Coupled Numerical Modelling of Railway Track Substructure with Vehicle-Track Interaction

Transcription

1 Paper 125 Civil-Comp Press, 2015 Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing, J. Kruis, Y. Tsompanakis and B.H.V. Topping, (Editors), Civil-Comp Press, Stirlingshire, Scotland Coupled Numerical Modelling of Railway Track Substructure with Vehicle-Track Interaction R.E. Shaltout, C. Ulianov and H.-M. Chen NewRail Centre for Railway Research Newcastle University, United Kingdom Abstract The track substructure is a vital and essential part of the railway track system which supports the track, and its properties have a strong influence on the overall track behaviour. In the research presented in this paper, a methodology for coupling the numerical models of the railway superstructure with substructure part is developed. The dynamic interaction between vehicle and railway track is presented taking into account the complexity of the modelling of the ballast bed, railpads, under sleeper pads and its effect on the determination of the overall track stiffness. The paper presents a framework to investigate the dynamics of overall vehicle track systems with emphasis on theoretical modelling of the track substructure and superstructure components as well as numerical simulation of modelled solutions. A connection has been established between the multibody simulation package, used in the dynamic analyse of the whole vehicle-track system, and the finite element software used in the analysis of the track substructure. Then, the track dynamic properties have been updated simultaneously to the multibody simulation program for each track section. The proposed methodology has been used in the dynamic analysis of different track designs for increased axle load applications. Keywords: railway track modelling, substructure modelling, coupled numerical modelling, vehicle-track interaction, finite element, multibody. 1 Introduction The necessity for the enhancement of performance of railway systems, including the track as well as the vehicle, and obtaining more safety and comfort conditions for railway vehicles leads to more complex definitions and descriptions for all parameters affecting the model simulation of the railway systems [1]. The dynamic interaction between the vehicle and track systems presents significant problems for railway systems. These kinds of problems are usually generated from the defects in 1

2 the railway track and/or defects in the vehicle systems especially at the level of the wheel-rail interaction. Several methodologies have been developed by many authors for the study of the vehicle-track dynamics (see the surveys in [2-5]). Generally, the simplicity of the models describing vehicle track interactions is lost when the rail is considered as having discrete supports and when nonlinearities are associated with the properties of ballast, under sleeper pads (USP), railpads and wheel rail contact [6]. The complications in railway models can be generated from the complex geometry of the vehicle and track components including wheels and rails; the non-linearities in the calculation of the contact forces in the interface between the wheel and rail surfaces; and the number of degrees of freedom of the whole system [7, 8]. Modelling of track substructure in both static and dynamic conditions, with respect to the vehicle-track interaction, is important not just for the optimisation of new track design solutions, but also for the understanding and analysis of track behaviour in order to develop and implement an efficient and reliable maintenance system. There have been developments and successes in providing a universal agreement for modelling the behaviour of the superstructure of the track, but no agreement has been made for the substructure. Insufficient knowledge of non-linear and dynamic characteristics of the ballast, sub-ballast and subgrade materials has been the major reason for the lack of a suitable model of the substructure, not to mention the understanding of the interaction between the superstructure and the substructure and how this affects track performance. The construction of modern tracks requires high quality of sub-ground preparation in combination with enhanced superstructure components [9, 10]. The track stiffness has a major effect on the distribution of the forces on the track elements including (rails, under rail pads, sleepers and sleeper-ballast interface). Tracks with lower stiffness allow a better distribution of the track forces, reducing the loads on every single element while increasing the bending stresses in rails. In the case of stiff tracks, the rail stresses are reduced but on the other hand there is an increase of the loads affecting each single component of the track. In the current work, the track substructure was modelled using a finite element modelling program, PLAXIS, to build a complete model of the track substructure part including the ballast layer, subgrade, formation, etc. The vehicle dynamic analysis was performed using VAMPIRE software. A connection has been established between the multibody simulation and finite element software. The coupling between both numerical models allows updating the dynamic properties of track substructure (including the track stiffness and track damping as well as the track response under the running conditions) at each section of the track. 2 Methodology for coupled vehicle-track numerical modelling Modelling and simulation in the field of railway dynamics is a complex interdisciplinary topic. The existing computational tools used in the dynamic analysis are required not only for purposes of enhancement of these systems, but 2

3 also for design purposes and maintenance operations of the railway systems, in order to avoid time and material loses in producing prototypes for the study of the behaviour of the analysed system parts. The definition of a suitable methodology for the dynamic modelling of the vehicle track interaction is crucial, and requires special attention. This modelling approach should be capable to accurately describe the vehicle and track dynamic behaviour in different operating conditions [11]. Figure 1: Proposed methodology for coupled vehicle-track modelling The presented research proposes an integrated modelling methodology, as shown in Figure 1. The methodology employs a coupled numerical modelling of the substructure and superstructure parts, with respect to the interfaces and dependencies between them. The modelling order shown in Figure 1 begins with modelling the track substructure, then the superstructure part and, finally, the definition of the coupling between the substructure model and vehicle-track interaction models. The proposed approach uses suitable and compatible computing tools for the definition and modelling of different track bed solutions and vehicle-tract interaction scenarios. Therefore, the use of such an integrated modelling approach, considering both the substructure and the dynamic interactions between vehicle and track, is threefold: Structural analysis of track design and validation of new solutions; Analysis of key properties and optimisation of new track designs; Prediction of long-term behaviour, considering the vehicle-track interaction, vibrations, environmental issues, etc. 3

4 3 Coupled track vehicle modelling procedure The procedure followed to perform the coupling between the numerical models of the track substructure and the superstructure is shown in Figure 2. All data required to perform the analysis is entered into a Data Centre which is responsible for the distribution of input data to blocks assigned for the vehicle or the track parameters. Figure 2: Work flow of the coupled vehicle-track numerical modelling methodology The analysis begins with the modelling of the substructure part of the track system, in which the railway track is divided into sections. At each section of the track, all the geometrical and mechanical properties of the track are defined and provided to the finite element model used in the analysis of the track superstructure. Afterwards, the track superstructure is modelled and the dynamic properties of its components are defined according to loading conditions. The importance of modelling the contact problem has a great influence on vehicle dynamics because all the forces produced from reactions on the vehicle are transmitted through the contact patch. The contact model used in the analysis is a non-linear multipoint contact model. All necessary data including wheel and rail profiles, as well as the track irregularity files are provided from the data centre. A connection has been established, through special subroutines, between the multibody simulation software VAMPIRE and the finite element software PLAXIS. For each section of the track, all the analysis results extracted from the finite element model of the track is fed into the multibody model to update the dynamic properties of the track section in the different operation conditions. 4

5 3.1 Modelling of track substructure Due to the large non-linearities associated with the track substructure layers, including the ballast and sub-ballast layers, track stiffness may undergo significant changes. These changes in track stiffness will cause variations in the train/track interaction forces. The force variations give rise to track degradation such as track differential settlement due to permanent deformation of the ballast and in the underlying structure [12, 13]. The determination of vertical track stiffness of the railway tracks is crucial, as it plays an important role in maintenance activities and overall track maintenance costs. The definition of track stiffness at each section of the track provides a better estimation of the life cycle cost especially for ballasted tracks. Therefore, it was necessary to build a numerical model that can clearly determine the vertical track stiffness in different operation scenarios. In the presented paper, the track stiffness was determined by simulating both static and dynamic loading of the vehicle in interaction with the track, with different substructure layer designs. A finite element model of the railway track was developed and used, where the load transmitted to the ballast surface was provided from the moving train. By defining the relation between the amount of deformation and stress values of each layer of the track substructure, the vertical track stiffness was determined at each section of the track and used to update track dynamic properties in the multibody simulation tool used for the dynamic analysis Geometrical parameters of the model In the modelling of selected track substructure solutions, the cross section of a single-line ballasted track was modelled in 2D by using the finite element method (FEM). Although the wheel-induced stresses primarily decreased after the depth of approximately 2B (with B as length of sleeper) beneath the track bed, for assurance, the depth of subgrade is supposed to be 15m in the model Mechanical properties of the track and substructure The primary purpose of the study is to comprehensively investigate the ballast and sub-ballast elasto-plastic behaviour effects on track performance and pressure on the sleeper. Hence, the rail and sleeper materials are assumed to be elastic and other materials are considered elasto-plastic using Mohr-Coulomb criteria. The critical parameters and properties of the material for track components which are used in the modelling have been identified, reviewed and selected from relevant previously published research [14, 15]. In the proposed modelling procedure, the following parameters have been used as an input to the track substructure modelling program: Modulus of subgrade (E v,sg ), sub-ballast (E v,sb ), ballast (E b ). Friction angle of the ballast and sub-ballast. Bearing capacity and stiffness of subgrade and unbound sub-ballast that might change seasonally. 5

6 3.1.3 Numerical modelling of track substructure Finite element method (FEM) and Finite difference method (FDM) are widely used for numerical modelling and analysing the general behaviour of track components in certain conditions. In addition, the discrete element method (DEM) is used to describe the local mechanical behaviour of discontinuous bodies such as unbound ballast. Currently, the design methods treat the ballast as a continuous medium. Thus both FEM and FDM are feasible to simulate the ballast section performance. Programs based on FEM are particularly capable to perform very detailed analysis of displacements, stresses and strains of track components. In this paper, the finite element method (FEM) is used for numerical modelling and analysing the behaviour of track components in certain conditions. Advanced constitutive models have been used for the geotechnical analysis of deformation, stability and soil-structure. A simulation was performed to analyse the non-linear, time-dependent and anisotropic behaviour of soils and rocks which are main components of the track substructure. 3.2 Dynamic modelling The main objective of vehicle track interaction modelling is to combine the components of the compound structure so that their complex dynamic interaction is represented properly. Various numerical methods for simulation and nonlinear dynamic analysis of the interaction between a train and a railway track have been presented [16, 17]. Some of these models were expanded to account for statedependent track properties like the work presented by Nielson [18]. In the current research, a complete model of the whole vehicle-track system was built using commercial software VAMPIRE which takes into account the dynamic properties of the vehicle as well as track superstructure and substructure components. The elastic half space theory for a multi-layered system has been used for modelling the track substructure layers. A design optimisation procedure was followed taking into account the gradual increase in the stiffness from bottom (natural ground or embankment) to top (ballast) Track model parameters When simulating an infinite railway track of periodic structure of finite length, it is important to determine the length of the track structure. Many authors have investigated the vertical response of the track model with different sleeper numbers, measured from the point of application of harmonic excitation in both sides. It was found that the resonance curves for tracks with 32 sleepers and 64 are identical. In the presented research, the simulation track was divided into a number of sections. Each track section used in the simulation has 32 sleepers. The track dynamic properties for each section of the track were provided from the finite element model of the track substructure to update the values of the track bed stiffness and track damping coefficient. A generic model of the track section used in 6

7 the simulation program is presented in below Figure 3. The track flexibility is modelled differently in the vertical and lateral directions. Laterally, the rails can move independently of the sleepers. Thus, the lateral model has rail to sleeper lateral flexibility, as well as sleeper to ground flexibility. Figure 3: Track section model Table 1 shows the key parameters defining the track model. The features of the program allow the simulation of any changes on track parameters, such as track flexibility, to be specified with respect to the distance along the track. These inputs are either provided by the FE model of the track substructure, or user defined parameters, which are stored in the program data centre. Parameter Description Remarks/notes K ZP Vertical track stiffness under left rail Provided by the FE model Vertical track damping under left rail of the track substructure C ZP K YG C YG K ZG Sleeper to ground lateral stiffness Sleeper to ground lateral damping Sleeper to ground Vertical stiffness C ZG Sleeper to ground lateral damping K YP Rail to sleeper lateral stiffness Input data provided from Rail to Sleeper lateral damping the program Data Centre C YP Table 1: Track dynamic parameters used in the simulation program Various solutions for the track substructure design have been studied taking into account different light and heavy traffic applications. An extended analysis was presented for extreme operating conditions with increased axel load. On the other hand, the superstructure components including: Under sleeper pads, sleepers, under rail pads and the rails have been modelled to match the applied operating conditions especially for the increased axle load applications. 7

8 3.2.2 Vehicle model parameters Various computational packages have been developed on the market and are being used in the dynamic analysis of the vehicle track interaction. Most of these packages use the Multibody methodology in the analysis of the vehicle dynamics and track performance. Generally, all the computational tools used in this type of analysis share the same functionality and basic foundations of the work done on railway systems to predict or to analyse the performance of vehicles in different operation scenarios. Examples of such powerful packages used for railway dynamic analysis include: SIMPACK, VAMPIRE, GENSYS, NUCARS, ADAMS/Rail and UNIVERSAL MECHANISM. In most of these simulation tools, the theoretical basis of the mathematical modelling is mature and reliable. Some of the mentioned programs are text based programs, where professional users are required to deal with the analysis performed by the necessary files to run the analysis. On the other hand, other programs use friendly graphical interfaces which allow the users to interact and make changes on the dynamic analysis of the railway systems. The vehicle model used in the simulation purpose in the presented research was modelled using the multi-body system formulation implemented in the VAMPIRE simulation tool. Each rigid body in the model is assigned with 6 degrees of freedom, whereas a constant speed V is prescribed for the forward motion of the centre of gravity. An example of vehicle model that can be used for simulation purposes is the heavy transport wagon with three-piece bogies, shown in Figure 4. The entire wagon set is subdivided into elementary units, as follows: The wagon body, three-piece bogie assembly (including the bolster and side frames) and wheelsets are all modelled as a rigid bodies; The primary suspension elements are defined by the pedestal or the so-called adapter plus, connecting the side frame with the wheelsets; The secondary suspension elements consist of the friction wedges between the bolster and side frames and the elements in the side bearers and the central plate, connecting the bolster to the wagon body. Figure 4: Typical iron ore wagon [21] 8

9 Table 2 shows the main characteristics of the vehicle, defining the model used in the simulation [21, 22]. Parameter / Specification Wagon Bogie Bogie total mass (incl. brake and Weight of empty wagon wheelsets) Weight of loaded wagon Mass of bolster Distance between centre plates Mass of side frame Wagon total length Semi-distance of two bogie mass centres Wheelset Wheelset mass Mass moment of inertia of wheelset about X, Z axis Mass moment of inertia of wheelset about Y axis Mass moment of inertia of wheelset about X, Z axis Wheelset base Wheel diameter Table 2: Vehicle parameters 4 Analysis of numerical modelling results Various track designs, including ballasted and non-ballasted track solutions, as well as operational conditions, considering both passengers and freight traffic on light, conventional and heavy traffic freight lines, were initially assessed to identify the common features and properties, and understand the specific modelling aspects and possible outcomes. The connection between the substructure modelling part and the superstructure modelling part was designed in a flexible form that permits the study of different configurations of the railway vehicles as well as various track combinations. Relevant examples of possible outcomes of the static and dynamic analyses carried out using the proposed methodology are further presented. The results concerning the analysed systems have been assessed in order to validate the functionality of the proposed coupled modelling approach, considering the analysis of the vehicle, as well as the track system. 4.1 Analysis of substructure modelling results The main objective of substructure modelling is to identify the optimised design solutions for the track substructure, according to the operating and loading conditions. The design procedure comprises the identification and selection of possible track layers, calculation and/or identification of their mechanical and geometrical properties according to the applied loads and operational conditions, and, finally, the optimisation of the thickness and composition of each layer. 9

10 A specific freight traffic case with increased axle load conditions has been modelled and analysed for verifying the proposed methodology. The primary selection of technologies and track solutions for such extreme axle load conditions is listed and followed by a summary in Table 3, varying ballast layer thickness and blanket layer layout at the same loading conditions (extremely increased payload, heavy haul 40 t/axle-load), namely: Substructure Solution 1 conventional design with only ballast layer of minimum thickness on formation, for freight line with increased payload; Substructure Solution 2 & 3 improved design for increased payload, with minimum thickness ballast layer and sub-ballast layer with increased thickness; Substructure Solution 4 & 5 conventional design with only ballast layer of increased thickness and rock formation for increased payload conditions. Characteristics Solution Short Name Ballast Layer Sub-ballast Layer Thickness (mm) Thickness (mm) Axle load 1 HH t/axle 2 HH 300S t/axle 3 HH 300S t/axle 4 HH t/axle 5 HH t/axle Table 3: Selected substructure solutions for freight line with increased payload From the finite element analysis of the substructure layers of the track, it was noted that the maximum pressure at the ballast surface is found for the HH500 case as shown in Figure 5. The presence of a sub-ballast layer not only largely increases the track deformation from rail, sleeper, ballast to sub-ballast layer, but also enlarges the loading pressure transmitted to the lower structure. Since ballast and sub-ballast are assumed as isotropic continuum media in the numerical modelling, the results showing higher pressure (the designs with sub-ballast layer) may not accurately describe the real case. Figure 6, shows the maximum ballast surface displacement for the different analysed solutions for increased axle load heavy haul applications, which proves that the sub-ballast designs have reduced the track bed stiffness and resulted in higher risk of track bed instability and more maintenance activities to the ballast layer etc. It was noted that a maximum of 2.5 mm was reached in the HH300S+ case. 10

11 Max. Ballast surface Pressure (kn/m2) HH 300 HH 400 HH 500 HH 300S HH 300S+ Figure 5: Maximum ballast surface pressure for different substructure solutions 3 Max. Ballast surface Displacement (mm) HH 300 HH 400 HH 500 HH 300S HH 300S+ 0 Figure 6: Maximum ballast surface displacement for different substructure solutions The determination of vertical track stiffness is crucial in railway system engineering for both a design and maintenance point of view. Global track stiffness is an important parameter in the design of railway tracks that can affect the wheelrail interaction as well as the track degradation [19, 20]. On the other hand, the local track stiffness presents the stiffness of the components and layers of the track model. The local stiffness in the presented analysis was determined from the finite element analysis of the substructure track model. The HH500 solution was selected, as an example, to be modelled in order to determine the vertical and lateral track stiffness provided to the multibody simulation program. The HH500 solution is a conventional ballast layer located directly on a rock based foundation. Figure 7 shows the stress distribution in the vertical directions. The stress values are extracted from the FE model of the track substructure layers under the increased axel load (40t/axle) conditions. 11

12 Figure 7: Cartesian effective stress distribution Figure 8: Total displacements U y in vertical direction Figure 8 depicts the vertical and lateral displacement of the track substructure layers under the determined loading conditions. As the track substructure layers had most impact on the total track modulus, the values of the applied forces and amount of deflection at each layer has been identified. The track bed stiffness has been determined for each section of the simulation track by defining the relation between the stresses and displacements of each layer. From the stress and displacement levels extracted from the FEA of the selected track design solution, it was found that the maximum obtained stiffness of the track bed can reach an approximate value of 270kN/mm. At each section of the track during the simulation, the calculated values of the track bed stiffness obtained from the substructure modelling are provided to the simulation program used for the dynamic analysis of the vehicle-track interaction. 12

13 4.2 Analysis of dynamic simulation results It is obvious that track geometry deviations and/or track geometry quality act as major sources of vehicle movement, influencing thus key aspects such as wheel rail forces, accelerations, wear, damage and safety issues (as a cause for derailment). In the current work, a track with different types of irregularities has been used to assess effect of the track irregularities on the dynamic response of the modelled track systems as well as the vehicle dynamic response. Figure 9 shows the lateral and vertical irregularities applied to the simulation model. The presented data shows measured track irregularities for a typical freight UK line Analysis of track irregularities impact The track irregularities have a big effect on the vehicle-track interaction forces generated at the wheel and rail interface. Figure 10 depicts the lateral forces on both wheels of the leading wheelset of the Iron ore vehicle running with a speed of 60 km/h on the defined track presented in the wheelset frame of reference. Due to the increased axle load in combination with large fluctuations of the lateral irregularities, the lateral forces on the left and right wheel varies significantly along the track as it can be shown in the following figure. The values of the forces are the dynamic forces affecting each wheel without taking into account the static load of the wheel. Figure 9: Lateral and vertical track irregularities of typical UK freight line 13

14 Figure 10: Lateral forces on the left and right wheels of the leading wheelset The simulation results on a track with good track geometry quality will lead to low assessment quantities, and simulations on track with bad track geometry quality will lead to high assessment quantities, which may be beyond the limit values and the vehicle will be rejected from approval. The lateral or vertical displacements of the rails are due to the flexibility of the track stiffness. Figure 11 shows the lateral displacement of the left and right rails relative to the ground. All geometric outputs are defined in the track axis system located at the plane of the track. Each wheelset in the model is assigned to a track axis system moving with a speed equal to the vehicle speed. Figure 11: Lateral displacement of the left and right rails relative to the ground Figure 12 depicts the absolute vertical displacement of the track under the leading wheelset. The measured data shows the track vertical movement due to the vertical flexibility of the track used in the simulation. 14

15 Figure 12: Absolute vertical displacement of the track at leading wheelset Analysis of track stiffness influence The vehicle track interaction model used in the simulation has been used to determine the influence of track stiffness on track response by comparing various quantities including (Lateral forces on left and right wheels, displacements of left and right rails, sleepers displacement). In this analysis the influence of the track stiffness was presented. A comparison is defined between two models of track with different stiffness. The first track (T1) has a vertical stiffness value of 270kN/mm, and the second track (T2) is a stiffer track with vertical stiffness of 400kN/mm. An example of the simulation outcomes from the both tracks is presented in Figures below. Figure 13 depicts a comparison between the results from both track T1 and T2 for the sleeper lateral displacement under the leading wheelset of the vehicle moving with a velocity of 80km/h. Figure 13: Lateral displacement of the sleeper - vehicle speed of 80km/h 15

16 The track stiffness has a major effect on the distribution of the forces on the track elements including rails, rail and under sleeper pads, fastenings and sleepers, and the sleeper-ballast interface. Tracks with lower stiffness allow better distribution of the track forces, reducing the loads on all elements while increasing the bending stresses in rails. In the case of stiff tracks, the rail stresses are reduced but on the other hand there is an increase of the loads affecting each single component of the track. 5 Conclusions In this paper, a compatible numerical modelling approach for the railway substructure was investigated and developed to be used with both static and dynamic modelling of railway track superstructure and vehicle-track interactions, in order to analyse the track performance from light and conventional lines to heavy haul lines. A methodology has been proposed for the modelling of the track substructure and superstructure components. The first step was to model the track substructure layers with a finite element modelling program. The second step was to model the track superstructure part. Finally the coupling between the two numerical models was achieved by updating values of the track stiffness from the FE model for each section of the simulation track and addressing its effect on generated contact forces at the wheel-rail interface. Various track designs, including ballasted and non-ballasted track solutions, as well as operational conditions, were initially assessed to identify common features and properties, and to understand the specific modelling aspects and possible outcomes. A specific case study has been presented for freight tracks with increased axle load applications. A model for simulating the dynamic interaction of the railway track and Iron ore wagon system has been presented. The effect of the track irregularities in addition to the vertical track stiffness has been addressed with extreme axel load conditions. The suggested methodology is possible to achieve design optimisation for the improved performance of wagon and track as well as the study of the effect of changing the dynamic properties of the track superstructure components. References [1] O. Polach, M. Berg, S. Iwnicki, Simulation, in Handbook of railway vehicle dynamics, S. Iwnicki, Editor, CRC press, [2] S.L. Grassie, R.W. Gregory, D. Harrison, K.L. Johnson, The dynamic response of railway track to high frequency vertical excitation, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 24 (2),77 90, [3] K.L. Knothe, S.L. Grassie, Modelling of railway track and vehicle/track interaction at high frequencies, Vehicle System Dynamics, 22, ,

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