Metamodelling of wheel–rail normal contact in railway crossings with elasto-plastic material behaviour

A metamodel considering material plasticity is presented for computationally efficient prediction of wheel–rail normal contact in railway switches and crossings (S&C). The metamodel is inspired by the contact theory of Hertz, and for a given material, it computes the size of the contact patch and the maximum contact pressure as a function of the normal force and the local curvatures of the bodies in contact. The model is calibrated based on finite element (FE) simulations with an elasto-plastic material model and is demonstrated for rail steel grade R350HT. The error of simplifying the contact geometry is discussed and quantified. For a moderate difference in contact curvature between wheel and rail, the metamodel is able to accurately predict the size of the contact patch and the maximum contact pressure. The accuracy is worse when there is a small difference in contact curvature, where the influence of variation in curvature within the contact patch becomes more significant. However, it is shown that such conditions lead to contact stresses that contribute less to accumulated plastic deformation. The metamodel allows for a vast reduction of computational effort compared to the original FE model as it is given in analytical form

Towards simulation-based optimisation of materials in railway crossings

Railway crossings are subjected to an intense load environment\ua0caused by the rail discontinuities needed to accommodate\ua0the passage of wheel flanges in intersecting traffic directions.\ua0This gives rise to high costs associated\ua0with repair and maintenance.\ua0For given traffic conditions, several approaches can be undertaken\ua0to mitigate the material degradation and hence reduce the life\ua0cycle cost.\ua0In the present thesis, the option of selecting a more suitable\ua0crossing material is explored.To obtain a guideline for material selection, the in-track\ua0performance of different materials during the life of a\ua0crossing needs to be predicted.\ua0In this work, an existing simulation methodology is extended to\ua0improve robustness and computational efficiency.\ua0The methodology is able to account for the\ua0dynamic vehicle-track interaction, resolve the\ua0elasto-plastic wheel-rail contact, and account for the main\ua0damage mechanisms related to the running surface of a crossing.In this thesis, the methodology is updated with a metamodel\ua0for plastic wheel-rail normal contact that is introduced to meet\ua0the computational challenge of a large number of finite\ua0element simulations.\ua0The metamodel is inspired by the contact theory of Hertz, and\ua0for a given material it computes the size of the contact patch and the maximum contact pressure as a function of the normal force and the local curvatures of the bodies in contact. The model is calibrated based on finite element simulations with an elasto-plastic material model.\ua0It is shown that the metamodel can yield accurate results\ua0while accounting for the inelastic material behaviour.Furthermore, the simulation methodology is\ua0employed to compare the performance of two rail steel\ua0grades that are used in crossings: the fine-pearlitic steel\ua0R350HT and the austenitic rolled manganese steel Mn13.\ua0A representative load sequence generated by means of Latin hypercube\ua0sampling, taking into account variations in worn wheel profile, vehicle speed and\ua0wheel-rail friction coefficient, is considered.\ua0After 0.8 MGT of traffic, it is predicted that the use of rolled Mn13\ua0will result in approximately two times larger ratchetting strain as\ua0compared to the R350HT

On the influence of crossing angle on long-term rail damage evolution in railway crossings

The rails in railway crossings are subjected to severe load environment leading to degradation of running surface due to wear and accumulated plastic deformation. To compare long-term degradation of three fixed crossings with different crossing angles, nominally designated 1:12, 1:15, and 1:18.5, a multidisciplinary simulation methodology is applied to predict damage of the crossing rail. For a given traffic scenario, including up to 65 MGT of facing move passenger traffic in through route, the results show that damage increases with increasing crossing angle. The ratio between the maximum damage for the crossings with the largest and smallest crossing angles is found to be about three in terms of wear and about two for plastic deformation. Initially high rate of plastic deformation reduces significantly after the first 2–5 MGT, and after 10–30 MGT it approaches a nearly constant value that is significantly lower than the wear rate

Long-term rail profile damage in a railway crossing: Field measurements and numerical simulations

Railway crossings are subjected to a severe load environment leading to a degradation of rail profiles due to wear and accumulated plastic deformation. This damage is the result of the high magnitudes of contact pressure and traction generated in the wheel–rail contact during each wheel transition between wing rail and crossing nose. An extensive measurement campaign has been carried out at a test site in Austria in a particularly severely loaded crossing manufactured from an explosion depth hardened (EDH) manganese steel grade. For an accumulated traffic load of 65 Mega-Gross-Tonnes (MGT), the evolution of profile degradation for 16 cross-sections along the crossing rail has been recorded on multiple occasions. The results from the measurement campaign are used to validate a previously presented multidisciplinary and iterative simulation methodology for the prediction of long-term rail damage. It is shown that the predicted rail profile degradation exceeds the measured degradation for some of the cross-sections but generally a good qualitative agreement is observed. Possible reasons for the higher predicted damage are the uncertain distribution of traffic at the test site and differences in material properties between the crossing in the field and the test specimens used for calibration of the cyclic plasticity model. The influence of the frequency of updating the rail profiles in the iterative simulation methodology, and the compromise between computational cost and the number of load cases accounted for in the applied load sequence, are addressed

Fast simulation of 3D elastic response for wheel–rail contact loading using Proper Generalized Decomposition

To increase computational efficiency, we adopt Proper Generalized Decomposition (PGD) to solve a reduced-order problem of the displacement field for a three-dimensional rail head exposed to different contact scenarios. The three-dimensional solid rail head is modeled as a two-dimensional cross-section, with the coordinate along the rail being treated as a parameter in the PGD approximation. A novel feature is that this allows us to solve the full three-dimensional model with a nearly two-dimensional computational effort. Additionally, we incorporate the distributed contact load predicted from dynamic vehicle-track simulations as extra coordinates in the PGD formulation, using a semi-Hertzian contact model. The problem is formulated in two ways; one general ansatz which considers the treatment of numerous parameters, some of which exhibit a linear influence, and a linear ansatz where multiple PGD solutions are solved for. In particular, situations where certain parameters become invariant are handled. We assess the accuracy and efficiency of the proposed strategy through a series of verification examples. It is shown that the PGD solution converges towards the FE solution with reduced computational cost. Furthermore, solving for the PGD approximation based on load parameterization in an offline stage allows expedient handling of the wheel-rail contact problem online

Modeling and experimental characterization of large biaxial strains and induced anisotropy in pearlitic rail steel

Large shear strains accumulate in the near-surface region under the running band of railway rails. In this region, rolling contact fatigue cracks often initiate, causing major problems for the railway industry. However, characterization of the constitutive and fatigue behavior of the material in this region is difficult due to the high strain gradient. The solution proposed in this thesis is to produce highly deformed cylindrical test bars: An axial-torsion test rig is used to predeform the bars in torsion while subjected to axial compressive loading. The obtained material state is found to be similar to that of field samples of rails at a depth between 50 and 100 μm. Using this predeformation method, the evolution of the yielding behavior is evaluated. The predeformed test bars are re-turned and drilled out to form thin-walled test bars, which can be used to measure yield surfaces. It is found that the degree of anisotropy quickly evolves with increasing predeformation and then saturates. Furthermore, the quadratic Hill yield criterion describes the anisotropic yield surfaces well. To better optimize rail maintenance and material selection, there is an industrial need for a model capable of predicting rail deterioration. An important component of such a model is an accurate material model that captures the relevant physical phenomena. A hyperelasto-plastic framework for finite strain material models is adopted in this thesis. As a first study, the predeformation method was simulated using 2D axisymmetric elements. It is shown that very good results can be achieved by using material models with advanced kinematic hardening laws. Next, an improved simulation methodology for axial, torsional and pressure loading is developed, resulting in an efficient 1D formulation. This methodology includes material removal to simulate the re-machining of the test bars into tubular bars. Using this methodology, 3 different distortional hardening models are evaluated in terms of how well they fit and predict the experimental data. The two phenomenological models perform better than the crystal plasticity model. However, these models should be further developed to improve their predictive abilities

Wheel–Rail Impact Loads and Track Settlement in Railway Crossings

Turnouts (Switches & Crossings, S&C) are critical components of a railway track requiring regular maintenance and generating high life cycle costs. A main driver for the high maintenance costs is the need to repair and replace switch rails and crossings as these components are subjected to a severe load environment. Dynamic wheel--rail contact forces with high magnitudes are often generated in the switch and crossing panels due to the discontinuities in rail profiles, resulting in a degradation of track geometry. One critical contribution to the track geometry degradation is track settlement. It is a phenomenon where the horizontal level of the ballasted track substructure decreases in height over time when subjected to traffic loading. Due to the design of the turnout and the variation in track support conditions, the load transferred into the track bed is not uniform and the resulting variation in settlement leads to irregularities in track geometry. Poor quality in track geometry induces higher dynamic wheel--rail contact forces and increases the degradation rate resulting in further differential track settlement, and possibly increased wear, plastic deformation and rolling contact fatigue of the rails. Thus, it is important to understand how settlement evolves under repeated loading to support product development and maintenance procedures of S&C, to provide a more uniform load distribution on the ballast and a more stable track geometry. The current work aims to provide a methodology to increase the understanding of track settlement in railway turnouts. Different numerical models are used to simulate the dynamic vehicle--track interaction and predict the wheel--rail impact loads in the crossing panel.The calculated contact pressure between sleepers and ballast is used as input for calculating the track settlement. Both empirical and constitutive settlement models are applied to predict settlement for a large number of load cycles (wheel passages). The material behaviour of the track substructure under repeated loading is investigated using a three-dimensional finite element model. A parameter study is performed to determine the influence of train and track parameters on the impact load generated at the crossing. The investigated train parameters include vehicle speed, lateral wheelset position and wheel profile, while the track parameters are rail pad stiffness, sleeper base area and implementation of under sleeper pads (USP). The study shows that the magnitude of the impact load is influenced more by the wheel--rail contact geometry than by the rail pad stiffness. Among the investigated parameter combinations, the most effective mitigation measures to reduce sleeper--ballast contact pressure are the implementation of USP and increasing the sleeper base area

Safety investigation of partially filled railway tank cars

The adverse effects of liquid cargo slosh on dynamic responses and safety performance of partially filled road vehicles are well known. The general-purpose railway tank car may also encounter partial fill conditions due to variations in density of the liquid cargo and track load limit. The additional slosh forces and moments from the partially filled state of the tank may further affect the wheel-rail forces, dynamic response, and safety of the rail vehicles. The coupled sloshing cargo and vehicle system dynamics have been investigated in only a few studies because of complexity and high computation demand. The objective of this study is to investigate the influence of liquid cargo sloshing on the dynamic performance of railway tank cars. Other than detail modelling, the topics of lateral dynamics, curving performance and switch passing responses of partially filled railway tank cars through a co-simulation approach have been addressed in this dissertation. The nonlinear damping characteristics of friction wedges in the secondary suspension of a freight wagon are investigated considering non-smooth unilateral contact, multi-axis motions, slip-stick conditions, and geometry of the wedges. The parameters of the contact pairs within the suspension were identified to achieve smooth and efficient numerical solutions while ensuring adequate accuracy. The friction wedge model was integrated into the multibody dynamic model of a three-piece bogie to study the effects of wedge properties on hunting characteristics. The resulting 114-degrees-of-freedom wagon model incorporated constraints due to side bearings, axle boxes, and the centre plates, while the wheel-rail contact forces were obtained using the FastSim algorithm. The simulation results were obtained to study hunting characteristics of the wagon in terms of critical speed and the predominant oscillation frequency. The study also examined the effects of wedge friction and geometry on lateral stability characteristics of the freight car. The results showed subcritical Hopf bifurcation of dynamic responses of the wagon. The parametric study showed an increase in the wedge angle, friction coefficient, and springs free length to yield higher critical speed. The validated dynamic model of the wagon is further used to investigate the effects of liquid sloshing on hunting speed of partly filled tank car. An analytical liquid slosh model is used to capture dynamic response of the liquid cargo in a horizontal cylindrical tank using up to five fundamental modes in the roll plane under lateral as well as yaw motions of the tank car. The liquid slosh model is co-simulated with the comprehensive nonlinear model of a railway tank car to evaluate the lateral dynamic response of the tank car. The results suggest that fill levels and the corresponding slosh forces can adversely affect the lateral stability performance and yield lower critical hunting speed of railway tank car. The influence of liquid cargo sloshing on the dynamic performance of railway tanker in a typical curve negotiation is further examined using the proposed coupled co-simulation model. The performance measures include car roll angle, unloading of the wheelset and derailment quotient. The results clearly demonstrate that partial state of the tank car and resulting slosh could lead to a significantly larger dynamic response of the system and may result in separation of wheel and rail contact at lower forward speed in comparison to the rigid cargo assumption. Dynamic simulations of partially filled railway tank cars without fluid slosh consideration will thus lead to underestimation of overturning critical conditions on the curving manoeuvres. Above performance measures in a switch-passing manoeuvre is finally examined for different fill ratios and switch geometries. The results obtained for the coupled vehicle and liquid slosh model clearly showed strong interactions between the switch-induced transient liquid slosh and vehicle dynamics for the partial-fill ratio of 60% and less. The effect of fluid slosh on the car body roll angle and wheelset unloading ratio was observed to diminish with fill ratio above 90%. Neglecting the contributions due to dynamic slosh force and roll moment may lead to overestimation of the critical speed in switch-passing manoeuvres if the car is partially filled