Interaction study of train–bridge–track systems using Maxwell model

The investigation of problems related to the interaction of train, bridge and track systems has been accelerated by the emergence of high-speed trains. Such studies are required, not only for the endurance issues regarding bridge and tracks, but to assure trains’ functionality and performance. The suspension mechanism of train systems is of prime importance in defining the functionality of high-speed trains, and accurate mathematical models of the mechanism are imperative. This paper introduces a numerical technique for an interaction study of train–bridge–track systems based on Maxwell (three-element type) modeling of the suspension mechanisms of vehicles. Track irregularity in sinusoidal form is also integrated into the mathematical model. Although the proposed technique is simple in formulation, it offers phenomenal accuracy in representing the interaction of train, track and bridge systems. In a numerical example, the dynamic behavior of a train–bridge system has been studied. Results of this analysis provide a valuable insight into the contributing roles of different parameters in this subject.     

Influence of long-wavelength track irregularities on the motion of a high-speed train

Vertical track irregularities over viaducts in high-speed rail systems could be possibly caused by concrete creep if pre-stressed concrete bridges are used. For bridge spans that are almost uniformly distributed, track irregularity exhibits a near-regular wave profile that excites car bodies as a high-speed train moves over the bridge system. A long-wavelength irregularity induces low-frequency excitation that may be close to the natural frequencies of the train suspension system, thereby causing significant vibration of the car body. This paper investigates the relationship between the levels of car vibration, bridge vibration, track irregularity, and the train speed. First, this study investigates the vibration levels of a high-speed train and bridge system using 3D finite-element (FE) transient dynamic analysis, before and after adjustment of vertical track irregularities by means of installing shimming plates under rail pads. The analysis models are validated by in situ measurements and on-board measurement. Parametric studies of car body vibration and bridge vibration under three different levels of track irregularity at five train speeds and over two bridge span lengths are conducted using the FE model. Finally, a discontinuous shimming pattern is proposed to avoid vehicle suspension resonance.     

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

The 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.     

Dynamic response of the train–track–bridge system subjected to derailment impacts

Derailments on bridges, although not frequent, when occurs due to a complex dynamic interaction of the train–track–bridge structural system, are very severe. Furthermore, the forced vibration induced by the post-derailment impacts can toss out the derailed wagons from the bridge deck with severe consequences to the traffic underneath and the safety of the occupants of the wagons. This paper presents a study of the train–track–bridge interaction during a heavy freight train crossing a concrete box girder bridge from a normal operation to a derailed state. A numerical model that considers the bridge vibration, train–track interaction and the train post-derailment behaviour is formulated based on a coupled finite-element – multi-body dynamics (FE-MBD) theory. The model is applied to predict the post-derailment behaviour of a freight train composed of one locomotive and several wagons, as well as the dynamic response of a straight single-span simply supported bridge containing ballast track subjected to derailment impacts. For this purpose, a typical derailment scenario of a heavy freight train passing over a severe track geometry defect is introduced. The dynamic derailment behaviour of the heavy freight train and the dynamic responses of the rail bridge are illustrated through numerical examples. The results exhibit the potential for tossing out of the derailed trains from the unstable increase in the yaw angle signature and a lower rate of increase of the bridge deck bending moment compared to the increase in the static axle load of the derailed wheelset.     

Vibration control in train–bridge–track systems

To study the problems associated with vibration control of train–bridge–track systems a mathematical model with the capability of representing supplementary vibrational control devices is proposed. The train system is assumed as rigid bodies supported on double-deck suspension mechanism with semi-active features. The bridge system is modeled using the modal approach. Vibration control for bridge responses is provided by tuned mass dampers. A non-classical incremental Eigen analysis is proposed to trace the system characteristics across the time. In an example, the capability of the proposed model in investigating the vibration control prospects of a bridge–train system is shown. The results indicate the effectiveness of active suspension mechanism in reducing train's body movements, particularly the pitching angle and the vertical accelerations. Accordingly, the results also verify the potential of TMD devices in reducing the bridge responses at resonance motions.     

Adaptive backstepping control of train systems with traction/braking dynamics and uncertain resistive forces

Although backstepping control design approach has been widely utilised in many practical systems, little effort has been made in applying this useful method to train systems. The main purpose of this paper is to apply this popular control design technique to speed and position tracking control of high-speed trains. By integrating adaptive control with backstepping control, we develop a control scheme that is able to address not only the traction and braking dynamics ignored in most existing methods, but also the uncertain friction and aerodynamic drag forces arisen from uncertain resistance coefficients. As such, the resultant control algorithms are able to achieve high precision train position and speed tracking under varying operation railway conditions, as validated by theoretical analysis and numerical simulations.     

Train–track–bridge dynamic interaction: a state-of-the-art review

ABSTRACT

Train–track–bridge dynamic interaction is a fundamental concern in the field of railway engineering, which plays an extremely important role in the optimal design of railway bridges, especially in high-speed railways and heavy-haul railways. This paper systematically presents a state-of-the-art review of train–track–bridge dynamic interaction. The evolution process of train–bridge dynamic interaction model is described briefly, from the simplest moving constant force model to the sophisticated train–track–bridge dynamic interaction model (TTBDIM). The modelling methodology of the key elements in the TTBDIM is systematically reviewed, including the train, the track, the bridge, the wheel–rail contact, the track–bridge interaction, the system excitation and the solution algorithm. The significance of detailed track modelling in the whole system is highlighted. The experimental research and filed test focusing on modelling validation, safety assessment and long-term performance investigation of the train–track–bridge system are briefly presented. The practical applications of train–track–bridge dynamic interaction theory are comprehensively discussed in terms of the system dynamic performance evaluation, the system safety assessment and train-induced environmental vibration and noise prediction. The guidance is provided on further improvement of the train–track–bridge dynamic interaction model and the challenging research topics in the future.     

Ride comfort of high-speed trains travelling over railway bridges

The ride comfort of high-speed trains passing over railway bridges is studied in this paper. A parametric study is carried out using a time domain model. The effects of some design parameters are investigated such as damping and stiffness of the suspension system and also ballast stiffness. The influence of the track irregularity and train speed on two comfort indicators, namely Sperling's comfort index and the maximum acceleration level are also studied. Two types of railway bridges, a simple girder and an elastically supported bridge are considered.

Timoshenko beam theory is used for modelling the rail and bridge and two layers of parallel damped springs in conjunction with a layer of mass are used to model the rail-pads, sleepers and ballast. A randomly irregular vertical track profile is modelled, characterized by its power spectral density (PSD). The ‘roughness’ is generated for three classes of tracks. Nonlinear Hertz theory is used for modelling the wheel-rail contact. The influences of some nonlinear parameters in a carriage-track-bridge system, such as the load-stiffening characteristics of the rail-pad and the ballast and that of rubber elements in the primary and secondary suspension systems, on the comfort indicators are also studied. Based on Galerkin's method of solution, a new analytical approach is developed for the combination between the rigid and flexural mode shapes, which could be used not only for elastically supported bridges but also other beam-type structures.     

Vibration control in train-bridge-track systems

To study the problems associated with vibration control of train-bridge-track systems a mathematical model with the capability of representing supplementary vibrational control devices is proposed. The train system is assumed as rigid bodies supported on double-deck suspension mechanism with semi-active features. The bridge system is modeled using the modal approach. Vibration control for bridge responses is provided by tuned mass dampers. A non-classical incremental Eigen analysis is proposed to trace the system characteristics across the time. In an example, the capability of the proposed model in investigating the vibration control prospects of a bridge-train system is shown. The results indicate the effectiveness of active suspension mechanism in reducing train's body movements, particularly the pitching angle and the vertical accelerations. Accordingly, the results also verify the potential of TMD devices in reducing the bridge responses at resonance motions.     

考虑附加变形的公路-磁浮合建桥车桥耦合动力响应研究

为了解温度变化和汽车荷载布置引起的附加变形对大跨度公路-磁浮合建桥及磁浮列车动力性能的影响,以某三塔四跨公轨合建大跨度斜拉桥为背景,采用UM及ANSYS软件建立磁浮列车、桥梁、悬浮控制器模型,分析温度、汽车荷载作用下的附加变形对车桥动力响应的影响。结果表明:温度附加变形对桥梁及磁浮列车的动力响应影响较小;汽车偏载作用对桥梁和磁浮车辆的横向动力响应影响较明显,6车道对称布载作用对磁浮列车的加速度和Sperling指标的影响不大,但悬浮间隙波动范围增大了30%;汽车荷载对公轨合建桥梁车桥动力响应的影响较大,需予以重点考虑。     

Measurements of car-body lateral vibration induced by high-speed trains negotiating complex terrain sections under strong wind conditions

Assessment of the vibration of high-speed trains negotiating complex sections of terrain under strong wind conditions is very important for research into the operation safety and comfort of passengers on high-speed trains. To assess the vibration of high-speed trains negotiating complex sections of terrain under strong wind conditions, we performed a field measurement when the train passes through typical sections of complex terrain along the Lanzhou–Xinjiang high-speed railway in China. We selected the lateral vibration conditions, including the roll angle and lateral displacement of car-body gravity centre through two typical representative sections (embankment–tunnel–embankment and embankment–rectangular transition–cutting) for analysis. The results show that the severe car-swaying phenomenon occurs when the high-speed train moves through the test section, and the car-body lateral vibration characteristic is related significantly to the state of the terrain and topography along the railway. The main causes for this car-swaying phenomenon may be the transitions between different windproof structures, and the greater the scale of the transition region between different windproof structures or landform changes, the more obvious the car-swaying phenomenon becomes. The lateral vibration of the car-body is relatively steady when the train is running through terrain with minor changes in topography, such as the windbreak installed on the bridge and embankment, but the tail car sways more violently than the head car. When the vehicle runs from the windbreak installed on the embankment into the tunnel (or in the opposite direction), the tail car sways more intensely than the head car, and the head car runs relatively stable in the tunnel.     

Dynamic analysis of a pantograph-catenary system using absolute nodal coordinates

The dynamic interaction between the catenary and the pantographs of high-speed trains is a very important factor that affects the stable electric power supply. In order to design a reliable current collection system, a multibody simulation model can provide an efficient and economical method to analyze the dynamic behavior of the catenary and pantograph. In this article, a dynamic analysis method for a pantograph-catenary system for a high-speed train is presented, employing absolute nodal coordinates and rigid body reference coordinates. The highly flexible catenary is modeled using a nonlinear continuous beam element, which is based on an absolute nodal coordinate formulation. The pantograph is modeled as a rigid multibody system. The analysis results are compared with experimental data obtained from a running high-speed train. In addition, using a derived system equation of motion, the calculation method for the dynamic stress in the catenary conductor is presented. This study may have significance in providing an example that a structural and multibody dynamics model can be unified into one numerical system.     

高速列车外观设计的进展和发展趋势

随着科学技术的不断发展和进步,我国高速列车成为一种高速度、高载能力的现代化轨道交通工具,其外观设计也成为高速列车整体设计的重点内容。为了在高速列车外观设计中把美观性和实用性进行有效的结合,本文针对高速列车外观设计的进展和未来发展趋势进行了分析和研讨,对高速列车外观设计中的造型、色彩、空气动力学、地域文化等多种因素的影响进行了研究分析,通过对我国高速列车外观设计的进展进行研究分析,对未来我国高速列车外观设计的发展趋势进行了展望,希望可以为我国高速列车外观设计的研究提供一些参考。     

A structural articulation method for assessing railway bridges subject to dynamic impact loading from track irregularities

This paper discusses the importance of track irregularities in railway bridge design, and presents a new technique for calculating the dynamic impact load induced by such irregularities: the structural articulation method. The properties of the combined bridge-suspension system are coupled through global mass, stiffness, and damping matrices. Under the proposed method, the true suspension system over a particular point on the bridge girder at time t is divided into equivalent suspension systems attributed to adjacent finite-element nodes of the bridge. The time-dependent effects of a moving mass are thereby included in the equation of motion.     

A semi-active control suspension system for railway vehicles with magnetorheological fluid dampers

The high-speed train has achieved great progress in the last decades. It is one of the most important modes of transportation between cities. With the rapid development of the high-speed train, its safety issue is paid much more attention than ever before. To improve the stability of the vehicle with high speed, extra dampers (i.e. anti-hunting damper) are used in the traditional bogies with passive suspension system. However, the curving performance of the vehicle is undermined due to the extra lateral force generated by the dampers. The active suspension systems proposed in the last decades attempt to solve the vehicle steering issue. However, the active suspension systems need extra actuators driven by electrical power or hydraulic power. There are some implementation and even safety issues which are not easy to be overcome. In this paper, an innovative semi-active controlled lateral suspension system for railway vehicles is proposed. Four magnetorheological fluid dampers are fixed to the primary suspension system of each bogie. They are controlled by online controllers for enhancing the running stability on the straight track line on the one hand and further improving the curving performance by controlling the damper force on the other hand. Two control strategies are proposed in the light of the pure rolling concept. The effectiveness of the proposed strategies is demonstrated by SIMPACK and Matlab co-simulation for a full railway vehicle with two conventional bogies.     

Transverse Vibration of Train-Bridge and Train-Track Time Varying System and the Theory of Random Energy Analysis for Train Derailment

Summary In this paper, the fundamental problems in the calculation of transverse vibration of train-bridge and train-track time-varying system (hereinafter referred to as the system) are expounded. That is, (1) Proper solution to transverse vibration of the system cannot be obtained by establishing separate transverse vibration equation groups for the car and the bridge (or track); (2) The exciting source of transverse vibration of the system has not been made definite; (3) It is difficult to carry out the random analysis of vibration of the time varying system as the theory of the random vibration analysis for the time varying system has not been established. Our thinking and methods to solve these problems are introduced. On the above-mentioned basis, the theory of random energy analysis for train derailment is presented. The main contents of this theory are as follows: method of random energy analysis of transverse vibration of the system; geometric criterion of derailment; mechanism of derailment caused by the combined track irregularity and energy increment criterion for derailment evaluation; calculation of the entire derailing process; method of improvement of track parameters for preventing straight line speed-raise freight trains from derailment and of the calculation of the safety coefficient against derailment. This theory is used to calculate a case of freight train derailment, which corresponds to an actually occurred accident. A train in another derailment test is judged to be not derailed and its maximum vibration responses are calculated. The field test results are well responded.     

Stochastic vibration of the vehicle–bridge system subject to non-uniform ground motions

A study of a train moving along a cable-stayed bridge is performed by considering both the stationary track irregularity and a non-stationary earthquake. A detailed bridge model with 3972 degrees of freedom is established while the train model consists of two locomotives and eight carriages. The equations of motion of the coupled system are obtained by using the displacement continuous condition at the contact, with track irregularities. The earthquake is assumed to occur once the train has entered the bridge. The pseudo-excitation method is used to find the random responses of the coupled system, and the results indicate that the effect of the earthquake is much greater than that of the track irregularities. The paper discusses the influence of the intensity of the earthquake, the wave propagation velocity, the speed of the train, and the dynamic interaction between the vehicles and the bridge.     

Structural analysis of 3D high-speed train–bridge interactions for simple train load models

Three-dimensional models are developed for analysing the dynamic interaction that occurs between high-speed trains and bridges. The reliability and accuracy of developed models are verified by comparing the results from analysing field tests on high-speed trains. A number of train load models are proposed and their performances are compared in order to identify possible models that would reduce the computational and modelling efforts while maintaining suitable accuracy. The results show that at least 16 cars out of a 20-car train should be modelled to achieve results that are comparable to those obtained using the highly detailed 20-car model. Regarding the simplified train load model, more accurate results are obtained employing the 3D moving vehicle model for power cars, the heaviest cars of a high-speed trainset, and a moving force model for other cars, power passenger cars, and passenger cars, compared with highly detailed 20-car model.     

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.     

Effect of temperature- and frequency-dependent dynamic properties of rail pads on high-speed vehicle–track coupled vibrations

The soft under baseplate pad of WJ-8 rail fastener frequently used in China’s high-speed railways was taken as the study subject, and a laboratory test was performed to measure its temperature and frequency-dependent dynamic performance at 0.3?Hz and at ?60°C to 20°C with intervals of 2.5°C. Its higher frequency-dependent results at different temperatures were then further predicted based on the time–temperature superposition (TTS) and Williams–Landel–Ferry (WLF) formula. The fractional derivative Kelvin–Voigt (FDKV) model was used to represent the temperature- and frequency-dependent dynamic properties of the tested rail pad. By means of the FDKV model for rail pads and vehicle–track coupled dynamic theory, high-speed vehicle–track coupled vibrations due to temperature- and frequency-dependent dynamic properties of rail pads was investigated. Finally, further combining with the measured frequency-dependent dynamic performance of vehicle’s rubber primary suspension, the high-speed vehicle–track coupled vibration responses were discussed. It is found that the storage stiffness and loss factor of the tested rail pad are sensitive to low temperatures or high frequencies. The proposed FDKV model for the frequency-dependent storage stiffness and loss factors of the tested rail pad can basically meet the fitting precision, especially at ordinary temperatures. The numerical simulation results indicate that the vertical vibration levels of high-speed vehicle–track coupled systems calculated with the FDKV model for rail pads in time domain are higher than those calculated with the ordinary Kelvin–Voigt (KV) model for rail pads. Additionally, the temperature- and frequency-dependent dynamic properties of the tested rail pads would alter the vertical vibration acceleration levels (VALs) of the car body and bogie in 1/3 octave frequencies above 31.5?Hz, especially enlarge the vertical VALs of the wheel set and rail in 1/3 octave frequencies of 31.5–100?Hz and above 315?Hz, which are the dominant frequencies of ground vibration acceleration and rolling noise (or bridge noise) caused by high-speed railways respectively. Since the fractional derivative value of the adopted rubber primary suspension, unlike the tested rail pad, is very close to 1, its frequency-dependent dynamic performance has little effect on high-speed vehicle–track coupled vibration responses.