Dynamic Response of a Six-axle Locomotive to Random Track Inputs

Spectral analysis techniques are employed to analyze the dynamic response of a six-axle locomotive on tangent track to vertical and lateral random track irregularities. The locomotive is represented by a thirty-nine (39) degrees of freedom model. A linear model is employed by considering small displacements, linear suspension elements and a linear theory for the wheel-rail interaction. Power spectral densities of displacements, velocities and accelerations and the statistical average frequencies of the system are obtained for each degree of freedom. Comparison of the calculated dominating frequencies with existing experimental values shows good agreement. The technique of spectral analysis is an effective tool for model validation, and for the determination of rail vehicle response to track irregularities. The probability functions for the response can be used as a measure for the ride quality of rail vehicles and for the study of fatigue damage of components.     

Direct Covariance Analysis for the Calculation of Creepages and Creep-Forces for Various Bogies on Straight Track with Random Irregularities

SUMMARY

In this paper creep-forces and creepages for an ICE express train coach and an electric locomotive BR 120 of the DB on straight track with random irregularities are investigated. The calculations are made with the multibody program MEDYNA using direct covariance analysis. One of the aims of this article is to emphasize the advantages of the direct covariance method (time domain) compared with the power spectral density method (frequency domain).     

Random Response of Tractor-Semitrailer System

SUMMARY

This work describes an analytical study of the dynamic behaviour of a tractor-semitrailer vehicle. A digital computer simulation was used to describe the longitudinal, vertical, and pitching motions of the vehicle travelling over a stationary random road surface. A man-seat model was also incorporated into the simulation. Vehicle response to road irregularities has been studied by assuming two different roads for loaded and unloaded cases.

Numerical results are presented for vehicle, showing system eigenvalues, power spectral densities and root mean square values of the linear and angular accelerations and displacements. Vehicle acceleration response is compared with the ISO riding comfort standard. All results for the loaded and unloaded cases and for smooth and rough roads indicated that an uncomfortable ride would result from vehicle response.     

Lateral Vibration of Railway Bridge-Vehicle System Caused by Track Irregularities

SUMMARY

The lateral vibration of the bridge-vehicle system caused by track irregularities is investigated in this paper by means of frequency spectral analysis method. A railway cable-stayed bridge is taken as the model to study, on which a theoretical analysis is made to compare with the practical results measured. The method proves to be feasible. Then it is applied to studying the interaction between a long-span railway cable-stayed bridge and a freight car as well as the effect of track irregularities on the dynamic characteristics of the bridge-vehicle system, thus leading to a couple of conclusions of considerable significance.     

Extended applications of track irregularity probabilistic model and vehicle–slab track coupled model on dynamics of railway systems

Track irregularities are inevitably in a process of stochastic evolution due to the uncertainty and continuity of wheel–rail interactions. For depicting the dynamic behaviours of vehicle–track coupling system caused by track random irregularities thoroughly, it is a necessity to develop a track irregularity probabilistic model to simulate rail surface irregularities with ergodic properties on amplitudes, wavelengths and probabilities, and to build a three-dimensional vehicle–track coupled model by properly considering the wheel–rail nonlinear contact mechanisms. In the present study, the vehicle–track coupled model is programmed by combining finite element method with wheel–rail coupling model firstly. Then, in light of the capability of power spectral density (PSD) in characterising amplitudes and wavelengths of stationary random signals, a track irregularity probabilistic model is presented to reveal and simulate the whole characteristics of track irregularity PSD. Finally, extended applications from three aspects, that is, extreme analysis, reliability analysis and response relationships between dynamic indices, are conducted to the evaluation and application of the proposed models.     

Influence of uneven rail irregularities on the dynamic response of the railway track using a three-dimensional model of the vehicle–track system

A mathematical model of the vehicle–track interaction is developed to investigate the coupled behaviour of vehicle–track system, in the presence of uneven irregularities at left/right rails. The railway vehicle is simplified as a 3D multi-rigid-body model, and the track is treated as the two parallel beams on a layered discrete support system. Besides the car-body, the bogies and the wheel sets, the sleepers are assumed to have roll degree of freedom, in order to simulate the in-plane rotation of the components. The wheel–rail interface is treated using a nonlinear Hertzian contact model, coupling the mathematical equations of the vehicle–track systems. The dynamic interaction of the entire system is numerically studied in time domain, employing Newmark's integration method. The track irregularity spectra of both the left/right rails are taken into account, as the inputs of dynamic excitations. The dynamic responses of the track system induced by such irregularities are obtained, particularly in terms of the vertical (bounce) and roll displacements. The numerical model of the present research is validated using several benchmark models reported in the literature, for both the smooth and unsmooth track conditions. Four sample profiles of the measured rail irregularities are considered as the case studies of excitation sources, examining their influences on the dynamic behaviour of the coupled system. The results of numerical simulations demonstrate that the motion of track system is significantly influenced by the presence of uneven irregularities in left/right rails. Dynamic response of the sleepers in the roll direction becomes more sensitive to the rail irregularities, as the unevenness severity of the parallel profiles (quantitative difference between left and right rail spectra) is increased. The severe geometric deformation of the track in the bounce–pitch–roll directions is mainly related to such profile unevenness (cross-level) in left/right rails.     

Dynamic Interaction between Wheel and Track - A Parametric Search towards an Optimal Design of Rail Structures

SUMMARY

The dynamic vertical interaction between a moving rigid wheel and a flexible railway track is investigated. A round and smooth wheel tread and an initially straight and noncorrugated rail surface are assumed in the present optimization study. A symmetric linear three-dimensional beam structure model of a finite portion of the track is suggested including rail, pads, sleepers and ballast with spatially nonproportional damping. The full interaction problem is numerically solved by use of an extended state-space vector approach in conjunction with a complex modal superposition for the track. Transient bending stresses in sleepers and rail are calculated. The influence of seven selected track parameters on the dynamic behaviour of the track is investigated. A two-level fractional factorial design method is used in the search for a combination of numerical levels of these parameters making the maximum bending stresses a minimum.     

Energy Dissipation Due to Vehicle/Track Interaction

SUMMARY

The effects of track irregularities and wheel profile on the amount of energy dissipated in railroad freight vehicles is examined. A nonlinear computational model is used to determine the average dissipation in the vehicle suspension and the wheel/rail contact patches. This dissipation is a component of the total resistance force acting on the vehicle. Parametric results are presented showing the effects of track geometry, wheel profile, suspension design, and hunting on train resistance. Track geometry studies consider the effects of track quality and curving. The AAR 1:20 wheel profile and the Heumann wheel profile are compared under various operating conditions. Compared with the Heumann profile, the AAR 1:20 profile is shown to have lower average resistance on good quality tangent track, but higher average resistance in steady curves. A trade-off exists between the two profiles when dynamic curve entry is considered.     

Influence of long-wavelength track irregularities on the motion of a high-speed train

Vertical track irregularities over viaducts in high-speed rail systems could be possibly caused by concrete creep if pre-stressed concrete bridges are used. For bridge spans that are almost uniformly distributed, track irregularity exhibits a near-regular wave profile that excites car bodies as a high-speed train moves over the bridge system. A long-wavelength irregularity induces low-frequency excitation that may be close to the natural frequencies of the train suspension system, thereby causing significant vibration of the car body. This paper investigates the relationship between the levels of car vibration, bridge vibration, track irregularity, and the train speed. First, this study investigates the vibration levels of a high-speed train and bridge system using 3D finite-element (FE) transient dynamic analysis, before and after adjustment of vertical track irregularities by means of installing shimming plates under rail pads. The analysis models are validated by in situ measurements and on-board measurement. Parametric studies of car body vibration and bridge vibration under three different levels of track irregularity at five train speeds and over two bridge span lengths are conducted using the FE model. Finally, a discontinuous shimming pattern is proposed to avoid vehicle suspension resonance.     

Robust control and actuator dynamics compensation for railway vehicles

A robust controller is designed for active steering of a high speed train bogie with solid axle wheel sets to reduce track irregularity effects on the vehicle’s dynamics and improve stability and curving performance. A half-car railway vehicle model with seven degrees of freedom equipped with practical accelerometers and angular velocity sensors is considered for the H_∞ control design. The controller is robust against the wheel/rail contact parameter variations. Field measurement data are used as the track irregularities in simulations. The control force is applied to the vehicle model via ball-screw electromechanical actuators. To compensate the actuator dynamics, the time delay is identified online and is used in a second-order polynomial extrapolation carried out to predict and modify the control command to the actuator. The performance of the proposed controller and actuator dynamics compensation technique are examined on a one-car railway vehicle model with realistic structural parameters and nonlinear wheel and rail profiles. The results showed that for the case of nonlinear wheel and rail profiles significant improvements in the active control performance can be achieved using the proposed compensation technique.     

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

Abstract

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.     

Critical Speed and Limit Speed in Phenomena of Lateral Instability on Railway Vehicles

SUMMARY

A comparison between theoretical calculations on dynamic lateral behaviour of railway vehicles and experimental results shows quite a sizeable difference between the calculated critical speed and the actual speed at which side impact phenomena will repeatedly occur between wheel flange and rail (running speed limit), such impact speed being remarkably lower than calculated.

Another typical experimental aspect is that the running speed limit will considerably vary for the same vehicle depending on the test track conditions. Such difference is usually attributed to alterations of the wheel-rail contact surfaces, only.

This paper will discuss some concurrent causes which may prove far from negligible, such as the effects of track defects, an amplification of the dynamic lateral displacement between wheel and rail on approaching the critical speed, the track mechanical properties, and in particular the track lateral rigidity.

The influence of some geometrical factors typical of the wheel-rail contact, such as side clearance and linearized conicity, will also be discussed. The approach is based on the application of statistical methods to dynamic linear systems.     

Validation of a MATLAB Railway Vehicle Simulation Using a Scale Roller Rig

SUMMARY

A 1/5 scale roller rig has been constructed for use in analysing the dynamic behaviour of railway vehicles. The roller rig includes a servo hydraulic system to allow a realistic input of track irregularities at the rollers and instrumentation is fitted to allow measurement of the position and acceleration of the bodies. This paper reports on the first stage in validating the behaviour of the roller rig using a relatively simple, linear computer model constructed in MATLAB. Initial results show good correlation between the behaviour seen on the roller rig and that predicted by the model.     

Modelling,validation and analysis of a three-dimensional railway vehicle–track system model with linear and nonlinear track properties in the presence of wheel flats

This paper presents dynamic contact loads at wheel–rail contact point in a three-dimensional railway vehicle–track model as well as dynamic response at vehicle–track component levels in the presence of wheel flats. The 17-degrees of freedom lumped mass vehicle is modelled as a full car body, two bogies and four wheelsets, whereas the railway track is modelled as two parallel Timoshenko beams periodically supported by lumped masses representing the sleepers. The rail beam is also supported by nonlinear spring and damper elements representing the railpad and ballast. In order to ensure the interactions between the railpads, a shear parameter beneath the rail beams has also been considered into the model. The wheel–rail contact is modelled using nonlinear Hertzian contact theory. In order to solve the coupled partial and ordinary differential equations of the vehicle–track system, modal analysis method is employed. Idealised Haversine wheel flats with the rounded corner are included in the wheel–rail contact model. The developed model is validated with the existing measured and analytical data available in the literature. The nonlinear model is then employed to investigate the wheel–rail impact forces that arise in the wheel–rail interface due to the presence of wheel flats. The validated model is further employed to investigate the dynamic responses of vehicle and track components in terms of displacement, velocity, and acceleration in the presence of single wheel flat.     

Dynamic Interaction of Railway Train and Bridges

SUMMARY

An analytical method for obtaining the dymanic responses of a train of locomotives moving on bridges is presented. The ratio of dynamic response to maximum static response is called the amplification factor, and its maximum absolute value minus one is called the impact. Each four-axle locomotive is modelled as a rigid body with three degrees of freedom: bounce, pitch and roll, and with a suspension system consisting of springs mounted on wheels. The locomotives are assumed to be connected by frictionless joints to form the train. The bridge is modelled as a three dimensional structure, with the masses lumped at the truss joints. All joints, including the floor beam connections, are assumed to be rigid, except those for the bracing members, which are assumed to be hinged. Vertical displacements are considered as the only dynamic degree of freedom. The mathematical formulation is described briefly, and a numerical example is given. Locomotive and truss member properties, together with stresses in some typical members, are given in the tables. The amplification factors of the responses in some typical bridge members are shown in the figures.     

Investigation of the impact of locomotive creep control on wear under changing contact conditions

This paper presents the locomotive traction controller performance with respect to the track wear under different operation conditions. In particular, an investigation into the dynamic response of a locomotive under changing wheel–rail friction conditions is performed with an aim to determine the effect of controller setting on track wear. Simulation using a full-scale longitudinal–vertical locomotive dynamic model shows that the appropriately designed creep threshold, controller, settings can effectively maintain a high tractive effort while avoiding excessive rail damage due to wear, especially during acceleration under low speed.     

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.     

Dynamics of Actively Guided Vehicles

SUMMARY

In spite of considerable interest in active controls for a wide variety of road and rail vehicles comparatively little work has been carried out on the dynamics of actively guided vehicles in which steering is carried out in response to signals from a controller seeking to follow a given path or track. Drawing from the relevant fields of guided rubber tyred vehicles, rail vehicles and mobile robots the common basis of the dynamics of active guidance is discussed,and this simple theoretical framework is then followed by a review of work in this field. Attention is restricted to wheeled vehicles.