Railway Vehicle Model Research Articles

Modelling of the shape of railway transition curves from the point of view of passenger comfort

In the past, railway transition curves were not used. Instead of it, a simple connection of the straight track and circular arc was applied. Nowadays, such simplicity is not allowed due to the increasing vehicle operating velocities. It is mainly visible in the high-speed train lines, where long curves are used. The article aims to develop a new shape of railway transition curves for which passenger travel comfort will be as high as possible. Considerations in this paper concern the polynomials of 9th- and 11th-degrees, which were adopted to the mathematical model of the mentioned shape of curves. The study's authors applied a 2-axle rail vehicle model combined with mathematically understood optimisation methods. The advanced vehicle model can better assign the dynamical properties of railway transition curves to freight and passenger vehicles. The mentioned model was adopted to simulate rail vehicle movement in both cases of the shape of transition curves and the shape of circular arc (for comparison of the results). Passenger comfort, described by European Standard EN 12299, was used as the assessment criterion. The work showed that the method using the 2-axle railway vehicle model combined with mathematically understood optimisation works correctly, and the optimisation of the transition curve shape is possible. The current study showed that the 3rd-degree parabola (the shape of the curve traditionally used in railway engineering) is not always the optimum shape. In many cases (especially for the long curves), the optimum shape of curves is between the standard transition curves and the linear curvature of the 3rd-degree parabola. The new shapes of the railway transition curves obtained when the passenger comfort is taken into account result in new railway transition curves shapes. In the authors' opinion, the results presented in the current work are a novelty in optimisation and the properties assessment of railway transition curves.

실시간 시뮬레이터를 활용한 철도차량 PMSM 제어시스템의 시계열 기반 안정도 추정

This paper deals with numerical analysis method for system stability, which is applied to the mathematical model of permanent magnet synchronous motor for railway vehicle as one of the application of real-time digital simulation. Specifically, this study deals with bifurcation numerical analysis, one of analytic method to study nonlinear dynamics of a system, for system design or its inspection technique of the system model. XPPAUT is used to analyze the electrical motion of this complex system, so it can introduce theoretical approach to design real-time computing environment based on OPAL-RT for electrification system parts of railroad vehicle model. Within the real-time simulation framework, the paper also provides time-series based system stability estimation by performing statistical processes for auto-regressive model construction. The proposed approach can reduplicate verification process by screen studying of the model for improvement during real-time simulation or further hardware-in-the-loop test system.

Influence of suspension parameter for derailment analysis of a full railway vehicle model cruising on a curved track

The main intention of this research work is to study the derailment response of high speed railway vehicle (HSRV) cruising on a curved track. In previous research work, lower degree of freedom (DOF) has been considered for the derailment analysis which may not give more accurate results. Hence, a 31 DOF bondgraph model of HSRV has been developed which consist of carbody, two truck frames and two selfsame wheelsets for each truck frame. Vertical, lateral, roll, yaw and pitch motion are considered for carbody and bogie and except pitch motion all the other motion are considered for wheelsets. Non-linearities in terms of heuristic nonlinear creep model and flange contact has been employed to simulate the derailment response at high speed. The effect of vehicle speed running on a curved track was investigated for derailment quotient. The main aim of present research work to evaluate derailment quotient at the speed range of 150 kmph to 600 kmph for hard and soft suspension parameter. Derailment quotient has been calculated for both linear and nonlinear creep models and it is seen that DQ for linear model has a lower value compare to non linear creep. The major advantages of the proposed model are that, the presented model can actively predict the derailment of a railway vehicle, and also precisely determine the nonlinear critical hunting speeds.

Vehicle/track interaction under the conditions of high speed railway operation

This paper deals with the issue of dynamic effects of a high-speed railway vehicle on the track. Some aspects of vehicle/track interaction at higher speeds are described. In this context, a multi-body model of high-speed railway vehicle was created and several simulation scenarios were performed with this model. Furthermore, the simulations were evaluated with a focus on selected characteristics of the vehicle/track interaction.

Dynamic simulation of a high-speed train with interconnected hydro-pneumatic secondary suspension

A secondary suspension configuration that integrates the Interconnected Hydro-Pneumatic Struts (IHPS) to the air spring system is proposed in this investigation for railway vehicles. Using the dynamic performance of IHPS, this suspension aims to provide smaller vertical supporting stiffness and larger anti-roll resistance compared to the traditional configuration, the air spring is connected to an emergency rubber spring in series with quite large stiffness. By replacing the rubber spring with IHPS, the proposed suspension configuration contributes to vibration absorption as well as anti-roll stiffness of the vehicle. The IHPS has two hydraulic cylinders installed in parallel to support the suspended mass. Each hydraulic cylinder has three oil chambers, and the oil chambers between the left and right struts are cross-connected through pipelines. Considering the oil compressibility and the vibration of liquid in the interconnected pipes, the mathematical model of IHPS is formulated and established in MATLAB. A multi-body dynamic railway vehicle model is built in SIMPACK, into which the IHPS is integrated through a co-simulation technique. Model validations on the IHPS are performed and its static and dynamic stiffness is examined. Numerical simulations show that the IHPS suspension reduces the vertical acceleration on the car body floor at a frequency between 1 and 3 Hz than the traditional air spring system with/without an anti-roll bar configuration. The vertical Sperling index of the vehicle using the IHPS suspension is smaller than that of the traditional suspensions, and it is more significant when the air spring deflates. However, the vertical acceleration with IHPS is larger than the traditional suspensions at 13∼55 Hz when the air spring deflates.

Evaluation of effectiveness of pneumatic suspensions: Application to liquid sloshing problems

In this investigation, a pneumatic suspension model with orifice damping is developed and used to evaluate the performance of the air suspension in comparison with the coil-spring suspension in railroad and highway transportation systems. In railcars, air springs are used to isolate the car from vibrations caused by track irregularities, while in highway trucks, air springs are often used in their rear suspensions to allow adjusting the suspension characteristics depending on the load conditions. The air spring formulation is validated by comparing the dynamic stiffness with the stiffness of other models reported in the literature. Different motion scenarios are considered to quantify effectiveness of the air spring in liquid sloshing problems. To capture the large displacements experienced by the liquid, the finite element (FE) absolute nodal coordinate formulation (ANCF) is used with a penalty approach to model the fluid/tank contact forces. In the railroad vehicle models, the wheel/rail contact is modelled using a nonlinear three-dimensional elastic contact formulation that accounts for the creep forces and spin moment, while in the highway-truck model, the wheel/ground interaction forces are modeled using a discrete-element tire model. In addition to comparing with coil springs, the paper discusses the differences between the pneumatic and active suspensions. The simulation results show that using air springs reduces the railcar mean vertical acceleration, maximum roll angle, and variations in the wheel/rail contact forces. The mean vertical acceleration of the truck tank is found to be lower when air springs are used, resulting in a reduction of the force exerted by the fluid on the tank walls.

Suppression of the flexible carbody resonance due to bogie instability by using a DVA suspended on the bogie frame

A novel method is proposed to suppress the flexible carbody resonance due to bogie instability by hanging a dynamic vibration absorber (DVA) to the bogie frame. The aim is to design the DVA to change the frequency of the bogie hunting motions, which can ensure the bogie does not operate at the resonant frequency of the objective mode of the flexible carbody. Firstly, the resonance phenomenon of the flexible carbody is introduced. The reason is revealed that the unstable frequency of the bogie hunting motions matches the resonance frequency of the carbody diamond mode, which is identified experimentally by modal testing. Then the unstable behaviour of the bogie with a suspended DVA is studied theoretically by building a simple lateral dynamics model of a bogie system. The basic mechanism of the effect of a DVA on the hunting frequency jump characteristic is explored. It is then adopted to suppress the carbody resonance due to bogie instability in the rigid-flexible multi-body dynamics model of a high-speed railway vehicle. The optimum parameters of the DVA suspension are determined numerically by deigning the unstable frequencies away from the objective natural frequency of the flexible carbody, and its effect on resonance suppression is confirmed.

Indirect identification of wheel rail contact forces of an instrumented heavy haul railway vehicle using machine learning

Rail car safety and stability are important factors for good performance. The most used safety index to quantify railway safety is the ratio between the lateral and vertical wheel rail contact forces (L/Q). This study aims to use machine learning (ML) models to evaluate the viability of estimating the wheel rail contact forces from sensors in a regular instrumented railway vehicle (IRV). A virtual model of a BRA1 railway vehicle was created to generate an artificial dataset with variables measured with the actual BRA1 vehicle plus different variables measured by other IRVs found in the literature. The desired output variable is the L/Q ratio for each wheel of the leading bogie. Exploratory data analysis was done to clarify the correlation between the variables while model explainability techniques were applied to evaluate the contribution of these input variables to the output (L/Q). A total of 24 embedded machine learning models were trained and optimized using the tree-based pipeline optimization tool (TPOT) to generate a ML pipeline capable of producing an accurate L/Q ratio as the output for different cases of sampling rate, input variables and track irregularities. The results show that machine learning models can predict the wheel rail contact forces indirectly – without using instrumented wheelsets – with the highest mean squared error being equal to 0.01113.

Improved lateral-dynamics-intended railway vehicle model involving nonlinear wheel/rail interaction and car body flexibility

To study the vehicle hunting behavior and its coupling with car body vibrations, a simplified lateral-dynamics-intended railway vehicle model is developed. A two-truck vehicle is modeled as a 17 degrees-of-freedom rigid system, into which the car body flexural vibrations of torsion and bending modes are further integrated. The wheel/rail interaction employs a real-time calculation for the Hertzian normal contact, in which the nonlinear curvatures of wheel and rail profiles are presented as functions of wheelset lateral movement and/or yaw rotation. Then the tangential/creep forces are analytically expressed as the Hertzian contact patch geometry, and lead to a continuous and fast calculation compared to a look-up table interpolation. It is shown that the hunting frequencies of the vehicle model and a truck model differ significantly, which verifies the necessity of the whole vehicle model. In the case of low wheel/rail conicity, the hunting frequency increases linearly with vehicle speed, whereas it rises slowly at high speed for a large conicity. Comparison of hunting frequency and damping ratio between various conicities shows that first hunting (car body hunting) may occur when the vehicle is operated at a low speed in a small conicity case, while a second hunting (truck hunting) appears when the vehicle is operated at a high speed in a large conicity case. Stability analysis of linear and nonlinear vehicle models was carried out through coast down method and constant speed simulations. Results tell that the linear one overestimates the lateral vibrating. Whereas the structural vibrations of car body can be ignored in the stability analysis. Compared to existing simplified models for hunting stability study, the proposed simplified vehicle model released limitations in the nonlinear geometries of wheel/rail profiles, and it is suitable for a frequency-domain analysis by deriving the analytical expressions of the normal and tangential wheel/rail contact forces.

Effect of Rail Vehicle–Track Coupled Dynamics on Fatigue Failure of Coil Spring in a Suspension System

In a rail vehicle, fatigue fracture causes a significant number of failures in the coil spring of the suspension system. In this work, the origin of these failures is examined by studying the rail wheel–track interaction, the modal analysis of the coil springs and the stresses induced during operation. The spring is tested experimentally, and a mathematical model is developed to show its force vs. displacement characteristics. A vertical 10-degree-of-freedom (DOF) mathematical model of a full-scale railway vehicle is developed, showing the motions of the car body, bogies and wheelsets, which are then combined with a track. The springs show internal resonances at nearly 50–60 Hz, where significant stresses are induced in them. From the stress result, the weakest position in the innerspring is identified and a few guidelines are proposed for the reduction of vibration and stress in rail vehicles.

A simple active carbody roll scheme for hydraulically actuated railway vehicles using internal model control

The paper presents the first classical internal model control (IMC) design in the context of railway carbody roll control. We propose a simple control approach for a recent hydraulically actuated vehicle body roll concept that offers limited carbody roll. The IMC approach addresses both preview- and nulling-type tilt setups, highlighting related benefits and limitations. The design provides a model simplification process that facilitates PI and PID-type control structures without the need for complex optimization. A simple, yet practical, tool for the industrial rail rolling stock engineer in vehicle control design is offered. Vehicle roll performance is rigorously studied on the deterministic (curving acceleration response) and stochastic (ride quality) trade off. Simulations are performed on an in-house multibody dynamics software package employing a realistic nonlinear railway vehicle model and allow to appropriately assess the performance of preview and nulling type tilt performance. The results obtained confirm that preview tilt control offers the better tilt performance as it utilizes a tilt command reference, and highlighted that nulling-type tilt performance remains at a relatively comparable level with the former.

Fatigue life prediction for locomotive bogie frames using virtual prototype technique

Current research papers use simulated load spectrums to assess bogie frames’ fatigue life but seldom consider traction and braking loads. Traction and braking loads play important roles in predicting fatigue life in high-speed and heavy haul operational scenarios. Hence, there is a research gap in terms of the consideration of longitudinal load spectrums while assessing bogie frames’ fatigue life. This paper presents research about this topic. A virtual prototype technique available in literature has been extended for this purpose; it uses multibody dynamics and finite element techniques to simulate the behaviour of bogie frames under real operational service loads. As a result, the special simulation methodology has been developed in this work and it includes the unique integration of simulation approaches that includes train dynamics, locomotive dynamics with the consideration of a traction control algorithm and the adopted fatigue life calculation method. This paper gives numerical examples of a rigid-flexible coupled dynamic railway vehicle model subjected to longitudinal forces. Road Environment Percent Occurrence Spectrum (REPOS) load spectrums of the bogie frame were developed from a whole-trip train simulation on a real route. The spectrums are then used to predict locomotive the bogie frame’s fatigue life. The results of the bogie frame fatigue life evaluation performed in this paper show that fatigue lives at the roots of traction rod seats under longitudinal load spectrums are shorter than their fatigue life under vertical load spectrums.

Investigation of Thermal Sensation in a Railway Vehicle during Cooling Period

The paper presents an investigation of local thermal comfort of passengers in a railway vehicle. The railway vehicle model includes five different parts called modules, and each module had different properties such as passenger capacity and seating arrangement. A virtual manikin model was developed and added to the numerical model which includes convection and radiation heat transfer between the human body and the environment. The numerical simulation was conducted according to the EN 14750-1 standard describing the thermal comfort conditions for different climatic zones. Two different cases were performed for steady-state conditions. Meanwhile, measurements were taken in a railway vehicle cabin to validate the numerical simulation, and the numerical results were in good agreement with the experimental data. It is observed that the local heat transfer characteristics of the human body have significant importance for the design of an effective heating, ventilation, and air conditioning (HVAC) system because each module had different heat transfer and air flow characteristics. It is also shown that the thermal sensation (TSENS) index helps railway vehicle HVAC researchers to determine the reasons for discomfort zones of each occupant. Another important result is that using a single air flow channel did not meet the thermal comfort demands of all passengers in this railway vehicle. Therefore, multiple air flow channel design configurations should be considered and developed for these vehicles. Local thermal comfort models allow HVAC systems to achieve better comfort conditions with energy saving. The numerical model can be used for effective module design, including seating arrangements, to achieve better thermal comfort conditions.

Suspension parameter design of underframe equipment considering series stiffness of shock absorber

In this article, a vertical rigid–flexible coupling model between the vehicle and the equipment is established. Considering the series stiffness of hydraulic shock absorbers, the underframe equipment is like a three-element-type Maxwell model dynamic vibration absorber. The carbody is approximated by an elastic beam and the three-element-type dynamic vibration absorber for general beam system was studied by fixed-point theory. The analytical solution of the optimal suspension parameters for the beam system subjected to harmonic excitation is obtained. The dynamic vibration absorber theory is applied to reduce the resonance of the carbody and to design the suspension parameters of the underframe equipment accordingly. Then, the railway vehicle model was established by multi-body dynamics simulation software, and the vibration levels of the vehicle at different speeds were calculated. A comparative analysis was made between the vehicles whose underframe equipment was suspended by the three-element-type dynamic vibration absorber model and the Kelvin–Voigt-type dynamic vibration absorber model, respectively. The results show that, compared with the vehicle whose underframe equipment is suspended by the Kelvin–Voigt-type dynamic vibration absorber model, the vehicle whose underframe equipment is suspended by the three-element-type dynamic vibration absorber model can achieve a much better ride quality and root mean square value of the vibration acceleration of the carbody. The carbody elastic vibration can be reduced and the vehicle ride quality can be improved effectively using the designed absorber.

The effect of gear meshing on the high-speed vehicle dynamics

The gear transmission system is a key part to transmit power for the electrical multiple unit (EMU) and to move the train forward. Its dynamic vibrations affect the operation safety and the dynamic characteristics of the vehicle. Based on the parameters of a certain type of high-speed EMU in China, a rigid-flexible coupling dynamics model of railway vehicle is developed. A flexible gear meshing dynamics model is built and it is incorporated into the vehicle system dynamics model. With the numerical method, the effect of the gear transmission on the dynamics of the high-speed vehicle is investigated. A field experiment is carried out and the measured accelerations of the gearbox are employed to validate the simulation results. The investigation results reveal that the gear meshing forces get large as the operation speed of the vehicle increases. Gear meshing affects the operation safety indexes and the vibrations of the bogie frames, motors and gearboxes, but has negligible effect on the vibrations of the carbody. The difference between the results with the flexible gear meshing model and the results with the rigid gear meshing model is negligible. The simulation acceleration is slightly smaller than the field test result of the gearbox.

Frequency-domain approach for the parametric identification of structures with modal interference

This study aims to improve the accuracy of the parametric estimation of systems with modal interference in the frequency domain. The theory of modal identification states that the frequency response function can be expressed as a rational function form by using the curve fitting technique, and the modal parameters can then be estimated from rational fractional coefficients. The conventional common denominator model only indicates the frequency response function of a single-degree-of-freedom system; thus, it cannot acquire the mode shape information. In this paper, we propose the matrix-fractional coefficient model constructed by the frequency response functions of a multiple-degree-of-freedom system for modal identification. To avoid the phenomenon of omitted modes caused by the distortion from modal interference among the vibration modes of systems during modal estimation, we use a system model with higher-order matrix-fractional coefficients, but fictitious modes may be caused by numerical computation. Structural and fictitious modes can be effectively separated by using a different-order constructed stabilization diagram. Modal identification can be implemented by solving the eigenproblem of the companion matrix yielded from least-square estimation. Numerical simulations, including a full model of sedan and one-half railway vehicle in the form of a linear 2D model, as well as the experimental testing of an actual plate, confirm the validity and robustness of the proposed parametric-estimation method for a system with modal interference under noisy conditions.

An innovative model for the prediction of wheel - Rail wear and rolling contact fatigue

One of the issues in the railway field is the damage caused by wear and RCF which deeply affects wheel and rail. These phenomena are closely connected and directly impact both on vehicle dynamics (comfort, stability, safety, etc.) and on the costs (line management, maintenance, etc.), decreasing the useful life of wheel and rail. To face these problems and detect abnormal operating conditions, this work aims at developing a modelling approach for railway and tramway applications that effectively combines wear and RCF models. The former has been validated by means of on-field experimental data whereas the latter through specific laboratory tests carried out on a dedicated test-rig. The proposed approach is capable of simultaneously predicting both the profiles shape evolution due to wear and the total RCF damage along the wheel and rail profiles, reaching a good compromise between accuracy and efficiency. Thanks to the high numerical efficiency, the wear-RCF model can be easily implemented into complex multibody models of railway and tramway vehicles to perform large-scale simulations.

On the nonlinear dynamics of a high-speed railway vehicle with nonsmooth elements

• A comprehensive lateral mathematical model of a high-speed railway vehicle with nonsmooth elements is built. • Numerical methods are presented to investigate the nonlinear dynamics of high-speed railway vehicles. • Nonlinear dynamics of a Chinese high-speed railway vehicle is investigated. • Influences of primary system parameters on the nonlinear dynamics of a Chinese high-speed railway vehicle are illustrated. A comprehensive lateral mathematical model of a high-speed railway vehicle with 17 degrees of freedom is built to study its nonlinear dynamics on a straight line. The hunting stability is explored by using eigenvalue analysis , bifurcation diagrams and the first Lyapunov coefficient. Due to the non-smoothness in the wheel/rail contact table and the secondary suspension elements such as anti-yaw dampers, bump stops , etc., an event-driven strategy is applied in the integration process of the ODEs . As an example, the nonlinear dynamics of a Chinese Railway High-speed (CRH) vehicle (named CRH2) is investigated. The result shows that the stable equilibrium of the high-speed railway vehicle loses its stability through a supercritical Hopf bifurcation with the increase of the forward speed, and the stable periodic solution loses its stability through a grazing bifurcation with the decrease of the forward speed. The influence of primary system parameters on the hunting stability of the high-speed railway vehicle is also investigated.

Prediction of the Pantograph/Catenary Wear Using Nonlinear Multibody System Dynamic Algorithms

In this investigation, computational multibody system (MBS) algorithms are used to develop detailed railroad vehicle models for the prediction of the wear resulting from the pantograph/catenary dynamic interaction. The wear is predicted using MBS algorithms for different motion scenarios that include constant-speed curve negotiation and acceleration and deceleration on a tangent (straight) track. The effect of the vehicle vibration in these different motion scenarios on the contact force is further used to study the wear rates of the contact wire. The wear model used in this investigation accounts for the electrical and the mechanical effects. The nonlinear finite element (FE) absolute nodal coordinate formulation (ANCF), which is suitable for implementation in MBS algorithms, is used to model the flexible catenary system, thereby eliminating the need for using incremental-rotation procedures and co-simulation techniques. In order to obtain efficient solutions, both the overhead contact line and the messenger wire are modeled using the gradient-deficient ANCF cable element. The pantograph/catenary elastic contact formulation employed in this study allows for separation between the pantograph panhead and the contact wire, and accounts for the effect of friction due to the sliding between the pantograph panhead and the catenary cable. The approach proposed in this investigation can be used to evaluate the electrical contact resistance, contribution of the arcing resulting from the panhead/catenary separation, mechanical and electrical wear contributions, and the effect of the pantograph mechanism uplift force on the wear rate. Numerical results are presented and analyzed to examine the wear rates for different motion scenarios.

Fatigue analysis of the gearbox housing in high-speed trains under wheel polygonization using a multibody dynamics algorithm

To examine the effect of the wheel polygonization on the fatigue of the wheelset-mounted gearbox housing of a high-speed train, a three-dimensional multibody system (MBS) railway vehicle model, which accounts for the flexibilities of gearbox housing and wheelset and the nonlinear wheel-rail contact, is established to perform the finite element and multibody dynamics analysis simultaneously. Field measurements on the wheel wear, within a total running distance of 140,000 km, were conducted to state the evolution of polygonal wear with a dominant order of 20 on the wheel. Then this uneven wear on the wheel is treated as excitations in the wheel-rail interaction, followed by numerical analysis on the dynamics stress distribution on the gearbox housing under the effect of a variable amplitude of polygonal wear on the wheel. It shows that the stress distribution on the gearbox housing is significantly affected by the deformation of the wheelset. Furtherly, the Kernel density estimation (KDE) method is employed to extrapolating the dynamic stress on the gearbox to obtain the stress with a total running distance of 140,000 km, then its fatigue damage is estimated. Comparative analysis in the fatigue damage of gearbox housing with or without the wheel polygonization states that the fatigue damage with a 20th order polygonal wear is 63% larger than that without the polygonal wear on the wheel.