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Refining the modelling of vehicle–track interaction
Abstract
An enhanced model of a passenger coach running on a straight track is developed. This model includes wheelsets modelled as rotating flexible bodies, a track consisting of flexible rails supported on discrete sleepers and wheel–rail contact modules, which can describe non-elliptic contact patches based on a boundary element method (BEM). For the scenarios of undisturbed centred running and permanent hunting, the impact of the structural deformations of the wheelsets and the rails on the stress distribution in the wheel–rail contact is investigated.
... Refs. [11][12][13]), is a convenient alternative that allows for the efficient and yet precise modelling of a wide range of 2D and 3D contact problems, either frictionless or with friction, static or rolling, and steady state or transient. Since it is a Boundary Element Method, in which the contact surface is discretized rather than the volume of the contacting bodies, its computational costs in the solution of large elastostatic, small-displacement, concentrated contact problems are far lower than those of FEM, especially when detailed results at the contact surface are sought. ...
... Doing this, specifically the B xn at the same lateral position than the loaded element (i.e. with α = 0) would be computed as indicated in Eq.(16). This is obtained exchanging the s and x coordinates in the formula for B sn in Eq.(13). In this equation, A w x+n = (A w xx + A w nn )/2, A w xx and A w nn are individual ICs of the wheel, and α x is the angular difference in the wheel surface orientation in longitudinal direction (analogous to α in the lateral direction). ...
... The effective elastic properties obtained with Eq.(14) are used to calculate modified A ij , designated as A ij . These A ij are then used in Eq.(13) for the B ICs presented in Section 3. This extended version of the B ij is designated as B ′ ...
The exact contact theory is an efficient alternative to the more general yet computationally expensive Finite Element Method for the detailed study of elastostatic contact problems. For its application in conformal contact problems, the exact contact theory needs to be fed with influence coefficients (ICs) appropriate for non-planar solids. An analytical approximation of the ICs for non-planar solids was proposed in a previous work, avoiding the involved process generally necessary to obtain ICs accurately. This work presents further developments of this approximation, further comparison with numerically obtained ICs, and evaluates the errors incurred when using approximated ICs in conformal contact.
... Therefore, a vehicle-track model, in which these two effects are combined, seems to be reasonable and desirable. Such a refined and extended modelling of a vehicle-track system is presented in the earlier works [4] and [5] by one of the authors. In [4], the modelling concepts for the flexible wheelsets and the flexible rails are described. ...
... In [4], the modelling concepts for the flexible wheelsets and the flexible rails are described. The essential progress beneath further improvements presented in [5] is the integration of a non-elliptic wheel-rail contact model, which replaced the simpler model based on the Hertzian theory. Both works [4] and [5] focus in particular on the extended modelling; for a demonstration of the functionality of the modelling and as a first check of the plausibility, the scenarios of centred running and of permanent hunting were investigated. ...
... The essential progress beneath further improvements presented in [5] is the integration of a non-elliptic wheel-rail contact model, which replaced the simpler model based on the Hertzian theory. Both works [4] and [5] focus in particular on the extended modelling; for a demonstration of the functionality of the modelling and as a first check of the plausibility, the scenarios of centred running and of permanent hunting were investigated. ...
The hunting motion of a passenger coach is investigated using a multibody system in which the wheelsets and the rails can be modelled as flexible bodies. By comparing the results for different model variants, in which the structural flexibilities of the wheelsets and of the rails are either taken into account or neglected, the impact of the flexibilities is analysed. It turns out that the flexibilities of both the wheelsets and the rails have a significant impact on the hunting behaviour by increasing the lateral motions of the wheelsets and lowering the critical speed. In order to investigate the impact of the flexibilities under different operating conditions, the calculations are carried out for track geometries using different rail profiles (60E1, 60E2) and different rail cants (1:40, 1:20) and for different values for the friction coefficient (0.25…0.4) at the wheel–rail contact. The results show that the influence of the flexibilities is the strongest for high lateral forces, which occur e.g. for contact geometries leading to high hunting frequencies and for high values of the friction coefficient. The results also show in some cases a strong impact of the flexibilities on the position of the wheel–rail contact on the running surface of the rail, which is of particular interest with respect to wear simulation.
... However, frequency-domain method gets its limit when comes to nonlinear components in wheel-rail contact and vehicle suspension. To take consideration of the effect of nonlinearities in the track and in wheel-rail contact, train-track interaction models in time domain are widely studied today: in [4][5][6][7][8][9][10][11][12][13][14], the train-track interaction is defined in time domain with the vehicle and/or the track model defined using the finite element method. ...
... Baeza et al. [10] developed a cyclic boundary track model based on modal substructuring. Di Gialleonardo et al. [13] investigated the effect of different levels of track flexibility on running behaviours of both tangent and curved tracks. To investigate the wheelset dynamics, efforts have been made to develop detailed rotating flexible wheelset model. ...
... To investigate the wheelset dynamics, efforts have been made to develop detailed rotating flexible wheelset model. Arnold et al. [5] and Kaiser et al. [7,13], proposed the use of a semi-analytical solution of a rotational symmetric structure in two dimensions, using Navier's equations. Baeza et al. [8,11], on the other hand, modelled the rotating wheelset based on Brown and Shabana's formulation [15,16] of kinematics of flexible rotating structure using a Lagrangian coordinate. ...
A mathematical model of dynamic wheelset–track interaction is proposed in this paper. The model is defined in the time domain in order to introduce and correctly evaluate nonlinear and time-variant phenomena related to the contact model and boundary conditions which play a very important role in rail surface degradation phenomena. The complete model can be divided into three main components: the model of the wheelset, the model of the track and the model of wheel–rail contact forces. In the paper, the wheelset is described as a rotating flexible body, and the gyroscopic and inertial effects associated with wheelset rotation are introduced to this model using an ‘Eulerian’ finite element approach based on 3D quadratic solid elements. The discrete supported track is modelled using finite Timoshenko beam element, which takes into account both the vertical and the lateral rail vibration valid up to 1500 Hz. The wheelset and the track are coupled by means of a contact model based on the nonlinear Hertz and Kalker theories. The flexible components of the interaction model make it possible to describe the train–track dynamics in a relatively high-frequency range, which allows the investigation of specific aspects such as rail corrugation. Some numerical results are presented in terms of contact forces and rail–wheel vibration speed in the paper. The effect of wheelset and track flexibility in specific frequency range on train–track interaction dynamics is briefly discussed.
... In an earlier work by one of the authors [2], a detailed model for a coupled vehicle-track system has been developed. Special features of this model are: 1.) ...
... In contrast to [2] only two model variants are used in the present paper. For the sake of brevity the model, in which the wheelsets are considered as rigid bodies and the simple track model is used, will be referenced as the "rigid model", while the refined model, in which the structural flexibilities of the wheelsets and the rails are taken into account, will be referenced as the "flexible model". ...
... As mentioned before, the influence of the structural flexibilities of wheelsets and rails on the hunting behaviour has been investigated in [2]. Since this impact will be compared with other influences, a short overview of the effects of the structural flexibilities will be given here. ...
... More recently, the need to widen the frequency range of analysis led to the incorporation of wheelset flexibility in the models, leading to a more realistic representation of wheel-rail interaction effects at higher frequencies. For the study of rail corrugation and wheel polygonalisation, generally a modal synthesis is introduced to reduce the size of the problem [5 -7], whereas in case the frequency range of interest is up to 1kHz and above (such as for the study of rolling noise) a Finite Element model of the wheel or the wheelset is used without condensation [8,9]. Only very recently, a further model refinement was introduced to consider the inertial effects due to wheelset rotation [10,11]. ...
... Considering Eqs. (8) and (9) and taking into account that matrix ω is anti-symmetric, the following equation is obtained: ...
... An alternative approach would be to compute the position of the contact point and the contact parameters at each time step of the numerical integration, considering also the deformation of the wheelset as in [9]. However, this approach would entail a much more CPU intensive calculation, whereas the focus in this work is to keep the computational effort as low as possible, while retaining in the model the main effects of wheelset flexibility for the problem studied. ...
Train–track interaction has been extensively studied in the last 40 years at least, leading to modelling approaches that can deal satisfactorily with many dynamic problems arising at the wheel/rail interface. However, the available models are usually not considering specifically the running dynamics of the vehicle in a curve, whereas a number of train–track interaction phenomena are specific to curve negotiation.
The aim of this paper is to define a model for a flexible wheelset running on a flexible curved track. The main novelty of this work is to combine a trajectory coordinate set with Eulerian modal coordinates; the former permits to consider curved tracks, and the latter models the small relative displacements between the trajectory frame and the solid. In order to reduce the computational complexity of the problem, one single flexible wheelset is considered instead of one complete bogie, and suitable forces are prescribed at the primary suspension seats so that the mean values of the creepages and contact forces are consistent with the low frequency curving dynamics of the complete vehicle.
The wheelset model is coupled to a cyclic track model having constant curvature by means of a wheel/rail contact model which accounts for the actual geometry of the contacting profiles and for the nonlinear relationship between creepages and creep forces.
The proposed model can be used to analyse a variety of dynamic problems for railway vehicles, including rail corrugation and wheel polygonalisation, squeal noise, numerical estimation of the wheelset service loads. In this paper, simulation results are presented for some selected running conditions to exemplify the application of the model to the study of realistic train–track interaction cases and to point out the importance of curve negotiation effects specifically addressed in the work.
... The effect of a flexible wheelset was found mainly on the transient forces after the impact due to wheel flat. The effect of the wheelset flexibility was also found to affect the vehicle running behaviour in [12]. ...
... If there are N elements in contact, Eqs. (11) and (12) are discretised to ...
... By superimposing the measured roughness onto the smooth transverse profiles of the wheel and rail, a three-dimensional mapping of the wheel and rail surface geometry in the flat spot region can be obtained, as shown in Fig. 7. This will be used as the profile difference z c input in Eq. (12) for the numerical contact model. It should be noted that, as this was an artificial flat spot, the surface is actually slightly concave which would not occur for a naturally occurring wheel flat. ...
Railway impact noise is caused by discrete rail or wheel irregularities, such as wheel flats, rail joints, switches and crossings. In order to investigate impact noise generation, a time-domain wheel/rail interaction model is needed to take account of nonlinearities in the contact zone. A nonlinear Hertzian contact spring is commonly used for wheel/rail interaction modelling but this is not sufficient to take account of actual surface defects which may include large geometry variations. A time-domain wheel/rail interaction model with a more detailed numerical non-Hertzian contact is developed here and used with surface roughness profiles from field measurements of a test wheel with a flat. The impact vibration response and noise due to the wheel flat are predicted using the numerical model and found to be in good agreement with the measurements. Moreover, compared with the Hertzian theory, a large improvement is found at high frequencies when using the detailed contact model.
... Similar approaches are commonly called as Eulerian approach as opposed to Lagrangian one that is traditionally applied in multibody dynamics. The Eulerian approach is proposed in recent publications (Baeza et al. 2008;Vila et al. 2011;Frigerio, 2010;Kaiser and Popp, 2006;Kaiser et al. 2007;Kaiser, 2012). The main advantage of the Eulerian approach (coordinates) consists in small displacements of contact points between the wheel and rail relative to the local coordinate system of the wheelset. ...
... In papers (Kaiser and Popp, 2006;Kaiser et al. 2007;Kaiser, 2012), flexible displacements of the wheelset are considered relative to the attached coordinate system not rotating around main axis. Cylindrical coordinates are introduced. ...
Two simulation techniques for analyzing flexible wheelset dynamics are presented. They are applied within multibody approach and implemented in "Universal mechanism" software. Equations of wheelset motion are derived using floating frame of reference and component mode synthesis methods. Modal analysis is carried out in external FEA software. Kinematics of a wheel profile is described taking into account flexible displacements of wheelset nodes. In the first techniques, Lagrangian approach is applied to obtain all terms of equation of motion including inertia forces. In the second one, Eulerian approach is simulated in the stage of integration of equation of motion. Non-rotating finite element mesh of the wheelset is considered using the interpolation of flexible displacements in the nodes. The first simulation results obtained using both approaches are presented. These results confirm correctness of the suggested techniques.
... Similar approaches are commonly called as Eulerian approach as opposed to Lagrangian one that is traditionally applied in multibody dynamics. The Eulerian approach is proposed in recent publications ( Baeza et al. 2008;Vila et al. 2011;Frigerio, 2010;Kaiser and Popp, 2006;Kaiser et al. 2007;Kaiser, 2012). The main advantage of the Eulerian approach (coordinates) consists in small displacements of contact points between the wheel and rail relative to the local coordinate system of the wheelset. ...
... In papers (Kaiser and Popp, 2006;Kaiser et al. 2007;Kaiser, 2012), flexible displacements of the wheelset are considered relative to the attached coordinate system not rotating around main axis. Cylindrical coordinates are introduced. ...
The computer simulation of railway wheelset (WS) dynamics taking into account elasticity allows analyzing WSs high frequency oscillations and vibroaccelerations of parts connected with them, modeling wheelsets strain, estimating the WS deformation impact upon force distributions in gears of locomotive drives, and also solving other problems. In the paper there are offered two approaches to the analysis of the dynamics of elastic WSs within the limits of which their finite element models with the rotating and non-rotating grid are under consideration. The WS kinematics is presented as a sum of its motion as an absolute solid together with the jointed coordinates and small elastic displacements related to modal coordinates. There are presented algorithms for the calculation of generalized forces of moving loads in the wheel/rail contact taking into account WS elasticity. The first results of modeling confirming the correctness of the methods offered are shown.
... In order to simplify the large dimension FE integration, the 'Arbitrary Lagrangian-Eulerian' (ALE) approach has been widely used for the flexible wheelset and track model although the term ALE may have not been adopted. To investigate wheelset dynamics, Baeza et al. [3,8,9] and Kaiser et al. [10][11][12][13] proposed the use of the ALE approach introducing an intermediate reference frame that moves with the rotating wheelset, so that a fixed longitudinal position of the contact point can be considered. Baeza et al. [8] evaluated the gradients of the shape function by making a linear transformation of Brown and Shabana's formulation [14,15] of kinematics of flexible rotating structure in a Lagrangian coordinate into a Eulerian coordinate. ...
... As far as track models are concerned, besides modelling the rail as Euler-Bernoulli [16] or Timoshenko beam elements [17,18], a recent trend considers modelling the rail as a generic elastically deformable structure. The track model developed by Kaiser in [12,13] consists of a modal synthesis performed on the rails considered as elastically deformable prismatic structures and assumes harmonic waveforms in longitudinal direction. Since the equations of the rails are written in a non-moving reference system, this method becomes increasingly computationally expensive when longer lengths travelled by the wheelset are considered. ...
A novel numerical model for train-track interaction is proposed in this paper to deal with wheel–rail interface dynamics in high frequency range. The complete model consists a 3D rotating flexible wheelset model, a 3D track model considering the discrete support of the rail and a non-linear, non-Hertzian model of wheel–rail contact. The wheelset and the track models are both defined using an ‘Arbitrary Lagrangian–Eulerian’ Finite Element approach in combination with modal synthesis. This allows an efficient treatment of the problem, compared to a classical Finite Element approach. The proposed model is suitable to represent train-track interaction effects in a frequency range up to 7 kHz thanks to the detailed description of wheelset and rail deformability. Wheel–rail contact forces and rail vibration under excitation produced by different types of railhead irregularity are investigated in the paper, assessing the effect of different models of wheelset and track flexibility. The results obtained show that the outputs of the model mostly relevant to the investigation of rail corrugation and rolling noise, i.e. wheel–rail contact forces and rail vibration, are highly sensitive to the wheelset and track model adopted.
... Commercial MBS software has been commonly used for this assessment, and can include very complex vehicle models including friction elements, non-linear bushings, air-springs and so on. However, track model is usually assumed to be rigid or rigid multi-body that will lead to overestimates of the vehicle critical speed and underestimates of the dynamic contact forces [2,3]. Furthermore, consideration of a flexible track has a significant influence for the stress and frictional power density distributions occurring in the wheel/rail contact [3]. ...
... However, track model is usually assumed to be rigid or rigid multi-body that will lead to overestimates of the vehicle critical speed and underestimates of the dynamic contact forces [2,3]. Furthermore, consideration of a flexible track has a significant influence for the stress and frictional power density distributions occurring in the wheel/rail contact [3]. As a result, track dynamic behaviour plays an important role for the assessment of vehicle dynamics and contact mechanics. ...
Accurate modelling of railway ballasted track dynamics is an important issue for a variety of applications such as the assessment of wheel/rail contact force and critical speed of the vehicle. Track design and assessment against safety and stability criteria can now rely on a number of advanced and validated dynamic models. However, there is a large range of different models that can be used to predict ballasted track dynamics. They vary from fast and simple rigid multi-body models as used in commercial Multibody System approach (MBS) vehicle dynamics calculations, to more complex and expensive three-dimensional (3D) Finite Element (FE) models. This paper investigates the influence of different modelling options up to 2000 Hz for characterising ballasted track dynamics with the aim of providing guidelines for simplifying the model and summarising the advantages and limitations of each option. Five different models, a two-degrees-of-freedom (2 dof) multi-body track model, 2D FE model, 3D FE models with/without consideration of sleeper flexibility, and a 3D FE track model with homogeneous ballast layer are used to represent the ballasted track as a two-layer support and compared against an analytical solution. Consideration is given to the flexibility of the sleepers, inclusion of ballast density and geometry, element discretization level and FE model length. Equivalent parameters to convert input data from one model to another are summarized.
... In the second step, it is checked whether the assumptions are true; if an assumption turns out to be false, the calculated value is corrected before starting the next iteration cycle. Although KVM achieves high computational accuracy, and although it has apparently been successfully integrated into a coupled vehicle-track model [9,24,25], the necessary iterative solution procedure of a high-order system of linear equations, which describes the contact mechanics, still requires an extremely high computational effort. This low computational efficiency becomes even more crucial since the iterative solution of the equations describing the contact mechanics has to be carried out for each wheel-rail contact in each step of the calculation of the multibody model. ...
Computational robustness is a fundamental requirement for wheel–rail dynamic interaction simulations. To improve the computational robustness of a wheel–rail non-Hertzian contact model (NHM) for cases with sudden changes in the wheel–rail initial contact point and lateral extreme of the contact area, in this paper, we develop a robust wheel–rail non-Hertzian contact model (RNHM) by improving the original MKP+FASTSIM model. Four improved strategies are applied in the RNHM: improving the wheel–rail contact angle, the wheel–rail rigid slip, the virtual penetration region reduction factor, and the ellipse-equivalent method for the nonelliptical contact area. The computational accuracy and robustness of the RNHM are validated by taking the robust Kalker variational method (RKVM) and other NHMs without model improvements as references, and the contact behavior between a worn wheel and a standard rail is used to verify the model. The simulation results indicate that the RNHM exhibits good computational accuracy and robustness in both the wheel–rail static contact analysis and the wheel–rail dynamic contact analysis and that all four improvement strategies are effective and necessary for increasing the computational robustness of the NHM. The improvement of the wheel–rail contact angle and the wheel–rail rigid slip significantly improve the calculation robustness of wheel–rail lateral force and wheel–rail longitudinal force, respectively; the improvement of the virtual penetration region reduction factor and the ellipse-equivalent method improves the calculation robustness of both the wheel–rail lateral force and the wheel–rail longitudinal force.
... The wheel-rail contact point should be searched prior to computing the contact forces. The entire process is quite complicated when a flexible wheelset is considered [28,29]. First, the position of the wheel tread should be revised. ...
Irregularities of rail joints ordinarily induce high-frequency impacts on wheel–rail contact systems, which may further influence vehicle–track interaction. In this study, a three-dimensional locomotive-track coupled dynamics model that uses the wheelset flexibility was developed. The wheelset rigid motion and elastic deformation are calculated based on the multi-body dynamics theory and finite element method, respectively. The effectiveness of this model was validated. The effect of wheelset flexibility on locomotive–track interaction due to rail weld irregularities is analysed by comparing the dynamic responses obtained using the rigid model and the proposed rigid–flexible coupled model. The proposed model is applied to the sensitivity analysis of the wheelset response to the rail weld geometry irregularity. The results show that the dominant frequency of the wheel–rail force or axle–box acceleration is 81 Hz, which is the 1st bending modal frequency of the wheelset. The P2 resonance frequency is easily excited owing to impacts of rail weld irregularities, which may induce the formation of locomotive wheel polygonization. The wheelset acceleration was more sensitive to the wavelength than the depth of the rail weld irregularities. The wavelength characteristics can be significant in vehicle vibration-based condition monitoring of rail weld irregularities.
... The influence of the flexible wheelset model was found mainly on the temporal forces after the impact caused by a flat spot. It was revealed in [17] that the wheelset flexibility also influences the behavior of the vehicle in motion. An efficient spatiotemporal model of the wheel-rail interaction was proposed in [18]. ...
... This is formalized by incorporating global deformations in the reference state. The mapping could be decomposed into parts, separating rigid body motion from flexible bending, as used in [30]. Here we focus on the combined result of these different motions. ...
This paper proposes a new way of considering wheel–rail contact in multibody systems simulation that goes beyond the traditional planar constraint and elastic approaches. In this approach, wheel–rail interaction is modelled as a force element with pressures and shear stresses distributed over a contact area that may be curved, supporting conformal contact situations. This by-passes the selection of the contact reference location and reference angle, which are delicate aspects of planar contact approaches.
The idea is worked out introducing the curved reference surface as the new backbone for the computations, instead of the tangent plane used previously in planar contact approaches. The steps are described by which the curved reference is constructed in CONTACT, using generic facilities for markers, grids, and coordinate transformations, by which generic wheel/rail configurations can be analyzed in a fully automated way.
Numerical results show the capabilities of the new method for measured, worn profiles, suppressing discontinuities in the forces when multiple contact patches split or merge. A further application concerns the evaluation of strategies used in planar contact approaches. There we find that the tangent plane’s inclination is of the biggest importance. This should be defined in an averaged way to achieve maximum correspondence to the more detailed curved contact approach.
... The influence of the flexible wheelset model was found mainly on the temporal forces after the impact caused by a flat spot. It was revealed in [17] that the wheelset flexibility also influences the behavior of the vehicle in motion. An efficient spatiotemporal model of the wheel-rail interaction was proposed in [18]. ...
... 24,[30][31][32] Finally, there are other approaches taking advantage of the finite element method to include flexibility in the dynamic analysis of railway vehicles. 23,[33][34][35][36] These approaches decrease the expensiveness of the procedure by representing the track components as unidimensional or lumped elements, and employing reduction techniques, such as modal synthesis, or cyclic boundaries. ...
The interaction between the rolling stock and the infrastructure plays a crucial role in railway vehicle dynamics. The standard approach consists of using a multibody formulation to model the railway vehicles running on simplified tracks. The track model can be rigid, if it comprises only a geometric description of the rail; semi-rigid, if it considers an elastic foundation underneath the rail; or a moving track model, if it comprises a track section underneath each wheelset traveling with the same speed of the vehicle. Despite their computational inexpensiveness, these approaches do not provide a complete representation of track flexibility and disregard coupling effects with the vehicle and among the track components. This work proposes a methodology to automatically generate finite element models of railway tracks comprising its relevant flexible components, i.e., rails, pads, fastening systems, sleepers, and ballast or slab. The finite element mesh is generated based on a parametric description of the track that allows an accurate description of its geometry, including curvature, cross-level, grade, and irregularities. The methodology is demonstrated with a case study in which a track with a complex geometry is loaded with two different approaches. The first approach prescribes moving loads, which is a typical approach used to design or analyze the infrastructure. The second approach applies loads retrieved from the dynamic analysis of a complete vehicle. The results show the benefits of this method and reveal that prescribed loading underestimates the forces resulting from the vehicle dynamics, which is an important issue on curved sections.
... Many suitable train-track interaction models have been developed over the last 40 years, incorporating more recently flexibility in the wheelset in order to widen the frequency range of analysis [1,4]. Finite Element (FE) models have strongly entered in railways research to extend the frequency range above 1 kHz to address the rolling noise phenomenon [5,6] and, only very recently, further works have considered the inertial effects due to wheelset rotation running on a tangent [3] and curved track [7]. ...
As it is well known, there are various phenomena related to railway train–track interaction, some of them caused by the high frequency dynamics of the system, such as rolling noise when the vehicle runs over the track, as well as squeal noise and short-pitch rail corrugation for curved tracks. Due to these phenomena and some others unsolved so far, a large effort has been made over the last 40 years in order to define suitable models to study the train–track interaction. The introduction of flexibility in wheelset and rail models was required to have a more realistic representation of the wheel–rail interaction effects at high frequencies. In recently published train–track interaction models, the rails are modelled by means of Timoshenko beam elements, valid up to 1.5 kHz for lateral rail vibration and up to 2 kHz for vertical vibration. This confines the frequency range of validity for the complete train–track model to 1.5 kHz.
With the purpose of extending the range of validity above 1.5 kHz, a 3D track model based on the Moving Element Method (MEM) is developed in this paper to replace the Timoshenko beam considered in earlier studies, adopting cyclic boundary conditions and Eulerian coordinates. The MEM approach considers a mobile Finite Element (FE) mesh which moves with the vehicle, so the mass of the rail ‘flows’ with the vehicle speed but in the opposite direction through the mesh. Therefore, the MEM permits to fix the contact area in the middle of a finitely long track and to refine the mesh only around the contact area, where the forces and displacements will be more significant. Additionally, a modal approach is adopted in order to reduce the number of degrees of freedom of the rail model. Both strategies lower substantially the computational cost. Simulation results are presented and discussed for different excitation sources including random rail roughness and singularities such as wheel flats. All the simulation cases are carried out for a Timoshenko beam and a 3D MEM track model in order to point out the differences in the contact forces above the range of validity of the Timoshenko beam.
... Effects include centripetal forces while following the curved path (t 1 ) of a beam and due to separation (t 2 to t 3 ) of the oscillator -A survey on bridge-vehicle interaction strongly relies on the knowledge of the mass of the involved car, train or maglev system and may be motivated by vibration and by fatigue issues of the bridge structure; see, e.g., [9,10,22]. -Fatigue is further addressed by investigations on the train-track dynamics, but the unsprung wheel mass is of essential importance here [6,14]. -The dominant aspect to examine the pantograph-catenary interaction is to design the system in such a way that the contact between both components is retained and the energy supply of the train is guaranteed; see, e.g., [7,18,24]. ...
The introduction of moving loads in the Floating Frame of Reference Formulation is presented. We derive the kinematics and governing equations of motion of a general flexible multibody system and their extension to moving loads. The equivalence of convective effects with Coriolis and centripetal forces is shown. These effects are measured numerically and their significance in moving loads traveling at high speed is confirmed. A method is presented to handle discontinuities when moving loads separate from the flexible structure. The method is extended from beam models to general flexible structures obtained by means of the Finite Element Method. An interpolation method for the deformation field of the modal representation of these bodies is introduced.
The work is concluded by application of the method to modern mechanical problems in numerical simulations.
Rail transportation is regarded as a reliable, quick, and secure mode of transportation. The wheel-rail contact interaction is crucial to the railway operation since it is responsible for supporting, traction, braking, and steering of railway vehicles. Improper wheel-rail interactions may produce or exacerbate wheel-rail interface issues such as rolling contact fatigue (RCF) and wear, which can threaten the vehicle’s running safety and stability. A review of the evolution and recent literature on wheel-rail contact mechanics and tribology is presented here. Topics covered include the basics of wheel-rail contact problem and methodologies for modeling both the normal contact (Hertzian and non-Hertzian) and tangential contact (Kalker’s theories including CONTACT and FASTSIM algorithms, Polach’s theory, USETAB program, etc.). The paper also reviewed various effects of contaminants and environmental conditions (water, leaves, sand, temperature, humidity, etc.) in wheel-rail contact. Various wheel-rail empirical adhesion models like the Water-induced low adhesion creep force model (WILAC) model and adhesion models based on elastohydrodynamic lubrication (EHL) theory (Greenwood-Tripp [GT] and Greenwood-Williamson [GW] models) are also reviewed. Lastly, the paper discusses the need and challenges for developing and integrating the wheel-rail non-Hertz contact model and adhesion model, as well as open areas for further research.
The use of detailed wheel/rail contact models has long been frustrated by the complicated preparations needed, to analyse the profiles for the local geometry and creep situation for the planar contact approach. A new software module is presented for this that automates the calculations in a generic way. Building on many components developed by others, this greatly simplifies the running of CONTACT for generic wheel/rail contact situations. Fully 3-d contact search algorithms are implemented. This uses the contact locus approach, that's simplified for wheel-on-rail situations and extended to wheel-on-roller contacts.
A main characteristic of the new module is its extensive use of the multibody formalism, using markers to represent coordinate systems, using a newly designed, generic, object oriented-like software foundation. The contact geometry is analysed twice; first for the location of contact patches, and then for the local geometry of the contact patches. The contact search starts from profiles in their actual, overlapping positions. This yields the extent of interpenetration areas as needed for the potential contact definition. Different strategies may be employed for the tangent plane needed in the planar contact method. Creepages are formed automatically using rigid body kinematics, including wheel and track flexible bending. Numerical results illustrate the viability, generality, and robustness of the approach. The extension to conformal contacts is presented in an accompanying paper.
The stresses between railway wheels and rails can be computed using different types of contact models: simplified methods, half-space-based boundary element approaches and finite element models. For conformal contact situations, particularly the contact between flange root and rail gauge corner, none of these models work satisfactorily. Finite element methods are too slow, half-space approaches ignore the effects of conformality, and simplified approaches schematise the elasticity of the material even further.
Vertical dynamic train–track interaction at high vehicle speeds is investigated in a frequency range from about 20Hz to 2.5kHz. The inertial effects due to wheel rotation are accounted for in the vehicle model by implementing a structural dynamics model of a rotating wheelset. Calculated wheel–rail contact forces using the flexible, rotating wheelset model are compared with contact forces based on rigid, non-rotating models. For a validation of the train–track interaction model, calculated contact forces are compared with contact forces measured using an instrumented wheelset. When the system is excited at a frequency where two different wheelset mode shapes, due to the wheel rotation, have coinciding resonance frequencies, significant differences are found in the contact forces calculated with the rotating and non-rotating wheelset models. Further, the use of a flexible, rotating wheelset model is recommended for load cases leading to large magnitude contact force components in the high-frequency range (above 1.5kHz). In particular, the influence of the radial wheel eigenmodes with two or three nodal diameters is significant.
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