Short-wave Irregularities Research Articles

Spectral element method for random vibration analysis of the vehicle-track coupling system

In this paper, we propose a new random vibration analysis model for the vertical vehicle-track coupling system, which combines the symplectic method and the spectral element method (SEM) to enhance calculation efficiency and accuracy. The model assumed that the vehicle is composed of a multi-rigid body with 10 DOFs, and its motion equation is derived using the traditional frequency analysis method. Tracks are considered periodic structures, and the part between sleeper support points is considered a substructure. The motion equation of the periodic track-substructure is established by spectral element method (SEM), and the propagation of vibration wave between the substructures is calculated by the symplectic method. The frequency responses of the vehicle-track coupling system are calculated by using the German low-interference irregularity spectrum and short-wave irregularity spectrum as excitation. Then, the rationality of this method is verified by comparing it with the results from the traditional symplectic method and simulations using Universal Mechanism software. The comparison shows that this method surpasses the traditional symplectic method in high-frequency accuracy while maintaining high computational efficiency. Although the finite element method also has the capability for high-frequency analysis, this method can calculate the high-frequency vibration of an infinitely long track using just one element, making it more suitable for the efficient analysis of vehicle-track coupling systems. Finally, the model is applied to analyze the distribution characteristics of the vibration response of the coupled system in the frequency domain.

Compilation of wheel-rail comprehensive irregularity spectrum for subway vehicle

The irregularity excitation experienced by subway vehicles is mainly the result of the interaction between the track and wheel. However, in the early system design and simulation analysis of subway vehicles, most only used the traditional standard track irregularity spectrum as the input excitation, ignoring or underestimating the contribution of the wheel irregularity. Based on our statistical analysis of 200,000 kilometers of tracking test data of subway vehicle wheel irregularities, we found that the short-wave irregularity caused by the wheels far exceeds the traditional standard track irregularity. The service condition of the vehicle is seriously affected, especially in the final stage of a wheel re-profile period. To address the above issues: Firstly, the sensitive wavelength range (16. 67∼2500 mm) of subway vehicles was derived based on the axle box acceleration spectrum of IEC61373: 2010, which was very close to the wavelength range (50∼2627 mm) of the wheel irregularity spectrum proposed later, demonstrating the importance of compiling a wheel irregularity spectrum; Secondly, based on the large number of tracking test data of wheel out-of-roundness, a calculation method of the wheel irregularity quantile spectrum under the Johnson non-normal transformation system was proposed; Thirdly, according to the different stages of the wheel re-profile period, the wheel irregularity spectrum is introduced to correct the short-wave segments of the traditional standard track irregularity spectrum to compile a wheel-rail comprehensive irregularity spectrum.

Evolution Characteristics of Aluminum Thermal Weld Irregularity and Damage in Heavy-Haul Railway under Different Service Conditions

Aluminum thermal welding joints are widely used in the maintenance welding of heavy-haul railways due to their easy handling and high efficiency. However, due to their inherent welding characteristics, welding results in certain differences in the material’s physical properties at the welding zone compared to adjacent base materials, leading to the occurrence of short-wave irregularity under long-term wheel–rail interactive forces. In order to explore the evolution characteristics of weld irregularity, dynamic characteristics, and plastic deformation under long-term wheel–rail impact, a detailed tracking test was conducted on a normal aluminum weld, and the process from being put on the track to being damaged and replaced was evaluated. At the same time, a rigid–flexible coupling model was established for subsequent analysis, and plastic damage was analyzed using the finite element model. The results show that the service life of the weld can be divided into three different stages: the initial stage, the intermediate stage, and the damage stage. In the damage stage, a temporary separation occurred between the wheel and rail, leading to a sudden change in the wheel–rail interaction. The weight of 250 MT at the weld reached the repairment control limit. The concentration effect of equivalent plastic deformation was most serious at 2~5 mm below the rail head.

Research on the influence of flexible wheelset rotation effect on wheel rail contact force

PurposeUnder the high-speed operating conditions, the effects of wheelset elastic deformation on the wheel rail dynamic forces will become more notable compared to the low-speed condition. In order to meet different analysis requirements and selecting appropriate models to analyzing the wheel rail interaction, it is crucial to understand the influence of wheelset flexibility on the wheel-rail dynamics under different speeds and track excitations condition.Design/methodology/approachThe wheel rail contact points solving method and vehicle dynamics equations considering wheelset flexibility in the trajectory body coordinate system were investigated in this paper. As for the wheel-rail contact forces, which is a particular force element in vehicle multibody system, a method for calculating the Jacobian matrix of the wheel-rail contact force is proposed to better couple the wheel-rail contact force calculation with the vehicle dynamics response calculation. Based on the flexible wheelset modeling approach in this paper, two vehicle dynamic models considering the wheelset as both elastic and rigid bodies are established, two kinds of track excitations, namely normal measured track irregularities and short-wave irregularities are used, wheel-rail geometric contact characteristic and wheel-rail contact forces in both time and frequency domains are compared with the two models in order to study the influence of flexible wheelset rotation effect on wheel rail contact force.FindingsUnder normal track irregularity excitations, the amplitudes of vertical, longitudinal and lateral forces computed by the flexible wheelset model are smaller than those of the rigid wheelset model, and the virtual penetration and equivalent contact patch are also slightly smaller. For the flexible wheelset model, the wheel rail longitudinal and lateral creepages will also decrease. The higher the vehicle speed, the larger the differences in wheel-rail forces computed by the flexible and rigid wheelset model. Under track short-wave irregularity excitations, the vertical force amplitude computed by the flexible wheelset is also smaller than that of the rigid wheelset. However, unlike the excitation case of measured track irregularity, under short-wave excitations, for the speed within the range of 200 to 350 km/h, the difference in the amplitude of the vertical force between the flexible and rigid wheelset models gradually decreases as the speed increase. This is partly due to the contribution of wheelset’s elastic vibration under short-wave excitations. For low-frequency wheel-rail force analysis problems at speeds of 350 km/h and above, as well as high-frequency wheel-rail interaction analysis problems under various speed conditions, the flexible wheelset model will give results agrees better with the reality.Originality/valueThis study provides reference for the modeling method of the flexible wheelset and the coupling method of wheel-rail contact force to the vehicle multibody dynamics system. Furthermore, by comparative research, the influence of wheelset flexibility and rotation on wheel-rail dynamic behavior are obtained, which is useful to the application scope of rigid and flexible wheelset models.

Influence of wheelset structural flexibility on dynamic properties of a wide-gauge six-axle heavy-haul locomotive

Wheelset structural flexibility, that is the elastic deformation of the wheelset as a structure, has an important influence on the dynamic properties of railway locomotive vehicles at medium and high frequencies. Based on the practical structural parameters, this paper proposes a multi-degree of freedom rigid-flexible coupling dynamic model of a wide-gauge freight electric locomotive with C0-C0 bogies with an axle suspension driving system. The wheelset with the interference-fit large gear is made flexible using the finite element method, and then the rigid-flexible coupling vehicle model with elastic wheelsets is established in the software SIMPACK 2020. A short-wave irregularity superposed on the American fifth-grade track irregularity is used as the track excitation to study the performance at higher frequencies. From the modal analysis of the vehicle, it is obtained that the lowest frequency at which the elastic deformation of the wheelset occurs is 24.631 Hz. The lateral vibration responses of the vehicle with elastic wheelsets are reduced mainly in the frequency range of 30-150 Hz. There are two resonances in the lateral vibration responses at the mode frequencies of the vehicle over 50 Hz, which are close to the wheelset’s first mode frequency. Taking the ГОСТ standard of wide-gauge countries as the main reference, simulations are separately taken in straight-line and curved-line cases. Results show that the wheelset structural flexibility mainly influences the vehicle lateral stability and safety.

The role of 3D contact geometry in modeling dynamic wheel-rail interaction at short-wave irregularities on rail surface

Modelling wheel-rail interaction at short-wave irregularities is an important issue under the context of vehicle-track system dynamics for analyzing and preventing severe impact. The present paper broadens the applicability of vehicle-track dynamics model to account for 3D short-wave irregularities on rail surface. The key is developing a meshing grid approach combined with the accurate conjugate gradient (CG) method for contact mechanics under arbitrary 3D contact geometry. Therefore, both the global dynamics and local contact solutions can be provided. In this study, short-pitch rail corrugation is employed for investigating the role of 3D contact geometry in modelling dynamic wheel-rail interaction. The traditional vehicle-track coupled dynamics model using Hertzian spring is used for comparison. The results show short-pitch rail corrugation contributes two different aspects, i.e., wheel center trajectory and time-varying contact stiffness. These two aspects are found to be the root causes for explaining the influence of the varying 3D geometry irregularity size on dynamic wheel-rail contact force.

Performance of Floating Slab Track with Rubber Vibration Isolator

This study systematically introduces a floating slab track (FST) with rubber vibration isolator (RVI) and investigates its behavior in urban rail transit. The FEM is used for modal analysis to clarify the modal parameters of the FST system. A vehicle–slab track coupling sub-model and a tunnel–soil coupling sub-model were established and the propagation law was analyzed by calculating the vertical vibration accelerations beneath the shield wall as well as the vertical vibratory acceleration levels of the surrounding soil. A wheel-set drop test was carried out to verify the actual vibration isolation effect compared with the numerical models. The results reveal that the vibratory acceleration levels at the distance of 20[Formula: see text]m from the tunnel center-line basically meet the requirements for vibration in most areas of a city. The variation trend of the vibratory acceleration level measured in laboratory tests agrees well with the calculated values from the numerical simulation. The attenuation amplitude of the levels reaches 19.33[Formula: see text]dB with the German high disturbance irregularity and 20.05[Formula: see text]dB with the short-wave irregularity in the simulation, and the levels are reduced by 45–58[Formula: see text]dB in laboratory tests which demonstrate the FST with RVI performs well in vibration isolation.

Influence of shortwave irregularity on increasing the vehicle running speed on bi-block ballastless track lines

Compared with slab ballastless track, bi-block ballastless track has the advantages of simpler constructed components and better economy, and has been used in high-speed railways for nearly 20,000 km in China. During the construction, the position deviation between sleepers and the disturbance of sleeper position caused by track bed concrete pouring can easily lead to shortwave irregularity with wavelength of 1 ∼ 2 m of bi-block ballastless track. Massive detection data on several high-speed railway lines showed that the standard deviation of vertical wheel-rail contact forces on bi-block ballastless track was about 58% higher than that on slab ballastless track. In this paper, a vehicle-track coupled dynamic analysis model was established, which can consider 1 ∼ 2 m shortwave irregularities of the track. Under the current construction and operation control standards, the dynamic responses of vehicles and tracks under different running speeds were studied. The results showed that vertical shortwave irregularity mainly affected the dynamic response of the wheel and rail, and rarely affected the dynamic response in other components. Compared with no shortwave irregularity, when the track had shortwave irregularity with σv = 0.8 mm, the peak value of the vertical acceleration of wheelset increased by 4.1 times, the standard deviation of wheel-rail contact force increased by 3.9 times, the vertical acceleration of frame increased by 1.7 times, and the vertical acceleration of track bed increased by 1.8 times, while the vibration acceleration of car body had almost no effect. When the track had shortwave irregularity with σh = 0.8 mm, the lateral acceleration of wheelset increased by 2.3 times. When the track had shortwave irregularity with σv = 0.8 mm and the vehicle speed increased to 450 km·h−1, the wheel load reduction rate reached 0.85, which exceeded the safety limit. Consider the results of this study, following suggestions can be obtained:(1) the shortwave irregularity with wavelength of 1 ∼ 2 m can be measured indirectly by the standard deviation of wheel-rail vertical contact force or wheelset vibration acceleration. (2) To control the wheel load reduction rate within 0.6, the standard deviation of random vertical irregularity should be controlled within 0.6 mm when running speed is 350 km/h, and within 0.4 mm when running speed is 400 km/h or above.

A joint vibro-acoustic method for periodic track short-wave defect identification

The present track short-wave irregularity inspection and evaluation method, based on the vibration signals collected by accelerators mounted on the axle box of high-speed comprehensive inspection train, is relatively a proven technology. However, with data analysis and check on-site, it finds out that the periodic defects exist in the sections where the dynamic responses are weak. When vibration signals are used for short-wave analysis, it may have the problems of inaccurate frequency identification, lack of energy concentration, etc., which is easy to cause missing or misjudgment of defects. As a result, the stability and robustness of present method need to be enhanced and refined. This article analyzes measured acoustic signals for a supplement to vibration signals. Based on vibration signals of axle box and acoustic signals collected by microphones mounted on the bogie frame of high-speed comprehensive inspection train, a new joint vibro-acoustic method for periodic track short-wave defect identification is proposed. The vibration and acoustic signals are processed and evaluated by Adaptive Chirp Mode Decomposition (ACMD), Gini Index (GI) and modal recombination. Energy Factor of Vibration Mode (EVM), Energy Factor of Acoustic Mode (EAM) and Energy Factor of Vibro-acoustic Mode (EVAM) are introduced for evaluating the periodic component in signals. By analyzing three groups of signals, it proves that, combining vibration and acoustic signals, the energy concentration of periodic components can be enhanced without losing the information of other signal components, and the periodic track short-wave defects can be effectively identified.

Influence of Short Wave Irregularity on Elastic Vibration Characteristics of ATP Antenna Beam of High-speed EMU

Influence of Short Wave Irregularity on Elastic Vibration Characteristics of ATP Antenna Beam of High-speed EMU

Weak Fault Feature Extraction of Axle Box Bearing Based on Pre-Identification and Singular Value Decomposition

The axle box bearing is one of the core rotating components in high-speed trains, having served in complex working conditions for a long time. With the fault feature extraction of the vibration signal, the noise interference caused by the interaction between the wheels and rails becomes apparent. Especially when there is a shortwave defect in the rail, the interaction between wheels and rails will produce high-amplitude impulse interference. To solve the problem of the collected vibration signals of axle box bearings containing strong noise interference and high amplitude impact interference caused by rail shortwave irregularities, this paper proposes a method based on pre-identification via singular value decomposition technology to select the signals in sections and filter the noise, followed by feature extraction and fault diagnosis. The method is used to analyze the axle box bearing fault simulation signal and the weak fault signal collected by the railway bearing comprehensive experimental platform, and these signals are then compared with the random screening signal and the manual screening signal to verify the effectiveness of the method.

Analysis of the influence of the track vertical profile irregularity on the vibration of the vehicle and the track under high speed moving train

A high speed train-track coupling system vertical dynamics model is established by considering the nonlinear wheel-rail contact, and the cross iteration method for solving the train-track nonlinear coupling system dynamics equations is proposed. Four kinds of track irregularities, i.e. the smooth track, the track random irregularity, the short-wave irregularity, and the combined track random irregularity and short-wavelength irregularity, on the vibration responses of the train and the track are analyzed with thismodel. The calculated results show that the vehicle and the bogie passing frequencies are the main excitation sources of the track vibration displacement and velocity, whereas the short-wave irregularity is the main excitation source of the track vibration acceleration. The track random irregularity, the short-wave irregularity and the sleeper spacing have great influence on the wheel-rail force, and the wheelset and the bogie vibration acceleration, while the car-body vibration acceleration is mainly affected by the track random irregularity.

Influence of Shortwave Irregularity on Increasing the Vehicle Running Speed on Bi-Block Ballastless Track Lines

Influence of Shortwave Irregularity on Increasing the Vehicle Running Speed on Bi-Block Ballastless Track Lines

On the modelling of normal wheel-rail contact for high-frequency vehicle–track dynamics analyses

ABSTRACT A transient wheel–rail rolling contact (RC) model and a vehicle–track coupled dynamics (CD) model are separately developed for a Hertzian contact in elasticity to calculate normal wheel–rail interactions at high frequencies. Short-wave irregularities with a wavelength of 20 ~ 400 mm are considered for a speed of 50 ~ 500 km/h. Results of 180 cases show that contact forces predicted by the CD model are significantly different from those by the RC model, suggesting that ignored or greatly simplified structural and wheel-rail flexibilities, transient effects, finite contact patch, etc. in the CD approach, play important roles in high-frequency interactions. Using the RC predictions as reference, a modified non-linear Hertzian spring is developed to improve the accuracy of the CD model. Such a modification provides references for determination of contact spring and contact filter effect at high frequencies, even though not applicable in a direct way.

Influence factors of short-wave irregularity based on inertial reference method

Influence factors of short-wave irregularity based on inertial reference method

The Influence of an Integration Time Step on Dynamic Calculation of a Vehicle-Track-Bridge under High-Speed Railway

In order to study the influence of an integration time step on dynamic calculation of a vehicle-track-bridge under high-speed railway, a vehicle-track-bridge (VTB) coupled model is established. The influence of the integration time step on calculation accuracy and calculation stability under different speeds or different track regularity states is studied. The influence of the track irregularity on the integration time step is further analyzed by using the spectral characteristic of sensitive wavelength. According to the results, the disparity among the effect of the integration time step on the calculation accuracy of the VTB coupled model at different speeds is very small. Higher speed requires a smaller integration time step to keep the calculation results stable. The effect of the integration time step on the calculation stability of the maximum vertical acceleration of each component at different speeds is somewhat different, and the mechanism of the effect of the integration time step on the calculation stability of the vehicle-track-bridge coupled system is that corresponding displacement at the integration time step is different. The calculation deviation of the maximum vertical acceleration of the car body, wheel-sets and bridge under the track short wave irregularity state are greatly increased compared with that without track irregularity. The maximum vertical acceleration of wheel-sets, rails, track slabs and the bridge under the track short wave irregularity state all show a significant declining trend. The larger the vibration frequency is, the smaller the range of integration time step is for dynamic calculation.

Mechanical characteristic variation of ballastless track in high-speed railway: effect of train\u2013track interaction and environment loads

Due to the fact that ballastless tracks in high-speed railways are not only subjected to repeated train–track dynamic interaction loads, but also suffer from complex environmental loads, the fundamental understanding of mechanical performance of ballastless tracks under sophisticated service conditions is an increasingly demanding and challenging issue in high-speed railway networks. This work aims to reveal the effect of train–track interaction and environment loads on the mechanical characteristic variation of ballastless tracks in high-speed railways, particularly focusing on the typical interface damage evolution between track layers. To this end, a finite element model of a double-block ballastless track involving the cohesive zone model for the track interface is first established to analyze the mechanical properties of the track interface under the loading–unloading processes of the negative temperature gradient load (TGL) followed by the same cycle of the positive TGL. Subsequently, the effect of wheel–rail longitudinal interactions on the nonlinear dynamic characteristics of the track interface is investigated by using a vehicle-slab track vertical-longitudinal coupled dynamics model. Finally, the influence of dynamic water pressure induced by vehicle dynamic load on the mechanical characteristics and damage evolution of the track interface is elucidated using a fluid–solid coupling method. Results show that the loading history of the positive and negative TGLs has a great impact on the nonlinear development and distribution of the track interface stress and damage; the interface damage could be induced by the wheel–rail longitudinal vibrations at a high vehicle running speed owing to the dynamic amplification effect caused by short wave irregularities; the vehicle dynamic load could produce considerable water pressure that presents nonlinear spatial–temporal characteristics at the track interface, which would lead to the interface failure under a certain condition due to the coupled dynamic effect of vehicle load and water pressure.

Effect of rail pad stiffness on the wheel/rail force intensity in a railway slab track with short-wave irregularity

In this paper, a two-dimensional numerical model is developed to investigate the effect of rail pad stiffness on the wheel/rail force in a slab track with harmonic irregularity. The model consists of a vehicle, nonlinear Hertz spring, rail, rail pad, concrete slab, resilient layer, concrete base, and subgrade. The rail is simulated using the Timoshenko beam element for considering the effects of high-frequency excitation produced by short-wave irregularity. The results obtained from the model are compared with those available in the literature and from the field to prove the validity of the model. Through a parametric study, the effect of variations in rail pad stiffness, vehicle speed, and harmonic irregularity on the wheel/rail force is investigated. For the slab track without any irregularity, the wheel/rail force is at maximum when the vehicle speed reaches the critical speed. As the rail pad stiffness increases, the critical speed increases. When the amplitude of irregularity is high, wheel jumping phenomenon may occur. In this situation, as the vehicle speed and rail pad stiffness are increased, the dynamic wheel/rail force is increased. In the low-frequency range, the wheel/rail force increases as the rail pad stiffness increases. In the high-frequency range, the wheel/rail force increases as the rail pad stiffness is decreased.

Algorithms and Instrument for Rapid Detection of Rail Surface Defects and Vertical Short-Wave Irregularities Based on FOG and Odometer

Defects and vertical short-wave irregularities significantly influence the maintenance of the railway tracks and the train safety, and hence, they need to be detected and eliminated in the early stages of formation. We studied the principles and algorithms to detect the defects and to measure the vertical short-wave irregularities by using a fiber optical gyroscope and an odometer, and the associated software was also developed. The principles of deformation index, namely, the ratio of angular rate to velocity and the method to determine the threshold of defects detection, are expatiated. The influence of the transfer function in measuring the vertical irregularities has long been a tough issue. The relation between the characteristics of deformation index and the wavelength of irregularities is studied by converting the deformation index from the time domain to the spatial domain. The post-processing module utilizes the results of the spectrum analysis of the deformation index to determine the wavelength of the track irregularities and eliminate the influence of the transfer function. To improve the accuracy of the calculation results, we analyzed the characteristics of the output of the gyroscope and the odometer and designed a series of targeted error-elimination methods. The forward and reverse dead-reckoning method is utilized to reduce the error accumulation, especially a high frequency noise when calculating the magnitude of the vertical short-wave irregularities. The experimental results show that the repeatability is 0.038 mm when the chord length is 1 m and 0.65 mm when the chord length is 10 m. The accuracy is 0.05 mm when compared with the results obtained using a ruler of 1 m. The moving speed of the instrument was approximately 0.6–1.2 m/s during the experiment. Both the accuracy and the efficiency can fulfill the requirements for the measurement of the short-wave irregularities.

Study on Sensitive Wavelength Characteristics of Track Short Wave Irregularity Based on High Frequency Wheel/rail Contact Model

Study on Sensitive Wavelength Characteristics of Track Short Wave Irregularity Based on High Frequency Wheel/rail Contact Model