Evaluation of track stiffness and track damping

Correct estimation of track stiffness and track damping is essential for predicting the dynamic wheel loads of railway vehicles running on rough tracks. While several analytical procedures have been developed in the past to estimate track stiffness, there is no procedure readily available for estimating track damping. Experimental techniques involving the use of impulse tests have been used in this study to estimate track stiffness and track damping, on several different track structures on the Indian Railways. The results of these tests are presented.     

SOUND RADIATION FROM A VIBRATING RAILWAY WHEEL

The sound radiation characteristics of a railway wheel are investigated by using boundary element calculations. The axisymmetry of the wheel allows an axi-harmonic formulation to be used, in which the wheel is defined by a two-dimensional mesh of its cross-section and the motion is decomposed into harmonics of different numbers of nodal diameters. The radiation ratios of the wheel, vibrating in its various normal modes, are calculated for a range of frequencies. The effects of variation in the wheel radius, web thickness and tyre depth are also investigated. From these results, simple formulae are proposed that allow the radiation ratios to be approximated closely. These are more convenient than the boundary element calculations for calculating the rolling noise from a wheel since they are a function of a few simple geometrical parameters. The directivity of wheel radiation is also considered, with comparisons with measured data indicating that simple monopole and dipole characteristics can be applied.     

地铁车辆直型辐板阻尼环车轮声振特性分析

为探究地铁车辆阻尼环扩张状态对阻尼环车轮声振特性影响,在半消声室内进行阻尼环车轮自由状态下的声振特性实验研究,结合有限元仿真对实验结果进行分析。研究表明,环-轮组合振动固有频率与原车轮相比变化不大,但阻尼环使车轮的模态阻尼比显著增加,有效抑制了车轮各模态的振动幅值。改变阻尼环扩张状态,阻尼环降噪效果发生非线性变化,幅值在5.6 dB(A)之内。阻尼环扩张状态可通过调节非闭合阻尼环两端扩张装置来改变。阻尼环处于非最大扩张状态W_3时,可获得最佳降噪效果。     

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。     

用波尔共振仪研究混沌现象

用半导体激光器作为光源,用鼠标作为位移传感器,将波尔共振仪摆轮的振动转化为鼠标的运动轨迹,并通过Ghost Mouse-Setup软件记录鼠标轨迹,最后通过Labview软件对记录的轨迹进行信号处理,通过观察分析吸引子来研究波尔共振仪中的混沌现象。实验结果表明:波尔共振仪中摆轮做阻尼振动时,其振动振幅出现随时间逐渐减小,最终停止摆动的确定性规律,但每一次摆轮的运动过程都是随机的,各不相同。只要时间足够长,摆轮最终都会收缩成一点,形成稳定的焦点,即混沌吸引子。这就是波尔共振仪中摆轮做阻尼振动出现的混沌现象。     

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.     

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。     

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.     

阻尼贴片式高速列车车轮振动声辐射试验分析

为了研究辐板不同阻尼贴片装置对高速列车车轮的减振降噪效果,在半消声室内进行标准车轮与阻尼贴片式车轮自由状态下的振动声辐射试验研究,并基于有限元法对车轮模态进行了仿真计算。研究结果表明：施加辐板阻尼贴片后,两种阻尼贴片车轮的固有频率与标准车轮相比变化不大,但对于频率在1600Hz以上各阶模态阻尼比显著增加。径向与轴向激励下的降噪效果均达到10dB(A)以上,可见两种阻尼贴片装置均具有良好的降噪效果。其中在多了0.3mm铝合金薄板的情况下,W2车轮的降噪效果要略优于W1车轮,轴向激励下更加明显。     

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.     

Experimental Modal Damping Identification of a Mechanical Structure Using Video Magnification Technique

Vibration can be introduced in all mechanical fields in our life. Engineers try to avoid its negative effect leading in some cases to deformation in the machines. Many researches are dedicated to study the identification of damping especially in multi degree of freedom systems with particular attention to the source of energy dissipation. They focus on developing new tools or methods which may be used in real problems to obtain accurate results about the amount (or value) and the location of energy dissipation in the structure. The aim of this paper is to present an original procedure aims to experimentally determine the modal damping ratio of a mechanical structure. The proposed procedure consists of extracting the Frequency Response Function of the vibrating system using the video magnification method and then calculate the modal damping ratio using the 3-dB method. These experimental measurements are carried out by giving an external force on a cantilever beam, then the modal damping ratios are extracted using motion magnification. The obtained results show a relative error less than 4.2% between the experimental measurements and the analytical calculation for the Frequency Response Function (FRF) curves. The novelty of the paper is to combine the video magnification technique and the 3dB method in a procedure that aims to experimentally measure the modal damping of a mechanical structure. The proposed procedure in this paper represents the damping identification as a simple and easy engineering application.     

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.     

A dynamic model for an asymmetrical vehicle/track system

A finite element model to simulate an asymmetrical vehicle/track dynamic system is proposed in this paper. This model consists of a 10-degree-of-freedom (d.o.f.) vehicle model, a track model with two rails, and an adaptive wheel/rail contact model. The surface defects of wheels and rails can be simulated with their geometry and an endless track model is adopted in the model. All time histories of forces, displacements, velocities and accelerations of all components of the vehicle and track can be obtained simultaneously. By using this model, one can study the effect that wheel/rail interaction from one side of the model has on the other. This can be done for many asymmetrical cases that are common in railway practice such as a wheel flat, wheel shelling, out-of-round wheel, fatigued rail, corrugated rail, head-crushed rail, rail joints, wheel/rail roughness, etc. Only two solutions are reported in this paper: steady state interaction and a wheel flat.     

Experimental study of the effect of viscoelastic damping materials on noise and vibration reduction within railway vehicles

Interior noise and vibration reduction has become one important concern of railway operating environments due to the influence of increased speeds and reduced vehicle weights for energy efficiency. Three types of viscoelastic damping materials, bitumen-based damping material, water-based damping coating and butyl rubber damping material, were developed to reduce the vibration and noise within railway vehicles. Two sleeper carriages were furnished with the new materials in different patterns of constrained-layer and free-layer damping treatment. The measurements of vibration and noise were carried out in three running carriages. It is found that the reduction effect of damping treatments depends on the running speed. The unweighted root-mean-square acceleration is reduced by 0.08–0.79 and 0.06–0.49 m/s² for the carriage treated by bitumen-based as well as water-based damping materials and water-based damping material, respectively. The first two materials reduce vibration in a wider frequency range of 63–1000 Hz than the last. It turns out that the damping treatments of the first two reduce the interior noise level by 5–8 dBA within the carriage, and the last damping material by 1–6 dBA. However, the specific loudness analysis of noises shows that the noise components between 125 and 250 Hz are dominant for the overall loudness, although the low-frequency noise is noticeably decreased by the damping materials. The measure of loudness is shown to be more accurate to assess reduction effect of the damping material on the acoustic comfort.     

On derivation of the analytical expression for damping ratios in a low-viscosity approximation

The damping ratios of waves and oscillations in nonlinear dispersion equations are found for planar, cylindrical, and spherical geometries as applied to finite-volume liquids. For a cylindrical jet and a plane interface between viscous liquids, the damping ratios are determined for the first time. When the radius of curvature of the liquid jet surface decreases, so does the damping ratio of capillary waves. In a system of immiscible liquids, the damping ratio may be both larger and smaller than that for the pure liquid depending on the viscosity of the liquids and the ratio of their densities. This is because the damping ratio depends on the kinematic viscosities of pure liquids. The damping ratio is also estimated for waves arising at the liquidgas interface due to a tangential discontinuity of the velocity field.     

SOME OBSERVATIONS ON THE CHARACTERIZATION OF STRUCTURAL DAMPING

This paper deals with the characterization of damping in dynamical structural systems. In particular, the problem of how the modal damping ratios change with different boundary conditions is addressed. It is shown that only Rayleigh-type damping is actually independent of boundary conditions and modal damping ratios can be easily converted from one boundary condition to another. This condition applies independently to continuous, discrete and discretized systems.     

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.     

移动闭塞条件下线路弯道对列车交通流影响的研究

在NaSch模型的基础上,针对铁路线路特点提出了一种用于模拟铁路线路弯道的多列车追踪运行的元胞自动机模型.应用该模型,进行了计算机数值模拟,研究了具有不同弯道半径、不同外轨超高和不同弯道长度的线路弯道对铁路交通流的影响.模拟结果表明:建立的模型能够准确的反映出特殊线路交通流情况,线路弯道对列车的行车安全有较大的影响,同时再现了时走时停的交通波现象,根据仿真结果得出了随着弯道半径的增大,列车的晚点时间逐渐减少,合理选择弯道半径、外轨超高值和弯道长度,可以显著提高线路的通行能力,减低轮轨磨耗,保证列车的安全、舒适运行.所得结果对铁路线路选线设计和运营管理有一定的指导意义.