Vertical Track Irregularities Research Articles

Dynamic response of steel-concrete composite bridges loaded by high-speed train

The paper focuses on dynamic analyses of a series of simply-supported symmetric composite steel-concrete bridges loaded by an ICE-3 train moving at high speeds up to 300 km/h. The series includes five bridges with span lengths ranging from 15 m to 27 m, with repeatable geometry of the superstructures. The objects, designed according to Polish standards valid from 1980s to 2010, are modelled on the bridges serviced on the Central Main Line in Poland since 1980s. The advanced, twodimensional, physically nonlinear model of the bridge-track structure-high-speed train system takes into account unilateral nonlinear wheel-rail contact according to Hertz\'s theory and random vertical track irregularities equal for both rails. The analyses are focused on the influence of random track irregularities on dynamic response of composite steel-concrete bridges loaded by an ICE-3 train. It has been pointed out that certain restrictions on the train speed and on vertical track irregularities should be imposed.

Influence of the Vertical Track Irregularities upon the Wheel - Rail Dynamic Forces

Influence of the Vertical Track Irregularities upon the Wheel - Rail Dynamic Forces

Mechatronic suspension design for full rail vehicle system

In this paper, an analytical mechatronic dynamic design model of a full rail vehicle system is developed. Based on the rail vehicle motion, its degree of freedom can be reduced to only 38. This reduction is necessary for the model simplicity. The developed model is validated with experimental result and compared with other one from literature. The real characteristics of the actuators are discussed, and its controller is designed. A mechatronic model that expresses the controlled tracking error as function of the vehicle dynamics and the actuator characteristics is developed. This model is used by the linear quadratic regulator approach to identify the mechatronic rail vehicle proportional–integral–derivative controller’s gains. The mechatronic rail vehicle comfort is evaluated in terms of the passenger displacement, acceleration and frequency as a response of a rail irregularities caused by a lateral and two vertical track irregularities. The simulations of vibration analysis are obtained in time and frequency domains and compared with railway vehicle status. The robustness of the designed mechatronic rail vehicle is verified by simulations, carried out for the cases of car body mass variations. The results show the effectiveness of the proposed mechatronic rail vehicle design which improves significantly the transportation of passengers.

Wheel-rail dynamic forces induced by random vertical track irregularities

The present paper investigates the wheel-rail dynamic forces produced by railway vehicles in motion, which are an important issue especially for the high-speed rail transport from the point of view of traffic safety, ride quality and undesirable effects on vehicles, on track and on the land in the vicinity of railways. The research is carried out on a model which includes track system, vehicle unsprung mass, vehicle primary suspension and the bogie sprung mass. The wheel-rail dynamic overloads are evaluated assuming random vertical irregularities of the track. The estimation of wheel-rail dynamic forces is made for a range of vehicle speeds up to 300 km/h and the influence of track and vehicle various parameters is investigated.

Vertical Track Irregularity Influence on the Wheel High-Frequency Vibration in Wheel-Rail System

A three-dimensional deformable finite element model of wheel-rail system is established. The vertical vibration natural frequencies are calculated by modal analysis. The improved central difference method by ABAQUS explicit nonlinear dynamics module is chosen to calculate the vertical vibration of wheel axle. Through the vibration measurement experiment ofLMAwheel by China Academy of Railway Sciences, the contact parameter is optimized and the model is modified. According to the nonlinear simulation results, the important influence of vertical track irregularity on the wheel set high-frequency vibration is discovered. The advantage frequencies through spectrum are close to the vertical vibration natural frequencies of seventh, eighth, ninth, and tenth mode. When the velocity is 350 km/h, system’s nonlinear dynamic characteristic is higher than the results at 200 km/h. The critical wavelength of vertical track irregularity on the wheel vertical vibration is about 0.8 m. In addition, a particular attention should be paid to one situation that the main dominant frequency amplitude is more than 50% of the acceleration amplitude even if the peak acceleration is low.

Nonstationary Random Vibration Performance of Train-Bridge Coupling System with Vertical Track Irregularity

In order to study the random vibration performance of trains running on continuous beam bridge with vertical track irregularity, a time-domain framework of random analysis on train-bridge coupling system is established. The vertical rail irregularity is regarded as a random process. A multibody mass-spring-damper model is employed to represent a moving railway car and the bridge system is simulated by finite elements. By introducing the pseudo excitation algorithm into the train-bridge interaction dynamic system, expressions of the mean value, standard deviation, and power spectral density of the nonstationary random dynamic responses of bridge and vehicles are derived. Monte-Carlo simulations are implemented to validate the presented method. A comprehensive analysis of the train-bridge coupling system with vertical track irregularity is conducted focusing on the effect of the randomness of the vertical rail irregularity on the dynamic behavior of the running train and the three-span continuous concrete bridge. Moreover, stochastic characteristics of the indicator for assessing the safety and the riding quality of the railway cars running on continuous beam bridge are carried out, which may be a useful reference in the dynamic design of the bridge.

Effect of temperature difference load of 32 m simply supported box beam bridge on track vertical irregularity

In order to study the effect of temperature difference load (TDL) along the vertical direction of a simply supported beam bridge section on the vertical irregularity, a rail-bridge-piers calculation model was established. Taking 32 m simply supported box beam bridge which is widely used in the construction of passenger dedicated line in China as an example, influences of the temperature variation between the bottom and top of the bridge, temperature curve index, type of temperature gradient, and beam height on track vertical irregularity were analyzed with the model. The results show that TDL has more effects on long wave track irregularity than on short one, and the wavelength mainly affected is approximately equal to the beam span. The amplitude of irregularity caused by TDL is largely affected by the temperature variation, temperature curve index, and type of temperature gradient, so it is necessary to monitor the temperature distribution of bridges in different regions to provide accurate calculation parameters. In order to avoid the irregularity exceeding the limit values, the height of 32, 48, and 64 m simply supported box beam bridges must not be less than 2.15, 3.2, and 4.05 m, respectively.

On the Wheelset Vibration due to the Stochastic Track Vertical Irregularities

The track vertical irregularities are the originator of the vertical vibrations in the wheelset. These vibrations are further conveyed to the suspended masses of the vehicle, thus generating and maintaining their vibrations. The study of the vibrations behavior of the wheelset plays an important role in the research dealing with the improvement of the vehicle dynamic performance, mainly at high velocities. This paper examines the vibrations behavior of the wheelset during running at speed of up to 200 km/h on a track with stochastic vertical irregularities, which are mathematically represented via the power spectral density. As underlain on numerical simulations, a series of basic features of the wheelset vertical vibrations will stand out, in correlation with the velocity, track quality and its damping. The observations herein prove that the maximum level of vibrations is visible at the frequency resonance of the wheelset on the track. Similarly, it is evident that the wheelset vibrations behavior increases during the running at high velocities on a track with weak damping and low quality.

Analysis of the dynamic response in the railway vehicles to the track vertical irregularities. Part II: The numerical analysis

The paper examines the dynamic response of a two-bogie vehicle to the symmetrical and antisymmetrical excitations, due to bounce and pitch of the axles’ planes, derived from the track vertical irregularities. Part I introduced the theoretical model and the response functions of the vehicle, as well as the theoretical elements required for the analysis of the dynamic response of the vehicle to the track stochastic irregularities. Part II comprises the results of the numerical analysis of the vehicle dynamic response in three reference points of the carbody, based on which a series of properties of the vertical vibrations behaviour of the railway vehicle is pointed out at. The excitation modes that trigger the carbody response in its reference points are identified. Hence, the influence of the geometrical filtering effect of the excitation modes upon the ride quality and ride comfort is established.

Analysis of the Dynamic Response in the Railway Vehicles to the Track Vertical Irregularities. Part I: The Theoretical Model and the Vehicle Response Functions

The paper herein focuses on the dynamic response of a two-bogie vehicle to the excitations derived from the track vertical irregularities. The symmetrical and antisymmetrical modes due from the bounce and pitch motions of the axles’ planes in the two bogies are being considered. The analysis of the dynamic response in the vehicle relies on the response functions in three reference points of the carbody, composed by means of these response functions to the symmetrical and antisymmetrical excitation modes. Similarly, the dynamic response of the vehicle to the track stochastic irregularities is examined and expressed as a power spectral density of the carbody vertical acceleration and the root mean square of the acceleration and the index of the partial comfort to the vertical vibrations is calculated. The paper is structured into two parts. The Part I includes all the theoretical elements required for the analysis of the dynamic response in the vehicle, while Part II introduces the results of the numerical analysis.

Track and ground vibrations generated by high-speed train running on ballastless railway with excitation of vertical track irregularities

Track irregularities generated during the running service of high-speed railways aggravate vibrations of the track and the surrounding ground environment. To better understand the propagation of vibrations induced by high-speed train running on irregular tracks, a 2.5-dimensional (2.5D) finite element model combining with thin-layer elements was applied to establish a vehicle–track–foundation coupled dynamic analysis model. A quarter-car model was used to derive the equation for wheel–rail interaction force considering track irregularity. The track structure and the underlying foundation were simulated using the 2.5D finite element model, and the subsoil boundary was simulated using thin-layer elements. Compared with the field measurements of the Beijing–Shanghai high-speed railway, the reliability of the established numerical model in analyzing vibration response was verified. A spectrum analysis of the response data obtained from the field measurements reveals that for a newly constructed high-speed railway, track alignment is in good condition due to the operation of grinding and leveling, and vehicle parameters dominate the vibration response of the track structure. Then influences of track irregularities of four typical wavelengths on the vibrations of the track and the surrounding ground environment were investigated. It is found that track irregularities of smaller wavelengths induce higher vibration frequencies and significantly higher vibration responses from the track and the ground compared to track irregularities of longer wavelengths. However, the low-frequency vibrations induced by the latter propagate to a longer distance compared to the former. The critical velocity of the ballastless slab track–ground system is greater than the Rayleigh wave velocity of the soft layer of the subsoil. When train speed is lower than the critical velocity, track irregularity substantially affects the vibrations of the track and the surrounding ground. When the train speed exceeds that critical velocity, the ground vibration is determined by the train wheel weight.

Effect of vertical track irregularities on the dynamics of freight railway wagon

This paper describes mathematical modelling of a freight railway wagon of Indian railways. The freight wagon is modelled as nine-degrees of freedom system. The equations of motion are derived using Newtonian approach. Rail surface vertical profile irregularity of sinusoidal type is taken as input for both the wheels. The frequencies at which these irregularities occur correspond to the natural frequency of the carbody. The equations of motion are solved by MATLAB using a fourth order Runga-Kutta algorithm with a fixed step size. Time domain responses are obtained for different input frequencies and loading conditions while maintaining the wagon speed constant. The effect of variation of the input frequencies of track irregularities and the loading condition on the dynamic behaviour of the carbody is discussed. It has been observed that the empty carbody gets excited to a severe level of acceleration even at lower resonant frequency and a dense region appears near the resonant frequency peak in FFT. The phase trajectories show quasi-periodic nature of response for empty carbody.

Capturing Riding Characteristics of Double-Deck Bridges under Multi-Lane Moving Vehicles

This paper investigates the characteristics of riding comfort of double-deck bridges under multi-lane moving vehicles based on a framework for spatial dynamic analysis of double-deck bridges carrying both road vehicles and monorail trains taking into account road surface roughness and both vertical and lateral track irregularities. The bridge is modelled by finite elements with proper boundary conditions. And the road vehicle is modelled as a mass-spring-damper system with 7 degrees of freedom (DOFs) while that of the monorail train has 15 DOFs. Then holistic bridge-vehicle interaction system was assembled using a fully computerized approach and solved by direct integration method. The riding characteristics of an authentic long-span bridge carrying both road vehicles and monorail trains are investigated in details as per ISO 2631.

Vertical vibrations of composite bridge/track structure/high-speed train systems. Part 3: Deterministic and random vibrations of exemplary system

Abstract Based on the one-dimensional quasi-exact physical and mathematical modelling of a composite (steel-concrete) bridge/track structure/high-speed train system (BTT), developed in Part 2, advanced computer algorithms for the BTT numerical modelling and simulation as well as a computer programme to simulate vertical vibrations of BTT systems are developed. The exemplary bridge under numerical quasi-static and dynamic analysis, designed according to Polish standards, has a 15.00 m span length and belongs to the SCB series-of-types developed in Part 1. The bridge is loaded by a German ICE-3 high-speed train moving at the resonant and maximum operating speeds. A continuously welded ballasted track structure adapted to high operating velocities is applied. The output quantities include: time-histories of the vertical deflection of the main beams at the midspan, time-histories of the longitudinal normal stress in the bottom fibres of the main beams at the midspan, time-histories of the vertical acceleration of the bridge deck at the midspan, time-histories of the vertical accelerations of the suspension pivots in car-bodies, time-histories of the dynamic pressures of the wheel sets of moving rail-vehicles. The design quantities, understood as the extreme values of the output quantities, are used to verify the design conditions. The basic random factor, i.e. vertical track irregularities of the track, is taken into consideration. Basic statistics of the design quantities treated as random variables are calculated and taken into account in the design conditions.

Vertical vibrations of composite bridge/track structure/high-speed train systems. Part 2: Physical and mathematical modelling

A theory of one-dimensional physical and mathematical modelling of the composite (steel-concrete) bridge/track structure/highspeed train system is developed including viscoelastic suspensions of rail-vehicles with two two-axle bogies each, non-linear Hertz contact stiffness and one-sided contact between wheel sets and rails, the viscoelastic and inertia features of the bridge, the viscoelastic track structure on and beyond the bridge, approach slabs, and random vertical track irregularities. Compared to the state-of-the-art, the physical model developed in the study accurately reproduces dynamic processes in the considered system. Division of the system into the natural subsystems, a method of formulation of the equations of motion partly in implicit form and the finite element method are applied. Vibrations in the vertical plane of symmetry are described by more than nine matrix equations of motion with constant coefficients. Couplings and non-linearity are hidden in the generalized load vectors. The equations of motion are integrated using the implicit Newmark average acceleration method with linear extrapolation of the interactions between the subsystems.

Vibrations of Bridge / Track Structure / High-speed Train System with Vertical Irregularities of the Railway Track

The study presents the vibration theory and random dynamic analysis of the series-of-types (designed by the author) of composite (steel-concrete) bridges loaded by a German ICE-3 high-speed train. The vibration theory includes: a continuously welded ballasted track structure, viscoelastic suspensions of rail-vehicles with two two-axle bogies each, non-linear Hertz contact stiffness and one-sided contact between the wheel sets and the rails, the viscoelastic and inertia features of the bridge, the viscoelastic track structure on and beyond the bridge, approach slabs. The basic random factor, i.e. vertical track irregularities of the track, is taken into consideration.

Identification of the power spectral density of vertical track irregularities based on inverse pseudo-excitation method and symplectic mathematical method

A new method is proposed to identify the power spectral density (PSD) of vertical track irregularities. A vertical coupled vehicle–track dynamic model is established. In this model, a vehicle is simplified as a multi-rigid-body model with 10 degrees of freedom, and a track is treated as a three-layer discrete elastic support model in which the rail, which is supported discretely by the sleepers, is described by Bernoulli–Euler beam theory. The vehicle and track models are coupled by a linearized Hertzian spring. The axle box acceleration is selected as the measurement data, and the stationary PSD of the axle box acceleration is simply transformed into its displacement PSD. The PSD of the vertical track irregularities is identified using a combination of the inverse pseudo-excitation method and the symplectic mathematical method. The accuracy of the proposed method is investigated for the different measurement noise levels, vehicle speeds, primary suspension parameters and PSD classes. The numerical results indicate that the proposed method can accurately identify the PSD of the vertical track irregularities.

21116 3次元接触を考慮した車輪・レール系の挙動解析について(GS-25【振動(2)】)

The purpose of this study is to formulate a three-dimensional motion of a wheelset considering contact geometry by applying techniques of multibody dynamics and to analyze behavior of a wheelset on the rail with vertical track irregularity. The differential algebraic equation is solved by the augmented formulation with Lagrange multipliers, using generalized coordinates and non-generalized surface parameters that describe the contact point. The slip at the contact point between wheel and rail is generated and the creep forces are caused. Due to the creep force, the hunting motion occurs. The increase of rolling speed and the amplitude of the track irregularity is very effective on the fluctuation rate of wheel load.

Waveband Analysis of Track Irregularities in High-Speed Railway from On-Board Acceleration Measurement

This paper is focused on waveband analysis of the lateral and vertical track irregularities from the on-board acceleration measurement of in-service high-speed trains. The track irregularities play important roles to determine dynamic stability of vehicles and ride quality of passengers, so that their amplitude and wavelength should be monitored continuously and carefully. Measuring acceleration at the axle-box or bogie of the trains has been under consideration for low-cost implementation and robust to a harsh railway environment. To estimate the track irregularities, lateral and vertical vibration caused by the wheel/track interaction is measured by the axle-box and bogie mounted accelerometers of an in-service high-speed train. A Kalman filter is used to prevent unrealistic drifts in the estimation. By applying the waveband-pass and compensation filters to the estimated displacement, it is possible to estimate the track irregularities. A distance-wavelength representation is used to identify their waveband in an intuitive way. It is verified by comparing with a commercial track geometry measurement system. From their comparison, it confirms that the representation can produce a satisfactory result.

주행 안전을 고려한 고속철도 자갈궤도 및 콘크리트궤도 레일패드의 강성 상한 결정

본 연구에서는 고속철도의 자갈궤도와 콘크리트궤도에서 열차 주행 안전 측면에서 관리해야 할 레일패드 강성의 상한값을 차량 및 궤도의 동특성과 운영환경을 고려하여 결정하는 방법을 제시하였다. 차량-궤도의 상호작용해석의 중요 입력 파라메타인 궤도틀림과 관련하여 프랑스 및 독일에서 제시한 고저틀림 PSD(파워 스펙트럼 밀도)와 경부고속철도 1단계 구간 자갈궤도 및 콘크리트궤도에서 계측한 고저틀림 자료를 통하여 얻은 PSD를 기초로 하여 넓은 범위의 주파수 영역에서 적용할 수 있는 자갈궤도와 콘크리트궤도의 고저틀림 PSD를 제시하였다. 제시된 PSD 기준 모델을 사용하여 시간 영역에서의 고저틀림 입력을 난수 생성(random number generation)을 통하여 구한 후 차량-궤도 상호작용 해석기법을 사용하여 레일패드 강성에 따른 윤중 감소율을 산정하였다. 산정된 윤중 감소율에 대하여 국내 철도차량 안전기준에 관한 규칙의 탈선계수 규정을 적용하여 주행 안전 측면에서 허용할 수 있는 레일패드 강성의 상한값을 제시하였다. In this study, proposed is the methodology to determine the upper limit for stiffness of rail pad for the ballasted and concrete track in high-speed railway in the viewpoint of running safety, considering the dynamic characteristics of train and track and the operation environment. For the track irregularity, one of the most important input parameters for traintrack interaction analysis, the reference vertical track irregularity PSDs(power spectral densities) for the ballasted and concrete track in a wide range of frequencies were proposed based on those presented in France and Germany and that obtained from the measured data at Kyeong-Bu 1st phase high-speed railway line. Using these reference PSD models, the input data for the vertical track irregularity data were regenerated by random generation process, and then, the wheel load reduction rates according to the stiffness of the rail pads have been calculated by the train-track interaction analysis technique. Finally, by comparing the wheel load reduction rates calculated with the derailment criteria prescribed in the Korean standards for railway vehicle safety criteria, the upper limits for the stiffness of rail pad have been proposed.