Prediction of rail corrugation using a rotating flexible wheelset coupled with a flexible track model and a non-Hertzian/non-steady contact model

This paper presents a model for simulating vehicle–track interaction at high frequencies for investigations of rail roughness growth. The dynamic interaction model developed employs a substructuring technique and the whole system consists of a number of substructures that can be modelled independently. The systems are coupled through the forces at the wheel–rail contact and the railpad. A coupled, rotating flexible wheelset, a flexible track model and a non-Hertzian/non-steady contact model have been implemented and results are presented here for a free wheelset on a symmetrical track system with initial random and sinusoidal roughness. Both rigid and flexible wheelsets are considered.     

Denoising of sensor signals for the flange thickness measurement based on wavelet analysis

A railway wheelset is subject to normal wear due to large part to friction contact between the wheelset and the rail. Because the wear of wheelset will bring the hidden security troubles to the operation of the railway, it is very important to measure the wheelset's geometrical parameters, especially the flange thickness. The optoelectronic method is proposed and can dynamically measure the flange thickness on line. Fast Fourier transform and wavelet analysis methods are used to denoise the sensor's signals. It is found that the wavelet transform produces a much better way of denoising of the signals compared with the fast Fourier transform. Comparisons of the flange thickness measurement with the wheelset creeping and the optoelectronic system are presented. The root-mean-square errors of the flange thickness with the manual measurement with the wheelset creeping and the optoelectronic method measurement with the wavelet analysis are 0.22 and 0.18, respectively. The changing range of manual measurement is much larger than that of the optoelectronic method because of the difference between every operator's measuring standard. Measurement results of the optoelectronic method show that the system has better repeatability and reliability compared to the manual measurement.     

Dynamic optimization of track components to minimize rail corrugation

In this paper, the influence on corrugation of the most significant track parameters has been examined. After this parametric study, the optimization of the track parameters to minimize the undulatory wear growth has been achieved. Finally, the influence of the dispersion of the track and contact parameters on corrugation growth has been studied. A method has been developed to obtain an optimal solution of the track parameters which minimizes corrugation growth, thus ensuring that this solution remains optimum despite dispersion of track parameters and wheel–rail contact uncertainties. This work is based on the computer application RACING (RAil Corrugation INitiation and Growth) which has been developed by the authors to predict rail corrugation features.     

A Novel Method for non-contact measuring diameter parameters of wheelset based on wavelet analysis

A railway wheelset is subject to normal wear due to large part to friction contact between the wheelset and the rail. It is very important to measure the diameter parameter of wheelset for the safety of trains. The optoelectronic method is introduced and can dynamically measure the diameter parameter. Fast Fourier transform and wavelet analysis methods are used to denoise the detected signals of wheelset diameters. The results show that the wavelet analysis provides a much better way of denoising of the signals compared with the fast Fourier transform method. Comparisons of the diameter parameter measurements with the manual apparatus and the optoelectronic system are presented. The measurement accuracy of diameter parameter was within 1.0 mm. The root-mean-square error of the diameter is 0.51 and 0.15, respectively. The accuracy meets the measuring requirement of diameter parameters on line and shows that the system has better repeatability and reliability compared to the manual measurement.     

Theoretical development of a simplified wheelset model to evaluate collision-induced derailments of rolling stock

A theoretical method is proposed to predict and evaluate collision-induced derailments of rolling stock by using a simplified wheelset model and is verified with dynamic simulations. Because the impact forces occurring during collision are transmitted from the car body to the bogies and axles through suspensions, rolling stock leads to derailment as a result of the combination of horizontal and vertical impact forces applied to the axle and a simplified wheelset model enforced at the axle can be used to theoretically formulate derailment behaviors. The derailment type depends on the combination of the horizontal and vertical forces, the flange angle and the friction coefficient. According to collision conditions, wheel-climb, wheel-lift or roll-over derailment can occur between the wheel and the rail. In this theoretical derailment model of a simplified wheelset, the derailment types are classified as Slip-up, Slip/roll-over, Climb-up, Climb/roll-over and pure Roll-over according to the derailment mechanisms between the wheel and the rail and the theoretical conditions needed to generate each derailment mechanism are proposed. The theoretical wheelset model is verified by dynamic simulation and its applicability is demonstrated by comparing the simulation results of the theoretical wheelset model with those of an actual wheelset model. The theoretical derailment wheelset model is in good agreement with the virtual testing model simulation for a collision-induced derailment of rolling stock.     

Dynamic instability of a wheel moving on a discretely supported infinite rail

The parametric instability of a wheel moving on a discretely supported rail is discussed. To achieve this, an analysis method is developed for a quasi-steady-state problem which can represent an exponential growth of oscillation. The temporal Fourier transform of the rail motion is expanded by a Fourier series with respect to the longitudinal coordinate, and then the response of the rail deflection due to a quasi-harmonic moving load is derived. The wheel/track interaction is formulated by the aid of this function and reduced to an infinite system of linear equations for the Fourier coefficients of the contact force. The critical velocities between the stable and unstable states are calculated based on the nontrivial condition of the homogeneous matrix equation. Through these analyses the influences of the modeling of rail and rail support on the unstable speed range are examined. Moreover, not only the first instability zone but also other zones are evaluated.     

Dynamic train-track interaction at high vehicle speeds—Modelling of wheelset dynamics and wheel rotation

Vertical dynamic train-track interaction at high vehicle speeds is investigated in a frequency range from about 20 Hz to 2.5 kHz. The inertial effects due to wheel rotation are accounted for in the vehicle model by implementing a structural dynamics model of a rotating wheelset. Calculated wheel-rail contact forces using the flexible, rotating wheelset model are compared with contact forces based on rigid, non-rotating models. For a validation of the train-track interaction model, calculated contact forces are compared with contact forces measured using an instrumented wheelset. When the system is excited at a frequency where two different wheelset mode shapes, due to the wheel rotation, have coinciding resonance frequencies, significant differences are found in the contact forces calculated with the rotating and non-rotating wheelset models. Further, the use of a flexible, rotating wheelset model is recommended for load cases leading to large magnitude contact force components in the high-frequency range (above 1.5 kHz). In particular, the influence of the radial wheel eigenmodes with two or three nodal diameters is significant.     

A finite element study on rail corrugation based on saturated creep force-induced self-excited vibration of a wheelset-track system

The present work proposes friction coupling at the wheel-rail interface as the mechanism for formation of rail corrugation. Stability of a wheelset-track system is studied using the finite element complex eigenvalue method. Two models for a wheelset-track system on a tight curved track and on a straight track are established. In these two models, motion of the wheelset is coupled with that of the rail by friction. Creep force at the interface is assumed to become saturated and approximately equal to friction force, which is equal to the normal contact force multiplied by dynamic coefficient of friction. The rail is supported by vertical and lateral springs and dampers at the positions of sleepers. Numerical results show that there is a strong propensity of self-excited vibration of the wheelset-track system when the friction coefficient is larger than 0.21. Some unstable frequencies fall in the range 60-1200 Hz, which correspond to frequencies of rail corrugation. Parameter sensitivity analysis shows that the dynamic coefficient of friction, spring stiffness and damping of the sleeper supports all have important influences on the rail corrugation formation. Bringing the friction coefficient below a certain level can suppress or eliminate rail corrugation.     

The influence of the contact zone on the excitation of wheel/rail noise

Rolling noise is excited by surface roughness at the wheel/rail contact. The contact patch is known to attenuate the excitation at wavelengths that are short in comparison with its length. A distributed point-reacting spring (DPRS) model is used with measured roughness data to determine the contact filter effect, and this result is compared with analytical predictions. It is found that the analytical model gives an attenuation that is too large at short wavelengths but is usable for wavelengths down to somewhat smaller than the length of the contact patch. Additionally, variations in the detailed geometry of the profile can cause the contact point on the wheel and rail to oscillate laterally. This introduces an oscillating moment that can induce additional vibration and noise. The DPRS model and rolling noise prediction model are both extended and used together to allow an estimate of the contribution to the radiated noise. It is found that, while the direct roughness excitation is still more important, the moment excitation can be significant, particularly for conforming profiles.     

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.     

A precise integration method for solving coupled vehicle–track dynamics with nonlinear wheel–rail contact

A new method is proposed as a solution for the large-scale coupled vehicle–track dynamic model with nonlinear wheel–rail contact. The vehicle is simplified as a multi-rigid-body model, and the track is treated as a three-layer beam model. In the track model, the rail is assumed to be an Euler-Bernoulli beam supported by discrete sleepers. The vehicle model and the track model are coupled using Hertzian nonlinear contact theory, and the contact forces of the vehicle subsystem and the track subsystem are approximated by the Lagrange interpolation polynomial. The response of the large-scale coupled vehicle–track model is calculated using the precise integration method. A more efficient algorithm based on the periodic property of the track is applied to calculate the exponential matrix and certain matrices related to the solution of the track subsystem. Numerical examples demonstrate the computational accuracy and efficiency of the proposed method.     

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.     

Simple and fast rail wear measurement method based on structured light

In this paper, a fast and accurate rail wear measurement method based on simple equipments is presented. The inner rail profile is measured by a line structured light vision sensor. Using the centers of the big and small circle from the rail waist profile as control points, the measured rail profile is registered to the reference profile. The rail wear, including the vertical and horizontal rail wear, is computed by comparing the registered measured profile with the reference profile. The method has three key contributions: (1) the rail waist light stripe center points in the images are located fast and accurately by first tracking the region containing the rail waist light stripe using the Kalman filter and then computing the sub-pixel precision image coordinates by Hessian matrix at pixels. (2) The rail waist profile is segmented automatically into arcs of big and small circles by thresholding the normal angle curve of the measured rail waist profile. The centers of the two circles are used as control points for registering the measured rail profile to the reference profile. (3) The fast location of rail wear points in the images is realized by projecting the rail wear constraint points to the image, which simplifies the problem of computing rail wear from 2d image processing to 1d searching along the line segment connecting two rail wear constraint points. Experiments show that the proposed method can achieve 500 fps measurement frequency. At a train speed of 350 km/h, the interval between two consecutive measurements is about 190 mm. The system is tested on a real running train, and the measurement results are compared with those rail wear measured manually by special gage. The RMS errors of vertical and horizontal rail wears are 0.34 and 0.30 mm, respectively.     

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.     

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.     

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.     

Time-domain prediction of impact noise from wheel flats based on measured profiles

Railway impact noise is caused by discrete rail or wheel irregularities, such as wheel flats, rail joints, switches and crossings. In order to investigate impact noise generation, a time-domain wheel/rail interaction model is needed to take account of nonlinearities in the contact zone. A nonlinear Hertzian contact spring is commonly used for wheel/rail interaction modelling but this is not sufficient to take account of actual surface defects which may include large geometry variations. A time-domain wheel/rail interaction model with a more detailed numerical non-Hertzian contact is developed here and used with surface roughness profiles from field measurements of a test wheel with a flat. The impact vibration response and noise due to the wheel flat are predicted using the numerical model and found to be in good agreement with the measurements. Moreover, compared with the Hertzian theory, a large improvement is found at high frequencies when using the detailed contact model.     

Simplified simulation of fretting wear using the method of dimensionality reduction

We study the problem of wear of a rotationally symmetric profile subjected to oscillations with small amplitude. Under these conditions, sliding occurs at the boundary of the contact area while the inner parts of the contact area may still stick. In a recent paper, Dimaki with colleagues proposed a numerically exact simulation procedure based on the method of dimensionality reduction (MDR). This drastically reduced the simulation time compared with conventional finite element simulations. The proposed simulation procedure requires carrying out the direct and the inverse MDR transformations in each time step. This is the main time consuming operation in the proposed method. However, solutions obtained with this method showed a remarkable simplicity of the development of wear profiles in the MDR space. In the present paper, we utilize these results to formulate an approximate model, in which the wear is simulated directly in the one-dimensional space without using integral transformations. This speeds up the simulations of wear by further several orders of magnitude.     

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.     

平行磨削非轴对称非球面光学元件表面形貌

结合砂轮表面仿真及磨削过程的运动学仿真获得工件表面轮廓、形貌和粗糙度预计,可以作为磨削过程中的理论依据,是精密磨削加工技术中主要的研究内容之一。平行磨削技术是加工非轴对称非球面光学元件的重要手段,而相关的仿真过程报道还很少。提出一种基于平行磨削的精密磨削加工非球面表面生成的仿真方法,该方法主要包含使用高斯方法生成具有不同统计学特征的随机砂轮表面形貌,建立单磨粒运动轨迹方程和圆弧砂轮细分后与工件表面点接触的运动关系,据此给出平行磨削加工表面生成的数值算法,并对不同加工参数下的工件表面形貌进行仿真。仿真结果和测量结果的一致性验证了所给算法的正确性和有效性