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.     

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.     

Wheel/rail noise—Part III: Impact noise generation by wheel and rail discontinuities

This paper is part of a series of publications dealing with wheel/rail noise [1–4]. Except for comparing the relative importance of impact noise with rolling noise, this paper concerns itself exclusively with the impact noise generated by such discontinuities as rail joints, frogs, switches, and wheel flats.Studies show that above a certain critical train speed the wheel separates from the rail when the interface encounters certain types of discontinuities. This critical train speed is an important acoustical parameter, because the noise generation process obeys completely different laws in the speed ranges below and above it. From the geometry, the kinematics, and the dynamics of the wheel/rail system, analytical models have been developed to identify the major variables controlling the generation of impact noise. The validity of these models has been confirmed by both scale-model and full-scale experiments.The results of the study show the following: (1) at rail joints, the height difference—and not the width of the gap—is the controlling parameter; (2) below critical train speed, impact noise increases with increasing train speed and does not depend on the direction of travel; (3) above critical train speed, the intensity of impact noise increases with increasing train speed for travel in the step-up direction but is independent of the train speed for travel in the step-down direction; (4) in generating impact noise, wheel flats are equivalent to step-down rail joints, provided flat height equals height difference at the joint; (5) both the magnitude and spectrum of impact noise produced by wheel and rail discontinuities can be predicted from a simple wheel drop test. With the knowledge gained from both the analytical and the experimental studies, we have been able to identify feasible measures for the control of impact noise.     

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.     

Sources and mechanisms of wheel/rail noise: state-of-the-art and recent research

A review is presented of wheel/rail research studies, published since 1978. Additionally a study is presented which is focussed on the magnitudes and relative importance of vertical and horizontal forces in the wheel/rail contact zone. In the specific case and the frequency range 50–2000 Hz the vertical force appeared to be 3–10 times larger than the lateral (axial) force. Nevertheless radiation due to axial excitation of the wheel dominates the wayside sound pressure level in several one-third octave frequency bands. Another significant contribution to the wayside A-weighted sound pressure level is attributed to vertical excitation of the rail.     

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.     

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 .     

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.     

Experimental analysis of wheel noise emission as a function of the contact point location

Recent analyses show that the wheel noise emission depends on the lateral position of the contact patch area on the wheel tyre. This displacement from the nominal position is such that different wheel modes are excited, resulting in a different frequency and amplitude composition of the wheel related noise component. In this paper the results of a test programme held on the ETR500 Italian high-speed train are shown. Thanks to a special device mounted under the axle box comprising a microphone and a windshield, it has been possible to measure the wheel noise continuously up to 300 km/h in tangent track and in curves. The behaviour of wheels in different condition of line curvature is shown, together with the results from a new type of constrained layer damped wheel.     

Wheel/rail noise—means for control

Wheel/rail noise is one of the primary sources of noise from rail system operations—in many cases, the primary source. This paper is a review of the methods available for controlling all three types of wheel/rail noise: squeal, impact, and roar (rolling noise). The acoustical performance, non-acoustical benefits, problems, constraints, and additional research and testing requirements for each noise control treatment are presented.     

Band/wheel system vibration under impulsive boundary excitation

Measurements of band vibration undertaken here show that passage of the butt weld connecting the ends of continuous band over wheels excites vibration in the band/wheel system. A displacement impulse occurs each time the weld initially contacts and separates from the wheels. The excitation is periodic, and it can excite instability. The vibration and stability of the coupled band/wheel system under impulsive boundary displacements are analyzed in this paper. The theoretical and experimental findings show that resonance occurs in the system when the weld passage (impulse) period is an integer multiple of any system natural period.     

The influence of noise on the logistic model

The behavior of the logistic system which is generated by the functionf(x =ax (1–x) changes in an interesting way if it is perturbed by external noise. It turns out that the chaotic behavior which was predicted by Li and Yorke for orbits of period 3, becomes visible and that a sequence of mergence transitions occurs at the critical parameter. The change of the invariant probability density and the Lyapunov exponents are examined numerically. The power spectrum for the period 3 orbit for different fluctuations is calculated and a recursion formula for the time evolution of the probability density is presented as a discrete-time analog of a Chapman-Kolmogorov equation.     

A numerical investigation of curve squeal in the case of constant wheel/rail friction

Curve squeal is commonly attributed to self-excited vibrations of the railway wheel, which arise due to a large lateral creepage of the wheel tyre on the top of the rail during curving. The phenomenon involves stick/slip oscillations in the wheel/rail contact and is therefore strongly dependent on the prevailing friction conditions. The mechanism causing the instability is, however, still a subject of controversial discussion. Most authors introduce the negative slope of the friction characteristic as a source of the instability, while others have found that squeal can also occur in the case of constant friction due to the coupling between normal and tangential dynamics. As a contribution to this discussion, a detailed model for high-frequency wheel/rail interaction during curving is presented in this paper and evaluated in the case of constant friction. The interaction model is formulated in the time domain and includes the coupling between normal and tangential directions. Track and wheel are described as linear systems using pre-calculated impulse response functions that are derived from detailed finite element models. The nonlinear, non-steady state contact model is based on an influence function method for the elastic half-space. Real measured wheel and rail profiles are used. Numerical results from the interaction model confirm that stick/slip oscillations occur also in the case of constant friction. The choice of the lateral creepage, the value of the friction coefficient and the lateral contact position on the wheel tread are seen to have a strong influence on the occurrence and amplitude of the stick/slip oscillations. The results from the interaction model are in good qualitative agreement with previously published findings on curve squeal.     

Wheel/rail noise—Part II: Wheel squeal

A model is presented for the intense pure-tone noise generated by American subway cars and German trams when traversing tight curves. Squeal is presumed to arise from lateral crabbing of the wheels across the rail head, which results from the finite length of the truck (or bogie). This lateral sticking and slipping causes vibrations in the wheel to increase until a stable amplitude is reached. The stick-slip mechanism is described by a negative damping coefficient that varies with vibration amplitude. The model is used to predict the intensity of wheel squeal as a function of train speed, curve radius, and truck length. Damped and resilient wheels were tested and found effective at reducing wheel squeal.     

Propagation of noise from rail lines

This paper presents models for predicting the effects of geometric attenuation, air absorption, ground attenuation, and barrier insertion loss on the propagation of noise from railcars and locomotives. Predictions based on these models are compared with available field data.     

The differing annoyance levels of rail and road traffic noise

The results of a study on the relative annoyance by rail or road traffic noise in urban and rural areas are reported. Fourteen areas with rail and road traffic noise with differing levels of loudness (L_eq) were investigated. The annoyance was assessed by means of a questionnaire. The analysis of the relationship between annoyance and L_eq—performed separately for rail and road traffic noise—shows that the same amount of annoyance is reached for railway traffic noise at L_eq levels 4–5 dB(A) higher than for road traffic noise (railway/traffic noise “bonus”). The estimation for the difference values vary for the different variables of annoyance. Furthermore, the difference levels tend to be higher in urban than in rural areas.     

Some mechanisms of excitation of a railway wheel

Railway wheel vibrations are caused by a number of mechanisms. Two of these are considered: (a) gravitational load reaction acting on different points of the wheel rim, as the wheel rolls on, and (b) random fluctuating forces generated at the contact patch by roughness on the mating surfaces of the wheel and rail. The wheel is idealized as a thin ring, and the analysis is limited to a single wheel rolling on a rail. It is shown that the first mechanism results in a stationary pattern of vibration, which would not radiate any sound. The acceleration caused by roughness-excited forces is much higher at higher frequencies, but is of the same order as that caused by load reaction at lower frequencies. The computed acceleration level (and hence the radiated SPL) caused by roughness is comparable with the observed values, and is seen to increase by about 10 dB for a doubling of the wagon speed. The driving point impedance of the periodic rail-sleeper system at the contact patch, which is used in the analysis, is derived in a companion paper.