison betweenesults from round wheels (solid lines) and wheels with OOR (dashed-dottedines).

he pinned-pinned rail resonance (around 940 Hz) generate theighest wheel–rail contact forces.

Fig. 10 compares the wear depth spectrum after one bogieassage assuming either round wheels or wheels with OOR.he wear depths are presented as one-third octave band spectra.

t is observed that rail wear depth levels after one bogie passage

ith wheel OOR are higher, especially for wavelengths shorter

han 8 cm, than the levels obtained after passage of the sameogie with round wheels.

ig. 11. Calculated rail roughness developed after 1 year of train traffic for leftupper figure) and right rail (lower figure). Comparison of results assuming eitheround wheels (solid line) or wheel OOR. The influence of using one (dashed-otted line), two (dotted line) or four (dashed line) iterations to study 1 yearf train traffic is studied. In each iteration, the wheels are rotated before theimulation of dynamic train-track interaction is started. The initial roughness isndicated by the lowest dashed line.

e5tttw

F(ii

ear 262 (2007) 1296–1307

Fig. 11 shows a comparison of rail roughness levels devel-ped after 1 year of train traffic when wheel OOR is accountedor in different ways. First, 1 year of train traffic is consid-red by performing only one iteration, see Fig. 4, either withound wheels or with one sample of wheel OOR. Alternatively,year of traffic is simulated by performing two or four iterations

including rotation of the wheelsets between each iteration). Thiseans that one loop in the iteration scheme corresponds to one,

ne half or one quarter of a year of X2 train traffic. It is evidenthat the number of iterations has an important influence on theredicted rail roughness level. Using more iterations to cover 1ear of traffic leads to an averaging effect of the irregular wearnd a slower roughness growth rate. Most of the results thatnclude wheel OOR generate higher roughness levels than if theheels are round. However, a “convergence” towards a level

lose to the results for round wheels is observed. This can alsoe seen in Fig. 12, which shows the roughness after 1 year ofrain traffic versus number of iterations. The roughness is givenas root mean square values) for the single one-third octave bandith centre wavelength 5.0 cm.In order to study the influence of wheelset flexibility, some

imulations were performed including eight modes of a free-ree wheelset modelled with Euler-Bernoulli-Saint-Venant finiteeam elements for the wheelset axle and lumped masses for theigid wheels. Three bending modes (multiple frequencies) andwo torsional modes with eigenfrequencies lower than 400 Hzere included. No significant change in the developed rail cor-

ugation was observed.Another simulation was performed in order to study the influ-

nce of train speed on the developed irregularity. For train speed0 km/h and increased applied torque according to the available

raction effort curve, it was found that the normal force magni-udes decreased, compared to the results for 200 km/h, whereashe longitudinal creepage magnitudes increased. The developedear depth was dominated by wavelengths corresponding to the

ig. 12. Calculated rail roughness developed after 1 year of train traffic for leftupper figure) and right rail (lower figure). Results from different numbers ofterations with wheel OOR (dash-dotted line). The result for round wheels (oneteration) is indicated by the solid line.

A. Johansson, J.C.O. Nielsen / W

Fig. 13. Calculated rail roughness developed after 1 (two lowest lines), 2, 3, 4, 5oCt

p(

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wwslmrnothe influence of corrugated wheels on rail corrugation growth

r 6 years of train traffic (bold solid and dotted lines). Wheel OOR is neglected.omparison to rail roughness measured after approximately 10 years of train

raffic.

eaks at 570 Hz (2.5 cm) and the P2 resonance around 55 Hz25 cm).

Roughness level spectra evaluated in one-third octave bandsorresponding to 6 years of train traffic are compared to mea-ured roughness levels in Fig. 13. Based on conclusions drawnrom Figs. 11 and 12, wheel OOR is neglected. Good agreements observed for the shape of the broad peak for wavelengthsetween 3 cm and 7 cm. However, for longer wavelengths (i.e.–16 cm), the numerical model underestimates rail roughnessrowth. An appropriate value for the scaling factor (i.e. theumber of passing bogies accounted for in each iteration) wasssessed by comparing results obtained with different trial scal-ng factors. Given that the wheels are round, it was found thatncluding 1 year of train traffic in each iteration generated veryimilar results as compared to if each iteration accounted foralf a year of train traffic.

The results in Fig. 13 indicate that the present model tendso overestimate the corrugation growth rate. Roughness levelsbserved in the field after about 10 years are obtained after 6ears of train traffic in the simulation model. Several possiblexplanations for this can be argued: The wear coefficient, asetermined by twin-disc experiments, varies between approx-mately 0 and 4.4 × 10−4 for a contact pressure up to about400 MPa, see [31]. In the present study, a constant value of.0 × 10−4 was chosen. Reducing the wear coefficient wouldeduce the corrugation growth rate. Other damage mechanisms,n combination with wear, may also be present. For example,lastic deformation of the corrugation peaks due to a higher localontact pressure has been suggested as a mechanism reducingeak-to-peak corrugation magnitudes [34]. Corrugation gener-ted by other vehicles (e.g. freight locomotives, passenger trainst other train speeds, with other wheelbases, etc.) will distribute

he wear to other wavelengths. This could however lead to eitherncreased or decreased corrugation growth in different wave-ength intervals. The wear is updated along the path of the

cnc

ear 262 (2007) 1296–1307 1305

heel–rail contact patch. From the numerical simulations, itas found that the lateral motion of the wheel–rail contact patchas of the order of 0.1 mm. However, the initial conditions were

he same for each iteration in the numerical model. In reality,ateral motion due to e.g. long wavelength lateral track irregu-arities could distribute the wear in the transverse direction ofhe rail surface and reduce the corrugation growth rate. Finally,n the numerical model it is assumed that all passing wheelsetsave the same transverse wheel profile. In a real application, dif-erent wheels may have different worn wheel profiles, causingheel–rail contact at different lateral positions. Thus, for many

easons, the present numerical simulation may be seen as a worstase scenario.

Despite all these uncertainties, the present numerical modelas shown to be a good prediction tool for rail corrugation. Theypothesis suggesting that powered X2 wheelsets, exerting highractive forces at uniform train speed, contribute significantly tohe rail corrugation has been verified. It should, however, beoted that also other powered units than X2 may contribute tohe rail corrugation. The wavelength interval and growth rate ofuch contributions depend on the current combinations of e.g.rain speed, wheelbase and magnitude of traction force.

. Concluding remarks

A numerical tool for qualitative and quantitative predictionf rail corrugation growth has been demonstrated. The validatedime domain model accounts for a wide frequency range ofynamic train-track interaction, and both wheel and rail irregu-arities are treated. Results from simulations of rail corrugationrowth have been compared to measurements and the agreementith respect to dominating corrugation wavelengths and annualrowth was satisfactory. It was found that the wide spectrum ofail corrugation with wavelengths ranging from 3 cm to 8 cm,bserved in field measurements, was partly explained by pas-ages of powered X2 wheelsets exerting high tractive forces atconstant train speed of 200 km/h. Bending modes of the rail,

onstrained by the two wheelsets in a bogie, were found to bemportant for the corrugation growth. However, the corrugationrowth rate seems to be overestimated by the current model.everal potential reasons for this, such as a conservative choicef wear coefficient, were discussed. Plastic deformation maylso decrease the growth rate, as well as lateral variations of theheel–rail contact positions for different wheelset passages.The wear depth after one bogie passage with corrugated

heels was found to be much larger as compared to if roundheels are present. However, due to an averaging effect from

everal passing wheels with different samples of wheel irregu-arities (in the simulation model accounted for by rotating the

easured wheel irregularities in each iteration relative to theail), the annual rail roughness growth decreased with increasingumber of iterations and converged to a level similar to the onebtained for perfectly round wheels. Thus, it is concluded that

an be neglected. However, wheel–rail contact forces are sig-ificantly higher for severely corrugated wheels traversing aorrugated rail than if the wheels are round. This shows that

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306 A. Johansson, J.C.O. Nielse

se of the cast iron scrubber brake as a service brake should bevoided. Another remedy would be to use sinter or compositerake blocks instead of cast iron blocks. Several benefits woulde obtained by a revision of the tread brake system, such aseduced wheel corrugation growth, reduced rolling noise levels,ncreased turning intervals and reduced risk of premature fatigueailure of vehicle and track components.

cknowledgements

This work was performed at the Department of Appliedechanics, Chalmers University of Technology in Goteborg,

weden. It forms part of the activities in the Centre ofxcellence CHARMEC (CHAlmers Railway MEChanics),ee www.charmec.chalmers.se. Professor Roger Lunden gavealuable comments on the manuscript. Dr. Stuart Grassie iscknowledged for discussions concerning the origin of the wheelorrugation and its influence on rail corrugation growth.

ppendix A

.1. Rail

The rail parameters given in Table A.1 are used in theayleigh-Timoshenko-Saint-Venant beam theory. The rail incli-ation is 1:30.

.2. Track support

The track support parameters given in Table A.2 were deter-ined by tuning of the model to obtain good agreement between

able A.1arameters of the rail model (UIC60 profile)

arameter Value

ending stiffness about lateral axis EIY (MNm2) 6.41ending stiffness about vertical axis EIZ (MNm2) 1.08aint-Venant torsional stiffness GKV (MNm2) 0.18ass distribution (kg/m) 60ross section area (m2) 7.69 × 10−3

oung’s modulus (GN/m2) 210oisson’s ratio 0.3

he bending stiffnesses have been calculated with respect to the principal axesf inertia through the centre of gravity of the cross-section.

able A.2arameters of the track support model

arameter X Y Z ϕX ϕY ϕZ

p (MN/m) or (kNm/rad) – – 120 – 225 –

b (MN/m) or (kNm/rad) – – 140 – 915 –

p (kNs/m) or (Nms/rad) – – 16.0 – 30 –

b, (kNs/m) or (Nms/rad) – – 165 – 1080 –

s (kg) or (kgm2) – – 125 – 2.0 –

ach parameter may hold three values which correspond to the translation direc-ions X (along rail), Y (across rail) and Z (vertical), and three values whichorrespond to the rotationsϕi for i = X, Y, Z. A dash (–) corresponds to a parameterot included in the model.

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ear 262 (2007) 1296–1307

alculated impact loads from a wheel flat and the correspondingeasured wheel–rail contact forces, see [24].

eferences

[1] S.L. Grassie, J. Kalousek, Rail corrugation: characteristics, causes andtreatments, in: Proceedings of the Institution of Mechanical Engineers,J. Rail Rapid Transit, part F 207 (1) (1993) 57–68.

[2] J.C.O. Nielsen, A. Ekberg, R. Lunden, Influence of short-pitch wheel/railcorrugation on rolling contact fatigue of railway wheels, in: Proceedings ofthe Institution of Mechanical Engineers, J. Rail Rapid Transit, part F 219(3) (2005) 177–187.

[3] J.C.O. Nielsen, A. Johansson, Out-of-round railway wheels—a literaturesurvey, in: Proceedings of the Institution of Mechanical Engineers, J. RailRapid Transit, part F 214 (2) (2000) 79–91.

[4] J.C.O. Nielsen, R. Lunden, A. Johansson, T. Vernersson, Train-track inter-action and mechanisms of irregular wear on wheel and rail surfaces, VehicleSyst. Dyn. 40 (1–3) (2003) 3–54.

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