1996 experimental validation of the twins prediction program for rolling noise - description of the...

8/14/2019 1996 Experimental Validation of the Twins Prediction Program for Rolling Noise - Description of the Model and Met

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Journal of Sound and Vibration (1996) 193(1), 123135

EXPER IMENTAL VALIDATION OF T HE TWIN S

PR EDICTION PR OGR AM FOR R OLLING NOISE,PART 1: DESCR IPTION OF T HE MODEL

AND METHOD

D. J. T

TNO Institute of Applied Physics (TPD), P.O. Box 155, 2600 AD Delft, The Netherlands

B. H

British Rail Research, P.O. Box 2, London Road, Derby DE24 8YB, England

N. V

Vibratec, 6 Chemin de lIndustrie, B.P. 69, 69572 Dardilly, France

(Received in final form 20 November 1995)

The C163 Expert Committee of the European Rail Research Institute (ERRI)concerned with Railway Noise, has been developing theoretical models for the generationof wheel/rail rolling noise. These models have been brought together into a softwarepackage, called TWINS (TrackWheel Interaction Noise Software). This is intendedas a tool with which different designs of wheel and track can be assessed in terms of theirnoise generation. This paper begins by describing briefly the various theoretical modelsincorporated, the assumptions made within these models and their limitations. On the basisof the input and output parameters, a methodology is derived for the validation of themodel by using full scale running tests. Two sets of experiments have been performed fora range of conditions in which the input parameters (the surface roughnesses of wheel andrail) were measured as fully as possible. As well as the sound pressure during train pass-by,a number of intermediate parameters were also monitored to allow validation of parts ofthe model.

1996 Academic Press Limited

1. INTRODUCTION

When a railway wheel rolls on straight or slightly curved track in the absence ofdiscontinuities, a broadband noise is emitted. Theoretical models for this rolling noise goback to Remington [1, 2], and have been substantially developed by Thompson [38].In recent years, through the initiative of the C163 expert committee of ERRI (EuropeanRail Research Institute), these theoretical models have been expanded further, and have

been assembled in a software package, called TWINS (TrackWheel Interaction NoiseSoftware) [9]. This is intended as a tool with which different designs of wheel and trackcan be assessed in terms of their noise generation. This paper begins by giving an overviewof the various theoretical models incorporated in TWINS, the assumptions made within

these models and their limitations. A methodology is then derived for the validationof the model using full scale running tests and experiments are described in which theinput parameters (the surface roughnesses of the wheel and the rail) have been measured

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as fully as possible. In addition to the sound pressure during train pass-by, a numberof intermediate parameters were also monitored to allow validation of parts of themodel. Comparisons between the experimental results and predictions are presented in acompanion paper [10].

2. THE TWINS MODEL

2.1.

The basis for the theoretical model contained in TWINS is summarized in Figure 1. It isnow generally agreed that rolling noise is generated by surface irregularities (roughness)on the wheel and/or rail running surface. These roughnesses introduce a relative vibrationbetween the wheel and the rail, the consequent wheel and rail vibrations radiating noise.By assuming linearity of the various parts of the model, most of the calculations can be

carried out in the frequency domain.Irregularities with a wavelength (in m) produce excitation at a frequency f= V/,

where Vis the train speed in m/s. Therefore, for a frequency range 1005000 Hz, andnormal train speeds (50160 km/h), roughness with wavelengths approximately 3450 mm

needs to be measured. For higher speeds, yet longer wavelengths are required. The

Figure 1. An overview of the TWINS model for rolling noise.


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roughness profile is usually measured with a pointed probe, which gives a profile differentfrom that experienced by the wheel/rail system. The input to TWINS consists of the spatialdata on a series of parallel lines covering the contact patch. The relative height of theselines is also required, which provides information about the transverse profile. A modelis included in TWINS to calculate the average roughness input to the system from these

data in the spatial domain. The wheel and rail surfaces are represented by an array ofindependent non-linear springs, which simulate the correct global properties of the contactzone. Wheel and rail radii of curvature are input, which allows the dependence ontransverse profiles to be allowed for. For more details, see reference [11]. This model

combines directly three aspects of roughness analysis as described in reference [12]: featuresin the surface which the wheel/rail geometry cannot fully follow are removed (e.g., smallholes in the surface), wavelengths short in comparison with the contact patch length areattenuated (contact filter) and variations in the roughness across the width of the contactpatch are allowed for. The latter may reduce the excitation if the roughnesses at oppositesides of the contact zone are uncorrelated.

Wheel and rail roughnesses are added together in the frequency domain, with theassumption that they are uncorrelated.

2.2. -

The model of the wheel/rail interaction has been published in references [4] and [7].This is shown schematically in Figure 2. The roughness induces a vertical relative

displacement between the wheel and rail or in the Hertzian contact spring, the motion ofeach depending on the relative amplitudes (and phases) of their receptances. The localcontact deflections are represented by a linearized incremental stiffness, which is valid onlyfor relatively small amplitudes, but allows the model to be implemented in the frequencydomain.

Coupling in the lateral direction is represented by a creep force element. This is asimplification of the transient creepage studied by Gross-Thebing [13] in which the lowfrequency creep force creepage law is represented by a damper, to which a spring isintroduced in series to simulate the high frequency transient effects; see reference [3].

Coupling can also be included in any other degrees of freedom at the contact (up to 6),although in the current results only the vertical and lateral translations are included. Thesewere found in reference [3] to be the most important.

Figure 2. Details of the wheel-rail interaction.


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2.3.

A railway wheel is a very lightly damped resonant body, which can be characterizedreadily by its normal modes. Axial modes are categorized by the number of nodaldiameters (n) and the number of nodal circles (m); radial modes are also important andare categorized by the number of nodal diameters. The free vibration of a wheel is modelledby using finite elements [5]. From the modal basis (natural frequencies and mode shapedata) derived from this finite element analysis, the frequency responses of the wheel(expressed as receptances, i.e. displacement divided by force) are predicted in TWINS byusing a modal summation, including the effects of wheel rotation [8]. The calculation ofthe wheel vibration response due to the wheel/rail interaction forces is done on the samemodal basis, and also includes the effects of rotation [8]. The wheel response during rollingis calculated at three positions axially on the web and in two directions on the tyre. It isfound to be important that all of these calculations are carried out in very small frequency

steps, especially around wheel resonances [14].

2.4.

Unlike the wheel, the rail is effectively an infinite structure. Its motion is therefore

not modal but consists of travelling waves. At low frequencies some resonances dooccur due to the behaviour of the track foundation (for example, bouncing on theballast stiffness) but these are much more heavily damped than the wheel resonances.Three complementary models are available in TWINS for the track dynamics [15] (seeFigure 3), although the results of the validation described here will be limited to trackmodels 1 and 2:

1. Continuously supported beam. This is a Timoshenko beam mounted on a two-layercontinuous support. It is similar to the continuous model of Grassie [16], although thedamping of the pads and ballast is modelled by hysteretic loss factors rather than viscous

dampers. Equivalent models are used separately for the vertical and lateral directions.2. Periodically supported beam [17]. This is similar to model 1, with the exception

that the periodicity of the support is included. Significant effects are found at the

Figure 3. Models for track vibration: (a) continuously supported beam model; (b) periodically supported beammodel; (c) continuously supported rail model including cross-sectional deformation.


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pinnedpinned frequencies (where sleeper separation equals half a bending wavelength).A limitation of the model as implemented is that the rail fasteners are represented by pointconnections between the rail and sleeper rather than distributed over an area, so that thepinnedpinned effects are found to be exaggerated.

3. Allowing for cross-sectional deformation[6]. The rail is represented by finite elements

so that it is modelled in much more detail, particularly important above 1 kHz. The railpad is represented by a distributed resilient layer under the rail foot. However, as withmodel 1, the support in this model is continuous and so the model cannot predictbehaviour associated with the pinnedpinned effects.

For track models 1 and 2, the cross-coupling between a vertical force and a lateralresponse is theoretically zero. In practice, although it is small, it is not negligible,for example, it is due to imperfections in the symmetry of the support (especially thesleeper), the inclination of the rail and the position of the contact on the rail head.An estimate of the cross-coupling is therefore made using a simple model. A parameter,X (assumed to be real) is chosen, giving the cross-receptance Axy , in terms of thegeometrical average of vertical receptance Axx and lateral receptance Ayy , as

Axy = XAxxAyy . The value of X is estimated from measurements (see section 4). Thisequation is motivated by the fact that for X= 1 it generally represents the maximumcross-receptance of a structure. It applies, for example, at each single resonance peak ofa multi-degree-of-freedom system with low modal overlap,

Axynxny /mn [2n ( 1 + in )

2] for n ,

where nx is the modal amplitude of mode n in the x direction, n is the resonancefrequency and n is the damping loss factor. When summing over many such modes, Xwill be less than 1. For a system with high coupling Xmay be close to 1, whereas forlow coupling,nywill be small when nxis large andvice versa, so that the correspondingvalue of X will be much lower. A rail, as an infinite structure, can be represented asthe limit of a multi-degree-of-freedom system for an infinite modal density. While not

rigorous, this approach does allow the cross-receptance to be estimated by using a singleparameter, independent of frequency, whichfrom measurementsappears to give usableresults.

The response of the rail to the wheel/rail interaction is predicted for each wave typeseparately (for models 1 and 2 there are two waves in each direction; for model 3 thereare as many waves as there are degrees of freedom in the rail cross-section considered).The attenuation with distance of each wave is an important parameter in determining theoverall vibration (and hence noise) of the rail. The lower this attenuation, the larger is theeffective radiating area of the rail. The average vibration is calculated over a length L , thewheel being assumed to be located at the centre of this section. The spatially averagedresponse uj for a particular degree of freedom j is given by

u2

j=

2

L

L/2

0uj(z)

2

dzr jr2

kFkkr

2

1 er L

rL

,

wherekrare the partial receptances giving the response in waver to a forceFkin direction

k, jr are the wave shapes, i.e., normalized responses in wave r for direction j and r isthe real part (decaying part) of the propagation constant for waver . It is possible to workwith measured track decay rates instead of predicted ones. The approximation in the above


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equation comes from evaluating the integral separately for each wave, which is strictlyvalid only for low decays.

2.5.

New models for the sound radiation from wheels and track have been implemented in

TWINS. The sound power is calculated by combining predicted vibration spectra withradiation efficiencies in one-third octave bands. For the wheel, semi-analytical expressionshave been derived for the radiation efficiency from the results of boundary elementcalculations. These allow for the number of nodal diameters in the corresponding mode

shape, so the wheel response has first to be separated into that corresponding to variousnumbers of nodal diameters. For the rail, an equivalent sources model has been developed[18] which models the radiation from an infinitely long structure (i.e., assumed to betwo-dimensional). For the sleeper, a model based on a baffled rectangular piston has beenused, which gives a radiation efficiency close to 1 for most frequencies considered.Radiation from the vibration of the ballast is ignored.

In order to make comparisons between different situations, or to compare the relativeimportance of sound radiation from the wheel, rail and sleeper, it is sufficient to workin terms of sound power. However, to compare results with experimental data, soundpressure predictions are also required. Therefore a simple propagation model has beenimplemented in which the wheels are represented as moving point sources and thetrack as a line source at high frequencies and a moving point source at low frequencies

where the response of the track decays rapidly with distance. Very simple directionalities(monopole and dipole) are used. The reflection from the partially absorbing ground isincluded, although without any account of the phase relationship between direct andreflected rays. The Doppler effect is neglected; its effect for train speeds up to 160 km/hwill be limited to a shift of at most13% in frequency, equivalent to one one-third octaveband.

T

1Tracks which have been included in the measurements

Track Rail Rail-pad Sleeper Sleeper spacing (m)

A UIC 54 High stiffness 45 mm ribbed Concrete bibloc 06B UIC 54 No rail-pad Wooden 06C UIC 60 Medium stiffness Concrete monobloc 06D UIC 60 Medium stiffness Concrete bibloc 06

T 2

Wheels which have been included in the measurements

Min. web Tyre TyreType of thickness width height Radius

Wheel Description braking (mm) (mm) (mm) (mm)

1. SBB EW4 Doubly curved web Disc 1013 135 55 4602. SNCF Corail Curved web Tread 25 135 60 4403. DB optimized Straight web Disc 25 135 50 4604. Freight Curved web Tread 2227 135 50 460


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T 3

Measurement configurations and speeds (in km/h) for passenger vehicle tests

Track A (bibloc) Track B (wood) Track C (monobloc)

1. SBB EW4 50, 80, 125, 160 50, 80, 125, 160 80, 125, 160

2. SNCF Corail 50, 80, 125, 160 50, 80, 125, 160 80, 125, 1603. DB optimised 80, 125, 160

3. VALIDATION

3.1.

With reference to Figure 1, the input to the model consists of the wheel and rail surfaceroughness profiles, while the output is the total sound pressure of wheel and track. Bothof these quantities can be measured. In order to assess the operation of the model in moredetail, as many other parameters as possible should also be measured.

Measurements of the dynamic properties of the wheel and track allow a check that thecorrect parameter values are used. For the wheel the measured modal damping values areused in the predictions, and the natural frequencies are checked. The rail pad and ballaststiffnesses are found by fitting predicted frequency responses to the measurements.

By measuring the vibrations of both wheel and track during running, an intermediatecomparison is provided. The following results can therefore be checked: sound pressure

calculated from roughness, wheel and track vibration calculated from roughness and soundpressure calculated from wheel and track vibration.

3.2.

In this section the main measurement campaign is described briefly. Reference [19]contains more details. The measurements took place in October 1992 and were performedfor three different types of track (AC) and three types of wheel (13), as listed in Tables 1and 2 (track D and wheel 4 were used in the freight tests; see section 5). All tracks wereof standard ballasted construction. The train speeds were chosen so that the same one-third

octave band roughness data could be used for each speed simply by shifting the frequencybase by a whole number of bands. The 25 combinations tested are listed in Table 3. TracksA and B were located in the same track section and so were measured in a single seriesof runs. For these sites the coaches with DB optimized wheels were unfortunately not

available.

Figure 4. The composition of the test train.


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Figure 5. A representation of the pass-by geometry. Four wheelsets move over a distance of 26 m. At the centreof this trajectory, the mid-point of the wheelsets is opposite the microphone positions. The shaded wheel is thetest wheel, which was instrumented.

For each type of wheel, two coaches were included next to each other in the test train

as shown in Figure 4. It is important in the trackside measurements (noise and trackvibration) that a single type of wheel can be isolated. To achieve this the two adjacentbogies at the centre of the pair of vehicles with nominally similar wheels were considered,predictions and measurements giving results in terms of the average during the passage

of these four wheelsets on two rails (see Figure 5). In each case one of the wheels wasinstrumented and is indicated as the test wheel.

The sound pressure measurements were made very close to the track (see Figure 6): threemicrophone positions at 3 m from the near rail, at heights of 05, 12 and 25 m abovethe rail head. Vibration was measured on the rail above a sleeper laterally and vertically.Measurements were made at a total of six positions on this cross-section, although in theanalysis attention has been concentrated on the vertical and lateral accelerations at the railhead, as shown in Figure 6. Additionally measurements were made at three positions

Figure 6. A Sketch of the positions of transducers on the wheels and tracks.


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vertically on the sleeper (two shown in Figure 6 and a third at the centre of the sleeper)and some measurements were also made on the rail between sleepers. A detection systemat the trackside allowed the exact time to be recorded at which each wheel passed themeasurement cross-section.

All measurements were analyzed by integrating over a fixed distance of train movement,

not a fixed integration time, so that the results for different speeds are consistent. It isimportant that all the rail vibration and noise emission from the chosen wheels should beacquired during the measurements. To achieve this, the trackside measurements were basedon an integration length corresponding to two half coach lengths (26 m) with the two

test bogies passing the test section at the centre of the time window (see Figure 5). If anyrail vibration from the test bogies is transmitted beyond this length, it is compensated forby vibration transmitted from the wheels before or after the test ones propagating intothe measurement window. A check was also made to ensure that the relatively noisytread-braked wheels did not introduce unwanted rail vibration or noise radiation duringthe time window corresponding to the other types of wheel.

On board the train, the accelerations on the test wheels were measured in the radialdirection on the tyre and the axial direction on the wheel web (see Figure 6) duringrunning over the measurement site, the signals being transmitted to the coach by usingtelemetry equipment. The position relative to the ground was also recorded. The data wereanalyzed over a time corresponding to 10 m of train movement centred on the tracksidemeasurement cross-section.

3.3.

Wheel roughness was measured by using an LVDT displacement transducer, asdescribed in reference [20]. For each type of wheel, the roughness has been measured forall eight wheels of the two middle bogies. One wheel per type was selected as a test wheel,for which roughness has been measured on 20 parallel lines (separated by 25 mm). Thesemeasurements were done on only three lines (separated by 10 mm) for the other sevenwheels. The Corail and SBB wheels were measured in detail before the running tests, and

as a check measurements were made on three lines on each wheel after the running testsas well, and little change was found. The roughness of the DB optimized wheels could bemeasured only at the end of the tests. It is therefore not clear to what extent their roughnesschanged during the tests, but since these wheels were delivered new for the tests it is quite

feasible that this could have occurred.Rail roughness has been measured by using a system developed for the DB [21] in

which an LVDT is pulled along a 12 m long measuring beam located on the rail.Measurements at the three locations were made over a total length of 11 m (centred onthe measurement cross-section) for both rails. Detailed measurements with 11 parallellines (separated by 2 mm) were taken on a 12 m test section at the measurementcross-section. The remainder of the measurements were made on only three parallel lines(separated by 10 mm), in separate portions of 12 m with an overlap of 02 m betweenadjacent portions. The length of the rail roughness device severely limits the frequency

resolution. In order to have data available at low frequencies, the requirement that severalfrequency lines of the narrow-band spectrum should fall in a one-third octave band hasbeen relaxed to one line. The low frequency results thus contain large uncertainty.

The wheel and rail roughness data on multiple parallel lines, available for the test

wheels and rail sections, have been analyzed in TWINS by using the model described insection 2.1. This produces an excitation (equivalent roughness) spectrum including thecontact filter effects. The wheel and rail roughnesses were processed separately.


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From the single line data, available for all eight wheels and 11 rail sections of a giventype, a significant variation was found between the roughness of the various wheels of aparticular type and the various rail sections at a particular location. Standard deviationsup to 5 dB were found, see reference [10]. Furthermore, the average roughness applyingto each situation (i.e., each wheel/rail type) differed by up to 5 dB from the (single line)

roughness on the test wheel/rail section. Since the measured noise and vibration iscaused by all wheels and rail sections, a correction is needed to the equivalent roughness,output from TWINS, for the single test wheel/rail. This correction was formed from thedifference between single line results for the test wheel/rail and the average over all eight

wheels or 11 rail sections of the given type.

4. TUNING OF WHEEL AND TRACK PARAMETERS

4.1.

For each test wheel, frequency response measurements have been carried out forhorizontal and vertical excitation. Natural frequencies have been identified which are usedto adjust the modal bases computed with finite elements before input to TWINS. Modal

damping values have also been measured and used in the predictions. Agreement betweenmeasured and predicted natural frequencies was found to be extremely good for the DBwheel (better than 2%), which was new, but less good for the Corail wheel which was worn(discrepancies up to 10%) or the SBB wheel. An example of the measured and predictedwheel frequency response functions (shown as accelerancesacceleration divided by force)is given in Figure 7. Good agreement can be seen, enhanced by the use of measured naturalfrequencies in the predictions.

4.2.

With hammer excitation, measurements were made for each track of the accelerancesin the vertical and lateral directions and the cross-accelerance, at mid-span and above asleeper. The ratio between rail and sleeper vibration was also measured. Wave decay rateswere also measured, by moving the excitation away from the response position in a series

Figure 7. Corail wheel radial accelerance: ; predicted; , measured.


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T 4

Track parameters derived from characterization tests

Track type

Parameter A B C D

Rail type UIC54 UIC54 UIC60 UIC60

Cross-receptance parameter, LX (dB) 15 10 10 10

Rail damping loss factor vertical 002 002 002 002Lateral 002 002 001 001

Pad stiffness, vertical (N/m) 13 109 5 1 08 35108 20108

Pad stiffness, lateral (N/m) 10 108 177108 50107 48108

Sleeper mass, 1/2 sleeper (kg) 122 30 162 120

Ballast stiffness magnitude vertical (N/m) 15 108 1 1 08 7 1 07 7 1 07

Ballast stiffness magnitude lateral (N/m) 75 107 1 1 08 11108 1 1 08

of steps. Track parameters were chosen to give the best fit to the characterization testresults. Values are listed in Table 4.An example of predicted and measured accelerances is given in Figure 8 for track C.

Further comparisons can be found in reference [22]. The vertical accelerances were

reasonably well predicted with track model 1. Around the pinnedpinned frequency (about1 kHz), this continuous model predicted a response which is part way between themeasured response above a sleeper and that at mid-span. The periodic model (model 2),on the other hand, correctly predicted the difference in accelerances between these twopositions, except at the pinnedpinned frequency itself, at which insufficient damping ledto an exaggerated effect (see reference [22]). As far as the lateral accelerance is concerned,the predictions were found to be 510 dB too low for track models 1 and 2. This can beexplained by the neglect of torsion and cross-sectional deformations in these models.Track model 3 gave much better results [22]. The level of the cross-accelerance is defined

in models 1 and 2 in terms of the single parameter, Lx = 20 logXsection 2.4. The best

Figure 8. Track C vertical accelerance: , predicted by using track model 1; , measured betweensleepers; , measured above sleeper.


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compromise was found forLXequal to 10 dB for the wooden and monobloc tracks and15 dB for the bibloc track. This corresponds to the fact that the block under the railin the case of the bibloc sleeper is rather symmetrical with respect to the rail centreline,whereas the other sleepers are asymmetrical relative to the rail.

At high frequencies, reasonable agreement between measured and predicted decay rates

for track model 1 could be achieved only by introducing a damping loss factor into therail itself with a value of 001002. In practice, this damping is almost certainly due toeffects of the fasteners which have a greater influence at high frequencies than the beammodels suggest, due to the cross-sectional deformation of the rail (see reference [15]). For

the periodic track model, the possibility is not yet available to introduce the fictitiousdamping on the rail itself to correct for high frequency effects. Track model 3 can predictthe high frequency effects of cross-section deformation and gives good approximations ofthe measured decay rates [22].

5. VALIDATION FOR A FREIGHT VEHICLE

A second series of tests was carried out in 1993 to validate the TWINS model for freight

vehicles. Details are very similar to those given above for passenger vehicles but withthe following differences. Train speeds of 60 and 100 km/h were used (typical of freighttraffic). Two tracks were studied (track C as above and track D, see Table 1). A singlewheel type was studied, typical of freight vehicles (type 4; see Table 2). A two-axlefreight vehicle was tested, so only two wheelsets are included in the measurement, and theintegration length is 14 m (the length of the vehicle). The microphone positions wereslightly different. In the light of experience in the first tests, account was taken of thewheel and rail transverse profiles from which the contact patch position could be estimated.Extra vibration measurements were carried out on the vehicle superstructure to estimateits contribution to the noise radiation. The results are presented in part 2 of this paper[10].

ACKNOWLEDGMENTS

The work described here has been performed under the direction and funding of ERRIexpert committee C163 (Railway Noise). The TWINS model has been produced forERRI by TNO-TPD and includes theoretical models developed by British Rail Research,Technical University of Berlin, Bolt Beranek and Newman, University of Keele and

TNO-TPD.

REFERENCES

1. P. J. R 1975 Journal of Sound and Vibration 46, 419436. Wheel/rail noise part IV:rolling noise.

2. P. J. R 1987 Journal of the Acoustical Society of America 81, 18051823. Wheel/railrolling noise I: theoretical analysis.

3. D. J. T 1990 Ph.D. Thesis, University of Southampton. Wheelrail noise: theoreticalmodelling of the generation of vibrations.

4. D. J. T1993Journal of Sound and Vibration 161, 387400. Wheelrail noise generation,part I: introduction and interaction model.

5. D. J. T1993Journal of Sound and Vibration 161, 401419. Wheelrail noise generation,part II: wheel vibration.

6. D. J. T1993Journal of Sound and Vibration 161, 421446. Wheelrail noise generation,part III: rail vibration.


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7. D. J. T1993Journal of Sound and Vibration 161, 447466. Wheelrail noise generation,part IV: contact zone and results.

8. D. J. T1993Journal of Sound and Vibration 161, 467482. Wheelrail noise generation,part V: inclusion of wheel rotation.

9. D. J. T and P. E. G 1993 Proceedings of Inter Noise 93, Leuven, 14631466.TWINS: a prediction model for wheelrail rolling noise.

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11. P. J. Rand J. W 1996Journal of Sound and Vibration 193, 83102. Estimation ofwheel/rail interaction forces in the contact area due to roughness.

12. D. J. T1996Journal of Sound and Vibration 193, 149160. On the relationship betweenwheel and rail surface roughness and rolling noise.

13. A. G-T 1993 Fortschritt-Berichte VDI Reihe 12 Nr. 199, Dusseldorf. LineareModellierung des instationaren Rollkontaktes von Rad und Schiene.

14. D. J. T 1994 Journal of Sound and Vibration 171, 427432. Authors reply.15. D. J. T and N. V 1995 Interaction of Railway Vehicles with the Track and its

Substructure,Vehicle System Dynamics Supplement 24, 8699. Track dynamic behaviour at highfrequencies, part 1: theoretical models and laboratory measurements.

16. S. L. G, R. W. G, D. Hand K. L. J 1982 Journal of MechanicalEngineering Science24, 7790. The dynamic response of railway track to high frequency verticalexcitation.

17. M. A. H1992Proceedings of DAGA 92, 10331036. Anregung von gekoppelten Wellen aufeinem Timoshenko-Balken mit aquidistanten Stutzstellen.18. M.-F. P, M. H, J. Band J. B1992 Proceedings of DAGA 92, 9971000.

Berechnung des Abstrahlmaes von Eisenbahnschienen anhand der Multipolsynthese.19. E R R I1995Question C163,Railway Noise,Report no. 21. Railway

rolling noise modelling. Description of the TWINS model and validation of the model versusexperimental data. Utrecht.

20. M. G. D, F . J. W. B, P. C. G. J. D, D. J. T 1994 RailEngineering International 23(nr 3), 1720. Wheel roughness and railway rolling noisetheinfluence of braking systems and mileage.

21. G. H, M. R and P. H 1990 Eisenbahn Technische Rundschau 39 (November),685689. Entwiklung eines hochempfindlichen Schienenoberflachenmegerats als Beitrag zuweiteren moglichen Larmminderungsmanahmen im Schienenverkehr.

22. N. V and D. J. T 1995 Interaction of Railway Vehicles with the Track and itsSubstructure. Vehicle System Dynamics Supplement 24, 100114. Track dynamic behaviour athigh frequencies, part 2: experimental results and comparisons with theory.

1996 experimental validation of the twins prediction program for rolling noise - description of the...

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