A Theory of Wheelset Forces for Two Point Contact Between Wheel and Rail

This paper describes a quasistatic theory of wheelset forces for an important practical case of the wheelset rolling when one of the wheels touches the rail in two contact zones. One of these zones lies on the tread and the other on the wheel flange. For such contact the specific problem of finding the distribution of forces between the tread and flange arises. The simultaneous frictional rolling contact problems for both contact zones have been described with Kalker×apos;s non-linear theory and wheelset equilibrium equations.

The numerical results presented are for an individual wheelset on straight track, the distribution of forces being described for a wide range of loading conditions. The influence of steering on the distribution of forces has also been presented.

This theory can be easily extended for quasistatic curving of railway vehicles and may assist wear studies for vehicles with worn wheels.     

Simulation of Multibody Vehicles Moving over Elastic Guideways1

This paper describes the present state of a general purpose computer program for calculating the dynamic response of vehicles travelling over guideways which may be elastic.

The linearized state-equations of motion for general multibody vehicles are constructed automatically by the program, these equations are supplemented by the equations for the active subsystems. Finally, the vehicle system equations are combined with the modal equations for elastic guideways and the complete set of coupled equations is solved simultaneously by numerical integration.     

Analysis of the Dynamic Response of a Rolling String-Type Tire Model to Lateral Wheel-Plane Vibrations

A theory has been developed for the analysis and prediction of the dynamic frequency response of lateral force and moment acting upon a pneumatic tire when the wheel is moved laterally and swivelled about the vertical axis. The theory establishes the force and moment response of a tire model which consists of a stretched circular string with mass, elastically supported to the wheel-center-plane. The analysis is confined to small deviations from rectilinear motion such that it is permissible to assume that sliding does not occur in the contact area. In this manner, the equations are kept linear.

The theory which gives an exact analysis of the dynamic response of the model adopted shows satisfactory qualitative agreement with experiments. The change in the moment response due to tire inertia reduces the tendency to shimmy at higher frequencies and higher speeds. The lateral force response, however, changes in an unfavorable fashion which, for castered wheels, may result in a decrease of the effective damping about the king-pin at higher speeds and frequencies.     

Additional 4WS and Driver Interaction

This investigation is based on a complex 4-wheel vehicle model of a passenger car that includes steering system and drive train. The tyre properties are described for all possible combined longitudinal and lateral slip values and for arbitrary friction conditions. The active part is an additional steering system of all 4 wheels, additionally to the driver's steering wheel angle input. Three control levels are used for the driver model that thereby can follow a given trajectory or avoid an obstacle.

The feedback control of the additional 4 wheel steering is based on an observer which can also have adaptive characteristics. Moreover a virtual vehicle model in a feedforward scheme can provide desired steering characteristics.

To get information for critical situations a cornering manoeuvre with sudden u-split conditions is simulated. Further a similar manoeuvre is used to evaluate the reentry in a high friction area from low friction conditions. And finally the performance of the controller is shown in a severe lane change manoeuvre.     

Zur Steuerbarkeit eines gebremsten Sattelschleppzuges

(Title: On Controllability of a Tractor-Semitrailer Truck During Braking)

The concept of controllability coming from linear system theory is applied to the motion of a tractor-semitrailer vehicle during straight-line braking. Some states of braking with locked up wheels at different axles are considered. The question whether the system is always controllable must be answered in the negative for locked up wheels at the tractors front axle. In other cases controllability in its mathematical meaning which, however, does not always appear to be fully adequate for practical problems, is possible.     

Survey of Wheel—Rail Rolling Contact Theory

This paper describes the theory of frictional rolling contact as far as it is significant for the wheel-rail system. It is divided into two parts.

The first part, mostly non-mathematical, contains a historical survey from the times of Carter and Fromm (1926) to the present day, in which all aspects of rolling contact theory are discussed. Included are a quantitative account of the results of Hertz theory (Section 3), and a table of the creepage and spin coefficients.

The second part gives a present day account of the simplified theory (Section 4), and of the exact linear and non-linear theory (Section 5).

The paper closes with some recommendations for future research, of which the most pressing is a thorough investigation of the accuracy of simplified theory.     

Railway Vehicle Modelling by the Constraint Equation Method*

A method for the dynamic analysis of railway vehicles is proposed. The method is based on both the using of constraint equations, and on the building of the mathematical model by means of the initial data.

The calculation models are nonlinear, due both to the connecting elements, and to the wheel-rail contact modelling. Solving of differential equations is achieved by time step integration. The method has been applied to the analysis of a freight wagon and a train unit.     

Comparison of All-Wheel Steerings in the System Driver-Vehicle

Different load or tires and a drive on an ice-coated road can overcharge a driver to such an extend, that the result may be an accident. Therefore the aim of development is a self-acting compensation of the vehicle to different vehicle transfer behaviour (invariant vehicle behaviour).

The calculation of so called optimal characteristics shows, that only rear-wheel steering cannot realize this aim of development. Therefore an additional front-wheel angle, which is not influenced by the driver, is necessary. A transfer function can be calculated in order to get controlled steering of the rear wheels without the influence of load.

It is not possible to realize optimal characteristics, because the parameters of the vehicle are difficult to measure. Only an optimal diagnosis and control of driving condition realize a relief for the driver in every driving situation in order to avoid most of the accidents.

The often demanded sideslip angle compensation only worsens driving conditions on ice-coated roads. Therefore systems which identify the driving condition themselves have to be favoured in any case.     

Active Suspension Control; Performance Comparisons Using Control Laws Applied to a Full Vehicle Model

Based on a mathematical model of an actively suspended vehicle, the effects of the following issues in deriving the control laws are studied:

(a)representation of the ground surface as integrated or filtered white noise.

(b)cross-correlation between left and right track inputs.

(c)wheelbase time delay between front and rear inputs.

The third of these issues is shown to be by far the most important. Considerable improvements at the rear suspension can be obtained if the control law includes the information that the rear input is simply a delayed version of the front input. Effectively this provides feedforward terms in the control law for the rear actuator. For the full state feedback case, these improvements are indicated by reductions in the rear body acceleration and rear dynamic tyre load of around 20% and 40% respectively with no increase in suspension working space.     

Optimization for Vehicle Suspension II: Frequency Domain

The objective of this study is optimizing the components design of a vehicle suspension system under excitation due to road roughness. The vehicle is modelled as a dynamic system made of masses interconnected by, linear, springs and dampers. The optimizing code provides values corresponding to the caracteristics of masses, dampers and springs which, within a range, minimize the objective function for a defined excitation. This objective function auantifies the vehicle comfort level.

The optimization method used is the sequential linear programming by iteratively applying the Simplex algorithm. The model response is obtained in frequency domain and the vehicle excitation can be either random or deterministic.

The exact nature of the optimization problem, objective function and restrictions, depend on the type of excitation considered.

In succeeding paragraphs, the problem formulation together with a comparison with other authors is presented.     

Natural Frequencies of Bernoulli-Euler Beams Resting on Two Elastic Supports: Application to Railway Vehicles

The purpose of the present study is to investigate the effect of the different parameters of the elastic supports upon which a deformable beam lies, upon the natural frequencies of the system.

The influence of support parameters is obtained by exploiting characteristic transcendental equations. The natural flexural vibrations of the beam are only affected by the stiffness of the supports over a very restricted range; outside this range the frequencies are those of a completely free beam or of a beam supported by two simple rigid supports (infinite stiffness).     

Messungen von Fahrbahn-Unebenheiten paralleler Fahrspuren und Anwendung der Ergebnisse

Measurement of two track road inputs and theoretical application of the results

The calculation of vehicle response to road-surface irregularity inputs requires the spectral densities of the left and right longitudinal track and their statistical dependence

This paper presents some resluts of parallel profile measurements, three typical german roads have been chosen

Random vibration of two vehicle types are digital-simulated. The dynamic tire load shows that independent suspension systems are more advantageous than beam axles, because by wheel tramp this type increases the dynamic tire load.     

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

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.     

Dynamic Behaviour of Ore Wagons in Curves at Malmbanan

The transportation of ore can be made more cost efficient by use of bigger and heavier trains. An increase in axle load is thereby wanted. The fleet of ore wagons of today at Malmbanan/Ofotbanan in northern Sweden and Norway has to be updated. It is of interest to find out if it is possible to allow a higher axle load on the track with new wagons

To be able to understand and predict the effects on track wear depending on what type of vehicle that is in use, the contact forces between wheels and rails have to be determined. A computer aided analysis has been made of the dynamic behaviour of three test vehicles equipped with different types of three-piece bogies running at Malmbanan. The vehicles are modelled and their interaction with the track is analysed using the multibody simulation package GENSYS

The simulations show that, even if the axle load is increased from 25 tons to 30 tons and the velocity is increased from 50 km/h to 60 km/h, it is possible to reduce lateral track forces and wear in curves by using a different bogie than the standard three-piece bogie used today.     

Nähere Untersuchungen zur stationären Kurvenfahrt von Einspurfahrzeugen

Detailed Investigations of the Steady State Turning of Single Track Vehicles

In the paper the steady state turning of single track vehicles on a horizontal, even road is investigated, supposing the air to be at rest. The vehicle model used has six degrees of freedom: rolling, yawing, pitching and bouncing of the vehicle, rotation of the front wheel system (steering) relatively to the main frame and distortion of the rear wheel system due to limited stiffness of its linkage, and also takes into account wind drag and gyroscopic effects generated by wheels and other vehicle components. A special importance is given to the geometry of the vehicle

The results show a comparison of two types of motorcycles with different geometries and tires. To characterize the vehicle behaviour the roll, side slip and steering angle as functions of the normal acceleration are used. A more detailed study in respect to the steering torque is added.     

The Lateral Dynamics of Motorcycles and Bicycles

The paper is a review of the state of knowledge and understanding of the steering behaviour of single-track vehicles, with the main accent on vehicle design, and vehicle design analysis and behaviour prediction.

The body of the paper consists of a chronological account of the steps which have been taken in establishing the current position. Scientific study of the motions of two-wheelers has been in progress for more than 100 years, but progress was slow and many conflicting conclusions were drawn until increasing understanding of tyre mechanics, systematic application of the laws of motion for systems of rigid bodies, digital computation and modern numerical methods, and improved mobile measurement, recording, and data processing capabilities allowed the pace to accelerate.

The current position, which is that a good understanding of the relationship between design and performance has been achieved, but that by no means have all the problems of significance been solved, is described at the end of the paper.     

Simulation and Visualisation of the Dynamic Behaviour of an Overhead Power System with Contact Breaking

For high speed rail traffic it is necessary to design overhead power systems which minimize the contact loss between pantograph head and contact wire. To predict how different design solutions will behave it is favourable to model and simulate the dynamic behaviour. In this paper a model of an overhead power system is specified and used in simulation. The model is suitable for simulation with contact loss since it includes specifications of impact conditions between pantograph head and contact wire. Two sets of equations of motion are specified, one for the contact case and one for the non-contact case. The model also includes lateral movement of the wire due to the zigzag span and friction between the pantograph head and the contact wire. It is shown how to make animations of the system behaviour using a MCAE-system. The animations are made using a geometrical model of the system together with results from numerical simulations.

Through the examples provided, use of the mathematical model and the geometrical model is presented. The response is visualised as time histories and phase plane diagrams of different coordinates and as animations of the total system response. The different types of visualisations make an excellent combination when studying the system behaviour of different design solutions.

In one example, simulation using the linearised set of equations gives the same results as simulation using the set of fully nonlinear equations, due to periodic response and the simple alternation of contact conditions. It is shown that the situation when any of the parameters vary suddenly is possible to simulate using the fully nonlinear equations of motion.     

Solution of the Multiple Wheel and Rail Contact Dynamic Problem

An unconventional method for calculating the forces developing in the wheel and rail contact patches of a railway vehicle has been implemented at the New Technology Laboratory of INRETS. It takes into account the elastic deformations of the materials in the Hertzian elliptical contact areas; the possibility of having simultaneously several contact patches on each wheel, is introduced in the simulation of the dynamic phenomena.

The theory is applied for a high speed bogie running on a perfectly straight track.     

Ride Quality and Dynamics of Rail Vehicle Models for Microcomputers

This paper describes mathematical and computer models for ride quality and dynamics of rail vehicles developed for running on personal computers. The purpose of the computer simulations is for prediction of ride quality in order to study the dynamic stability of the system and the effect of track quality and irregularities on ride quality.

In deriving the equations of motion for dynamic stability, the tangential forces acting on the contact areas between the wheels and rails are of fundamental importance in railway vehicles dynamics and are included in the analysis [1]. These forces are due to the creep phenomenon between the wheel and the rail on which it is rolling. Track irregularities are defined in terms of four components consisting of gauge, cross level, alignment and vertical surface profile [2]. Relation of allowable track irregularities versus speed is given by the FRA Track Safety Standards. Analytical representation of track irregularities should include both PSD (Power Spectral Density) for CWR (Continuous Welded Rail) as well as discrete inputs from track joints.

In this paper, the rail vehicle suspension analysis and dynamics mathematical and computer models are described. The computer models are written in Fortran 77 and designed to run on personal computer. The paper also discusses programming considerations that must be taken into account when programming for microcomputers under DOS (IBM's Disk Operating System) and MS or RM Fortran Compilers. Most of the considerations are however, valid in general with respect to engineering software development and programming for microcomputers.

Computer graphics is a powerful tool for visualization of the resulting solutions such as the display of the characteristic roots for the eigenvalues solution on a root locus plot and representation of acceleration levels versus the “Reduced Comfort Boundary” limits defined by the International Standards Organization” (ISO 2631-1985). In this paper some examples of these resulting outputs are presented and their significance discussed.     

A Driver Model Based on the Cerebellar Model Articulation Controller

A model of driver behavior is described which is based on a current theory of neurophysiological processes occurring in the cerebellum. The model learns to control the vehicle through experience, provides discontinuous ramp steer inputs to the vehicle, accepts discontinuous input data, and is applicable to all control situations.

The model is implemented on a simple simulation model of a car and learning is accomplished by the use of an explicit driver model which drives the vehicle along a specified trajectory.