Dynamic Interaction of Vehicles with Tracks and Roads

The principle problems of the new developing scientific field - dynamics of vehicles, tracks and roads - are defined. Basic theoretical models for the analysis of railway and road vehicles, tracks and roads and principle methods of their solution are shown. The dynamic interactions between vehicles and routes are emphasized and several basic equations are given to show the behaviour of their elements. The effect of some parameters, like speed, track or roads irregularities etc. is explained. The possibilities are described how to simplify the theoretical models to obtain a simple solution.     

On the Design and Development of a Magneto-Rheological Mount

This paper evaluates the performance of a Magneto-Rheological (MR) mount. The mount incorporates MR fluid in a conventional fluid mount to open and close an inertia track between the fluid chambers of the mount. It is shown that such switching of the inertia track improves the mount's isolation effect by eliminating the large transmissibility peak that commonly exists at frequencies larger than the notch frequency for conventional fluid mounts. The switching frequencies of the MR mount are evaluated based on the parameters of the mount. A simple control scheme for switching the mount between the open and closed states is proposed, and the performance of the controlled mount is compared with conventional mounts. A sensitivity analysis is conducted to evaluate the effect of parameter errors in estimating the switching frequencies and mount performance. The results show that the switching frequencies can be accurately determined from mount parameters that are easily measured or estimated.     

Vibrations Generated by Rail Vehicles: A Mathematical Model in the Frequency Domain

Movement of railway vehicles generates mechanical vibrations of a wide range of frequency. Depending on track materials, dissipation in form of viscous and hysteretic damping is present, and stiffness depends on strain-rate. In a previous paper (Castellani et al., 1998), a mathematical model to describe track materials has been developed in the frequency domain. The present paper applies this model, and attempts an analytical formulation of vehicle-track and soil interaction in the frequency domain. Rail vibrations during the passage of a vehicle are generated by three families of forces: a) the weight of the moving vehicle, b) the inertial reaction of the vehicle under the effect of corrugations over an undeformable rail, and, c) the vehicle inertial forces due to displacements of the rail. The first two groups of forces do not depend on the rail displacement, and the related mathematical formulation is a simple problem of forces at a mobile point of application. Formulation of the vehicle inertial forces, related to the rail vibration, requires reference to the acceleration of the rail, as seen by an observer in motion with the vehicle itself. Moreover, it is necessary to express the equilibrium equation of two dynamic systems, the vehicle and the track, at a the movable point of contact. There is no straight numerical procedure to solve this equation in the frequency domain. In the paper two theoretical propositions (Fryba, 1988; Grassie et al., 1982) are revisited with reference to the effect of the transit of a single wheel. Fryba infers that, in the absence of corrugations, the forces c) are null. Grassie et al. (1982) present a mathematical formulation of the interaction between wheel and rail, at mobile point of contact. At each position, the interaction force is of impulsive type. They presume that for a corrugation of harmonic type, of wavelength ?, the wheel is subject to a harmonic motion, of the frequency f = V/?, where V is the wheel velocity. All other frequency components, due to the impulse, are disregarded. Both these assumptions are shown to be inconsistent from a theoretical point of view, however they suggest suitable approaches to the solution.     

On the Design and Development of a Magneto-Rheological Mount

This paper evaluates the performance of a Magneto-Rheological (MR) mount. The mount incorporates MR fluid in a conventional fluid mount to open and close an inertia track between the fluid chambers of the mount. It is shown that such switching of the inertia track improves the mount's isolation effect by eliminating the large transmissibility peak that commonly exists at frequencies larger than the notch frequency for conventional fluid mounts. The switching frequencies of the MR mount are evaluated based on the parameters of the mount. A simple control scheme for switching the mount between the open and closed states is proposed, and the performance of the controlled mount is compared with conventional mounts. A sensitivity analysis is conducted to evaluate the effect of parameter errors in estimating the switching frequencies and mount performance. The results show that the switching frequencies can be accurately determined from mount parameters that are easily measured or estimated.     

Vehicle-Track Dynamics in the Mid-Frequency Range

During the last years railway companies have observed increasing problems with track damage like rail corrugation, deterioration of ballast or unround wheels. Since the origin of these damages is suspected in the mid-frequency dynamics, research activities in the frequency range from 50 up to 500 Hz have been initiated. The article demonstrates that in comparison to the low and high frequency range the knowledge about physical effects in the mid-frequency range is poor. Apart from a historical literature review on vehicle and track modelling, recently published methods and models are collated and problems in their mathematical treatise are mentioned. Regarding the vehicle, the paper shows the development starting with Klingel's massless wheelset model and ending with sophisticated elastic multibody system models. Concerning the track, different mathematical approaches in frequency and time domain are compared. In the mid-frequency range the pad, ballast and subsoil properties play an important role. Hence, the missing of experimentally validated models of these components is crucial. First attempts have been performed, which take into account the subsoil as layered half-space and the ballast as an assembly of viscoelastic rods. Besides the short time dynamics the article gives also an overview of the modelling of the wear phenomena mentioned above. An investigation of such long-term effects requires complex models of the entire vehicle-track system. The few wear models found in literature are discussed and first results are mentioned.     

Vehicle-Track Dynamics in the Mid-Frequency Range

During the last years railway companies have observed increasing problems with track damage like rail corrugation, deterioration of ballast or unround wheels. Since the origin of these damages is suspected in the mid-frequency dynamics, research activities in the frequency range from 50 up to 500 Hz have been initiated. The article demonstrates that in comparison to the low and high frequency range the knowledge about physical effects in the mid-frequency range is poor. Apart from a historical literature review on vehicle and track modelling, recently published methods and models are collated and problems in their mathematical treatise are mentioned. Regarding the vehicle, the paper shows the development starting with Klingel's massless wheelset model and ending with sophisticated elastic multibody system models. Concerning the track, different mathematical approaches in frequency and time domain are compared. In the mid-frequency range the pad, ballast and subsoil properties play an important role. Hence, the missing of experimentally validated models of these components is crucial. First attempts have been performed, which take into account the subsoil as layered half-space and the ballast as an assembly of viscoelastic rods. Besides the short time dynamics the article gives also an overview of the modelling of the wear phenomena mentioned above. An investigation of such long-term effects requires complex models of the entire vehicle-track system. The few wear models found in literature are discussed and first results are mentioned.     

Experimental and numerical investigation of the effect of rail corrugation on the behaviour of rail fastenings

This paper presents the results of a detailed investigation of the effects of rail corrugation on the dynamic behaviour of metro rail fastenings, obtained from extensive experiments conducted on site and from simulations of train–track dynamics. The results of tests conducted with a metro train operating on corrugated tracks are presented and discussed first. A three-dimensional (3D) model of the metro train and a slab track was developed using multi-body dynamics modelling and the finite element method to simulate the effect of rail corrugation on the dynamic behaviour of rail fastenings. In the model, the metro train is modelled as a multi-rigid body system, and the slab track is modelled as a discrete elastic support system consisting of two Timoshenko beams for the rails, a 3D solid finite element (FE) model for the slabs, periodic discrete viscoelastic elements for the rail fastenings that connect the rails to the slabs, and uniformly viscoelastic elements for the subgrade beneath the slabs. The proposed train–track model was used to investigate the effects of rail corrugation on the dynamic behaviour of the metro track system and fastenings. An FE model for the rail fastenings was also developed and was used to calculate the stresses in the clips, some of which rupture under the excitation of rail corrugation. The results of the field experiments and dynamics simulations provide an insight into the root causes of the fracture of the clips, and several remedies are suggested for mitigating strong vibrations and failure of metro rail fastening systems.     

Effects of rail thermal stress on the dynamic response of vehicle and track

A new method is proposed to obtain the dynamic responses of the vehicle–track coupling system under the conditions of rail thermal stress changes in high-speed railways. Exact models are established with different rail longitudinal forces, in which multibody dynamic models are used for vehicles and the direct stiffness method for structures. In order to provide a general, simple and flexible formulation to express longitudinal stress distribution, the accurate model of long slab track consists of many small units with parameters which can be initialised separately. The exact analytical equation of track frequency and modal function was obtained by the transition matrix method, which can be used in calculating the dynamic response of wheel–rail coupling model. The proposed model is verified through comparisons with other classical solutions. Under the influence of train velocities and track irregularities, the specific vibration performances that frequency shifted and amplitude peak enhanced with thermal force are demonstrated through examples. The results show that the response analyses of vehicle and track have great application potentiality for fast estimation of the rail longitudinal stress.     

Modelling of wheels and rail discontinuities in dynamic wheel-rail contact analysis

A classification of wheel-rail contact is given. Difference is made between modelling of a running wheel with continuous single-point-contact, as is common practice in wheel-rail contact analysis, and a wheel with transient double- or multi-point-contact, which may occur for rail irregularities with curvatures larger than that of the wheel circumference. It is shown that application of the first model for these irregularities will strongly underestimate the contact forces as it does not describe occurring mechanisms correctly. Further, it is shown that in principle it is not possible to describe the second type of contact fully correct with a lumped wheel model. Both wheel models are formulated mathematically for some basic contact cases. Afterwards, results are applied to a linear track model. Analytical closed-form solutions are found in the frequency domain for arbitrary type of contact and numerically transformed to the time domain. Finally, the necessity is shown to avoid situations where transient multiple-point-contact may occur (like rail joints) in practice.     

Modelling of wheels and rail discontinuities in dynamic wheel–rail contact analysis

A classification of wheel–rail contact is given. Difference is made between modelling of a running wheel with continuous single-point-contact, as is common practice in wheel–rail contact analysis, and a wheel with transient double- or multi-point-contact, which may occur for rail irregularities with curvatures larger than that of the wheel circumference. It is shown that application of the first model for these irregularities will strongly underestimate the contact forces as it does not describe occurring mechanisms correctly. Further, it is shown that in principle it is not possible to describe the second type of contact fully correct with a lumped wheel model. Both wheel models are formulated mathematically for some basic contact cases. Afterwards, results are applied to a linear track model. Analytical closed-form solutions are found in the frequency domain for arbitrary type of contact and numerically transformed to the time domain. Finally, the necessity is shown to avoid situations where transient multiple-point-contact may occur (like rail joints) in practice.     

Application of Sensitivity Analysis to the Development of High Performance Adaptive Hydraulic Engine Mounts

Summary In this paper, the sensitivity analysis is applied to the development of high performance adaptive hydraulic mounts. The analysis allows us to select the most effective design parameters for tuning an adaptive mount to different road and engine conditions. It is shown that in the low frequency road excitation, the upper chamber compliance and inertia of the fluid column in the inertia track are the most influential properties in changing the dynamic stiffness of the hydraulic mount. These properties for the high frequency engine excitations are the upper compliance and the inertia of the fluid column of the decoupler. For tuning the adaptive mount to different road and engine excitation, a global optimization technique is used to find the magnitude of the adjusting parameters to minimize objective functions in low and high frequency excitations. The results indicate significant improvement over conventional hydraulic mounts. It is further shown that when the upper compliance is used as the adjusting parameter, a simple on-off control which is triggered by the engine revolution and vehicle speed is sufficient for tuning the adaptive mount.     

Application of Sensitivity Analysis to the Development of High Performance Adaptive Hydraulic Engine Mounts

Summary In this paper, the sensitivity analysis is applied to the development of high performance adaptive hydraulic mounts. The analysis allows us to select the most effective design parameters for tuning an adaptive mount to different road and engine conditions. It is shown that in the low frequency road excitation, the upper chamber compliance and inertia of the fluid column in the inertia track are the most influential properties in changing the dynamic stiffness of the hydraulic mount. These properties for the high frequency engine excitations are the upper compliance and the inertia of the fluid column of the decoupler. For tuning the adaptive mount to different road and engine excitation, a global optimization technique is used to find the magnitude of the adjusting parameters to minimize objective functions in low and high frequency excitations. The results indicate significant improvement over conventional hydraulic mounts. It is further shown that when the upper compliance is used as the adjusting parameter, a simple on-off control which is triggered by the engine revolution and vehicle speed is sufficient for tuning the adaptive mount.     

High-frequency random vibration analysis of a high-speed vehicle–track system with the frequency-dependent dynamic properties of rail pads using a hybrid SEM–SM method

A hybrid Spectral Element Method (SEM)–Symplectic Method(SM) method for high-efficiency computation of the high-frequency random vibrations of a high-speed vehicle–track system with the frequency-dependent dynamic properties of rail pads is presented. First, the Williams-Landel-Ferry (WLF) formula and Fractional Derivative Zener (FDZ) model were, respectively, applied for prediction and representation of the frequency-dependent dynamic properties of Vossloh 300 rail pads frequently used in China's high-speed railway. Then, the proposed hybrid SEM–SM method was used to investigate the influence of the frequency-dependent dynamic performance of Vossloh 300 rail pads on the high-frequency random vibrations of high-speed vehicle–track systems at various train speeds or different levels of rail surface roughness. The experimental results indicate that the storage stiffness and loss factors of Vossloh 300 rail pad increase with the decrease in dynamic loads or the increase in preloads within 0.1–10,000?Hz at 20°C, and basically linearly increase with frequency in a logarithmic coordinate system. The results computed by the hybrid SEM–SM method demonstrate that the frequency-dependent viscous damping of Vossloh 300 rail pads, compared with its constant viscous damping and frequency-dependent stiffness, has a much more conspicuous influence on the medium-frequency (i.e. 20–63?Hz) random vibrations of car bodies and rail fasteners, and on the mid- (i.e. 20–63?Hz) and high-frequency (i.e. 630–1250?Hz) random vibrations of bogies, wheels and rails, especially with the increase in train speeds or the deterioration of rail surface roughness. The two sensitive frequency bands can also be validated by frequency response function (FRF) analysis of the proposed infinite rail–fastener model. The mid and high frequencies influenced by the frequency-dependent viscous damping of rail pads are exactly the dominant frequencies of ground vibration acceleration and wheel rolling noise caused by high-speed railways, respectively. Even though the existing time-domain (or frequency-domain) finite track models associated with the time-domain (or frequency-domain) fractional derivative viscoelastic (FDV) models of rail pads can also be used to reach the same conclusions, the hybrid SEM–SM method in which only one element is required to compute the high-order vibration modes of infinite rail is more appropriate for high-efficiency analysis of the high-frequency random vibrations of high-speed vehicle–track systems.     

Simulation of dynamic interaction between train and railway turnout

Dynamic train–track interaction is more complex in railway turnouts (switches and crossings) than that in ordinary tangent or curved tracks. Multiple contacts between wheel and rail are common, and severe impact loads with broad frequency contents are induced, when nominal wheel–rail contact conditions are disturbed because of the continuous variation in rail profiles and the discontinuities in the crossing panel. The absence of transition curves at the entry and exit of the turnout, and the cant deficiency, leads to large wheel–rail contact forces and passenger discomfort when the train is switching into the turnout track. Two alternative multibody system (MBS) models of dynamic interaction between train and a standard turnout design are developed. The first model is derived using a commercial MBS software. The second model is based on a multibody dynamics formulation, which may account for the structural flexibility of train and track components (based on finite element models and coordinate reduction methods). The variation in rail profile is accounted for by sampling the cross-section of each rail at several positions along the turnout. Contact between the back of the wheel flange and the check rail, when the wheelset is steered through the crossing, is considered. Good agreement in results from the two models is observed when the track model is taken as rigid.     

On the effect of unsupported sleepers on the dynamic behaviour of a railway track

The effect of unsupported sleepers on the dynamic behaviour of a railway track is studied based on vehicle–track dynamic interaction theory, using a model of the track as a Timoshenko beam supported on a periodic elastic foundation. Considering the vehicle's running speed and the number of unsupported sleepers, the track dynamic characteristics are investigated and verified in the time and frequency domains by experiments on a 1:5 scale model wheel–rail test rig. The results show that when hanging sleepers are present, leading to a discontinuous and irregular track support, additional wheel–rail interaction forces are generated. These forces increase as further sleepers become unsupported and as the vehicle's running speed increases. The adjacent supports experience increased dynamic forces which will lead to further deterioration of track quality and the formation of long wavelength track irregularities, which worsen the vehicles’ running stability and riding comfort. Stationary transfer functions measurements of the dynamic behaviour of the track are also presented to support the findings.     

Time Domain Model of the Vertical Dynamics of a Railway Track up to 5 kHz

The modelling of the vertical dynamics of a track at high frequencies requires rather complex approaches to take into account section deformations. Validation is usually made by comparing computed frequency responses with measured ones. In this study an experimental model of a railway track is proposed based on the analysis of recorded time histories of impact excitations and the corresponding vibrations of the rail with auloregressive (AR) techniques. Measurements are used not only as a convergence parameter that the model must approach, but are also entirely used to describe the dynamic behaviour of the rail in the frequency range 150 / 5000 Hz. Frequency response functions are reconstructed with a very high fidelity but the model obtained is not general, as it is applicable only to the measured track section under the hypothesis of linearity. The measurement details, the construction and the validation of the model are shown in this paper.     

Modelling of Railway Track and Vehicle/Track Interaction at High Frequencies

A review is presented of dynamic modelling of railway track and of the interaction of vehicle and track at frequencies which are sufficiently high for the track's dynamic behaviour to be significant. Since noise is one of the most important consequences of wheel/rail interaction at high frequencies, the maximum frequency of interest is about 5kHz: the limit of human hearing. The topic is reviewed both historically and in particular with reference to the application of modelling to the solution of practical problems. Good models of the rail, the sleeper and the wheelset are now available for the whole frequency range of interest. However, it is at present impossible to predict either the dynamic behaviour of the railpad and ballast or their long term behaviour. This is regarded as the most promising area for future research.