Track Coupling System Research Articles

Dynamics modeling of urban rail vehicle axle-box bearings with roller defect considering time-varying impact

Accurately simulating the vibration response of the axle-box bearing with a localized defect on the roller can guide the proposal of several health condition estimation methods. However, there is still a lack of discussion and analysis on the detailed motion process of the roller defect passing through the inner/outer race. For filling this gap, a roller defect model considering time-varying impact is proposed and applied to the vehicle–track coupling system considering axle-box bearings. In addition to the Hertz contact force due to the relative displacement between the roller and race, time-varying impact excitation is designed according to the law of the conservation of energy. At first, an onsite test and an experimental test are implemented to validate the accuracy of the roller defect model and the vehicle–track coupling model, respectively. Then, the effect of the roller defect on the vibration characteristics of the components in the vehicle system is investigated. Finally, the influence of the defect size and vehicle speed on the vibration response of the axle-box bearing is studied, and the change rule of the time-varying impact is also researched with the defect size. Besides, the axle-box vibration response is simulated under variable vehicle speeds, and order tracking technique is applied to analyze the simulated result.

A transient three-dimensional wheel-rail adhesion model under wet condition considering starvation and surface roughness

The objective of this paper is to propose a new three-dimensional wheel-rail adhesion model under wet condition which considers insufficient water supply, the measured surface roughness and dynamic effect of the vehicle and track coupling system. Firstly, a longitudinal vehicle/track coupling dynamic model (LVTDM) was developed to obtain the dynamic parameters and contact points trace in curved track. Then, an improved numerical method was used to solve the transient general starved Reynolds equations, utilizing the input dynamic parameters acquired from the LVTDM. The numerical model was validated under the starved steady condition for the smooth surface and subsequently applied to investigate wheel and rail contact behaviors under wet condition. The results show that the effect of starvation on the wheel-rail rolling contact behaviours becomes significant when the inlet film thickness is less than 1000 nm for smooth surface. The numerical results were also compared with experimental results conducted by a high-speed tribology facility. In addition, the time-dependent characteristics of the wheel-rail rolling contact were obtained at different time instants. The transient wheel-rail adhesion characteristics under wet condition for different train speeds were obtained. The transient wheel-rail adhesion modeling results shows that the train speed has a significant effect on the adhesion ability.

Dynamic impact of sleeper unsupported defects on the heavy haul locomotive-ballasted track coupling system

In this study, a dynamics analysis framework combining the multi-body dynamics method (MBD) and the discrete element method (DEM) capable of accounting for sleeper unsupported defects is proposed. Different sleeper hanging defects (e.g., number of unsupported sleepers and the hanging height) is an input for an analysis of the heavy haul locomotive dynamic behavior and related ballasted bed degradation in terms of ballast particle wear. Simulated results indicate that the sleeper hanging defects dramatically increase the average contact stress underneath the well-supported sleeper adjoining the sleeper hanging area and the corresponding ballasted bed stress, indicating that the unsupported height should be suppressed within 5 mm even if only there exist single or two consecutive unsupported sleepers. When occurring minor sleeper unsupported defects and not being maintained in time, the vibration acceleration and dissipation energy of the ballasted bed will further increase sharply, which will aggravate the wear of the ballast particles and may change the particle size distribution of the ballasted bed or even pollute it.

A Hybrid Method for Vehicle–Track Coupling Dynamics by Analytical and Finite Element Combination Technique

Globally, rail transit is developing toward higher speeds, larger axle weights, and greater environmental friendliness. The more and more complex wheel–rail interaction will result in the dynamic responses of vehicles, tracks and other structures needing more in-depth theoretical research. However, most existing models for dynamic simulations of the vehicle–track coupling system need to extend the model on both sides of the concerned region to eliminate the boundary effect. To a certain extent, this kind of process method increases the computational effort. To overcome this disadvantage, a hybrid model combined with the analytical method and finite element method was proposed. The moving support system (including transition nodes) was specially established referring to the analytical solution of rail deflection based on the Winkler elastic foundation beam theory to realize the combination of the two methods. Two examples were presented to verify the stability and accuracy of the proposed model. The comparison results show that simulation results of vertical wheel–rail forces and track vibrations are almost consistent with the existing model. Furthermore, the calculation efficiency was discussed and certificated under different long-marshalling trains, with an obvious speedup factor that could be more than 2.5 for 16-marshalling train. The proposed model has a wide application prospect in the vehicle–track coupling analysis of long-marshalling trains, especially for heavy haul railways with hundreds of vehicles.

Dynamic Analysis of the High Speed Train–Track Spatial Nonlinear Coupling System Under Track Irregularity Excitation

Track irregularity is the main factor that affects the safety and comfort of high-speed railway. It is important to study the influence of the track irregularity on the safety service of high speed train–track coupling system. In this paper, a vehicle–track spatial nonlinear coupled system dynamics model is developed with FEM. The model includes vehicle subsystem and track subsystem, which are coupled by wheel–rail interface. The vehicle subsystem is a 31-DOF spatial vehicle model, and the track subsystem is a three-dimensional slab track model composed of the rail, rail pad and track slab. Considering wheel tread profile and rail head profile, the wheel–rail spatial contact geometry relationship is established, and the “Trace method” and the “Minimum distance method” are used to search for wheel–rail contact points. Considering the nonlinear contact between the wheel and the rail, a numerical approach is presented, where the “Trace method” is embedded into the algorithm for solving the vehicle–track nonlinear coupling dynamics equation by cross iteration, realizing searching the wheel–rail contact points and solving the vehicle–track nonlinear coupling equation simultaneously, which greatly improves the efficiency of numerical analysis. As application examples, the dynamic responses of a high speed train–track spatial nonlinear coupled system excited by the track V-shaped local profile irregularity and the track torsional irregularity are analyzed. The results show that the algorithm is effective in solving the vehicle–track spatial nonlinear coupled system dynamics problem, and the track irregularity has significant influence on the dynamic response of vehicle and track structure.

Vibration analysis and multi-state feedback control of maglev vehicle-guideway coupling system

<abstract> <p>Due to the existence of elastic modes in the track, the suspension system of maglev train is prone to vehicle-track coupling vibration, which has become an important problem restricting the further development of maglev train technology. In view of the limitation of the existing rigid track suspension model, this paper establishes an electromagnet-controller-elastic track coupling system model. And then, the nonlinear maglev system is transformed into a linear system by Hartman-Grobman theorem. Since the elastic deformation of the track is difficult to measure, a tracking differentiator is presented to filter out the interference of the displacement signal and obtain the differential signal of the gap between the electromagnet and the track. In order to suppress the vehicle-track coupling vibration, a four-state feedback control method is proposed by introducing the gap differential feedback signal. According to the Hurwitz algebraic criterion, the stability of four-state feedback control system is compared with that of three-state feedback control system. Simulation results show that, the four-state feedback control method can provide the elastic deformation information of the track, and can suppress the coupling vibration between the vehicle and the elastic track effectively.</p> </abstract>

Impact of Rail Fastener Looseness on Vertical Dynamic Responses of High-Speed Vehicle and Ballastless Track

The fastener system is an essential component of the high-speed ballastless track system. A detailed analysis for the effect of fastener looseness on the vertical dynamic response of the vehicle–track coupling system is conducted from the time domain, frequency domain and time–frequency domain in this paper. A fine fastener system model is employed, which includes two spring rods and one rail pad. The preloaded force is proposed to simulate the defect of the fastener, and a looseness coefficient is defined to represent the loose degree of the fastener. First, three fastener system models are introduced into the model, respectively, and the difference in the vehicle–track dynamic is analyzed and compared. The results show that the proposed model is more consistent with the real situation and more suitable to simulate fastener defects. Then, the detailed analysis of vehicle and track dynamic responses is explored in the case of different degrees of loose fasteners and the case of completely loose fasteners. According to the simulation results, there is little impact on the dynamic response of the vehicle–track system when the looseness coefficient is less than 0.9. When the fasteners are completely loosened, the dynamic response of the wheelset and the rail significantly increases. The vibration responses of rail and wheelset enhance with the increase of the number of the completely loose fastener. The loose fasteners affect the low-frequency part of the wheelset vibration response and the high-frequency part of the rail vibration response. Finally, a time–frequency analysis method is used to analyze the system vibration response under the combined effect of the completely loose fastener and the track irregularity. The track irregularity still dominates the excitation of the system, and the vibration response of the wheelset and the rail is more sensitive to the fastener defect at low speed.

Dynamic Analysis of Tram Vehicles Coupled With the Track System Based on Staggered Iterative Algorithm

Abstract In recent years, a large number of tram–tracks have been constructed in typical soft soil area of China. Infrastructure defects due to the differential foundation settlement are serious issues in this area. To ensure the operation safety of the tram, the influence of different infrastructure defects on the dynamic response of the tram–track system has been investigated in this paper. A dynamic model of a five-module 100% low-floor tram vehicle coupled with a slab track system is developed based on a finite element (FE) method and multibody kinematics. The articulation between different vehicle modules, the wheel–rail nonlinear contact, pad failures, and a cavity in the subgrade have been taken into account in this model. The dynamic response of the vehicle–track coupling system to different operation speeds and infrastructure defects are calculated. Results indicate that the vibration energy of the vehicle body is mainly distributed in the frequency range below 1.5 Hz. This frequency range should be paid special attention in the durability design for the vehicle structure. When the number of the failure pads is larger than 3, the pad failure in tram–track has significant influence on the system dynamic response. A cavity in subgrade has a limited effect on high frequency vibrations (above 100 Hz) of the rail, while the low frequency vibrations (below 75 Hz) of the rail can be obviously increased by cavities in subgrade. The model can be used in the optimization of suspension parameters and the tram vehicle–track coupled vibration analysis.

Analysis of vertical vibration characteristics of the vehicle-flexible track coupling system under wind load and track irregularity

In this study, to overcome the inherent problem caused by simulating infinite rail using finite rail, a method that combines flexible rail embedded in SIMPACK and a flexible track board imported from ANSYS on a SIMPACK platform is first proposed, by which vehicle-flexible track coupling is effectively realized. The method takes into account the simulation precision and computational efficiency. Using the proposed method, and comprehensively considering wind load, track irregularity, and minor track elasticity, the dynamic characteristics of high-speed train are solved conveniently and quickly. They are simulated under the conditions close to the objective reality. On this basis, the influences of many factors on the vibration characteristics of the train are analyzed, which include car body state, track state, mode numbers of the car body, wind load, track irregularity, and vehicle speed. In addition, the simulation results are basically consistent with the test results. This work lays a solid foundation for subsequent research on noise, fatigue, and the reliability of the train.

Integration of car-body flexibility into train–track coupling system dynamics analysis

ABSTRACTThe resonance vibration of flexible car-bodies greatly affects the dynamics performances of high-speed trains. In this paper, we report a three-dimensional train–track model to capture the flexible vibration features of high-speed train carriages based on the flexible multi-body dynamics approach. The flexible car-body is modelled using both the finite element method (FEM) and the multi-body dynamics (MBD) approach, in which the rigid motions are obtained by using the MBD theory and the structure deformation is calculated by the FEM and the modal superposition method. The proposed model is applied to investigate the influence of the flexible vibration of car-bodies on the dynamics performances of train–track systems. The dynamics performances of a high-speed train running on a slab track, including the car-body vibration behaviour, the ride comfort, and the running safety, calculated by the numerical models with rigid and flexible car-bodies are compared in detail. The results show that the car-body flexibility not only significantly affects the vibration behaviour and ride comfort of rail carriages, but also can has an important influence on the running safety of trains. The rigid car-body model underestimates the vibration level and ride comfort of rail vehicles, and ignoring carriage torsional flexibility in the curving safety evaluation of trains is conservative.

Extended applications of track irregularity probabilistic model and vehicle–slab track coupled model on dynamics of railway systems

ABSTRACTTrack irregularities are inevitably in a process of stochastic evolution due to the uncertainty and continuity of wheel–rail interactions. For depicting the dynamic behaviours of vehicle–track coupling system caused by track random irregularities thoroughly, it is a necessity to develop a track irregularity probabilistic model to simulate rail surface irregularities with ergodic properties on amplitudes, wavelengths and probabilities, and to build a three-dimensional vehicle–track coupled model by properly considering the wheel–rail nonlinear contact mechanisms. In the present study, the vehicle–track coupled model is programmed by combining finite element method with wheel–rail coupling model firstly. Then, in light of the capability of power spectral density (PSD) in characterising amplitudes and wavelengths of stationary random signals, a track irregularity probabilistic model is presented to reveal and simulate the whole characteristics of track irregularity PSD. Finally, extended applications from three aspects, that is, extreme analysis, reliability analysis and response relationships between dynamic indices, are conducted to the evaluation and application of the proposed models.

A numerical train–floating slab track coupling model based on the periodic-Fourier-modal method

A numerical model based on the periodic-Fourier-modal method is proposed for the dynamic analysis of a train-floating slab track coupling system with random track irregularity. In the model, each vehicle of the train is modeled as a multiple-degree-of-freedom vibration system consisting of one car body, two bogies, four wheelsets, and two groups of spring-damper suspension devices. The floating slab track is modeled as a periodic-infinite structure with discrete supports and discontinuous slabs. Linear springs are used to couple the train and the track. In order to establish this numerical model, an efficient periodic approach named periodic-Fourier-modal method for solving the dynamic response of the floating slab track under a harmonic moving load is first developed. Based on this, a strategy is then proposed which can couple the moving train to the track with random irregularity and express the wheel–rail force as a superposition of a series of harmonic loads. With the solved wheel–rail force, the vehicle response can be directly calculated through vehicle dynamics, while track response can be calculated through the principle of superposition and the reuse of the initially proposed periodic-Fourier-modal method. Using this train–floating slab track coupling model, the solution of the dynamic response of the infinite track can be transformed to perform only within a single periodic range, which can save the calculation time significantly. The numerical results of the Beijing subway, based on the proposed model, are discussed in detail, and some important conclusions are drawn.

Dynamic Analysis of the High Speed Train and Slab Track Nonlinear Coupling System with the Cross Iteration Algorithm

A model for dynamic analysis of the vehicle-track nonlinear coupling system is established by the finite element method. The whole system is divided into two subsystems: the vehicle subsystem and the track subsystem. Coupling of the two subsystems is achieved by equilibrium conditions for wheel-to-rail nonlinear contact forces and geometrical compatibility conditions. To solve the nonlinear dynamics equations for the vehicle-track coupling system, a cross iteration algorithm and a relaxation technique are presented. Examples of vibration analysis of the vehicle and slab track coupling system induced by China’s high speed train CRH3 are given. In the computation, the influences of linear and nonlinear wheel-to-rail contact models and different train speeds are considered. It is found that the cross iteration algorithm and the relaxation technique have the following advantages: simple programming; fast convergence; shorter computation time; and greater accuracy. The analyzed dynamic responses for the vehicle and the track with the wheel-to-rail linear contact model are greater than those with the wheel-to-rail nonlinear contact model, where the increasing range of the displacement and the acceleration is about 10%, and the increasing range of the wheel-to-rail contact force is less than 5%.

Effects of rail thermal stress on the dynamic response of vehicle and track

A new method is proposed to obtain the dynamic responses of the vehicle–track coupling system under the conditions of rail thermal stress changes in high-speed railways. Exact models are established with different rail longitudinal forces, in which multibody dynamic models are used for vehicles and the direct stiffness method for structures. In order to provide a general, simple and flexible formulation to express longitudinal stress distribution, the accurate model of long slab track consists of many small units with parameters which can be initialised separately. The exact analytical equation of track frequency and modal function was obtained by the transition matrix method, which can be used in calculating the dynamic response of wheel–rail coupling model. The proposed model is verified through comparisons with other classical solutions. Under the influence of train velocities and track irregularities, the specific vibration performances that frequency shifted and amplitude peak enhanced with thermal force are demonstrated through examples. The results show that the response analyses of vehicle and track have great application potentiality for fast estimation of the rail longitudinal stress.

Dynamics of a vehicle–track coupling system at a rail joint

The dynamic behaviour at a rail joint is examined using a two-dimensional vehicle–track coupling model. The track system is described as a finite-length beam resting on a double-layer discrete viscous-elastic foundation. The vehicle is represented by a half car body and a single bogie. The influence of the number of layers considered, the number of elements between two sleepers, and the beam model is investigated. Parametric studies, both of the coupling model and the analytic formulae, are carried out in order to understand the influence of the main track and vehicle parameters on the P1 and P2 peak forces. Finally, the results in terms of P2 force from the proposed model are compared, not only with measured values but also with other simulated and analytical solutions. An excellent agreement between these values is found.

Nonlinearity and non-stationarity analysis of dynamic response of vehicle–track coupling system enhanced by Huang transform

A method is proposed to analysis the nonlinearity and non-stationarity of dynamic response of high speed vehicle–track coupling system, to understand the properties of signal and its underlying physical meaning. First, a space coupling model of high speed vehicle–track system is built according to the theory of coupling dynamics of vehicle–track system. Then, the dynamic response of vehicle–track system is processed by Ensemble Empirical Mode Decomposition (EEMD) to generate the intrinsic mode functions (IMFs). Next, the “Direct Quadrature” (DQ) method is used to calculate the local instantaneous frequency and instantaneous amplitude of the IMFs, the generalized zero-crossing method and the full wave zero-crossing method are applied to calculate the mean local frequency of the IMFs. Finally, the index and degree of nonlinearity and non-stationarity based on intra-wave frequency modulation (the deviation of the instantaneous frequency from the generalized zero-crossing frequency) and inter-wave frequency modulation (the deviation of the instantaneous frequency from the full wave zero-crossing frequency), are defined to quantify the nonlinearity and non-stationarity of dynamic response. The usefulness and capability of the proposed method are displayed through two cases, which are considered general enough to be the representatives of nonlinear and non-stationary dynamic response of vehicle–track coupling system.

Dynamic analysis of the train and slab track coupling system with finite elements in a moving frame of reference

Slab tracks are widely used worldwide in high-speed railways. In order to investigate the dynamic behavior of the train and slab track coupling system, a new approach, based on conceptions of the vehicle element and track element, is developed with finite elements in a moving frame of reference. By discretizing the slab track subsystem into track elements that flow with the moving vehicle, the proposed method eliminates the need for keeping track of the vehicle position with respect to the track model. The governing equations are formulated in a coordinate system traveling at a constant velocity, and the associated stiffness matrix, mass matrix and damping matrix for the track element in a moving frame of reference are derived. The vehicle element is introduced to model a car with primary and secondary suspension systems, which has 26 degrees of freedom, where 10 degrees of freedom are used to describe the vertical movement of the car, and 16 degrees of freedom are associated with the rail displacements. In the numerical study, four cases of application examples are presented taking into consideration the effects of track roughness, train speed and track parameters. The numerical solutions compare favorably with the results obtained by alternative methods. The method is shown to work for varying train speed and track parameters, and has several advantages over the conventional finite element method in a fixed system of reference.

Comments on “Analyses of dynamic response of vehicle and track coupling system with random irregularity of track vertical profile”

Comments on “Analyses of dynamic response of vehicle and track coupling system with random irregularity of track vertical profile”

ANALYSES OF DYNAMIC RESPONSE OF VEHICLE AND TRACK COUPLING SYSTEM WITH RANDOM IRREGULARITY OF TRACK VERTICAL PROFILE

A dynamic computational model for the vehicle and track coupling system is developed by means of finite element method in this paper. In numerical implementation, the vehicle and track coupling system is divided into two parts; lower structure and upper structure. The vehicle as the upper structure in the coupling system is a whole locomotive or rolling stock with two layers of spring and damping system in which vertical and rolling motion for vehicle and bogie are involved. The lower structure in the coupling system is a railway track where rails are considered as beams with finite length rested on a double layer continuous elastic foundation. The two parts are solved independently with an iterative scheme. Coupling the vehicle system and railway track is realized through interaction forces between the wheels and the rail, where the irregularity of the track vertical profile considered as stationary ergodic Gaussian random processes and simulated by trigonometry series is included. The amplitudes of vibrations, their velocities and the accelerations generated in the vehicle and rail and the interaction forces between the vehicle and the rail due to the random irregularity of the track vertical profile and different line grades and train speeds have been analyzed numerically by this model. Analyses of system responses are performed in time and frequency domains.