Modelling the Contact Between Wheel and Rail Within Multibody System Simulation

In modern railway industry the simulation of the behaviour of railway vehicles has become an important design method during the last years. Modern simulation packages offer modelling elements that are highly adapted for standard and unusual simulation scenarios. A specific application case is the simulation of a railway vehicle travelling through a switch. It makes high demands on the simulation software due to the inconvenient modelling elements needed: the changing rail profiles on the blade rail and in the crossing vee area as well as the guard rail with its additional contact at the back of the wheel. The article gives an overview over the state of the art in railway vehicle simulation and presents a simulation of a passenger car running through a switch as an application example.     

Modelling the Contact Between Wheel and Rail Within Multibody System Simulation

In modern railway industry the simulation of the behaviour of railway vehicles has become an important design method during the last years. Modern simulation packages offer modelling elements that are highly adapted for standard and unusual simulation scenarios. A specific application case is the simulation of a railway vehicle travelling through a switch. It makes high demands on the simulation software due to the inconvenient modelling elements needed: the changing rail profiles on the blade rail and in the crossing vee area as well as the guard rail with its additional contact at the back of the wheel. The article gives an overview over the state of the art in railway vehicle simulation and presents a simulation of a passenger car running through a switch as an application example.     

The Available Methods to Calculate the Wheel/Rail Forces in Non Hertzian Contact Patches and Rail Damaging

In the present paper, the methods used in railway dynamics to take into account the non Hertzian multi contact patches occurring on a wheel, are summarised. Some application cases are presented as well as an explanation of the so called “squat” rail deterioration.     

The Available Methods to Calculate the Wheel/Rail Forces in Non Hertzian Contact Patches and Rail Damaging

Abstract

In the present paper, the methods used in railway dynamics to take into account the non Hertzian multi contact patches occurring on a wheel, are summarised. Some application cases are presented as well as an explanation of the so called “squat” rail deterioration.     

Wheel/Rail Contact: Geometrical Study*

Before trying to ascertain the precise nature of the Wheel-Rail contact (internal stresses and strains, wear and friction, security against a derailment, dynamic behaviour of the vehicle, etc.) the geometrical problem must necessarily be solved. That is, for each position of the wheelset (this is defined by 6 parameters, of which only 4 are independent) the two dependent parameters and the coordinates of the points of contact of each wheel, and rail must be obtained. A new method is proposed of obtaining the spatial position of a wheelset with reference to the rails, from the most general point of view.     

Solution of the Multiple Wheel and Rail Contact Dynamic Problem

SUMMARY

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.     

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.     

The Geometrical Contact between Track and Wheelset

In previous publications the author has described a so-called first-order theory for the motion of a railway vehicle wheelset on a tangent track. In the present report the geometrical aspect of this theory is further evaluated and a method for solving the constraint equations between the coordinates of the wheelset is indicated.     

Behaviour of the Normal Contact Force Under Multiple Wheel/Rail Interaction

The wheel/rail contact forces are calculated in the frequency domain using a track model with multiple wheels on the rail. The effects of the wave reflections between the wheels on the contact force are studied. Different pad stiffnesses are used in the calculations to investigate the influence on the contact force. It is shown that the contact force can have up to four main peaks in the frequency region 550-1200?Hz due to the wave reflections between the wheels, so that the wavelengths of short pitch corrugation can be expected to be associated with multiple frequencies. As a conclusion, it is recommended that in a model for predicting short pitch corrugation the effects of multiple wheel/rail interactions need to be included.     

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.     

Wheel/Rail Non-linear Interactions With Coupling Between Vertical and Lateral Directions

Summary A theoretical model is developed to explore the high frequency wheel/rail interaction with coupling between the vertical and lateral directions. This coupling is introduced through the track dynamics due to the offset of the wheel/rail contact point from the rail centre line. Equivalent models of the railway track in the time domain are developed according to the rail vibration receptances in the frequency domain. The wheel is represented by a mass in each direction with no vertical-lateral coupling. The vertical wheel/rail interaction is generated through a non-linear Hertzian contact stiffness, allowing for the possibility of loss of contact between the wheel and rail. The lateral interaction is represented by a contact spring and a creep force damper in series and their values depend on the vertical contact force. The vibration source is the roughness on the wheel and rail contact surfaces which forms a relative displacement excitation in the vertical direction. Using the combined interaction model with this relative displacement excitation, the wheel/rail interactions with coupling between the vertical and lateral vibrations are simulated. It is found that the lateral interaction force caused by the offset is usually less than thirty percent of the vertical dynamic force. The lateral vibration of the rail is significantly reduced due to the presence of the lateral coupling, whereas the vertical interaction is almost unaffected by the lateral force.     

Wheel Vibrations and Transient Tire Forces

SUMMARY

This paper presents a survey of the state-of-the-art in predicting the wheel vibrations in a complex dynamic vehicle suspension system and their influence on the forces transduced in a high frequency area from the tire to the vehicle's body. Secondly it presents also the transient evolution of tire models used for prediction and understanding high frequency movements in the tire's contact area, producing the guiding forces and torques during vehicle handling.     

Wheel Vibrations and Transient Tire Forces

This paper presents a survey of the state-of-the-art in predicting the wheel vibrations in a complex dynamic vehicle suspension system and their influence on the forces transduced in a high frequency area from the tire to the vehicle's body. Secondly it presents also the transient evolution of tire models used for prediction and understanding high frequency movements in the tire's contact area, producing the guiding forces and torques during vehicle handling.     

Advanced Contact Mechanics-Road and Rail

The development of contact theories and numerical formula for various applications is a field which expands rapidly. This publication focuses on the rolling contact problem both for tire-road and wheel-rail contact. For the tire-road application a central problem is the modeling of the composite structure of the tire under internal pressure and axle load. One actual contact problem is the rolling on soft soil, which is discussed as the main application. In the wheel-rail case the contact area is much smaller and much more emphasis has been laid on the treatment of material changes, wear and creep phenomena. These approaches are discussed in detail as well as a more recent finite element formulation following the arbitrary Lagrange-Eulerian concept. Ideas about damage mechanisms finish the article.