Peter Torstensson

Simulation of dynamic vehicle–track interaction on small radius curves

A time-domain method for the simulation of general three-dimensional dynamic interaction between a vehicle and a curved railway track, accounting for a prescribed relative wheel–rail displacement excitation in a wide frequency range (up to several hundred Hz), is presented. The simulation model is able to capture the low-frequency vehicle dynamics simultaneously due to curving and the high-frequency track dynamics due to the excitation by, for example, the short-pitch corrugation on the low rail. The adopted multibody dynamics formulation considers inertia forces, such as centrifugal and Coriolis forces, as well as the structural flexibility of vehicle and track components. To represent a wheel/rail surface irregularity, isoparametric two-dimensional elements able to describe generally curved surface shapes are used. The computational effort is reduced by including only one bogie in the vehicle model. The influence of the low-frequency vehicle dynamics of the remaining parts of the vehicle is considered by pre-calculated look-up tables of forces and moments acting in the secondary suspension. For a track model taken as rigid, good agreement is observed between the results calculated with the presented model and a commercial software. The features of the model are demonstrated by a number of numerical examples. The influence of the structural flexibility of the wheelset and track on wheel–rail contact forces is investigated. For a discrete rail irregularity excitation, it is shown that the longitudinal creep force is significantly influenced by the wheelset eigenmodes. The introduction of a velocity-dependent friction law is found to induce an oscillation in the tangential contact force on the low rail with a frequency corresponding to the first anti-symmetric torsional mode of the wheelset. Further, under the application of driving moments on the two wheelsets and excitation by a discrete irregularity on the high rail, the frequency content of the tangential contact forces on the low rail is significantly influenced by the P2 resonance as well as by several wheelset eigenmodes.

Rolling Contact Fatigue Prediction for Rails and Comparisons With Test Rig Results

Tests in a full-scale roller rig, a full-scale linear test rig, and a twin-disc machine are numerically evaluated and compared in terms of rolling contact fatigue loading. From previously evaluated contact patch sizes, a Wöhler curve relationship is established and matched towards experimentally established fatigue lives. In addition, non-linear finite-element simulations are carried out. Key data needed for the numerical evaluations, as well as difficulties in translating experimental data to numerical models are highlighted. A key parameter here is the interfacial wheel—rail friction. Additional simulations were carried out to establish the latter. However, the conformal contact in the linear test rig makes such simulations very uncertain.

An Efficient Approach to the Analysis of Rail Surface Irregularities Accounting for Dynamic Train–Track Interaction and Inelastic Deformations

A two-dimensional computational model for assessment of rolling contact fatigue induced by discrete rail surface irregularities, especially in the context of so-called squats, is presented. Dynamic excitation in a wide frequency range is considered in computationally efficient time-domain simulations of high-frequency dynamic vehicle–track interaction accounting for transient non-Hertzian wheel–rail contact. Results from dynamic simulations are mapped onto a finite element model to resolve the cyclic, elastoplastic stress response in the rail. Ratcheting under multiple wheel passages is quantified. In addition, low cycle fatigue impact is quantified using the Jiang–Sehitoglu fatigue parameter. The functionality of the model is demonstrated by numerical examples.

The influence of rail surface irregularities on contact forces and local stresses

The effect of initial rail surface irregularities on promoting further surface degradation is investigated. The study concerns rolling contact fatigue formation, in particular in the form of the so-called squats. The impact of surface irregularities in the form of dimples is quantified by peak magnitudes of dynamic contact stresses and contact forces. To this end simulations of two-dimensional (later extended to three-dimensional) vertical dynamic vehicle–track interaction are employed. The most influencing parameters are identified. It is shown that even very shallow dimples might have a large impact on local contact stresses. Peak magnitudes of contact forces and stresses due to the influence of rail dimples are shown to exceed those due to rail corrugation.

Investigation of railway curve squeal using a combination of frequency- and time-domain models

Railway curve squeal arises from self-excited vibrations during curving. In this paper, a frequency- and a time-domain approach for curve squeal are compared. In particular, the capability of the frequency-domain model to predict the onset of squeal and the squeal frequencies is studied. In the frequency-domain model, linear stability is investigated through complex eigenvalue analysis. The time-domain model is based on a Green’s function approach and uses a convolution procedure to obtain the system response. To ensure comparability, the same submodels are implemented in both squeal models. The structural flexibility of a rotating wheel is modelled by adopting Eulerian coordinates. To account for the moving wheel–rail contact load, the so-called moving element method is used to model the track. The local friction characteristics in the contact zone are modelled in accordance with Coulomb’s law with a constant friction coefficient. The frictional instability arises due to geometrical coupling. In the time-domain model, Kalker’s non-linear, non-steady state rolling contact model including the algorithms NORM and TANG for normal and tangential contact, respectively, is solved in each time step. In the frequency-domain model, the normal wheel/rail contact is modelled by a linearization of the force-displacement relation obtained with NORM around the quasi-static state and full-slip conditions are considered in the tangential direction. Conditions similar to those of a curve on the Stockholm metro exposed to severe curve squeal are studied with both squeal models. The influence of the wheel-rail friction coefficient and the direction of the resulting creep force on the occurrence of squeal is investigated for vanishing train speed. Results from both models are similar in terms of the instability range in the parameter space and the predicted squeal frequencies.

An iterative methodology for the prediction of dynamic vehicle–track interaction and long-term periodic rail wear:

In this study, a versatile numerical method for the prediction of long-term growth of rail roughness is presented and its functionality is demonstrated for the development of rail corrugation on small radius curves. The procedure includes two sub-modules: (1) a time-domain model for the simulation of dynamic vehicle–track interaction in a wide range of frequencies by using a commercial software for multibody dynamics and (2) a post-calculation of sliding wear based on the Archard’s model in combination with a non-Hertzian and transient wheel–rail contact model. The structural flexibility of the wheelset is accounted for by using the finite element method. The rail wear generated by a large number of passing trains is assessed by recurrently updating the rail surface based on the wear depth calculated in each post-processing step. The current work sets out from a previous study in which a model for the prediction of long-term growth of rail roughness on small radius curves was developed in a general-purpose programming language. By transferring the model into a commercial software, the aim is to develop an engineering tool that is more applicable for different operational conditions, such as various vehicle and track designs and track alignments. The proposed method is verified by comparing the simulation results against those obtained with the pre-existing software. Conditions similar to a 120 m radius curve on the Stockholm metro exposed to corrugation growth on the low rail are considered. The corrugation is found to be generated by the leading wheelsets. The prevailing wavelength-fixing mechanisms are identified and discussed.

Hybrid Model for Prediction of Impact Noise Generated at Railway Crossings

A hybrid model for the prediction of impact noise at railway crossings is presented. The hybrid model combines the simulation of vertical wheel‒rail contact force in the time domain and the prediction of sound pressure level using a linear frequency-domain model. The time-domain model uses moving Green’s functions for the vehicle and track models (accounting for wheel flexibility and a discretely supported rail with space-variant beam properties) and a non-Hertzian wheel‒rail contact model. The time-domain and frequency-domain models are coupled based on the concept of an equivalent roughness spectrum. The model is demonstrated by investigating the influence of axle load, vehicle speed and wheel profile on generated impact noise levels. A negligible influence on impact noise is observed for axle loads in the interval 15–25 tonnes. On the other hand, increasing vehicle speed from 80 to 150 km/h, or comparing a nominal S1002 wheel profile with a severely hollow worn profile, result in substantially higher levels of impact noise; for the given wheel and track conditions the differences are in the order of 10 dB(A).

Rail Corrugation Growth on Curves – Measurements, Modelling and Mitigation

The development of rail corrugation (so called rutting corrugation) on a 120 m radius curve on the metro of Stockholm Public Transport was studied by field measurements, laboratory measurements and numerical simulations. The corrugation develops exclusively on the (inner) low rail with wavelengths of about 5 cm and 8 cm. A time-domain model for prediction of long-term roughness growth on small radius curves is developed and validated against measured data. The wavelength-fixing mechanisms of the corrugation are bending eigenmodes of the leading wheelsets. The application of a friction modifier effectively mitigates the problem.

High-Frequency Vertical Wheel–Rail Contact Forces at High Vehicle Speeds –The Influence of Wheel Rotation

Dynamic vehicle–track interaction at high vehicle speeds is investigated in a frequency range from about 20 Hz to 3 kHz. The inclusion of wheel rotation in the vehicle model is investigated by implementing a structural dynamics model of a rotating wheelset in an existing simulation environment. Calculated wheel–rail contact forces using this comprehensive flexible wheelset model are compared with contact forces based on less detailed, non-rotating wheelset models. Load cases including broad-band wheel–rail excitation due to vertical rail irregularities (rail corrugation) and impact excitation caused by a local deviation from the nominal wheel radius (wheel flat) are considered. Viewed from the excitation point, each wheelset resonance peak of multiplicity two splits into two peaks; the separation of the two peaks increases with increasing rotational speed. If the wheelset model is excited at a frequency where two different mode shapes, due to the wheel rotation, have coinciding resonance frequencies, the contact force calculated for the rotating wheelset model differs significantly from those of the non-rotating 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 1.5 kHz). In particular, the influence of the radial wheel eigenmodes with two or three nodal diameters is significant.