On the role of aerodynamically generated sound in determining wayside noise levels from high speed trains

The relative contributions of aerodynamic and wheel/rail noise to railway wayside noise levels are not well understood. Methods for predicting these contributions discussed in this paper include (i) an equation for turbulent boundary layer noise (the minimum wayside noise), (ii) an empirical formula for total aerodynamic noise based on airframe noise studies, and (iii) the Peters equation for wheel/rail interaction noise. Comparisons are made between predicted and measured noise levels for (i) a buoyant vehicle, (ii) the Linear Induction Motor Research Vehicle (LIMRV), and (iii) a magnetically levitated vehicle. Analysis of these results indicates that aerodynamic fluctuations could become the dominant source 3f wayside noise at train speeds of 240–280 km/h. This prognosis is for new high speed railway vehicles equipped with disc brakes and other innovations that reduce the wheel/rail noise contribution.     

The effects on noise of changes in wheel/rail system parameters

An analytical model has been developed that simulates the generation and propagation of wheel/rail noise. In the model, wheel/rail vibrations are induced by running surface roughness. The vibration responses are determined from considering contact stiffness effects and wheel/rail impedance interactions. Near field sound power levels are then calculated by combining the responses with radiation efficiencies, space-averaging the velocity squared on the wheel, and accounting for the decay of vibration along the rail. Finally, the noise levels predicted for the wayside are obtained from an analysis of the propagation that includes the effect of finite ground impedance. Good agreement exists between the analytical model and a series of validation measurements taken at DOT's Transportation Test Center in Pueblo, Colorado. A sensitivity analysis conducted for the parameters of a typical baseline system achieved significant changes in rolling noise only for reductions in wheel/rail contact stiffness, increases in wheel/rail contact area, and decreases in wheel/rail roughness through wheel truing and rail grinding.     

瓦状阻尼橡胶块对高铁车轮减振降噪的影响分析

依据声学测试标准,为了评价某型高铁车轮在安装不同形式橡胶块装置后的减振降噪效果,在半消声室内基于B&K振动噪声测试分析系统,对裸轮和橡胶块车轮开展振动声辐射室内测试实验,并基于有限元方法对车轮模态进行了仿真分析。测试结果可知:相比裸轮,WA、WB车轮模态阻尼比显著增加,车轮的减振效果明显,其中WA车轮的减振效果略优于WB车轮。径向激励下,WA车轮声功率级降低了8 dB(A),WB车轮声功率级降低了5.5 dB(A);轴向激励下,WA车轮声功率级降低了8.2 dB(A),WB车轮声功率级降低了6.2 dB(A)。分析可知橡胶块装置能有效抑制车轮的滚动噪声和曲线啸叫,对车轮的减振降噪有积极作用。     

A HYBRID MODEL FOR THE NOISE GENERATION DUE TO RAILWAY WHEEL FLATS

A numerical model is developed to predict the wheel/rail dynamic interaction occurring due to excitation by wheel flats. A relative displacement excitation is introduced between the wheel and rail that differs from the geometric form of the wheel flat due to the finite curvature of the wheel. To allow for the non-linearity of the contact spring and the possibility of loss of contact between the wheel and the rail, a time-domain model is used to calculate the interaction force. This includes simplified dynamic models of the wheel and the track. In order to predict the consequent noise radiation, the wheel/rail interaction force is transformed into the frequency domain and then converted back to an equivalent roughness spectrum. This spectrum is used as the input to a linear, frequency-domain model of wheel/rail interaction to predict the noise. The noise level due to wheel flat excitation is found to increase with the train speed V at a rate of about 20 log₀V whereas rolling noise due to roughness excitation generally increases at about 30 log₀V. For all speeds up to at least 200 km/h the noise from typical flats exceeds that due to normal levels of roughness. When the wheel load is doubled the predicted impact noise increases by about 3 dB.     

Development of elastic force model for wheel/rail contact problems

In this investigation, a new formulation for the wheel/rail contact problem based on the elastic force approach is presented. Crucial to the success of any elastic force formulation for the wheel/rail contact problem is the accurate prediction of the location of the contact points. To this end, features of multibody formulations that allow introducing additional differential equations are exploited in this investigation in order to obtain a good estimate of the rail arc length travelled by the wheel set. In the formulation presented in this paper, four parameters are used to describe the wheel and the rail surfaces. In order to determine the location of the points of contact between the wheel and the rail, a first order differential equation for the rail arc length is introduced and is integrated simultaneously with the multibody equations of motion of the wheel/rail system. The method presented in this paper allows for multiple points of contact between the wheel and the rail by using an optimized search for all possible contact points. The normal contact forces are calculated and used with non-linear expressions for the creepages to determine the creep forces. The paper also discusses two different procedures for the analysis of the two-point contact in the wheel/rail interaction. Numerical results obtained using the elastic force model are presented and compared with the results obtained using the constraint approach.     

Wheel/rail noise generation due to nonlinear effects and parametric excitation

Two models are developed, one in the time domain and another in the frequency domain, to explain when a wheel/rail noise generation model requires the inclusion of discrete supports, parametric excitation, and the nonlinear contact spring. Numerical simulations indicate the inclusion of discrete supports to describe low frequency response, and also at higher frequencies, especially where the rail is very smooth or has a corrugation/wavelength corresponding to the pinned-pinned frequency. With a corrugation, it may become essential to include the nonlinear contact spring, as contact loss occurs at high corrugation amplitudes. As nonlinearity causes force generation over a broad frequency range, some contributions excite wheel resonances, resulting in high radiation levels, that require the inclusion of wheel/rail nonlinear effects and parametric excitation for accurate prediction.     

A rational fraction polynomials model to study vertical dynamic wheel–rail interaction

This paper presents a model designed to study vertical interactions between wheel and rail when the wheel moves over a rail welding. The model focuses on the spatial domain, and is drawn up in a simple fashion from track receptances. The paper obtains the receptances from a full track model in the frequency domain already developed by the authors, which includes deformation of the rail section and propagation of bending, elongation and torsional waves along an infinite track. Transformation between domains was secured by applying a modified rational fraction polynomials method. This obtains a track model with very few degrees of freedom, and thus with minimum time consumption for integration, with a good match to the original model over a sufficiently broad range of frequencies. Wheel–rail interaction is modelled on a non-linear Hertzian spring, and consideration is given to parametric excitation caused by the wheel moving over a sleeper, since this is a moving wheel model and not a moving irregularity model. The model is used to study the dynamic loads and displacements emerging at the wheel–rail contact passing over a welding defect at different speeds.     

The natural and forced vibrations of a wheel disc

A mechanical model for a wheel disc with a flat web, based on Mindlin's plate theory, is considered. First the eigenfrequencies and mode shapes of the wheel are calculated with the assumption that a fixed point on the rim is connected elastically to the rail. Then the forced vibrations of the wheel are considered under the assumption that a harmonic force acts at the contact surface of the wheel and rail. Results are obtained for the point impedance and the acceleration due to a harmonic force as functions of the frequency of the excitation.     

复式降噪块地铁车轮减振降噪特性

为探究一种复式降噪块装置及其组合形式对某S型辐板地铁车轮的减振降噪效果和机理，在半消声室内，分别对1种自由状态下的标准车轮和3种形式的复式降噪块车轮开展振动声辐射特性及阻尼特性试验，并通过有限元建模对其进行了模态计算。结果表明：复式降噪块装置可在全频段内提高车轮阻尼比，并对车轮各部位有良好的减振效果，以轮辋和踏面的减振效果最为显著；其中，6个制振阻尼片形式的降噪块对车轮的降噪效果最显著，径向激励下的降噪量为13.1dB(A)，轴向激励下的降噪量为11.1dB(A)，降噪频段主要集中在1000Hz以上中高频。该文研究结果是对列车降噪研究领域的补充和发展。     

Vibration of a rolling wheel— preliminary results

Preliminary results are presented of the axial vibration of a railway wheel on a vehicle travelling at speeds of up to 100 miles/h. Frequency analysis shows that the wheel response is resonant, at modes of vibration which have been identified from static tests. Further developments of measurement and analysis techniques will be necessary before a more complete picture of the importance of wheel vibration on wheel/rail noise radiation can be determined.     

Local control of noise and vibration with KELTRACK™ friction modifier and Protector trackside application: an integrated solution

Wheel squeal is a source of continuing concern for many railroads and transits, as well as for their neighbours. The underlying mechanism for squeal noise has been well understood in the literature for some time. However an integrated abatement method addressing the underlying cause of the problem has not previously been reported.This paper describes practical experience using a water-based liquid Friction Modifier (KELTRACK™) applied using a top of rail trackside applicator (Portec Protector^®). The Friction Modifier and delivery equipment have been co-developed to provide an optimized product/delivery system that gives significant reduction of wheel squeal in curves.Wheels experiencing lateral creep in curves are subject to roll-slip oscillations as a result of the frictional characteristics of the interface layer between the wheel and rail. These roll-slip oscillations are amplified in the wheel web leading to the familiar squeal. Providing a thin film of material between the wheel and rail with positive friction characteristics can both in theory and practice greatly reduce the magnitude of these oscillations. The controlled intermediate friction characteristics of KELTRACK™ allow the material to be delivered to the top of both rails without compromising traction or braking.The positive friction aspects of the friction modifier are illustrated by published laboratory studies. Delivery of KELTRACK™ to the contact patch is achieved with a proprietary top of rail electric trackside applicator, the Portec Protector^®. The material is delivered to the top of both rails for optimum friction control.The integrated product/equipment technology is now successfully controlling noise at more than twenty transit sites. Typical sound level reduction is 10-15 dB, in some cases as high as 20 dB, depending on the initial sound level. Two case studies are presented illustrating the technology.     

The influence of track modelling options on the simulation of rail vehicle dynamics

This paper investigates the effect of different models for track flexibility on the simulation of railway vehicle running dynamics on tangent and curved track. To this end, a multi-body model of the rail vehicle is defined including track flexibility effects on three levels of detail: a perfectly rigid pair of rails, a sectional track model and a three-dimensional finite element track model. The influence of the track model on the calculation of the nonlinear critical speed is pointed out and it is shown that neglecting the effect of track flexibility results in an overestimation of the critical speed by more than 10%. Vehicle response to stochastic excitation from track irregularity is also investigated, analysing the effect of track flexibility models on the vertical and lateral wheel–rail contact forces. Finally, the effect of the track model on the calculation of dynamic forces produced by wheel out-of-roundness is analysed, showing that peak dynamic loads are very sensitive to the track model used in the simulation.     

The noise behavior of the wheel/rail-system— some supplementary results

Acoustical measurements were carried out on railroad coaches, on standard tracks and in the free field during test runs. In particular the influences of noise parameters like train speed, track condition, wheel type or locomotive propulsion were examined. Among other things, it appeared that the track conditions can vary considerably, a fact that has a great influence on all measurement values. One obtains a kind of “track profile” relatively independent of the train speed. Measurements both on the parts of the rail and in the free field during the pass-by of a train wheel, just as do the measurements of the wheel levels at the same time, indicate that the rail in the frequency range between 500 and 1200 Hz is the most important factor with regard to sound radiation. Only above this range is the wheel the essential radiator, mainly in the range around 2000 Hz. Further it could be ascertained that the total acceleration levels of the wheel rim have a greater speed exponent than the total acceleration levels of the rail. This can be important if one makes an extrapolation for high train speeds. Additional damping of coach wheels results in a greater noise reduction not only for the radiated sound but also for the structure-borne sound at the rails. This fact indicates the relatively strong coupling between rail and wheel. Furthermore it was ascertained that the levels generated by a locomotive in the upper frequency range are similar to those produced by damped coach wheels. A propulsion influence of an electrical locomotive on the radiated total sound level could not be ascertained. In the last section possible noise generating mechanisms are pointed out with regard to their importance as indicated by our present state of knowledge.     

Vehicle–bridge interaction analysis under high-speed trains

The dynamic interaction between high-speed train and simply supported girders is studied by theoretical analysis and field experiment in this paper. The dynamic interaction model of the train–bridge system is established, in which the rigid-body dynamics theory, finite element method and wheel–rail displacement corresponding assumption are adopted for the vehicle model, bridge model and wheel–rail interaction model, respectively. The measured track irregularities are taken as the system excitation. The responses of a 24 m-span PC box girder bridge are calculated. The proposed analysis model and the solution method are verified through the comparison between the calculated results and the measured results.     

Effect on vehicle and track interaction of installation faults in the concrete bearing surface of a direct-fixation track

Various installation faults can occur in fasteners in the construction of a direct-fixation track using the top-down method. In extreme cases, these faults may cause excessive interaction between the train and track, compromise the running safety of the train, and cause damage to the track components. Therefore, these faults need to be kept within the allowable level through an investigation of their effects on the interactions between the train and track. In this study, the vertical dynamic stiffness of fasteners in installation faults was measured based on a dynamic stiffness test by means of an experimental apparatus that was devised to feasibly reproduce installation faults with an arbitrary shape. This study proposes an effective analytical model for a train–track interaction system in which most elements, except the nonlinear wheel–rail contact and some components that behave bilinearly, exhibit linear behavior. To investigate the effect of the behavior of fasteners in installation faults in a direct-fixation track on the vehicle and track, vehicle–track interaction analyses were carried out, targeting key review parameters such as the wheel load reduction factor, vertical rail displacement, wheel load, and mean stress of the elastomer. From the results, it was noted that it is more important for the installation faults in the concrete bearing surface of a direct-fixation track to be limited for the sake of the long-term durability of the elastomer rather than for the running safety of the train or the structural safety of the track.     

Noise generation by railroad coaches

A systematic analysis was carried out on the acoustic behaviour of railroad coaches. Radiation of air-borne sound as well as structure-borne sound transmission from the wheel/rail contact area to the car body was investigated in laboratory and stationary tests and during test runs at high speeds (160–250 km/h). The aim of the experiments was to find out how much the individual components of the trailing bogie contribute to the transmission of structure-borne sound and the radiation of air-borne sound. A rank ordering of the individual transmission paths from the axle bearing to the bogie frame was set up. An identification of the main noise sources and an indication of the frequency range in which they are important was possible.     

Recent developments in wheel/rail noise research

A review is presented of wheel/rail noise research studies, published since 1976. The indications are that a forced vibration model for the mechanism of wheel/rail noise generation is consistent with the results obtained by various researchers. Further work is needed on the parameters governing the magnitudes of the forces in the wheel/rail contact zone, however, before a complete understanding of noise generation can be achieved, and hence control at source.     

On the impact noise generation due to a wheel passing over rail joints

Impacts occur when a railway wheel encounters discontinuities such as rail joints. A model is presented in which the wheel/rail impacts due to rail joints are simulated in the time domain. The impact forces are transformed into the frequency domain and converted into the form of an equivalent roughness input. Using Track-Wheel Interaction Noise Software (TWINS) and the equivalent roughness input, the impact noise radiation is predicted for different rail joints and at various train speeds. It is found that the impact noise radiation due to rail joints is related to the train speed, the joint geometry and the static wheel load. The overall impact noise level from a single joint increases with the speed V at a rate of roughly .     

弯管对末端带弹性障板充液管路辐射声能量的影响

基于声固耦合有限元方法建立了末端带弹性障板的充液管路数值模型,重点分析了不同激励下弯管对管口辐射声能量的影响.结果表明:弯管引入的高阶周向模式耦合使结构振动和流体声传播都发生明显改变,以致系统辐射声能量及主要能量贡献源也发生转移,并随激励方式和频率而不同.对本文管路模型,平面波激励下弯管系统在低频的结构辐射声能量明显增...     

Vertical dynamic response of non-uniform motion of high-speed rails

In this paper, a computational study using the moving element method (MEM) is carried out to investigate the dynamic response of a high-speed rail (HSR) traveling at non-uniform speeds. A new and exact formulation for calculating the generalized mass, damping and stiffness matrices of the moving element is proposed. Two wheel–rail contact models are examined. One is linear and the other nonlinear. A parametric study is carried out to understand the effects of various factors on the dynamic amplification factor (DAF) in contact force between the wheel and rail such as the amplitude of acceleration/deceleration of the train, the severity of railhead roughness and the wheel load. Resonance in the vibration response can possibly occur at various stages of the journey of the HSR when the speed of the train matches the resonance speed. As to be expected, the DAF in contact force peaks when resonance occurs. The effects of the severity of railhead roughness and the wheel load on the occurrence of the jumping wheel phenomenon, which occurs when there is a momentary loss of contact between the wheel and track, are investigated.