Vertical Dynamic Interaction Research Articles

A Simple Model for Vertical Dynamic Interactions among a Group of Strip Footings Rested on Homogeneous Half‐Space

A simple model for vertical dynamic interactions among a group of strip footings rested on half‐space is presented in this paper. An analytical method is presented to obtain the contact pressures and the impedance matrix for a group of surface strip footings. In order to conveniently solve the unknown contact pressures between the soil and footings, the soil‐footing interfaces are discretized into a series of strip elements. The Green function for each element under uniform harmonic force is derived and calculated by the piecewise integration and Cauchy principal value integral. The influences of footing and soil parameters on contact pressures and vertical dynamic impedances of footing groups are discussed in detail. The SSSI effect between adjacent footings increases with the decrease of the distance ratio S/L. For three footings in a group, the middle footing experiences greater cross‐interactional effect than the side ones. The present method has high accuracy, which is not only simple but also suitable for the high‐frequency analysis.

Analysis of train/turnout vertical interaction using a fast numerical model and validation of that model

A two-dimensional (2D) finite element model has been developed for simulation and analysis of train/turnout vertical dynamic interactions at a common crossing. The model has been validated through field measurements and simulation results obtained using a three-dimensional (3D) multi-body system (MBS) model. The dynamic behaviour of three turnouts on the Dutch railway network was simulated using the 2D model. The simulation results were compared with measured data collected from the instrumented crossings containing corresponding turnouts. It was observed that the values of the vertical acceleration of the crossing nose obtained from the simulations were in good agreement with the measured values. The 2D model was verified by adapting the more intricate 3D MBS model established in the VI-Rail software. The vertical geometry of the rail used in the 2D model was obtained using the wheel trajectory from the 3D model. It was observed that the dynamic wheel forces in the two models were close to one another. From these results it was concluded that the 2D model is able to simulate train/turnout interactions with a good accuracy and thus it can be used instead of complex time-consuming numerical simulations.

Vertical Dynamic Interaction of Trains and Rail Steel Bridges

Rail steel bridges are vulnerable to high impact forces due to the passage of trains; unfortunately the determination of these transient impact forces is not straightforward as these are affected by a large number of parameters, including the wagon design, the wheel-rail contact and the design parameters of the bridge deck and track, as well as the operational parameters – wheel load and speed. To determine these impact forces, a detailed rail train-track/bridge dynamic interaction model has been developed, which includes a comprehensive train model using multi-body dynamics approach and a flexible track/bridge model using Euler-Bernoulli beam theory. Single and multi-span bridges have been modelled to examine their dynamic characteristics. From the single span bridge, the train critical speed is determined; the minimum distance of two peak loadings is found to affect the train critical speed. The impact factor and the dynamic characteristics are discussed.

Influence of Parameters of Railway Track Construction on Vertical Dynamic Interaction Vehicle/Track

By analysing the dynamic interaction between the railway vehicle and the track we are able to explain complex interactive phenomena that are particularly important in the case of higher and high speed of a moving rail vehicle on railway track.The paper focuses on the solution of the above mentioned problem with the help of numerical computer simulations. The important step on the way to create a respective simulation model is setting objective entry parameters of railway track as well as taking its imperfections into consideration. These imperfections significantly influence the results of dynamic interaction. Out of the considered track imperfections, we particularly solve deformation resistance inhomogeneity of track grid subgrade and vertical irregularities of rail belt.

Simulation of dynamic train–track interaction with state-dependent track properties

A previously published numerical method for simulation of vertical dynamic interaction between a train and a railway track is expanded to account for state-dependent track properties. Track properties are separated into linear contributions corresponding to an unloaded track, and non-linear contributions that are dependent on the time-variant state of the different track components due to the dynamic loading from a moving train model. A complex modal superposition is adopted to decouple the equations of motion of the linear track model with a non-proportional spatial distribution of viscous damping. The state-dependent properties are accounted for by applying equivalent transient external forces to the corresponding nodes of the linear finite element model of the track. Simulations are carried out in the time domain with a moving mass model. The need for a state-dependent track model is discussed with respect to reported field and laboratory measurements. The numerical method and the state-dependent track model are validated versus field measurements of wheel–rail contact force and rail bending moment as caused by a 100 mm long and 0.9 mm deep wheel flat.

Simulation of Interaction Between a Train in General Motion and a Track

Summary An existing state-space based numerical method to simulate vertical dynamic interaction between a rolling train and a railway track is improved and extended. The model is extended to enable general three-dimensional motion of a train traversing a track. For the vehicle description a multibody dynamics method is used which allows for flexible components, for example, wheelsets. The track model is accordingly made three-dimensional in the sense that it allows for deflections and forces in all three directions at the wheel-rail contact. A track and a train in general motion imply two-dimensional modelling of the contact surface. Therefore, a linearised contact model including contact zone detection is proposed. The equations of motion of the system are formulated in a first-order form. The generalised dynamic train-track interaction model is verified against existing programs and good agreement of the results is obtained.

Simulation of Train-Track Interaction with Stochastic Track Properties

A numerical method to simulate vertical dynamic interaction between a moving train and a railway track was extended to account for stochastic properties in the track structure. The numerical simulations are carried out in the time-domain with a moving mass model. Full-scale measurements in the field and laboratory experiments were carried out to obtain data for the stochastic track model. The values of the stochastic variables are thus chosen to correspond to real tracks. To investigate the influence of the randomness of selected stochastic parameters in the track structure, the Latin Hypercube sampling method with correlation control was used to generate stochastic realisations.

Dynamic Train-Track Interaction: Variability Attributable to Scatter in the Track Properties

A numerical method to simulate vertical dynamic interaction between a rolling train and a railway track has been used to investigate the influence of stochastic properties of the track structure. A perturbation technique has been used to investigate the influence of the scatter in selected track properties. The train-track interaction problem has been numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the whole track structure. All numerical simulations have been carried out in the time-domain with a moving mass model. Properties such as rail pad stiffness, ballast stiffness, dynamic ballast-subgrade mass and sleeper spacing have been studied. To obtain sufficient statistical information from track structures, full-scale measurements in the field and laboratory measurements have been carried out. The influence of scatter in the track properties on the maximum contact force between the rail and the wheel, the maximum magnitude of the vertical wheelset acceleration, and the maximum sleeper displacement have been studied. Mean values and standard deviations of these quantities have been calculated. The effects of the variation of the investigated track properties are discussed.

Dynamic Train-Track-Ballast Interaction with Unevenly Distributed Track Properties

ABSTRACTA numerical method to simulate vertical dynamic interaction between a rolling train and a railway track has been extended to account for stochastic properties in the track structure. Here, the rail pad stiffness, the ballast stiffness, the dynamic ballast-subgrade mass and the sleeper spacing are modelled as random variables. The numerical simulations have been carried out in the time-domain with a moving mass model. Full-scale measurements in the field and laboratory experiments have been carried out to get realistic data for the selected stochastic variables. Two conceptual different methods (a perturbation and a Monte Carlo method) were used to investigate the influence of the randomness of selected stochastic parameters in the track structure. The investigated quantities have been the maximum value of the rail-wheel contact force, the maximum magnitude of the vertical wheelset acceleration and the maximum value of the sleeper displacement. Mean values and standard deviations of these quantities have been calculated. The effects of the variation of the investigated track properties are discussed.

Dynamic Train/Track Interaction Including State–Dependent Track Properties and Flexible Vehicle Components

ABSTRACTAn existing state—space based numerical method (see Reference [1]) to simulate vertical dynamic interaction between a rolling train and a railway track has been improved and extended. The modified method allows for non—linear track model properties and flexible vehicle model components. Track model properties are separated into linear contributions corresponding to a non—loaded track configuration and increments which are state—dependent. Linear finite element models represent the train and the track modelled as separate components. Model reduction techniques are employed for computational efficiency. State—dependent track model properties tire accounted for by applying counter—acting state—dependent forces to the corresponding nodes of the linear track model. The train/track simulations are carried out in the time—domain. The need for a state—dependent track model is discussed with respect to laboratory and field measurements.

Dynamic interaction between a lumped mass vehicle and a discretely supported continuous rail track

This paper describes the formulation and application of a numerical model that simulates the vertical dynamic interaction between a train vehicle and the rail track. The considered vehicle model is supported on two double-axle bogies at each end and is described as a 10-degree-of-freedom lumped mass system comprising the vehicle body mass and its moment of inertia, the two bogie masses and their moments of inertia, and four wheelset unsprung masses. The bogie sideframe mass is linked with the wheel unsprung mass through the primary suspension springs and linked with the vehicle body mass through the secondary suspension springs. In the track model, the rail is treated as an infinitely long beam discretely supported at rail/sleeper junctions by a series of springs, dampers and masses representing the elasticity and damping effects of the rail pads, the ballast, and the subgrade, respectively. Shear springs and dampers are also introduced between the ballast masses to model the shear coupling effects in the ballast. The mass, stiffness and damping values of these track components and the sleeper spacings can be arbitrarily varied, so that variations in track component properties and track geometric errors can be taken into account. The dynamic interaction between the wheelsets and the rail is accomplished by using the non-linear Hertzian theory. Example applications of the model are given.

MOVING FORCE IDENTIFICATION: A TIME DOMAIN METHOD

The solution for the vertical dynamic interaction forces between a moving vehicle and the bridge deck is analytically derived and experimentally verified. The deck is modelled as a simply supported beam with viscous damping, and the vehicle/bridge interaction force is modelled as one-point or two-point loads with fixed axle spacing, moving at constant speed. The method is based on modal superposition and is developed to identify the forces in the time domain. Both cases of one-point and two-point forces moving on a simply supported beam are simulated. Results of laboratory tests on the identification of the vehicle/bridge interaction forces are presented. Computation simulations and laboratory tests show that the method is effective, and acceptable results can be obtained by combining the use of bending moment and acceleration measurements.

Vertical Interaction between Train and Track with Soft and Stiff Railpads—Full-Scale Experiments and Theory

The vertical dynamic interaction between a running freight wagon and a tangent railway track has been investigated experimentally and numerically. Standard solid wheels without and with wheelflats were instrumented for measurement of transient vertical wheel/rail contact forces. Accelerations and strains in the track structure were measured in parallel. The location of the instrumented wheelset in relation to the instrumented portion of the track was determined at each instant of time. A portion of the track was equipped with railpads considerably stiffer than the soft ones used as standard in Sweden. The influence of train speed and axle load on dynamic responses was studied and compared for the two test sites. Track parameters determined at the test site were used as inputs to a mathematical model. Numerical results show reasonable agreement with measured responses. In the presence of wheelflats, measured dynamic contact forces were largely affected by pad stiffness and axle load. For some of the loading cases investigated, it was observed that soft pads did not always lead to lower contact forces. Maximum dynamic responses generally increased with increasing train speed.