Rolf Diehl, Reinhard Gorlich and Georg Holzl 2 1 Introduction In the speed range from about 60 to about 250 km/h rolling noise is the dominant noise f

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1 Rolf Diehl, Reinhard Gorlich and Georg Holzl 1 Acoustic Optimisation of Railroad Track Using Computer Aided Methods Rolf Diehl and Reinhard Gorlich Muller{BBM GmbH, D{82152 Planegg, Robert-Koch-Str. 11 Phone / -207, Fax Rolf.Diehl@mbbm.de Georg Holzl Deutsche Bahn AG, Forschungs- und Technologiezentrum, BT 511 D{80939 Munchen, Volckerstr. 5 Phone , Fax Georg.Hoelzl@bku.db.de Summary To improve the understanding of the rolling noise generation mechanism, a theoretical model called Rail/Wheel{Impedance{Model (RIM) has been developed. The model allows for the calculation of structure borne sound of the wheels, the rails and the sleepers and their radiation into the surrounding air as a trackside pass{by level. It is furthermore possible to study the excitation of constructions (e.g. bridges) through the track. The model has been extensively used to study the eects of track parameters on the emitted sound especially the acoustic relevance of design parameters of ballasted and slab tracks have been studied in detail. Approaches to acoustically optimised track designs are discussed. This includes the eects of stiness and damping of pads and of the resilient elastomer layer in the construction of slab track and the construction of sleepers. Keywords: rail/wheel interaction model, acoustics, vibration, noise prediction, pass{by level of trains, track optimization.

2 Rolf Diehl, Reinhard Gorlich and Georg Holzl 2 1 Introduction In the speed range from about 60 to about 250 km/h rolling noise is the dominant noise from railroad lines. In order to develop, investigate and optimize rolling noise reduction measures it is necessary to better understand the generation mechanism. The fundamental principles of rail/wheel roughness interacting with impedances have been published, e.g. in (Remington, 1987). Based on these principles for the excitation mechanism several prediction tools have been implemented, such as TWINS 1. Another rail/wheel noise prediction tool, RIM 2, has been developed by Muller{BBM in cooperation with Deutsche Bahn AG since This paper describes in brief the theory behind RIM and gives some examples of its applications 3. 2 The tool RIM As shown in Fig. 1a, the combined roughness of the running surfaces of wheel and rail is used as the source of excitation for the system. In a rst step the structure{ borne velocities of the system components are calculated. The pass{by levels are then estimated using a simple model for air borne sound propagation. 2.1 Structure{borne sound generation Pads and ballast are modelled by frequency dependent complex stinesses, including a loss factor. The ground is modelled as a spring or a substructure like a concrete plate, a halfspace, a bridge or another engineering construction specied 1 "Track/Wheel Interaction Noise Software" developed by ERRI (Thompson, 1993). 2 "Rad/Schiene{ImpedanzModell zur Rollgerauschprognose", (Muller-BBM, 1993). 3 See also (Holzl and Muller, 1995) vehicle body bogie wheel contact zone / roughness rail sleeper / baseplate foundation Figure 1: Left: a) Principle of the rail/wheel impedance model. Right: b) Impedance of rail on ballasted track, of the wheel and of the rail/wheel contact stiness.

3 Rolf Diehl, Reinhard Gorlich and Georg Holzl 3 by an impedance. Depending on the foundation impedance, estimates of vibration transmission into the structure/ground are possible. The rail is modelled as a beam on a continuous foundation using the well known dierential equation for the Euler{Bernoulli beam (optionally Timoshenko theory, including shear deformation and rotational inertia). From this equation a solution is developed, which leads to an equation of 4 th power for the wavenumbers k of the rail depending on the material parameters, the mass, the moment of inertia of the rail, the input impedance under its foot and the train velocity. Using these k's, formulations for the impedance of the rail and the velocity of the rail along its length are derived. The basic model is only taking vertical excitation and vibration into account. Using a cross mobility(vertical excitation / lateral response), as proposed in (TNO, 1996), a horizontal response can be introduced. The sleepers can either be calculated as simple masses, as appropriate e.g. for bi{bloc sleeper, or as a beam on a continuous foundation as appropriate for the mono{bloc sleeper. In addition to the lumped parameter model with the mass sleeper, having two resonances, this leads to a certain number of additional resonances caused by the beam sleeper (see Fig. 2a). The wheel input impedance and the average wheel velocity are calculated using modal superposition derived from the eigenfunctions expansion theorem (Cremer and Heckl, 1982, p. 280). The input values, modal frequencies, damping and masses, are derived from measurements or empirical estimates taking wheel size and construction into account. The vehicle body is only seen as a lumped mass on a bogie which is modeled by modal superposition of generalized masses and stinesses for the vertical degrees of freedom (dipping, rolling and pitching). The velocities at the contact point of wheel and rail are predicted from ltered Figure 2: Left: a) Impedance of the rail on slab track, on ballasted track with sleepers modelled as mass, as beam supported by ground of dierent stiness and a measurement result (As the track was unloaded a frequency shift due to the lower ballast and ground stiness is to be expected.). Right: b) A-weighted pass{ by level and contributions of the components rail, sleeper and wheel on ballasted track depending on train speed.

4 Rolf Diehl, Reinhard Gorlich and Georg Holzl 4 surface roughness under consideration of the input impedances (Fig. 1b). 2.2 Air{borne sound generation Based on the estimated structure{borne velocities a propagation model is applied for the sound radiation into full space. The wheels are looked upon as pointsources and the calculation of the pass{by level takes the wheel position into account. The rail is considered as a line source consisting of a number of point sources. The calculation of the rail velocity along its propagation length is based on an analytic solution for the propagation integral depending on the wavenumbers. Sleeper vibration levels are estimated using rail vibration and a level dierence for the transfer function. Fig. 2b shows the contrinutions of the three components to the overall level. Figure 3: Rail vibration at the rail/wheel contact point and at distances of 1 2,1,2, 4, 8 m. Left: a) ballasted track, Right: b) ballastless track. Figure 4: Prediction of air{borne noise of the components rail, sleeper/baseplate and the wheel. Left: a) ballasted track, Right: b) ballastless track.

5 Rolf Diehl, Reinhard Gorlich and Georg Holzl 5 3 Applications of RIM The model described above allows for parametric studies to nd optimum values for design parameters of the rail/wheel system. Concerning the wheel, variations in eigenfrequencies, damping and modal mass can be studied. The relation of these parameters to real constructions of wheels may be found using FE{calculations. Even more interesting are the possibilities to study the track: variations of parameters of the rail, dynamic stiness and loss factor of pads and ballast or the resilient layer, mass, damping and impedance behaviour of sleepers or baseplates, stinesses of foundation impedances consisting of track construction, e.g. subgrade or bridges, and the inuence of the amplitude / frequency distribution of the roughness of the running surfaces of wheel and rail. 3.1 Track design As can be seen from the predictions in Fig. 3, rail vibration is higher on ballastless track and better damped along the propagation path on ballasted track in the dominating frequency range leading to higher pass-by levels for slab track (Fig. 4). The sleeper embedded in ballast acts like a vibration absorber for the rail in the frequency range relevant for rail radiation. From the acoustic point of view the stiness of the pads should be fairly high in order to reduce rail vibration this is practically opposed to the requirements of track design where soft pads are needed in order to reduce rail and sleeper stress and ballast deterioration. The main dierences in the construction of ballasted and ballastless track concerning relevant structure borne vibrations are the reduced damping of elastomer materials compared to ballast and the reduced connection impedance at the rail foot due to the replacement of the sleeper with the baseplate. Fig. 5a shows the inuence of parameter variations on the A{weighted pass{by level as the tripling of the loss factor of elastomers is not very realistic, the introduction of a heavy mass promises to be successfull. The values for ballasted track (b 1, b 2) show, that the subgrade has very little inuence on the emitted sound whereas a very soft pad (b 3) completely uncouples the rail from the rest of the construction leading to very high levels on the rail. The gure shows furtheron, that for ballasted track constructions wheel radiation dominates the emitted sound pressure level. To improve the noise situation, it is hence necessary to introduce appropriate measures at the wheels. The eect of the sleeper / baseplate on the input impedance of the rail can be seen in Fig. 2a: in order to achieve a low noise slab track it is important to raise the input impedance and the propagation loss of the rail in the middle frequency range. In terms of construction, the present design of slab track may be revised as follows: 1) moving the elasticity of the elastomer layer, necessary to maintain the quasi static deection for comfort reasons, away from the rail: This could be a construction with booted sleepers (on an resilient layer) on a concrete slab, the

6 Rolf Diehl, Reinhard Gorlich and Georg Holzl 6 Figure 5: Left: a) Inuence of track parameters on the pass{by level: slab track (st 1), double mass of base plate (st 2), heavier rail (st 3), triple loss factor of the elastomer (st 4), sleeperlike mass instead of base plate (st 5), st 4 and st 5 combined (st 6), ballasted track on soft subgrade (b 1), on sti subgrade (b 2) and b 2 combined with soft pads (b 3). Right: b) Insertion loss of ballast mats of varying stiness c 1 : c 2 : c 3 =1:2:4on a steel bridge. rail being fastened to the sleeper via sti pads. A test track previously realized showed however, that such a conventional sleeper design is rather noisy. 2) introducing a heavy damper, as is the sleeper in ballasted track: To provide an acoustic optimization a damping mechnism for the rail and the booted sleeper has to be designed, that is eective also in the lower frequency range in order to reduce sleeper radiation. 3.2 Ground borne vibration To study the eect of mitigation measures for ground borne vibration and excitation of structures simple models have been developed e.g. for bridges, based on beams or plates. Using these base impedances the insertion loss of ballast mats on steel bridges were estimated. Fig. 5b shows the benecial eect of low stinesses of the mats. A high loss factor of the mats is to be recommended in the range of the resonance of the wheelset on the mats around 30 { 50 Hz (not shown in gure). 3.3 Surface roughness As the roughness of the wheel and rail running surfaces are regarded to be the source of the excitation of the predominant noise in the speed range from 60 to 250 km/h it has to be under control. The easiest requirement would be to ask for very smooth running surfaces, but as grinding costs are of vital interest to railroad companies there has to be a more precise specication. As shown in Fig. 6a, RIM allows the sensitivity of the roughness on A{weighted sound level to be calculated.

7 Rolf Diehl, Reinhard Gorlich and Georg Holzl 7 Taking this into consideration the limiting curve in Fig. 6b was developed, for which a pass{by level of 85 db(a) at 160 km/h is predicted. Tomaintain a noise standard for railway lines such a limiting curve should be established internationally. Figure 6: Left: a) Sensitivity of the surface roughness of running surfaces (variation of a single wave length band of 3 db) for 63, 80, 100, 125, 160, 200 and 250 km/h (peaks from left to right) on ballasted track on the A{weighted pass{by level at 25 m. Right: b) Proposal for a limiting curve for rail grinding. 4 Outlook Studying the rolling noise generation mechanism with the aid of a rail/wheel impedance model is usefull to understand the requirements for an acoustically optimized design of railroad track and vehicle: the input impedances of the contact partners have to be adapted to minimize the excitation, especially in frequency ranges of high radiation eciency as already proposed by (Heckl, 1995). Bibliography Cremer, L. and Heckl, M. (1982). Korperschall. Springer Verlag. Heckl, M. (1995). Das rollende Material der Zukunft Entwicklungstendenzen des Schallschutzes. In Osterreichisch{Deutsches Symposium " Leise Bahn\, 10.{11. Mai Holzl, G. and Muller, G. (1995). Anwendung von modernen Memethoden und von Simulationsprogrammen zur Erforschung von Schallreduzierungsmanahmen beim Schienenverkehr. ZEV + DET Glas. Ann., 119(9/10):453{461. Muller-BBM (1993). Rad/Schiene{Impedanzmodell zur Rollgerauschprognose. Muller{BBM report , for Deutsche Bahn ZTQ 15. Remington, P. J. (1987). Wheel/rail rolling noise. parts I and II. Journal of the Acoustical Society of America, 81:1805{1832. Thompson, D. J. (1993). Wheel{rail noise generation, parts I { V. Journal of Sound and Vibration, 161:387{482. TNO (1996). TWINS: Track-Wheel Interaction Noise Software. Theoretical Manual, version 2.3 TPD-HAG-RPT (revised), TNO Institute of Applied Physics.

EVALUATION OF THE EFFECTS OF TEMPERATURE ON RAILPAD PROPERTIES, RAIL DECAY RATES AND NOISE RADIATION

EVALUATION OF THE EFFECTS OF TEMPERATURE ON RAILPAD PROPERTIES, RAIL DECAY RATES AND NOISE RADIATION R. A. Broadbent, D. J. Thompson and C. J. C. Jones ISVR, University of Southampton, Southampton, SO7