Railway Vehicle Model Research Articles

Combined active suspension and structural damping control for suppression of flexible bodied railway vehicle vibration

ABSTRACTThe design trend for future high-speed trains is envisaged to be lightweight, rising the cost of structural vibration due to the extra flexibility. In this context, studies have looked into the suppression of such vibrations via the use of either (conventional actuators) active suspensions or by structural damping via piezoelectric actuators. The addition of extra macro-actuators will highly impact vehicle weight and is subject to location constraints, while the use of only piezo-actuators normally does not reach the required force levels for appropriate suppression. However, piezo-actuators provide appropriate complementary action with conventional active suspension. In this paper, we present a decentralised control scheme for suppressing the vertical vibration of the vehicle body, combining active structural damping via frequency-weighted control and active suspension control using skyhook damping via structured synthesis. A vertical side-view model of a flexible-bodied railway vehicle is used for the control study, with the configuration of piezoelectric actuators and sensors determined via structural norms. Stability robustness of the controller is analysed with respect to parametric and dynamic uncertainties using μ analysis techniques. Results illustrate the effectiveness of the proposed control scheme for both flexible and rigid modes while guaranteeing robustness to model uncertainty.

Estimation for Wheelset Angle of Attack by Kalman Filter Using Quasi-static Single Wheelset Model of Railway Vehicle

Estimation for Wheelset Angle of Attack by Kalman Filter Using Quasi-static Single Wheelset Model of Railway Vehicle

Parametric Analysis of the Car Body Suspended Equipment for Railway Vehicles Vibration Reduction

A generalized railway vehicle model is built to study the coupled vibrations between a flexible car body (CB) and the equipment suspended beneath it by taking the complex suspension characteristics of the equipment into consideration. Associated theories for the determination of the suspension parameters for CB suspended equipment are summarized systematically, including the vibration isolation methods and the dynamic vibration absorber (DVA) theories for both undamped and damped cases. The equipment is then grouped into four categories by weight, location, and the excitation that it is subjected to. A general principle for the determination of the suspension parameters is proposed for better vibration isolation effects concerning bogie hunting, the elastic modes of the CB and its excitations. Analysis based on DVA theory shows that 1) siting equipment heavier than 2 t near the CB center can reduce the structural vibrations of the CB considerably, 2) siting medium-weight equipment near one end of the CB is good for absorbing the vibrations resulting from bogie hunting, and 3) a rigid connection is suggested for light equipment. Furthermore, on-track field tests of a high speed train confirmed that the heavy equipment vibrated violently upon absorbing some of the CB vibration energy resulting from bogie hunting. However, solid proof of the vertical bending of the CB was not obtained yet because it was sufficiently damped and is not the first natural mode of a modern aluminum-alloy CB. Further research on the lateral flexibility of the CB and its coupled vibrations with the heavy equipment mounted near its center are in need.

Improved nonlinear model of a yaw damper for simulating the dynamics of a high-speed train

The aim of this paper is to establish a simple and accurate nonlinear model of a yaw damper for the dynamic numerical simulation of high-speed trains. An improved nonlinear yaw damper model is proposed based on the traditional Maxwell model. It comprises a piecewise linear force–displacement spring and a piecewise linear force–velocity damper in series. These nonlinear inputs for the model are retrieved from the dynamic performance tests of the damper, and the force–displacement and force–velocity curves are further modified to improve the modelling accuracy according to the test results. The proposed model can accurately simulate the damper's dynamic stiffness and dynamic damping characteristics with respect to the excitation frequency or displacement, which cannot be reproduced when using the traditional Maxwell model. Both the traditional Maxwell model and the improved nonlinear model presented in this work are integrated into a multibody dynamics railway vehicle model to simulate the typical dynamic problems of a high-speed train operating at 250 km/h in northeast China. Through comparative analysis, it was found that the numerical simulations are consistent with the field measurements. It can be concluded that the proposed nonlinear damper model is more suitable for studying railway vehicle system dynamics under various operating cases. By contrast, the input parameters of the traditional Maxwell model must be modified artificially according to the vehicle responses and the dynamic characteristics of the yaw damper.

Experimental and numerical investigation of the possibilities for the structural health monitoring of railway axles based on acceleration measurements

In this article, numerical and experimental investigations are carried out to assess the possible use of vibration measurements to identify the presence of a fatigue crack in railway axles, detecting components of axle vibration occurring at frequencies that are integer multiples of the axle’s frequency of revolution (N×Rev components). A model of a cracked axle is defined using the Timoshenko beam finite elements incorporating an equivalent beam element having cross-sectional area and moments which are periodically changing with the angular position of the axle turn to reflect the crack breathing mechanics. Two levels of validation are considered for this model: first, verification with numerical results from a solid model of railway cracked axle (solid model was built before using the solid finite element model) and, second, validation against experimental results obtained from full-scale tests performed on cracked axles using a rotating bending fatigue test rig available at the labs of Politecnico di Milano. To consider the effect of disturbances arising from train–track interaction, track irregularity and wheel out-of-roundness, a multi-body model of a complete railway vehicle is defined, incorporating one axle modelled as a flexible cracked axle. This model is used to evaluate the N×Rev components of axle vibration occurring in the presence of axle cracks having different positions along the axle and different depths, in combination with different sources of disturbance. The results show that the 2×Rev and 3×Rev components of the horizontal axle-box acceleration are well correlated to the size of the crack and are almost insensitive to the effect of all disturbances considered in this study. Hence, they can be used for the continuous monitoring of axel integrity. Finally, a criterion for crack detection is defined and applied to the experimental and numerical results, showing the possibility of detecting cracks with sizes in the order of 8% of the total section area.

A simplification of railway vehicle lateral vibration model based on LQG control strategy

ABSTRACTIn designing linear quadratic Gaussian (LQG) controller based on a full-size railway vehicle, the solutions for the coefficient matrices A, B, Q, R, and N can be quite difficult. Moreover, debugging the weighting coefficients of so many control indexes can be onerous, but the calculation results for a simplified vehicle model are very inaccurate. With these two factors taken into consideration, a seven degrees of freedom (DOFs) simplified railway vehicle model is proposed, in which the wheelset dynamic motion parameters are used as the input excitation. When an LQG controller is designed based on this model, the eight DOFs of the four wheelsets can be left out and the dimensions of the coefficient matrices A, B, C, D, Q, and N will be reduced by at least 16. Even so, the wheel-rail non-linear contact relation can be considered. It is found that the maximum deviations of the calculation results between the simplified model and the 62-DOF full-size three-dimensional model established in the software ADAMS/Rail are <16%. The weighting coefficients are defined by means of an analytic hierarchy process method, and a quite obvious control effect can be obtained by designing the LQG controller based on the simplified model.

Derailment analysis based on a new coupled multibody railway vehicle model

Derailment analysis based on a new coupled multibody railway vehicle model

Stress and Vibrational Analysis of an Indian Railway RCF Bogie

In the present work, static and dynamic finite element analyses are carried out on an Indian railway 6 ton RCF sleeper bogie. The geometrical CAD model of railway vehicle has been developed in UG-NX7.5 and has been exported to ANSYS12.1 package where finite element modelling and the required static and dynamic analyses have been performed. For dynamic response, modal, harmonic and transient dynamic analyses are carried out. First few natural modes of vibration of the bogie are extracted in Eigen frequency analysis and it is observed that the roll mode attained at a frequency which is well matched with the fundamental natural frequency calculated analytically. The harmonic peaks obtained are matching well with the natural frequencies obtained in modal analysis. Response to the ground excitation when the bogie passes over a bump is simulated in transient analysis.

Stability and bifurcation analysis of the non-linear railway bogie dynamics

It is a critical issue to maintain stability in high-speed railway vehicles and to ensure comfortable and safe driving. Multi-body models of railway vehicles have non-linear properties originated from the wheel–rail contact and characteristics of the suspension systems. The critical speed values at which the unstable oscillations and the amplitudes of the limit cycle-type vibrations take place vary by adjusting the design parameters; therefore, these effects on non-linear railway dynamics must be evaluated with a higher precision by using numerical and/or analytical methods to determine the bifurcation behavior. The main objective of this paper is to examine the non-linear phenomena in a railway bogie from a broad perspective, concentrating on non-linear analysis methods. Thus, non-linear equations of motion of a 12-degrees of freedom railway bogie involving dual wheelsets, non-linear wheel flange contact, heuristic non-linear creep model, and suspension system are solved in the time domain with small time steps by using ode23s (stiff/Mod.Rosenbrock) method. The critical speeds were calculated with respect to the effects of various lateral stiffness and damping coefficients. The bifurcation diagrams of the maximum lateral displacement of the leading wheelset were depicted within a wide speed range. In the case of the suspension parameter set where the subcritical/supercritical Hopf bifurcation takes place, the phase portraits and the symmetric/asymmetric oscillations of the leading wheelset at the critical speed were represented. The type of the Hopf bifurcation can be transformed from the subcritical state to the supercritical state by increasing the given suspension ratio. The Lyapunov exponents of the lateral displacement, lateral velocity, yaw angular displacement, and yaw angular velocity of the leading wheelset were evaluated above the critical speeds to examine chaotic motion. The effect of the suspension parameters on the non-linear dynamical behavior of the railway bogie at the stability limit and on the bifurcation type has been proved.

Impacts of wind shielding effects of bridge tower on railway vehicle running performance

When railway vehicles run by towers of long span bridges, the railway vehicles might experience a sudden load-off and load-on phenomenon in crosswind conditions. To ensure the running safety of the railway vehicles and the running comfort of the passengers, some studies were carried out to investigate the impacts of sudden changes of aerodynamic loads on moving railway vehicles. In the present study, the aerodynamic coefficients which were measured in wind tunnel tests using a moving train model are converted into the aerodynamic coefficients in the actual scale. The three-component aerodynamic loads are calculated based on the aerodynamic coefficients with consideration of the vehicle movement. A three-dimensional railway vehicle model is set up using the multibody dynamic theory, and the aerodynamic loads are treated as the inputs of excitation varied with time for kinetic simulations of the railway vehicle. Thus the dynamic responses of the railway vehicle passing by the bridge tower can be obtained from the kinetic simulations in the time domain. The effects of the mean wind speeds and the rail track positions on the running performance of the railway vehicle are discussed. The three-component aerodynamic loads on the railway vehicle are found to experience significant sudden changes when the vehicle passes by the bridge tower. Correspondingly, such sudden changes of aerodynamic loads have a large impact on the dynamic performance of the running railway vehicle. The dynamic responses of the railway vehicle have great fluctuations and significant sudden changes, which is adverse to the running safety and comfort of the railway vehicle passing by the bridge tower in crosswind conditions.

Effect of wind gusts on the dynamics of railway vehicles running on a curved track

Due to global warming, there is an increasing number of wind gusts that affect the stability of railway vehicles. A railway vehicle running on a curved track during a wind gust is subjected to multiple forces simultaneously, which include the centrifugal force and forces exerted by the wind gust and cant, and they significantly affect the vehicle’s dynamic characteristics as well as its safety. The forces increase the vibration of carbodies and the risk of derailment and overturning of cars; the effect is worse on irregular tracks. In order to review the phenomenon in detail, a 1/20 scale model of a railway vehicle was built to measure the aerodynamic coefficients in five directions—side force, lift force, roll moment, pitch moment, and yaw moment—through a wind tunnel test. The data collected were applied as external forces to a full-scale railway vehicle model traveling on a curved track. Using a multibody simulation software program, SIMPACK, a railway vehicle was modeled, which was then used in the simulation of the dynamic characteristics and safety of vehicles while traveling on a curved track during a wind gust. Using the actual measured track data from the curved zone, a comparison was made on the dynamic characteristics of the car traveling, with and without a wind gust, on a curved track with a railway curve radius of 599 m; also, the difference was analyzed with the direction of the wind gust blowing from inside and toward the center of curvature. The results showed that in the presence of a wind gust blowing from outside the curvature with an average speed of 25 m/s it is advisable to stop train services on grounds of safety.

Robustness analysis of bogie suspension components Pareto optimised values

ABSTRACTBogie suspension system of high speed trains can significantly affect vehicle performance. Multiobjective optimisation problems are often formulated and solved to find the Pareto optimised values of the suspension components and improve cost efficiency in railway operations from different perspectives. Uncertainties in the design parameters of suspension system can negatively influence the dynamics behaviour of railway vehicles. In this regard, robustness analysis of a bogie dynamics response with respect to uncertainties in the suspension design parameters is considered. A one-car railway vehicle model with 50 degrees of freedom and wear/comfort Pareto optimised values of bogie suspension components is chosen for the analysis. Longitudinal and lateral primary stiffnesses, longitudinal and vertical secondary stiffnesses, as well as yaw damping are considered as five design parameters. The effects of parameter uncertainties on wear, ride comfort, track shift force, stability, and risk of derailment are studied by varying the design parameters around their respective Pareto optimised values according to a lognormal distribution with different coefficient of variations (COVs). The robustness analysis is carried out based on the maximum entropy concept. The multiplicative dimensional reduction method is utilised to simplify the calculation of fractional moments and improve the computational efficiency. The results showed that the dynamics response of the vehicle with wear/comfort Pareto optimised values of bogie suspension is robust against uncertainties in the design parameters and the probability of failure is small for parameter uncertainties with COV up to 0.1.

Modelling of structural flexibility of the railway vehicles carbody

The accuracy in the models of railway vehicles in the ride comfort evaluation mainly derives from the modelling of the carbody structural flexibility. The former part of the paper herein reviews the ‘flexible carbody’ type methods used to represent the carbody structural flexibility in the approaches targeting the identification of certain methods to reduce the flexible vibrations in the carbody so as to improve the ride comfort of the railway vehicles. What seems to apply are the simple beam models such as Euler - Bernoulli or Timoshenko, structure type models and detailed multi-body, finite-element models or combinations of multi-body and finite-elements models. The latter part will feature a contrastive analysis regarding the comfort index coming from the numerical simulations based on ‘rigid carbody’ and ‘flexible carbody’ original models. It is highlighted that the comfort performance of a railway vehicle evaluated on the basis of a ‘rigid carbody’ mode is overrated.

ВЕРИФИКАЦИЯ ПРОСТРАНСТВЕННЫХ ДИНАМИЧЕСКИХ МОДЕЛЕЙ РЕЛЬСОВЫХ ЭКИПАЖЕЙ В SIMPACK RAIL ПРИ ИССЛЕДОВАНИИ ГОРИЗОНТАЛЬНЫХ КОЛЕБАНИЙ ЛОКОМОТИВОВ

ВЕРИФИКАЦИЯ ПРОСТРАНСТВЕННЫХ ДИНАМИЧЕСКИХ МОДЕЛЕЙ РЕЛЬСОВЫХ ЭКИПАЖЕЙ В SIMPACK RAIL ПРИ ИССЛЕДОВАНИИ ГОРИЗОНТАЛЬНЫХ КОЛЕБАНИЙ ЛОКОМОТИВОВ

Non-linear vibration analysis of a 2-DOF railway vehicle model under random rail excitation

With increase in the axle load and wagon speed, the cost of damage to rail track and wagon components increases significantly. This leads to widespread interests in the investigation of the dynamic interactions of the rail track and the wagon. Rail irregularities are one of the important vibration sources of the rail track structure and train. These irregularities have generally random distribution that are assumed to be stationary random and ergodic processes in space, with Gaussian amplitude probability densities and zero mean values. In this paper, the dynamic response of the railway vehicle due to random irregularity of rail track is analysed. The wagon is modelled as a two degrees-of-freedom non-linear model where includes non-linear spring and linear damper of primary suspension system. The Hertzian contact theory is used to obtain the relationship between normal contact force and the displacement of the mass centre of the wheel. Using the method of multiple scales the analytical approximate response of the railway vehicle due to track irregularities is obtained. The amplitudes of vibrations of the vehicle and the interaction forces between the vehicle and the rail for different line grades and train speeds have been analysed analytically by this model. According to the results, rail irregularities have more effect on the vertical acceleration of the vehicle than the train speed.

The use of a linear half-vehicle model for the optimization of damping in the passive suspension system of a railway car

The paper presents a methodology of optimizing the parameters of the passive suspension system of a railway vehicle. A linear half-vehicle model and an example of the procedure carried out to optimize a selected parameter of the model have been demonstrated. A method of the selection of damping in the suspension system of a railway vehicle, based on over 40-year achievements of the cited authors of publications in the field of motor vehicles, has been shown. The optimization of linear damping in the secondary suspension system of a passenger carriage moving on a track with random profile irregularities has been described in detail. The algorithms adopted for the calculations have a wider range of applicability; especially, they may be used for determining the optimum values of the other parameters of the railway vehicle model under analysis, i.e. stiffness of the secondary suspension system as well as stiffness and damping of the primary suspension system.

Robust control and actuator dynamics compensation for railway vehicles

ABSTRACTA robust controller is designed for active steering of a high speed train bogie with solid axle wheel sets to reduce track irregularity effects on the vehicle’s dynamics and improve stability and curving performance. A half-car railway vehicle model with seven degrees of freedom equipped with practical accelerometers and angular velocity sensors is considered for the H∞ control design. The controller is robust against the wheel/rail contact parameter variations. Field measurement data are used as the track irregularities in simulations. The control force is applied to the vehicle model via ball-screw electromechanical actuators. To compensate the actuator dynamics, the time delay is identified online and is used in a second-order polynomial extrapolation carried out to predict and modify the control command to the actuator. The performance of the proposed controller and actuator dynamics compensation technique are examined on a one-car railway vehicle model with realistic structural parameters and nonlinear wheel and rail profiles. The results showed that for the case of nonlinear wheel and rail profiles significant improvements in the active control performance can be achieved using the proposed compensation technique.

Study on Vibration Reduction Design of Suspended Equipment of High Speed Railway Vehicles

The design methods of the under-chassis equipment of a high speed railway vehicle based on dynamic vibration absorber (DVA) theory and vibration isolation theory are proposed, respectively. A detailed rigid-flexible coupled dynamic model of a high speed railway vehicle which includes car body flexibility and the excitation of the suspended equipment is established. The vibrations of the car body and the suspension equipment with the proposed design methods are studied. Results show that the elastic vibration of the car body can be decreased effectively by mounting the under-chassis equipment with elastic suspension. Comparing with vibration isolation theory, the method based on DVA theory is more effective for suppressing the car body flexible vibration, but it will increase the vibration of the equipment to a certain extent. The method based on vibration isolation theory can reduce the vibration of both the car body and the equipment at the same time. Therefore, the design method should be selected appropriately according to the specific requirement.

Hunting stability of high-speed railway vehicles on a curved track considering the effects of steady aerodynamic loads

Aerodynamic loads may have effects on the hunting stability, and the factor of curved track makes it more complicated. Therefore, considering the steady aerodynamic loads generated by crosswind and airflow in the opposite advancing direction of train, the hunting stability of high-speed railway vehicle on a curved track is studied in this paper. The changes of gravitational restoring force and creep coefficients which are caused by aerodynamic loads are considered, and the change of equilibrium position due to aerodynamic loads, centrifugal force and the factor of curved track is also in consideration. A mathematical model of a high-speed railway vehicle during curve negotiation with aerodynamic loads is set up. A program based on the model is written and verified. Using this program, the linear critical speed considering the effects of aerodynamic loads is determined by the eigenvalue analysis. This paper investigates the critical speeds in three aerodynamic conditions. Considering the aerodynamic loads, the dependence of critical speed on curve radius and super-elevation is analyzed, and the impact of aerodynamic loads on instability mode is analyzed as well. In addition, this paper obtains the dominant factors affecting critical speed and the variation tendency of critical speed with primary longitudinal stiffness by orthogonal experiments. The results show that the critical speed decreases or increases while the wind is blowing to outer rail or inner rail respectively. The aerodynamic loads produce obvious effects on the instability mode. The variation tendency of critical speed dependence on curve radius in the conditions with aerodynamic loads keeps consistent with the case without aerodynamic loads. It is seen from the orthogonal experiments that, aerodynamic loads and curve radius are the dominant factors affecting linear critical speed of vehicle on a curved track, and the linear critical speed decreases with the increasing of primary longitudinal stiffness.

Modelling of nonlinear hunting instability for a high-speed railway vehicle equipped by hollow worn wheels

One of the reasons for frequent vibrations of coaches and hunting instability are hollow worn wheels. The main purpose of this paper is to investigate the effect of the wheel surface hollowing on the inconstancy and vibrations of a wagon. Considering the nonlinearity of the hollow surface, as well as both single and double point wheel-rail contacts are the significant points of this study. In order to do this, 800 wheel profiles of 100 coaches were measured in a controlled manner in a period of six months as an infield study. Statistical methods were used to categorize the measured hollow wheel profiles and select eight of the most observed ones. Then, a nonlinear mathematical model of a high-speed railway vehicle with 21 degrees of freedom was used for dynamic analysis of a wagon equipped by the hollow worn wheels on a tangent track. In order to model the effect of hollowing on the dynamic behaviour of the vehicle, the nonlinearity of wheel profile was taken into account. Also, both single and double point wheel-rail contacts were considered for accurate modelling of the wheel-rail interaction forces. Based on the results of the study, the tread hollowing must be considered as an independent dimensional parameter in periodic inspections. Also, it was concluded that worn wheels should be inspected regularly and re-profiled before their false flanges exceed a limit of 2 mm, in order to prevent the hunting phenomenon, and ensure being away from derailment of a passenger railway vehicle. Validation of the mathematical modelling was performed through the modelling of vehicle in ADAMS/Rail and comparing the results.