Survey of Wheel—Rail Rolling Contact Theory

SUMMARY

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.     

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.     

Dynamic Behaviour of a Mobile Robot Vehicle with a Two Caster and Two Driving Wheel Configuration

The actual trajectory covered by a mobile robot in motion differs from the trajectory planned on the basis of the kinematic characteristics of its directional control system. This difference is essentially related to the behaviour of wheel-road contact, the influence of dynamic loads and the presence of caster wheels.

This paper presents a mathematical model (“ DDPP) which simulates the motion of a generic mobile robot vehicle with a propulsion and directional control system based on two independent driving wheels and two caster wheels.

The differential equations of motion have been obtained by applying modified equations of Lagrange.

The role played by the dynamic loads, the wheel-road contact features and the caster wheels is discussed hereof.     

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.     

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.     

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.     

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.     

Control Algorithms for Active Cab Suspensions on Agricultural Tractors

This paper describes active agricultural tractor cab suspensions based on optimal control theory. Control algorithms based on time invariant state feedback and on adaptive control are developed and studied. The influence of different observers and measurement noise levels on the vibration damping capacity are studied as well as the power consumption for the suspensions.

The principle for the adaptive algorithm is based on the parameters in the penalty matrices being varied so that the resulting controller always strives to make optimum use of available travel space. The feedback and observer gains are also changed depending on the characteristics of the vehicle's frame movements.

The results show that it is possible to design an effective active suspension, but that the choice of feedback gains must be dependent on the surface characteristics to reach satisfactory vibration damping performance.     

The Elastic Cross-Influence between Two Quasi-Hertzian Contact Zones

In this paper a type of contact between two bodies is considered, which leads to the formation of two separate contact zones. The contact zones considered are Hertzian ellipses if the distance between them is large. When the distance between the zones is finite it is necessary to take into account the elastic cross-influence of the two zones. In this paper an approximate method is proposed which allows the determination of the actual contact zones as Hertz's ellipses but without disregarding the cross-influence. Numerical results are presented for two, two-humped bodies pressed against each other and for steady state rolling of a flanged wheel along a steel rail.

It is shown that neglecting the cross influence for a flanged wheel leads to a negligible error in the contact forces but the forces are transmitted between wheel and rail through contact patches which are generally more slender than with the cross-influence neglected.     

Very-High-Speed Tests on the French Railway Track

The very-high-speed tests carried out by SNCF between the end of 1989 and May 1990, are an extension of the investigations which have been made for many years in order to acquire the control of high speeds. The high-speed run which ended the tests is well known [1], [2],[3].

In order to place the final test campaign in its context, we can recall progression made during the last decade.

In February 1981, the maximal speed of 380 km/h was reached with a TGV-PSE¹ train set, having the same configuration as the series, but only seven trailers instead of eight.

During the following years, until 1986, the pneumatic suspension and the new Y 231 carrying bogies designed for TGV-ATL train sets were developed, with numerous test runnings in the speed range from 300 to 350 km/h, in order to obtain certitudes as regards the stability of the bogies and the appropriate choice of anti-hunting devices for commercial speeds of 270 km/h (LGV-PSE) or 300 km/h (LGV-ATL).

These tests allowed the definition of the TGV equipment design principles, which are applied today as regards the critical speed of the bogies.

Between 1985 and 1988, the development of the prototype train set equiped with self-controlled synchronous motors (March 1988) led once more to numerous runnings at high speed, in December 1988 with the so-called “operation TGV 88”. During this operation, the speed range from 350 to 400 km/h was investigated (maximal speed 408,4 km/h on December 12th 1988).

Apart from the capability of the synchronous traction equipment to develop the required power and the performance consisting in the realization of such tests on a line kept in operation (LGV-PSE), the teachings gathered together during this test campaign were decisive for the pursuit of the operation.

On this occasion, we discovered that:

-with the single-phase GPU pantograph mounted on this train set, we could get the current collection under control without difficulties inside the studied speed range,

-the bogies presented a stability margin distinctly higher than that which had been estimated, according to the results of former experiences.

Consequently, the test campaign of the TGV 117 could be engaged with a great confidence in the capabilities of the TGV equipment to achieve markedly higher speeds with full safety. The preparation of this test campaign had begun in 1986 and was conducted in a parallel direction to the above mentioned experimentation.

The campaign was preceded by a preliminary test campaign with the train set TGV-ATL n° 308, with a reduced train composition, including eight trailers. The goal was the validation, until 390 km/ h, of the test field consisting in the TGV-ATL Aquitaine branch, as well for the track as for the overhead contact line, the achievement of which was just ended.

The operation TGV 117 was then carried out in two phases:

-in December 1989 the train set TGV-ATL 325 with a reduced train composition consisting in four trailers between two motor cars reached the maximal speed of 482,4 km/h on December 5th,

-in May 1990 the same train set, but with only three trailers, improved the performance unto the final record: the speed of 515,3 km/h was reached on May 18th.     

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.     

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.     

Railway Vehicle Active Suspensions

This paper reviews the state-of-the-art of active suspensions for use on railway vehicles. The primary focus of the paper is on ride quality control, both vertical and lateral, and on lateral stability control.

The section on theoretical considerations summarizes the results of a one-degree of freedom optimization and then investigates analytically the use of active suspensions for lateral ride and stability augmentation. It is shown that separate control structures using different measurements and actuator actions are very effective in controlling both ride quality and stability.

A section on a survey ofcurrent activities reviews published research on active railway suspension work around the world.

Finally a concluding section indicates future trends in active suspension applications.     

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.     

Vehicle Motion Analysis in Relation to Vehicle Safety

The influence of vehicle handling on the possible avoidance of accident situations is discussed. lit is shown that accident reconstruction at present does not provide the necessary information to relate the cause of accidents to the lack of road worthiness of vehicles. It follows that the vehicle behavior in proximity of its performance limit must be determined in order to infer its accident avoidance potential.

The paper presents a review of the state-of-the-art of vehicle modeling, simulation of vehicle maneuvers and full scale testing. The application of the direct method of the stability theory is suggested as a possible means of obtaining performance limit envelopes which are necessary for establishing standards of the performance of vehicles.     

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.     

Discomfort from feeling vehicle vibration

Vehicle refinement should include a consideration of the discomfort likely to be caused by vibration. This paper reviews the measurement, the evaluation, and the assessment of vehicle vibration felt by drivers and passengers.

The feeling of vibration that gives rise to judgements of vibration discomfort can be predicted using evaluation procedures that take into account human sensitivity to different magnitudes, frequencies, directions, and durations of vibration. The evaluation methods make it possible to optimise vehicles via dynamic modelling before the production of prototypes and they assist the testing and optimisation of prototypes and production vehicles.

Vibration evaluation provides imperfect predictions of discomfort when driver or passenger opinion is influenced by factors other than the vibration that is being measured and evaluated. Vibration evaluation can detect changes that are not detectable subjectively since smaller changes can be detected by measurement and evaluation than by subjective assessment.     

Berechnung des extremen Lenk- und Bremsverhaltens von Sattelkraftfahrzeugen

Simulation of Steering and Braking Behaviour of Tractor-Semitrailer Vehicles in Extreme Situations

This paper deals with the simulation of the behaviour of tractor-semitrailer vehicles at braking on wet, slippery road surface. The nonlinear model used for the computation enables to simulate extreme situations at wheel locking and swerving

The instabilities during braking such as jackknifing and trailer swing as well as non steerability are investigated. Straightline braking shows the influence of cornering on the behaviour during braking in a turn.