Out-of-round railway wheels-a literature survey

/Transit Engineers, Part F: Journal of Rail and Rapid
Proceedings of the Institution of Mechanical
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DOI: 10.1243/0954409001531351
2000 214: 79
Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit J. C. O. Nielsen and A Johansson
Out-of-round railway wheels-a literature survey
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Out-of-round railway wheelsÐa literature survey
J C O Nielsen1Ãand A Johansson2
1CHARMEC,Department of Solid Mechanics,Chalmers University of Technology,GoÈteborg,Sweden
2Frontec Research and Technology AB,GoÈteborg,Sweden
Abstract:This literature survey discusses the state-of-the-art in research on why out-of-round railway wheels are developed and on the damage they cause to track and vehicle components.Although the term out-of-round wheels can be attributed to a large spectrum of different wheel defects,the focus here is on out-of-round wheels with long wavelengths,such as the so-called polygonalization with1±5harmonics (wavelengths)around the wheel circumference.Topics dealt with in the survey include experimental detection of wheel/rail impact loads,mathematical models to predict the development and consequences of out-of-round wheels,criteria for removal of out-of-round wheels and suggestions on how to reduce the development of out-of-round wheels.
Keywords:railway wheel out-of-roundness,polygonalization,wheel/rail impact load detectors,removal criteria
1INTRODUCTION
Imperfections on the wheel tread can have a detrimental influence on both track and vehicle components such as sleepers,rails,wheelsets and bearings.Examples of imperfections are isolated wheelflats,causing severe re-peated high-frequency impact loads,and polygonal wheels with irregularity wavelengths of approximately1m,lead-ing to an increased low-frequency component of the dynamic wheel/rail contact force.These are both regarded here as types of wheel out-of-roundness(OOR).The disastrous Eschede accident in Germany in June1998may have started with a fatigue crack in the wheel rim caused by the fluctuating contact force on a non-round wheel tread.
The OOR also leads to impact noise and/or increased rolling noise.Thus,in order to minimize costs for repair and maintenance and to meet noise legislation,there is a large economic incentive for detecting and replacing non-round wheels in time.Also,the cause of OOR should be investigated in order to find suitable countermeasures. Current Swedish criteria for determining if a railway wheel should be replaced or not are based on the length of a wheelflat.However,recent studies have shown that there may be other wheel defects causing large impact forces that are not covered by the present criteria for wheel removal. For example,the depth of a flat may be more important than its length.Since it is desirable to remove all wheels that cause additional damage to trains and tracks,new criteria need to be developed as well as new methods for detection of wheel defects.
The objective of this literature survey is to describe the state-of-the-art in research on why out-of-round railway wheels are developed and on the damage they cause to track and vehicle components.The present survey,with56 references,stems from an original technical report[1] where119references are cited.Focus is on wheel defects with irregularity wavelengths in a range from about0.5m up to the full wheel circumference.
2CLASSIFICATION OF WHEEL TREAD IRREGULARITIES AND THE PROPOSED
ORIGIN OF THE DIFFERENT PHENOMENA
The sections below classify different types of defects on railway wheel treads.Emphasis is put on defects with longer wavelengths,but local defects and defects with shorter wavelengths are also dealt with.For the classifica-tion,reports[2]to[4]have been used.
2.1Eccentricity
Eccentricity is caused by misalignment in the fixation of the wheel during profiling or reprofiling,and it is present to some extent on all railway wheels.
2.2Discrete defect
This is a deviation of the wheel radius that is present over a small part of the tread.The deviation may be caused by a wheelflat or by inhomogeneous material properties.Plastic
79
The MS was received on14June1999and was accepted after revision for
publication on4January2000.
ÃCorresponding author:CHARMEC,Department of Solid Mechanics,
Chalmers University of Technology,SE-41296GoÈteborg,Sweden.
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deformation is common in conjunction with this wheel tread defect.
2.3Periodic non-roundness
This type of OOR has a periodic irregularity around the wheel circumference superimposed on the constant wheel radius.The wavelength of the irregularity ranges from 14cm to approximately one wheel circumference,while the amplitude is of the order of1mm.This defect has been detected only on disc-braked wheelsets.
According to Zacher[5],examples of periodic OOR with one,three and four periods around the wheel circumference have been found on wheels from ICE trains in Germany. Investigations carried out at DB AG by Rode et al.[6]state that the fixation(claw clamping)of the wheel during reprofiling may be a cause of a triple-shaped polygon.This initially small OOR is amplified during rolling.
Figures1and2are two examples taken from Pallgen[7], showing periodic OOR on ICE wheelsets.The wavelength contents of the different wheel tread defects are also given in the figures.A conclusion from the investigation is that the third harmonic dominates for solid steel wheels,while the second harmonic dominates for rubber sprung wheels. Based on experiments performed by an international workgroup(UNRA)on the Gotthard line,MuÈller et al.[8] state that OOR may be caused by inhomogeneous material properties around the wheel circumference.Another ex-perimental and theoretical investigation of periodic OOR has been carried out by Werner[9].Here,a coupling to the frequencies of natural vibration of the railway wheelset is used to explain the OOR.
2.4Non-periodic(stochastic)non-roundness
This type of OOR may be caused by unbalances in the wheelset or by inhomogeneous material properties of the wheel.As for periodic non-roundness,this defect has been observed only on disc-braked wheelsets.
So-called stochastic OOR has been detected on ICE wheels in Germany[7].An example of a non-periodic (stochastic)OOR is shown in Fig.3,where the wavelength content of the OOR is also illustrated.From the figure it can be concluded that the stochastic shape contains several different harmonics.
2.5Corrugation
This defect appears on wheel treads that are block braked. The dominating circumferential wavelength of this type of OOR is3±6cm,while the amplitude is smaller than 10ìm.Experimental and theoretical studies(numerical simulations)of the development of this type of defect have been performed by Vernersson[10,11].The proposed and verified hypothesis is that,during block braking,some regions on the wheel tread become warmer(formation of hot spots owing to a thermoelastic instability,TEI)than neighbouring regions.The heated regions protrude from the wheel surface owing to thermal expansion and they are therefore subjected to more wear than the other parts of
the
Fig.1Detected OOR of a solid steel wheel with dominantly three harmonics around wheel circumference.The bars indicate the distribution of different harmonics of the OOR.(From reference[7])
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wheel tread surface.When the wheel cools down,the volume of material at these hot spots decreases (valleys are formed),which results in a corrugation pattern.It is noted that corrugation is a main source of rolling noise.
2.6Roughness
The circumferential wavelength of this defect is in the order of magnitude of 1mm,while the amplitude is of the order of 10ì
m.
Fig.2Detected OOR of a rubber sprung wheel with dominantly two harmonics around wheel circumference.The
bars indicate the distribution of different harmonics of the OOR shape.(From reference [7
])
Fig.3Detected non-periodic OOR.The bars indicate the distribution of different harmonics of the OOR shape.
(From reference [7])
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2.7Flats
This type of defect is due to unintentional sliding(without rolling)of the wheel on the rail.The primary cause is that the braking force is too high in relation to the available wheel/rail friction.The reason for this may be that the brakes are poorly adjusted,frozen or defective.Another reason may be that there are regions where wheel/rail friction incidentally and locally becomes low.
2.8Spalling
Spalling is the term used for the rolling contact fatigue phenomenon occurring when surface cracks of thermal origin meet,resulting in part of the wheel coming away from the wheel tread.The thermal cracks may arise in the hard and brittle martensite that is developed owing to heating and rapid cooling of the wheel tread during and after block braking.
2.9Shelling
Shelling is a term normally used for all types of subsurface induced cracks.It is manifested by loss of flakes of material from the wheel tread.Excessive vertical wheel/rail contact forces with respect to the diameter of the wheel is the primary cause for this particular form of rolling contact fatigue.
3DETECTION AND SIMULATION OF OUT-OF-ROUND WHEELS
Impact loads due to wheel defects may cause rail fracture as discussed in reference[12].The risk of fracture increases at low temperatures.The most severe type of wheel defect is a newly developed wheelflat with sharp edges.Older wheelflats with rounded edges may also damage sleepers and ballast.Different types of wheel defects may also cause high-cycle fatigue of wheels and other vehicle components, such as bearing failures[12].
3.1Experimental detection of impact loads
The two most common approaches to detect impact loads are based on the use of either strain gauges or acceler-ometers.The Association of American Railroads(AAR) uses both methods.Details on the function of the two detector systems are given in report[13]:
1.The first approach is known as WILD(Wheel Impact Load Detector).This system is composed of a series of strain gauges in a shear gauge load circuit configuration on the web of the rail.Ten vertical load circuits are installed on each rail.The coverage of this system is not complete,since wheels with different diameters cause maximum impact loads at different positions on the rail.
2.In the second approach,seven accelerometers are placed on each rail.This system offers a coverage of nearly100 per cent for all wheel diameters.However,the registered acceleration does not give a quantitative measure of the size of the impact load.Therefore,approach1is more widely used in North America.
In1991,a series of wheel impact tests was performed at the Transportation Test Centre in Pueblo,Colorado,United States.These tests are discussed by Kalay et al.[14]and by Stone et al.[15].The two types of detectors described above were tested.Both accidental and machined wheel defects were considered.The investigation showed that both types of detectors clearly identified wheels with tread defects,but,because of long-wavelength OOR,the repeat-ability of measurements was not quite satisfactory.In Figs 4and5,the detection uncertainties of the different detectors,for a wheel with a long(0.5m)wavelength defect,are illustrated.
Impact loads and rail accelerations were found to increase with increasing depth of the wheel defects and as functions of train speed.The scatter in the measurements increased with increasing speed and increasing size of the wheel defects.The optimum impact load threshold level, where out-of-round wheels with long-wavelength defects were most easily identified by the WILD system,was found to be in the range60±80kips(267±356kN).The train speed at which most defective wheels were most easily identified was found to be40mile=h(64.4km=h). The corresponding values for the accelerometer-based detection system were200±300g and50mile=h (80.5km=h).Increased acceleration levels could also be measured on the rail opposite that hit by the defective wheel.Further,since loaded and non-loaded cars with the same wheel defects produced approximately the same acceleration levels,the same threshold limit can be adopted in both cases.
Kalay et al.have investigated impact loads as a function of train speed[16].Data are given for different lengths of wheelflat and depths of the longer-wavelength defects in Figs6and7respectively.Loads increase with the length of the wheelflat and with the depth of the long-wavelength defect.
Other examples of available techniques to measure wheel/rail contact forces include strain gauges mounted on wheelset axles or strain gauges applied to the wheel web (see reference[17]).Ohtani[18]reports that the East Japan Railway Company has developed a system for detecting wheelflats.The principle of the computer-based method is to detect shock waves in the rail caused by a rolling wheel with a wheelflat.
Another method for detection of wheelflats and corruga-tion defects is to analyse the frequency spectrum of the measured rail acceleration.A description of this method based on the so-called cepstrum function in conjunction with Fourier analysis is given by Braccialli et al.[19,20].
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3.2
Numerical simulation of the influence of out-of-round wheels
Several mathematical models for simulation of dynamic wheel/rail interaction in the presence of imperfections on the railhead and wheel tread have been developed.These are,for example,described in the literature surveys by Knothe and Grassie [21]and Nielsen [22].
Imperfections on the wheel tread,such as pits,flats and
thermally affected zones,may lead to large impact forces owing to dynamic interaction of the wheel and track.The studies by Jenkins et al.[23]and Newton and Clark [24]are contributions in this field that had a significant influence on the early understanding of the effects of out-of-round wheels.Jenkins et al.[23]carried out a theoretical and experimental study,where different types of impact forces were treated and suggestions of an improved wheel design were given.Experimental and
theoretical
Fig.4Impact loads due to a long-wavelength (0.5m)wheel defect measured with a WILD detector.
1kip 4:45kN and 1mile =h 1:609km =h.(From reference [15
])
Fig.5Measured accelerations due to a long-wavelength (0.5m)wheel defect.1g 9:8m =s 2and
1mile =h 1:609km =h.(From reference [14])
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approaches to investigate impact loading due to wheelflats were described by Newton and Clark [24].Results from calculations with three different mathematical models were given and compared with results from experiments.It was concluded that the models are applicable in different
frequency intervals of the impact loads,i.e.for different train speeds.
Impact loads present on the Northeast Corridor high-speed track in North America are dealt with in papers by Ahlbeck and Hadden [25,26].The studies report
both
Fig.6Experimental measurements of impact loads from wheelflats versus train speed.The different lines show
that the impact load increases with the size of the flat.1kip 4:45kN,1mile =h 1:609km =h and 1inch 25:4mm.(From reference [16
])
Fig.7Experimental measurements of impact loads from wheels with longer-wavelength defects (18±22in long
defects around the wheel circumference)versus train speed.The different lines show that the impact load increases with the depth of the wheel defect.1kip 4:45kN,1mile =h 1:609km =h and 1mil 0:0254mm.(From reference [16])
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experimental work and numerical investigations.The influ-ence of sleeper bending modes on impact loads is examined in a mathematical model and the loading on bearings is discussed.The wheel defects that were investigated were 25±40cm long and2±4mm deep.These caused peak impact loads whose amplitude was greater than400kN [25].It was concluded that wheel defects with long wavelengths often lead to large impact loads,and that these wheel defects are not always easily detected by visual inspection of the wheel.Therefore,other methods need to be used[26].
Ahlbeck and Harrison[27]measured wheel profiles and adopted a mathematical model to predict impact loads from these defects.It was concluded that high-frequency impact loads at the wheel/rail interface are substantially attenuated by the wheelset mass.However,longer-wavelength tread irregularities leading to lower-frequency excitation may result in significant loads on the bearings.It was found that these loads increase with the ratio of depth to wavelength of the OOR.
An early experimental and theoretical investigation of the effects of out-of-round railway wheels on railway bridges was carried out by FryÂba[28].Results from an investigation with the purpose of specifying geometry limits on allowable wheel irregularities are presented by Grassie[29].Predictions made by an adopted mathematical track model were found to correspond rather well to experimental data.It was found that the amplitude of measured and calculated responses for a wide variety of defects found in operational service varied essentially in proportion to speed.
Cai and Raymond[30]have developed a theoretical model for simulating dynamic wheel/rail interaction. Various types of wheel defects(wheelflat,randomly worn wheel)are studied.The authors conclude that the wheel/ rail impact behaviour is highly dependent on train speed and that one defective wheelset can also lead to large impact loading on the adjacent wheelset.The effect of loss of contact between wheel and rail is also covered in the numerical simulation.In reference[31],the influence of an impact load caused by,for example,a wheelflat on deflections,accelerations,stresses and strains in rail and sleepers and on ballast pressures is computed. Theoretical investigations on wheel/rail impact loads and comparisons of different mathematical train/track models have been carried out by Dong et al.[32].Non-linear effects such as loss of wheel/rail contact and sleeper lift-off from the ballast are taken into account.It is concluded that axle load and train speed determine the magnitude of the impact loads caused by rge impact forces are obtained when the length of the flat in conjunction with train speed excites the fundamental eigenfrequency of the coupled wheelset/track system.Impact forces transferred from rail to sleeper are strongly influenced by pad stiffness and sleeper mass.The authors claim that,in order to detect wheelflats,it is preferable to position accelerometers on the rail,since smaller flats are not always detected by strain gauges on the rail.Dong and Sankar conclude that the factors that influence the impact loads the most are the shape and size of the wheel defects,axle load,train speed and railpad stiffness[33].
4CRITERIA FOR REMOV AL OF OUT-OF-ROUND WHEELS
The use of an impact load detecting system has offered the opportunity to define criteria for removal of railway wheels that are not only based on visual inspection of wheel tread defects but also on the impact loads that are measured by the detectors.In reference[13],a review of changes to North American criteria for removal of out-of-round wheels is given.From January1996,a wheel shall be replaced if it causes a peak impact load larger than90kips (400kN).The allowable length of the wheel flat was increased from2in(50.8mm)to2.5in(63.5mm).Inves-tigations have shown that only half of the wheels that caused impact loads of100kips(445kN)had visual defects that were unacceptable,and also that the depth of a flat is a better criterion for condemning wheels than its length.Although different North American railway admin-istrations use different criteria,the limit for replacing railway wheels is approximately100kips(445kN)for most administrations.
A conceptual framework for investigating the economic consequences of high-impact wheels is proposed in reference[13].The objective is to determine at which impact load level it is economically beneficial to remove a defective wheel.It is concluded that,for North American conditions,wheels should be removed from service when they cause impact loads greater than85kips(378kN). Kalay and Hargrove discuss wheel tread defects in reference[34].An economic analysis is also given,the authors concluding that a large sum of money can be saved each year by developing proper removal criteria based on impact load detection.The tests that led to the new impact load-based AAR wheel removal criteria are described by Kalay et al.[16]and by Tajaddini and Kalay[35],along with an economic motivation for wheel removal criteria.
In Sweden,the criteria for wheel repair are as follows [36]:
1.If the length of the defect is40±60mm,or if there exists a material build-up but with a height smaller than 1mm,the train has to go to the nearest workshop for repair.On such an occasion and at temperatures below À108C,the train speed must not be higher than 10km=h.At higher temperatures,there are no restric-tions other than that the speed interval15±45km=h should be avoided since the risk of damaging the rails is largest at these speeds.
2.If the length of the damage is larger than60mm,or if the height of a material build-up is larger than1mm,
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the train must go to the nearest manned station at a speed not higher than10km=h.
For freight wagons,the measured wheel impact loads indicating that the length of a wheelflat is within one of the intervals specified in the above criteria are290and320kN respectively[12].
5METHODS TO PREDICT OUT-OF-
ROUNDNESS BY NUMERICAL SIMULATION
According to Meinke and Meinke[37],two important features introduced by modern high-speed trains,as com-
pared with conventional trains,are as follows:
1.The rotational speed of the wheels is higher since the wheel diameter is still of the same size.
2.Higher speeds lead to larger kinetic energies and require more brake power to stop the train.The wheelsets are thus equipped with more disc brakes,typically four discs instead of two.
Most mathematical models adopted to predict railway wheel OOR include:
(a)a model of the dynamic interaction between wheelset
and track to determine forces and creepages at the wheel/rail contact point,
(b)a wear model to account for the long-term wear
process of the wheel tread.
A review of the development of numerical methods for prediction of wear on the wheel and rail is given by Zobory [38].
One basic approach in most models addressing the development of OOR is the assumption of so-called multi-ple time-scales.In the dynamic interaction model,the time-scale of the vibrations can be expressed in seconds,while an order of108wheel revolutions is considered in the wear model.For the dynamic interaction model,this means that the geometries of the wheel tread and rail can be treated as constant and that a controlled motion of the wheelset can be simulated with given conditions on speed,load and track.The contact forces and the slip lead to wear,but the geometry of the running surfaces changes in a very slow process.
The coupling of the two models is often illustrated by a feedback loop,such as the one in Fig.8.An initial out-of-round profile,together with model parameters of train and track and disturbance parameters such as unbalanced rotating masses,is taken as input to the simulation.Contact forces and wear power in the contact patch are calculated by use of the interaction model.Material excavation versus location on the wheel tread is then calculated on the basis of a wear hypothesis.The out-of-round shape is modified by the wear and then included in the new input data.By this procedure,the long-term wear is monitored iteratively. Certain model parameters such as speed and track proper-ties can be varied from one iteration to another in order to simulate more realistic operating conditions.
The dynamics of a high-speed wheelset is to a large extent a matter of rotor dynamics.The effects of rotatory inertia and gyroscopic moments are therefore important [37].In numerical simulations used to predict longer-wavelength defects,rigid body dynamics in combination with a wear model is often adopted.
Morys et al.have investigated a rigid body model of an ICE carriage on an elastic track model[39±43].The wheel/ rail contact is modelled by use of a simplified theory according to Kalker[44].The adopted wear model is based on the assumption that the rate of mass excavation is proportional to wear power in the contact patch.The significant variations in vertical wheel/rail contact forces caused by the out-of-round profile lead to an excitation of the lower wheelset bending modes[40].At frequencies below200Hz,the wheels can be treated as stiff and rigidly coupled to the axle.Thus,the bending oscillation of the axle leads to lateral slip and material excavation at the contact patches.Longitudinal slip and spin play a minor role.Vertical resonances of the coupled train/track system lead to peaks in the vertical contact force at certain train speeds.For a stiffer track,the resonance train speed is higher.
The amplitude of the dominating lateral wear energy within the contact patch is mainly determined by lateral slip,lateral contact force and vertical contact force.In Fig. 9,an example of calculated wear energy,vertical contact force and wheel radius deviation versus time is illustrated. The phase shift between wear energy maxima and radius deviation maxima is important for whether a certain OOR will be enlarged or not.Depending on this phase shift,three significant ranges of excitation frequency can be defined. In the low-and high-frequency ranges,the excavation maxima are located at the falling and rising slopes of the radius deviation curve away from the maxima and minima. An enlargement of the existing OOR harmonic order will not occur in these two frequency ranges.However,for medium frequencies,the maximum excavation occurs approximately at the maximum and minimum of the OOR shape.Because of the higher excavation at the minimum radius,the OOR enlarges rapidly.Next to the
dominant Fig.8Scheme for numerical simulation of the growth of wheel OOR.Connection between short-term train/track dy-
namics and long-term wear process is illustrated.(From
reference[39])
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original OOR shape,higher harmonic orders develop.No precise limits of frequency ranges can be given because they strongly depend on track properties.In the case of an ICE running on a stiff track,the medium range is approximately 50±80Hz.
The development of a certain OOR order is dependent on train speed and track conditions.In Fig.10,three typical qualitative results of long-time wear simulations are shown.For all simulations,various speeds,both driving directions and stiff track properties were assumed.In Fig.10a a slow change from an eccentricity (first-order OOR)to a third-order OOR is observed.In Fig.10b a change from a second-order to a fourth-order OOR is shown.In Fig.10c an enlargement of a third-order OOR without changes in shape or phase is illustrated.It is interesting to note that,within the investigated high-speed range and based on the assumed track properties,only the third-order OOR harmonic increases,whereas all other orders develop into higher harmonic orders.
Unbalances in the wheelsets may be another cause of out-of-round wheels.This topic has been investigated by Meinke et al .[37,45]and Morys [41].The unbalances are modelled as point masses distributed on the wheelset at different radii on the wheels and disc brakes.Meinke suggests that dynamic unbalances have a stronger influence than static ones [37].According to Morys,dynamic unbalances cause large vibrations of the wheels and small vibrations of the disc brakes,whereas the opposite condi-tions hold for static unbalances [41].
A complete locomotive vehicle is simulated by Soua and Pascal [46]in order to investigate the initiation and evolution of three different wheel wear shapes with 1,2and 4harmonic OOR orders.The authors state that wheelset axle torsional vibrations in combination with lateral motion of the whole wheelset explain the generation and evolution of the wear pattern.
Numerical simulations of wheel polygonalization are presented by V ohla et al.[47±49].One hypothesis is that
excitation of the wheel eigenmodes may play an important role for the development of OOR since the number of nodal diameters in the wheel eigenmodes coincides with some periodic irregularities found on worn wheels.
Also,Frischmuth and Langemann [50,51]have
carried
Fig.9Example of calculated lateral wear energy W R ,vertical contact force F N and wheel radius deviation r OOR
(train speed 70m =s,third-order OOR,peak-to-peak OOR amplitude r OOR 0:3mm,stiff track).(From reference [40
])
Fig.10Calculated long-term wear development as a conse-quence of small initial radius deviations caused by,for example,manufacturing tolerances.(From reference [40])
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