REVIEW PAPER 1 Rail corrugation: characteristics, causes...

REVIEW PAPER 1

Rail corrugation: characteristics, causes, and treatmentsS L GrassieAbbauernring 1, 30900 Wedemark, Germany. email: [email protected]

The manuscript was received on 29 November 2008 and was accepted after revision for publication on 20 May 2009.

DOI: 10.1243/09544097JRRT264

Abstract: Rail corrugation is a phenomenon of great diversity but appears now to be substantiallyunderstood. This review proposes some differences in classification of the phenomenon to takeaccount of work undertaken since a widely cited review was published by Grassie and Kalousekin 1993, it attempts to fill holes in an overall understanding of the problem, and answers ques-tions that remained open in 1993 and several that have arisen since. All types of corrugationthat have been documented to date are essentially constant-frequency phenomena. By treat-ing the vehicle/track system in its entirety, treatments are proposed that impinge upon trackand vehicle design as well as upon the wheel/rail interface where corrugation appears. There isno neat solution to rail corrugation, but it can be treated comprehensively and in many casesalso prevented by using products that are already commercially available. Since the frequencyof common wavelength-fixing mechanisms varies roughly in the range 50–1200 Hz, trains travel-ling at different speeds can produce corrugation of substantially similar wavelength by differentmechanisms in different locations. Although historical data can no longer be checked, this is themost likely explanation of the belief that rail corrugation was a substantially constant-wavelengthphenomenon.

Keywords: rail corrugation, rail corrugation measurement, measuring equipment, vehicle–trackinteraction, wheel–rail interface, vehicle dynamics, rails, rail fastenings, friction modification

1 INTRODUCTION

Irregularities on wheels and rails give rise to noise,ground-borne vibration and more general dynamicloading, which increases damage of components ofboth vehicle and track. Both wheels and rails are proneto develop quasi-sinusoidal irregularities, which areknown as corrugation when their wavelength is lessthan about a metre. Longer wavelength irregularitiesare usually known as ‘waves’ when they occur on railsor ‘out-of-roundness’ on wheels. Although the effectsof irregularities are substantially the same whetherthey occur on wheels or rails, the mechanism by whichmost types of irregularities occur differs in significantrespects. Consequently while this article is relevant inseveral respects to irregularities on both wheels andrails, it concentrates on rail corrugation. Excellent ref-erences on wheel irregularities are the review paper byNielsen and Johansson [1] and the proceedings of aworkshop held at the Technical University of Berlin in1997 [2].

The overall mechanism by which corrugation arisesis illustrated in Fig. 1, which first appeared in thisform in reference [3], although a similar feedback

loop has been widely used. The initial longitudinal railprofile excites a so-called ‘wavelength-fixing mecha-nism’, which represents the dynamic behaviour of thevehicle/track system. This mechanism ‘fixes’ not onlythe wavelength but also the position of the eventualcorrugation along the track. Other parameters, partic-ularly the tangential forces between the wheel and rail(‘traction’) and the allowable limit of these forces (‘fric-tion’) have some effect on this dynamic mechanism.For example, if a corrugation arises from periodic slipof the wheel on the rail, this is more likely to occurwhen the tangential force is close to the limit that canbe sustained by friction. The dynamic force acts as theinput to a so-called‘damage mechanism’, which resultsin a change in the initial longitudinal rail profile.

The most common ‘damage mechanism’ on almostall types of railways is wear. Other damage mecha-nisms are plastic bending of the rail, which occurswhen the rail is bent beyond its yield point (rather likea wire coat hanger) and plastic flow. Rolling contactfatigue (RCF) is exacerbated by corrugation, but (con-trary to what is stated in reference [3]) does not itselfappear to be a damage mechanism of the same formas wear or plastic flow, which change the profile of a

JRRT264 Proc. IMechE Vol. 223 Part F: J. Rail and Rapid Transit

2 S L Grassie

Fig. 1 A general corrugation mechanism (from refer-ence [3])

surface in the manner represented in Fig. 1. The influ-ence of RCF on corrugation and vice versa is discussedfurther in section 5.

The dynamic force that is output from thewavelength-fixing mechanism may be normal to thewheel/rail contact or tangential, or indeed both. Forthose types of corrugation for which the damagemechanism is wear, a useful sub-classification can bemade into those types in which there is a periodicvariation in force normal to the wheel/rail contactand those in which the significant variation is longitu-dinal. A relatively simple, quasi-analytical treatmentof the former category of corrugation, in which thewavelength-fixing and damage mechanisms are mod-elled independently, is given in reference [4]. Evidencefrom the field suggests that lateral dynamic behaviourgives rise to corrugation in only a few cases where thereis a pronounced resonance (section 8).

This contribution summarizes significant character-istics of rail corrugation of different types, providesphotographs and measurements of corrugation tohelp identify different types of corrugation from theirappearance, suggests relatively simple methods thathave helped to identify specific types of corrugation,and states treatments that have been either shown towork or that should work. Although basic backgroundmaterial is provided for all types of corrugation, itconcentrates on work that has been done since 1993.The article also unashamedly reflects the author’s owninterests since 1993, which have been more in the areaof understanding and providing practical solutions ofthis problem than in modelling it.

Corrugation tends to be more prevalent in curves. Itis sometimes more severe on the high rail, sometimesmore severe on the low rail, and occasionally of similarseverity on both rails. The reason for this difference isexplained here and provides a treatment that may insome cases also be a solution.

2 CLASSIFICATION OF CORRUGATION

The most common types of corrugation that have beendocumented in the literature can be classified accord-ing to their wavelength-fixing and damage mecha-nisms, as shown inTable 1.The approximate frequency

Table 1 Types of corrugation, characteristics, references, and treatments

Treatments1

Type

Wavelength-fixingmechanism Where?

Typicalfrequency(Hz)

Damagemechanism

Relevantfigures References

Demonstrablysuccessful

Should besuccessful

1 Pinned–pinnedresonance(‘roaringrails’)

Pinned–pinnedresonance

Straighttrack, highrail ofcurves

400–1200 Wear 2–6 [5–23] Hard rails,controlfriction

Increase pinned–pinned frequencyso that corru-gation wouldbe <20 mmwavelength

2 Rutting Secondtorsionalresonanceof drivenaxles

Low rail ofcurves

250–400 Wear 2, 7–11 [5, 6, 24–36] Frictionmodifier, hardrails, reducecant excess,asymmetricprofiling incurves

Reduce appliedtraction in curv-ing, improvecurvingbehaviourof vehicles,dynamicvibrationabsorber

3 Other P2resonance

P2resonance

Straight trackor high railin curves

50–100 Wear 3, 6, 17, 18 [4, 24, 37] Hard rails,highlyresilienttrackforms

Reduce unsprungmass

4 Heavy haul P2resonance

Straight trackor curves

50–100 Plastic flowin troughs

10, 12–14 [38–40] Hard rails Reduce cant excesswhen corrugationis on low rail

5 Light rail P2resonance


50–100 Plasticbending

15, 16 [41] Increase railstrength andEI

Reduce unsprungmass

6 Trackform-specific

Trackformspecific


– Wear 19, 20 [24, 42] Hard rails,frictioncontrol

Avoid ‘peaky’resonances,improve steering

Note: 1Grinding or reprofiling more generally is a treatment for all types of rail corrugation. Irregularities in general, such as from welds andjoints, should also be reduced as far as possible.

Proc. IMechE Vol. 223 Part F: J. Rail and Rapid Transit JRRT264

Rail corrugation: characteristics, causes, and treatments 3

range associated with the wavelength-fixing mecha-nism is tabulated since it is now clear that all typesof corrugation are essentially constant-frequency phe-nomena. Their wavelength at a particular location isaccordingly

λ = v/f (1)

where v is the speed of those trains that give rise tothe corrugation and f is the frequency of the perti-nent wavelength-fixing mechanism. Identification ofthis frequency is a powerful instrument in determin-ing the type of corrugation at a particular location. Forexample, in a project undertaken in the USA in themid-1990s a simple measurement was made at eachsite with a ruler of the average corrugation wavelengthand this was used with the line speed for that sectionof track to give the effective corrugation ‘frequency’for the site [5, 6]. Frequencies of possible wavelength-fixing mechanisms, which were found from dynamictesting on track and vehicles, were shown on the samegraph. An example of this simple analysis is shownin Fig. 2. At three of the six sites the corrugation ‘fre-quency’ corresponds to the frequency of the secondtorsional resonance of driven wheelsets (which is thecase for the so-called ‘rutting’ corrugation, section 4),it is close to the pinned–pinned resonance frequencyat one site (section 3), and lies slightly above the fre-quency of the second torsional resonance at two sites.At one of these two sites there was a trackform thathad been associated with corrugation on this metroand others (section 8).

Treatments that have been demonstrably successfulor that should be successful are summarized in Table 1,relevant figures in this article are shown, and refer-ences are provided. The majority of references are for

Fig. 2 Correlation of corrugation frequency and fre-quency of possible wavelength-fixing mecha-nisms (from reference [5])

work that has been undertaken since 1993. The prin-cipal exceptions to this are for those areas in whichrelatively little work has been done in the interven-ing years: heavy haul, light rail, and trackform-specificcorrugation (sections 6–8). For the first two types ofcorrugation, this largely reflects the fact that a goodunderstanding already existed in 1993, from which asolution had been developed that the railways foundsatisfactory.

3 ‘ROARING RAILS’ OR ‘PINNED–PINNEDRESONANCE’ CORRUGATION

3.1 Characteristics

‘Roaring rails’ or ‘pinned–pinned resonance’ corru-gation occurs primarily in straight track and gentlecurves, where curving is undertaken with minimalflange contact. It is more likely to occur on the highthan on the low rail in curves and is associated alsowith track carrying relatively light axle load traffic, i.e.<20 tonne. Examples from a metro system and fromthe UK main-line railway are shown in Figs 3 and 4.

If there is a so-called ‘white phase’ in the runningband on the head of a rail, one of the first signs of

Fig. 3 ‘Pinned–pinned resonance’ and ‘P2 resonance’corrugation on the same rail


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Fig. 4 ‘Pinned–pinned resonance’ corrugation withmodulation over sleepers

corrugation is a periodic constriction in the band ofwhite phase. (Development of ‘white phase’ is not dis-cussed here since it is not fundamental to corrugationdevelopment. This material is an extremely shallow(50 μm), hard, martensitic layer that apparently devel-ops as a result of rapid heating and quenching of therail surface during wheel slip [43–45].)The corrugationshown in Fig. 4, which is typical of ‘roaring rails’ seenon the UK main-line railway system, would first haveappeared as a periodic constraint of one of the twobright running bands that lie along the rail. In somecircumstances the corrugation is very much clearerover and on the approach to sleepers (Fig. 4).

Corrugation measurements for the same rail on ametro system, before and after grinding, are shown inFig. 5. This illustrates the effect of modulation not onlyat sleeper pitch (∼0.9 m) but also, to a lesser extent,by a P2-resonance corrugation at a wavelength of∼300 mm. The filtered displacement in the 30–100 mmwavelength range and the one-third octave spectra (inthe format prescribed in reference [46]) are shown.

The irregularity shown in Fig. 5 is <100 μm (0.1 mm)deep but is nevertheless an extremely severe pinned–pinned resonance corrugation. A short wavelengthcorrugation of this amplitude would be sufficient forthere to be loss of contact in the corrugation troughsfor all but the lowest speed traffic, so that a wheelwould hammer along the track contacting only thecorrugation peaks. The magnitude of impacts in suchcases can be several times the static wheel load. It isunsurprising that such corrugation is often known as‘roaring rails’ and is associated with rapid deteriora-tion of ballast, sleepers, and fastening components.

When the speed of traffic is closely controlled, thereis a clear peak in the corrugation spectrum. This isthe case for the metro in Fig. 5, for which the pinned–pinned resonance corrugation has a wavelength of

Fig. 5 Measurements of corrugation before and after grinding: filtered displacement (30–100 mmwavelength) and one-third octave spectra



∼40 mm. However, if speeds vary there is a corre-spondingly broad peak in the spectrum, as was notedin early measurements of corrugation from the Britishmain-line railway [15].

When reprofiling is undertaken to a high standard,as has been done with the ground rail in Fig. 5, irregu-larities are not only extremely small but also show notrace of the periodicity of the original corrugation. Thesmall periodic irregularities at 10 and 20 mm, whichresult from a slowly moving grinding train, are of a sim-ilar length to the contact patch between a train wheeland the rail, and are rapidly removed by traffic.

3.2 Cause

At its pinned–pinned resonance the rail vibrates as ifit were a beam that was almost pinned at the sleep-ers (or periodic rail fastenings). The frequency of thisresonance is

f = π

2L2

√EIm

[1 − 1

2

(πrg

L

)2(

1 + 2(1 + υ)

K

)](2)

where m and EI are the rail’s mass per unit length andbending stiffness, respectively, L is the sleeper spacing,rg is the radius of gyration, and K (≈0.34) is the shearconstant of the cross-section. Clearly the corrugationwavelength is longer the greater the sleeper spacingand the lower the rail stiffness. A typical frequency isabout 770 Hz for 56 kg/m rail and a 0.7 m sleeper spac-ing or 1200 Hz for 60 kg/m rail and 0.6 m spacing. The40 mm corrugation wavelength in Fig. 5 correspondswell to the predominant speed of about 65 km/h and a460 Hz resonant frequency for rail at about 0.9 m spac-ing, and is similar to the wavelength of corrugationon main lines where speeds are very much higher.

Corrugation is worse over sleepers (Figs 4 and 5)because the support appears dynamically stiff andvertical dynamic loads are correspondingly greater.

The damage mechanism for pinned–pinned res-onance corrugation is wear. It can be shown fromrelatively simple dynamic models of the track andvehicle (e.g. reference [47]) that dynamic loads at thefrequencies of interest are high on corrugation peaksand low in the troughs. This behaviour encourages slipand wear of the troughs. A simple analytical methodto calculate the corrugation growth rate in such cir-cumstances is given in reference [4]. This analysissuggests that where vertical dynamic loads are simi-lar, corrugation would be more severe the greater thesteady-state wear rate. This corresponds to the evi-dence that pinned–pinned resonance corrugation incurves is usually more severe on the high rail.

It was proposed in reference [3] that resilient rail-pads should be effective in reducing this type ofcorrugation, but modelling suggests instead that theyhave relatively little effect on dynamic loads asso-ciated with the pinned–pinned resonance [10]. Thishas also been found in practice. For example, Fig. 6shows the filtered profile of corrugation in the 30–100 mm wavelength range and the one-third octavespectra for two sections of track with supports ofvery different resilience. These sections of track are<500 m apart between the same stations on the samemetro line, they are in curves of similar radius, andare both ground routinely at about the same time.Although the severity of pinned–pinned resonancecorrugation is very similar (RMS amplitudes are 13.8and 14.8 μm in the 30–100 mm wavelength rangeshown), there is a significant difference in longer wave-length corrugation, for reasons that are explained insection 5.

Fig. 6 Corrugation on resilient (dark) and stiff (light) trackforms: filtered displacement(30–100 mm wavelength) and one-third octave spectra


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The pinned–pinned resonant frequency is signifi-cantly higher than the frequency of other wavelength-fixing mechanisms and accordingly gives the shortestwavelength for a given train speed. An extremely prac-tical question that arises is why corrugation is seldommeasured with a wavelength of <30 mm and extremelyrarely with a wavelength of <20 mm.The answer to thisquestion is found in the influence of contact mechan-ics between the wheel and rail. This essentially as afilter that attenuates wavelengths of <20 mm [7, 12].

4 RUTTING

4.1 Characteristics

‘Rutting’ was identified as a specific type of corru-gation in reference [3] and there has since been awealth of work in this area, e.g. [4, 5, 21–36]. This typeof corrugation occurs primarily on the inside rail incurves, e.g. Figs 7 and 8, although it may also occurin straight track where traction or braking is particu-larly severe. Discrete irregularities such as welds andjoints (e.g. Fig. 7) are common ‘triggers’ for corrugationand often fix the position of corrugation along the rail.Rutting usually has an extremely uniform wavelengthand appearance and can develop quickly to a depth oftenths of a millimetre.Wear debris is sometimes appar-ent to the naked eye, which is seldom if ever the casefor other types of corrugation. Plastic flow can occuron a well-developed corrugation (Fig. 8).

4.2 Cause

In a broad study of corrugation on North Americantransit systems, it was found that rutting of the insiderail in curves was not only the most common corru-gation mechanism but was also associated with thesecond torsional resonance of driven wheelsets, e.g.Fig. 2 [5, 6]. The first and second torsional resonancesare illustrated in Fig. 9. The frequency of the secondtorsional resonance is commonly about 250–400 Hz.A frequency of 250 Hz corresponds to a corrugationwavelength of 50 mm for vehicles at 45 km/h, which isa common speed for metro vehicles.

Rutting occurs where the traction ratio (the ratio oftangential to normal force) on one wheel is close tothe friction limit, so that this wheel slips and drivesthe opposite wheel in the wheelset in a roll–slip oscil-lation. It is usually the wheel on the leading wheelsetin a bogie on the high rail that slips, since the tan-gential force from curving is greatest on this wheeland the coefficient of friction is often less (becausethe gauge face of the high rail is lubricated to reducewear, and there is often some migration of lubricant).Applied traction increases the tangential force on theouter leading wheel and reduces it on the lower leading

Fig. 7 ‘Rutting’ on the inside (low) rail in a curve

Fig. 8 ‘Rutting’ showing development of plastic flow

wheel, thereby increasing the difference in tangen-tial force across the wheelset and exacerbating thestick–slip oscillation. These influences are illustratedin Fig. 10 [31, 32], which shows the traction ratio atboth wheels on leading and trailing axles of a bogieas a function of curve radius and for two values ofapplied traction. The traction ratio shown comprises



Fig. 9 Torsional resonances of wheelset (from reference[6])

components from both curving and applied traction(T /N = 0 for a coasting vehicle; T /N = 0.28 for a loco-motive or metro vehicle with half the axles motored). Aconventional vehicle suspension and wheel/rail pro-files were modelled, and the coefficient of friction wasassumed to be 0.4 at all contacts. The trailing wheelset‘steers’ well for all cases, so there is a relatively lowtraction ratio at both outer and inner wheels (‘highrail’ and ‘low rail’ wheels, respectively). For the lead-ing wheelset under coasting conditions (T /N = 0), thetraction ratio from curving alone causes slip at theouter wheel for curves of less than about 600 m radius,in which the modulus of the traction ratio is limited bythe coefficient of friction of 0.4: these would be con-ditions to initiate roll–slip oscillations in such curves.If the applied traction ratio were as great as 0.28, con-ditions for roll–slip oscillation exist even in curves of>1000 m radius.

The damage mechanism for rutting is clearly wear,which is quasi-periodic with high peaks correspond-ing to the slip phase of a roll–slip oscillation. Theimportance of longitudinal slip is illustrated by thelongitudinal scuffing marks in Fig. 11, which showsthe low rail of a 200 m radius curve on a suburban rail-way that had been treated with the so-called ‘frictionmodifier’ to reduce both corrugation and other rail

Fig. 11 Longitudinal scuffing apparent in friction mod-ifier in low rail of 200 m radius curve

damage (section 9). Because the friction modifieraffects the slip phase of the roll–slip oscillation, ithas been a particularly effective treatment of rutting[28–30, 35].

In the German language there is an interesting dis-tinction between ‘Schlupfwellen’ (‘slip waves’), whichoccur in curves, and ‘Riffeln’ (‘ripples’), which occur instraight track. German research in the last 20 years hasconcentrated on ‘Riffeln’ and there has been very littlework on ‘Schlupfwellen’.

5 OTHER P2 RESONANCE CORRUGATION

5.1 Characteristics

Tassilly and Vincent associated the P2 resonance withlonger wavelength corrugation on the rapid transit

Fig. 10 Traction ratio on leading and trailing wheelsets of a bogie resulting from curving andapplied traction


8 S L Grassie

Fig. 12 ‘P2 resonance’ corrugation on a tram system

system (RATP) in Paris, although only as a factorthat exacerbated the effect of the fundamental tor-sional resonance of wheelsets [24]. Evidence from fieldmeasurements and observations undertaken over thelast 15 years indicates that the P2 resonance is sig-nificant not only in heavy haul and light rail cor-rugation (sections 6 and 7) but also as one of themost prominent and frequent causes of corruga-tion on a wide variety of railways. For example, thelonger wavelength corrugation in Fig. 3 has resultedfrom excitation of the P2 resonant frequency, andthis is the source of corrugation at 300–400 mm inthe measurements (from the same railway) shownin Fig. 6. Also, while it was proposed in reference[3] that corrugation on tramways (Fig. 12) resultedfrom excitation of the fundamental torsional reso-nance of axles, this appears instead to be caused bythe P2 resonance. In both ballasted and non-ballastedtrack the P2 resonance can cause long wavelengthcorrugation that is clear when enhanced artificiallyby rail grinding (e.g. Fig. 13), but is otherwise dif-ficult if not impossible to see with the naked eye.The difficulty of both seeing and measuring suchlong wavelength corrugation may well have led to itsrelative neglect.

The frequency of both the P2 resonance and the firsttorsional resonance of wheelsets is commonly in therange 50–100 Hz, so it is unsurprising that severe cor-rugation can result where both resonances are excited.This can occur in tight curves in metro systems,as noted by Tassilly and Vincent [24]. Corrugationthat has arisen from a resonance in this frequencyrange is a particular problem on metros because therelatively low-frequency ‘rumble’ is transmitted wellinto buildings and occasional amplified by structuralresonances that occur at similar frequencies.

Fig. 13 ‘P2 resonance’ corrugation on ballasted track,highlighted by grinding

5.2 Causes

The P2 resonance is, by definition, the wavelength-fixing mechanism for this type of corrugation andwear is the damage mechanism. If there are circum-stances in which the fundamental torsional resonancecan be excited and if the resonant frequencies coin-cide, this exacerbates the effects of the P2 resonancealone.

Empirical evidence from five transit systems citedin reference [6] suggested that corrugation resultingfrom the P2 resonance on ‘direct fixation’ fasten-ing systems was absent if the track support stiffnesswas less than about 30 MN/m per fastening assembly.This has been supported by subsequent measure-ments. For example, the measurements of Fig. 6 showthat P2-resonance corrugation is pronounced on atrackform in which timber sleepers embedded in con-crete are the main resilient layer, but is essentiallyabsent on a commercially available trackform (‘Pan-drol Vanguard’) whose support stiffness is ∼5 MN/mper assembly.



6 HEAVY HAUL CORRUGATION

‘Heavy haul’ corrugation is the term introduced in ref-erence [3] to describe the type of corrugation that hadbeen found to exist on so-called heavy haul railways.Summary information for this type of corrugation isgiven in Table 1 and a typical example is shown inFig. 14.

The dearth of literature in this area in the last 15years strongly suggests not only that the problem issatisfactorily understood but also that the treatmentsproposed have been similarly satisfactory. The treat-ment adopted is the use of hard rail to resist plasticflow combined with routine rail grinding to reduceirregularities that excite the P2 resonance.

Heavy haul corrugation is associated in the literaturewith straight track and the ‘high’ rail in curves. There isevidence that corrugation occurs by substantially thesame mechanism on the low rail of over-canted curveson mixed traffic railways that carry significantly loweraxle loads than on heavy haul railways (Fig. 15). Thereason for this is that plastic flow occurs more readilythe higher the traction ratio and normal contact stress[48]. For a vehicle curving at balance speed the tractionratio is greater at the high rail than on the low rail foralmost all circumstances (Fig. 10). It is accordingly rea-sonable to expect that plastic flow would occur morereadily on the high rail in these conditions, as in Fig. 14.However, when a bogie curves with cant excess, thetraction ratio on the low rail wheel increases signifi-cantly because the trailing wheelset moves in towardsthe low rail and the leading wheelset moves towardsthe high rail, thereby increasing the angle of attack.There are high lateral loads on the leading, low railwheel and also high contact stresses, because con-tact tends to occur towards the field side of the wheel,which is often slightly convex. The direction of plasticflow, towards the inside of the curve (Fig. 15), is consis-tent with lateral forces arising from the angle of attackof the leading wheelset.

Where corrugation occurs by this mechanism on thelow rail of mixed traffic lines, it is often because track

Fig. 14 ‘Heavy haul’ corrugation

Fig. 15 ‘Heavy haul’ corrugation on low rail of a mixedtraffic railway

Fig. 16 Spalling in the trough of a heavy haul corruga-tion

has been canted for a few high-speed passenger trains,whereas the more damaging traffic is higher axle load,lower speed freight trains.

An example is shown in Fig. 16 of spalling that hasdeveloped from RCF in the trough of a corrugation. Itappears more likely that RCF is a consequence of thehigh loads in the trough of such a corrugation ratherthan its cause, as was suggested in reference [3].

7 ‘LIGHT RAIL’ CORRUGATION

Corrugation that bears many similarities to that expe-rienced on heavy haul railways was identified in the1980s on track that is now operated by AustralianRail Track Corporation [41] but is also present else-where. The corrugation propagates from welds andhas a wavelength in the range 500–1500 mm (Fig. 17).As with heavy haul corrugation, the absence of recentliterature in this area suggests that the problem isnot only well understood but also that the treatmentsadopted for it are substantially satisfactory. Accord-ingly only summary information is provided in Table 1.


10 S L Grassie

Fig. 17 Profile of light rail corrugation, showing prop-agation from the rail ends (about 15 m raillength)

The principal difference between light rail and heavyhaul corrugation is that the damage mechanism forthe former is plastic bending of the rail, so that cor-rugation is measurable on both railhead and railfoot.The treatment that has been adopted is to straightenwelds and joints, thereby reducing the main irregular-ities that excite the P2 resonance, and to grind railsto eliminate existing corrugation. Modern rail steelsand more robust rail sections have a sufficiently highbending strength to resist damage by this mechanism.

8 TRACKFORM-SPECIFIC CORRUGATION

Some trackforms are associated with rapid corruga-tion formation, while corrugation on others occursless quickly. An example is shown for 20 m of trackin Fig. 18, where there is a different trackform to theleft and right of a weld. In some cases a trackform

performs quite acceptably in some circumstances, ifnot indeed in most, but corrugates quickly in othercircumstances.

Both Tassilly and Vincent [24] and Ahlbeck andDaniels [42] noted that corrugation occurred relativelyrapidly on the low rail in curved track on a trackformcomprising sleepers mounted in resilient boots. Suchtrackforms are often used in metro systems to reduceground-borne vibration. Guidance was given in refer-ences [24] and [42] as to how to reduce the severityof such corrugation, including lubrication in curves.However, these measures do not guarantee that suchcorrugation is avoided.

A different non-ballasted trackform has given riseto the corrugation in Fig. 19. The wavelength-fixingmechanism in this case is the lightly damped reso-nance of a large, resiliently supported baseplate on theresilience of the railpad, at a frequency of ∼400 Hz. Rel-atively stiff non-ballasted trackforms corrugate fromexcitation of the P2 resonance (section 5).

A common characteristic of trackforms on whichcorrugation occurs preferentially in some if not all cir-cumstances is a pronounced resonance. In the case of

Fig. 19 Corrugation (25–30 mm wavelength) resultingfrom resonance of baseplate on railpad

Fig. 18 Trackform-specific corrugation: different trackform to the left and right of the weld at15.725 km



‘booted sleeper’ trackforms, the significant resonanceis one for lateral excitation at the railhead [24, 42],whereas in others (e.g. for P2-resonance corrugationand the trackform in Fig. 19) the resonance is one inwhich there is a high vertical dynamic load.

9 CORRUGATION MEASUREMENT

The ‘CAT’ or corrugation analysis trolley (Fig. 20),which has been developed in the last 15 years, has pro-vided consistent, reliable corrugation measurementsthat enable conditions on different systems to be com-pared, e.g. Figs 5, 6, and 18. This instrument hasbeen widely used to measure both corrugation andacoustic roughness [4, 19, 22, 33, 49]. It is possibleto make long measuring runs (limited only by thestamina of the user and storage on the computer)at a walking speed of ∼1 m/s [51]. This equipment,Q1which is a development of Harrison’s trolley profilome-ter [23], is robust, reliable, and used by main-lineand metro railway systems, universities, consultan-cies, and grinding contractors worldwide. Equipmentsuch as this is essential in order to reliably demon-strate that rail has been reprofiled to the requirementsof the European Standard for reprofiling of rails [50]or that the rail is ‘smooth’ to the requirements of ISO3095 [46] or the evolving ‘technical specifications forinteroperability’.

10 CORRUGATION TREATMENT

Table 1 lists treatments of different types of corru-gation. The success of some treatments has been

Fig. 20 CAT in use

demonstrated, while in other cases the success of thetreatment should follow from the explanation of causethat is given here. Whether or not a treatment is a pre-ventative measure, a cure of an existing problem, orsimply a means of reducing the severity of corrugationdepends on several factors, including particular cir-cumstances, the type of corrugation, and whether thetreatment is applied in isolation or as one of severalmeasures. To take the simplest example, the classi-cal treatment of corrugation is rail grinding, which isregarded by many as a palliative rather than a cure.However, if corrugation is initiated by railhead irregu-larities (as is manifestly the case with heavy haul andlight rail corrugation, e.g. Fig. 17), removal of existingirregularities will often delay recurrence of corruga-tion sufficiently to be considered in practice as anextremely satisfactory treatment even if it does noteliminate the underlying mechanism that causes thecorrugation. This underlying mechanism does indeedexist on all tracks. It is also clear that corrugationdoes not occur everywhere that trains curve with cantexcess, but where it does there is excellent evidencethat reduction of cant would greatly reduce if noteliminate corrugation.

10.1 Reprofiling and removal of corrugation

It is clear from the basic mechanism that gives rise toany type of corrugation (Fig. 1) that reduction of rail-head irregularities is a basic treatment of all types ofcorrugation. In the case of heavy haul and light railcorrugation, where the damage mechanism involvesexceedence of some threshold (the shakedown limitto cause plastic flow or yielding of the rail in bending),removal of irregularities may itself be sufficient to pre-vent the recurrence of corrugation. Where the damagemechanism is wear, reprofiling is more of a treatmentthan a cure, albeit an extremely successful one if it isadministered satisfactorily.

An example of grinding that has satisfactorilyremoved corrugation is shown in Fig. 21(a), whereasa rail on which grinding has left a severe, periodic,quasi-transverse ‘signature’ is shown in Fig. 21(b).The distance between grinding scratches in the lat-ter case is simply L = v/f , where v is the speed ofthe grinding train and f is the rotational frequencyof the motors (typically 50 or 60 Hz). Corrugationwould recur relatively slowly on the rail with min-imal roughness and periodicity, but can grow par-ticularly quickly if the grinding signature excites apossible wavelength-fixing mechanism. A Europeanstandard now exists that states objective limits on thelongitudinal irregularities that should remain on a railafter reprofiling [50]. Measurements taken using theinstrument shown in Fig. 20 demonstrate that majorrail grinding companies routinely grind rail to thisstandard, in Europe and elsewhere.


12 S L Grassie

Fig. 21 Ground rail (a) with minimal residual longitudi-nal irregularity and (b) with residual periodicity

An alternative method for controlling the longitudi-nal profile is in principle offered by ISO3095, whichis intended to standardize the method of measur-ing rolling noise from rail vehicles [46]. This standardstates limits on rail roughness that can exist at a sitewhere vehicle testing is undertaken.

It is also important to reduce discrete irregularitiesat welds that ‘trigger’ corrugation. Rails of 80 m lengthare now common, with which there are many fewerwelds than with rails of 15 m length, such as those inFig. 17. A reasonable requirement for welds is that theyshould be finished to an irregularity of <1.5 mrad, i.e.<0.4 mm under a 1 m straight edge.

10.2 ‘Hard’ rails

Hard rails are a treatment of all types of corrugation.Insofar as the yield strength of these rails is high, theyresist plastic flow and are therefore a treatment ofheavy haul corrugation, while a high bending strengthresists light rail corrugation. If the threshold for plastic

flow or plastic bending is raised sufficiently, corruga-tion by these mechanisms may be eliminated entirelysimply by satisfactory rail selection.

It was proposed in reference [3] that hard railsshould alleviate those types of corrugation for whichwear is the damage mechanism. Although no evidenceexisted at the time that this was the case, the successof the treatment has since been demonstrated in testson main-line track in Germany in which corrugationdeveloped at about two-thirds of the rate on 350BHNrail as on 260BHN rail [16]. The reduced corrugationpropensity of open hearth rail steel, e.g. references[3] and [13], remains unexplained, and is now slightlyacademic since open hearth rail steel is rarely if everproduced.

10.3 Control of friction

Friction is potentially significant for all types of cor-rugation in which wear is the damage mechanism,insofar as the higher the coefficient of friction thegreater the potential wear rate. If the railhead fric-tion coefficient can be controlled to a value of about0.35, this is sufficient for vehicle traction and brak-ing while limiting damage from plastic flow and wear.Rain, rust, and a generally moist atmosphere are oftensufficient to maintain friction to modest levels. How-ever, in a dry environment, particularly in dry tunnels,the friction coefficient can approach 0.6, with severeconsequences for wear.

So-called ‘friction modifiers’ are commercially avail-able to control the coefficient of friction to levelsof about 0.35. These offer a demonstrably success-ful means of controlling all types of corrugation forwhich wear is the damage mechanism [28–30, 35]. Thetreatment is particularly effective in treating ‘rutting’,which results from a roll–slip oscillation of the wheelon the rail since these substances limit the reductionof friction with sliding speed, thereby eliminating thepotential instability associated with a falling frictioncharacteristic.

Although some control of railhead friction can beobtained by judicious adjustment of gauge face lubri-cation, this should be used only with great care. Toomuch oil or grease on the railhead can lead to trainsbeing unable to brake satisfactorily.

10.4 ‘Improved steering’ and reduction oftangential loads

Curves are particularly prone to corrugation as a resultof the high tangential forces that arise from steering,particularly in combination with applied traction.There are several ways of reducing these forces bydesign of the track, the vehicle or the wheel andrail profiles, as well as by controlling friction itself(section 10.3).



Curving forces are particularly damaging when thereis excessive cant. Reducing cant not only gives moresimilar tangential forces on opposite wheels in awheelset [31] but also reduces the tangential force onthe low rail. This reduces stick–slip oscillation, andthereby rutting, and heavy haul corrugation where thisoccurs on the low rail. Reduction of cant is also inher-ently safer since it reduces the angle of attack of thebogie and thereby also the potential for flange-climbderailment.

Wheel and rail profiles that increase rolling radiusdifference are an effective method of reducing curv-ing forces on an existing railway, and demonstrablysuccessful in reducing corrugation in curves. Profilesthat increase rolling radius difference encourage con-tact along the gauge shoulder and gauge corner ofthe rail, thereby increasing contact stresses. Conse-quently, such profiles are best designed judiciously asone component of a wheel/rail interface strategy thatconsiders vehicle dynamic behaviour as well as wheeland rail damage.

Applied traction causes stick-slip oscillation tooccur in less severe curves. Consequently, if corruga-tion was considered at an early stage in the design ofa railway system, it would be desirable to place curvesfar from stations.

Differences in wheelset diameter and misalign-ments of wheelsets within a bogie should be strictlycontrolled in order to minimize the resulting tangen-tial forces and thus the propensity for wheels to slip.Mono-motor bogies should be avoided for this reason.

10.5 Trackform

Classical ballasted track provides a combinationof resilience and damping that fortuitously avoidsunnecessary resonances and reduces the effect ofthose that do exist. One of several reasons that corru-gation is associated with metros is that non-ballastedtrackforms are common and there is little guidanceas to how corrugation might be avoided on suchtrackforms.

In order to reduce the potential for corrugation,a trackform should have a low P2 resonance, andhigh damping of any resonant behaviour that cannotbe avoided. The trackform in Fig. 6 for which thereis no long wavelength peak in the one-third octavespectrum has excellent characteristics in this respect.

‘Roaring rail’ corrugation appears to be an unavoid-able consequence of track that is supported periodi-cally and on which trains travel sufficiently quickly thatthe resulting corrugation is longer than the contactpatch. However, roaring rail corrugation tends to beshallow, so that it can be relatively easily controlled byroutine rail grinding. In principle a continuous sup-port should reduce the severity of roaring rail corru-gation. However, continuously supported track tendsto be relatively stiff, thereby increasing the likelihood

of P2-resonance corrugation. It is also more diffi-cult to control track geometry during construction.Introduction of an artificial aperiodicity in supportspacing appears intuitively attractive. However, thelikely effect for any practical aperiodicity is that thepinned–pinned resonance and anti-resonance wouldmove to those frequencies corresponding to the meansupport spacing, and the modulation of contact forcewould decrease slightly. The severity of corrugationwould decrease slightly but maintenance would besignificantly more expensive.

It was suggested in reference [3] that resilient rail-pads were a possible panacea for several types ofcorrugation. Experience in the meantime indicatesthat corrugation is affected relatively little by the rail-pad except where this provides the principal resilienceof the track support.

10.6 Wheelsets

When corrugation results from the torsional reso-nance of solid axles, modification of this dynamicbehaviour may significantly reduce the problem if notsolve it entirely [5, 6]. There is some evidence thatrutting is greatly reduced when the wheelset is tor-sionally resilient, as occurs with some types of resilientcoupling of driven axles. High torsional resilience ofnon-driven axles is rare. The opportunity still exists todevelop a torsional dynamic vibration absorber for anoperating vehicle to attenuate rutting corrugation, asproposed in reference [6].

10.7 Traffic

All types of corrugation whose cause has beenexplained to date are substantially constant-frequencyphenomena. Consequently, the more consistent thespeed of trains and the less varied the traffic, themore consistent the wavelength of any corrugationthat results from excitation of a particular wavelength-fixing mechanism. Consistency is the bane of anydynamic problem and variety can be at least part ofthe solution. Measurements have demonstrated thatpinned–pinned resonance corrugation resulting fromtrains travelling at one speed can actually be wornout by changing the train speed, and re-establishedat a different wavelength [22]. A true mixed traffic rail-way, with a mix of both vehicle type and train speed,is an ideal antidote to corrugation formation, but isincreasingly uncommon.

11 CONCLUSIONS

A review of rail corrugation by Grassie and Kalousekin 1993, which has been widely cited in the sub-sequent literature, proposed that the phenomenoncould be categorized by different ‘wavelength-fixing’


14 S L Grassie

and ‘damage’ mechanisms. Six different types of cor-rugation were thus identified at that time. In theintervening years there has been relatively little pub-lished work in the areas of light rail and heavy haulcorrugation, from which it could reasonably be con-cluded that these are not only well understood butalso that satisfactory treatments have been developedand are being implemented. Those treatments are pri-marily routine reprofiling of the rails, minimization ofirregularities at welds, and the use of hard rails (forheavy haul corrugation) or rails with greater bendingstrength (for light rail corrugation).

Evidence of heavy haul corrugation on the low railof curves on mixed traffic railways is examined here.Such corrugation occurs when curves are over-cantedfor lower speed, heavier freight traffic. A high angleof attack results from poor steering, causing leadingwheelsets to run in contact with the field side of thelow rail. High contact stresses result from these con-tact conditions and high tangential loads from poorsteering. Together these cause plastic flow. If curveswere instead canted for lower speed traffic, this wouldreduce both corrugation and other types of damagethat occur on the low rail in curves. This would alsobe inherently safer since the lower angle of attackdecreases the risk of flange climb derailment.

With hindsight it is clear that most research on cor-rugation from the 1970s until the late 1990s was onroaring rails. This research has demonstrated con-clusively that roaring rails are a constant-frequencyphenomenon whose wavelength-fixing mechanismis the rail’s pinned–pinned resonance. Although thiswavelength-fixing mechanism is unavoidable to theextent that it is desirable for track to be supportedperiodically, both hard rails and control of friction aretreatments for this type of corrugation. Where roar-ing rails occur on the high rail in curves, they can bereduced by any measure that improves curving andreduces wear of the high rail.

Since the mid-1990s there has been a wealth ofresearch worldwide on rutting. This has demonstratedconclusively not only that rutting is a roll–slip oscilla-tion associated with differential tangential force on thetwo wheels of a wheelset but also that the wavelength-fixing mechanism is the second torsional resonance ofthe wheelset. Rutting occurs preferentially on the lowrail in curves because the curving force on the outerleading wheel of a bogie is higher than on the insidewheel, thereby causing the outer wheel to slip anddrive a roll–slip oscillation on the inner wheel. Appliedtraction on driven axles causes the outer wheel to slipin curves of greater radius.

The trackform has a more significant effect on cor-rugation than was recognized in 1993, and there areseveral trackform-specific types of corrugation. Reso-nant behaviour should be avoided as far as possibleand those resonances that do exist should be welldamped. Damage from the P2 resonance can be

minimized by ensuring that a trackform has adequateresilience and damping.

Although it was thought in 1993 that RCF couldbe a distinct damage mechanism, it appears morelikely that RCF is a consequence of high loads thatresult from corrugation rather than being the meansby which the rail is initially damaged.

Considerable advances have been made that enablecorrugation to be treated and in many cases pre-vented. Substances that modify the coefficient offriction between the wheel and rail have been deliber-ately developed as a method of reducing corrugation.These have been widely and thoroughly tested, andare extremely successful treatments, particularly ofthe roll–slip oscillation that gives rise to rutting. Ithas been demonstrated that hard rails reduce corru-gation for which the damage mechanism is wear, aswell as being one of the principal components of thesuccessful treatments of heavy haul corrugation. P2-resonance corrugation has been essentially eliminatedon at least one commercially available, highly resilientnon-ballasted trackform that was developed primar-ily to reduce ground-borne vibration. Wheel and railprofiles offer a means for reducing corrugation, par-ticularly in curves, but should not be considered inisolation as profiles that improve curving behaviourcan exacerbate other problems. It remains the casethat any other method of reducing curving forces,such as the use of self-steering bogies, should alsoreduce corrugation in curves but demonstration of thisremains a challenge for the future.

Rail grinding remains the most widely used treat-ment of rail corrugation and will continue to beessential even if treatments are found that reducethe rate of corrugation development. Although manyrailways have developed their own grinding specifica-tions, a European standard has been developed in thelast 15 years that can be applied to control the qualityof rail grinding in an objective and readily quantifiablemanner. Equipment has been developed with whicha continuous measurement can routinely be madeof tiny amplitudes of corrugation over essentially anunlimited distance. This equipment can be used notonly to control grinding but has also provided a widelyused tool in corrugation research.

For decades it was thought by many (including theauthor) that corrugation was a phenomenon in whichthe wavelength varied relatively little with speed. Thisbelief was based on a substantial volume of circum-stantial evidence, such as that shown in Fig. 22, whichcontained data from a Midland Railway survey in1911, observations from Harrison’s doctoral researchon British railways in the 1970s, and from Vancou-ver Skytrain in the 1980s. It is no longer possible toexamine whether all these data arose from a singlecorrugation mechanism, but there is convincing evi-dence for an alternative explanation, summarizedhere in Table 1. This is essentially that corrugation



Fig. 22 Variation of corrugation wavelength with speed(from reference [3])

at lower speeds results largely from lower frequencywavelength-fixing mechanisms, whereas that at higherspeeds results from higher frequency wavelength-fixing mechanisms. To take some examples givenhere, roaring rail corrugation could result at a wave-length of 40–60 mm on a metro line with vehicles at65 km/h and a pinned–pinned resonance at 460 Hz,on a British main-line with vehicles at 160 km/h and apinned–pinned resonance at 770 Hz, and on a Germanmain-line with vehicles at 250 km/h and a pinned–pinned resonance at 1200 Hz. Rutting could occurat roughly the same wavelength on a metro withvehicles travelling at 45 km/h from the second axletorsional resonance at 250 Hz. The data in Fig. 22demonstrate the effect of what Prof Knothe has termed‘non-steady-state contact mechanics’ in ensuring thatalmost no corrugation is measured with a wavelengthof <20 mm [12].

There may exist a single, all-encompassing the-ory that explains all corrugation, and perhaps alsoexplains neatly why corrugation occurs from differ-ent mechanisms in different places. This contributionprovides guidance but no such neat solution. It insteadsurveys developments in the area of rail corrugationfrom the viewpoint of a practitioner and railwayman,whose interests lie more in providing solutions thathave a sound theoretical basis and whose effects arethoroughly documented and understood than in per-fecting the theory. The success in both explaining andtreating rail corrugation would not have been achievedwithout accepting not only that both theory and obser-vation have contributed immensely to this area, butalso that each has its limitations.

ACKNOWLEDGEMENTS

The author is grateful to Schweerbau GmbH for theuse of CAT measurements and of a photograph; toBrian Whitney, Principal Rail Management Engineer,Network Rail for the use of a photograph; and to

clients, colleagues and friends whose contributionsand support have helped him to question and developaccepted wisdom. He is immensely grateful to Profes-sor K L Johnson, his close colleague, friend and mentorfor many years. Although we may have been misled inthinking for so long that corrugation was a constantwavelength phenomenon, we probably got more rightthan wrong.

© Authors 2009

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JRRT264

Queries

S L Grassie

Q1 Reference 51 appears before reference 50. This is against the Journal style; hence please re-number thereference to maintain the order.

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