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.     

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.     

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.     

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.     

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.     

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.     

An inverse railway wagon model and its applications

An inverse wagon model was developed to estimate wheel-rail contact forces using only measurements of wagon body responses as inputs. The purpose of this work was to provide mathematical modelling to embed in low-cost devices that can be mounted on each freight wagon in a large wagon fleet. To minimize cost, complication, and the maintenance inconvenience of these devices, the constraint is imposed that transducers and connections are limited to locations on the wagon body. Inputs to the inverse model developed include only vertical and lateral translational accelerations and angular accelerations of roll, pitch, and yaw of the wagon body. The model combines the integration and partial modal matrix (PMM) techniques together to form an IPMM method. Besides wheel-rail contact forces some motion quantities such as the lateral and yaw displacements of wheelset are also predicted. Results from the inverse model were compared with data from full scale laboratory suspension tests for vertical suspension excitations. The inverse model was also compared with results from simulations completed in VAMPIRE^® for more complicated track input profiles. The model results and the applications of the model are discussed.     

Estimation of wheel–rail contact conditions and adhesion using the multiple model approach

This paper presents the development of a multiple model estimation approach for the identification of the adhesion limit to overcome the problem of the wheel slip/slide at the rail wheel-rail contact. The contact characteristics at the rail wheel-rail interface are both highly nonlinear and subject to changes due to exposure to external contaminations. The detection of adhesion and its changes is therefore scientifically challenging, but would provide a critical information in the control of trains to avoid undesirable wear of the wheels/track but also the safety compromise of rail operations. This study exploits the variations in the dynamic behaviour of the railway wheelset caused by the contact condition changes and applies a bank of Kalman filters designed at selected operation points for the adhesion estimation. A fuzzy logic system is then developed to identify the contact conditions by examining the residuals from the Kalman filters.     

Novel electronic braking system design for EVS based on constrained nonlinear hierarchical control

Both environment protection and energy saving have attracted more and more attention in the electric vehicles (EVs) field. In fact, regarding control performance, electric motor has more advantages over conventional internal combustion engine. To decouple the interaction force between vehicle and various coordinating and integrating active control subsystems and estimate the real-time friction force for Advanced Emergency Braking System (AEBS), this paper’s primary intention is uniform distribution of longitudinal tire-road friction force and control strategy for a Novel Anti-lock Braking System (Nov- ABS) which is designed to estimate and track not only any tire-road friction force, but the maximum tire-road friction force, based on the Anti-Lock Braking System (ABS). The longitudinal tire-road friction force is computed through real-time measurement of breaking force and angular acceleration of wheels. The Magic Formula Tire Model can be expressed by the reference model. The evolution of the tire-road friction is described by the constrained active-set SQP algorithm with regard to wheel slip, and as a result, it is feasible to identify the key parameters of the Magic Formula Tire Model. Accordingly, Inverse Quadratic Interpolation method is a proper way to estimate the desired wheel slip in regards to the reference of tireroad friction force from the top layer. Then, this paper adapts the Nonlinear Sliding Mode Control method to construct proposed Nov-ABS. According to the simulation results, the objective control strategy turns out to be feasible and satisfactory.     

基于库仑定律的滚动轮表面接触应力分析

针对滚动轮表面接触应力的分析误区,基于库仑定律对路面（材料）与滚动轮接触表面的应力进行分析,得出在滚动轮接触表面不仅有接触正应力,而且还有接触剪应力（或摩擦应力）的结论.并根据结论进一步分析,阐明了原分析误区不能解释的问题.     

Non-steady state modelling of wheel-rail contact problem for the dynamic simulation of railway vehicles

This paper deals with the solution of the non-steady state wheel-rail contact problem. Firstly, the existing models are analysed and it is concluded that none of them have the computational efficiency and/or accuracy characteristics required to be used in a railway simulation programme. Following this, a new solution is proposed to the problem that allows obtaining sufficiently accurate results with a relatively low computational cost. During the development of the proposed method it has been assumed that only one type of creepage is variable with respect to the time. Further work is necessary to extend it to more general cases.     

Non-steady state modelling of wheel-rail contact problem for the dynamic simulation of railway vehicles

Abstract

This paper deals with the solution of the non-steady state wheel-rail contact problem. Firstly, the existing models are analysed and it is concluded that none of them have the computational efficiency and/or accuracy characteristics required to be used in a railway simulation programme. Following this, a new solution is proposed to the problem that allows obtaining sufficiently accurate results with a relatively low computational cost. During the development of the proposed method it has been assumed that only one type of creepage is variable with respect to the time. Further work is necessary to extend it to more general cases.     

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.     

Nonlinear tire-road friction control based on tire model parameter identification

A hierarchical control structure is a more suitable structural scheme for integrated chassis control. Generally, this type of structure has two main functions. The upper layer manages global control and force allocation, while the bottom layer allocates realized forces with 4 independent local tire controllers. The way to properly allocate these target forces poses a difficult task for the bottom layer. There are two key problems that require attention: obtaining the nonlinear time-varying coefficient of friction between the tire and different road surfaces and accurately tracking the desired forces from the upper layer. This paper mainly focuses on longitudinal tire-road friction allocation and control strategies that are based on the antilock braking system (ABS). Although it is difficult to precisely measure longitudinal tire-road friction forces for frequently changing road surface conditions, they can be estimated with a real-time measurement of brake force and angular acceleration at the wheels. The Magic Formula model is proposed as the reference model, and its key parameters are identified online using a constrained hybrid genetic algorithm to describe the evolution of tire-road friction with respect to the wheel slip. The desired wheel slip, with respect to the reference tire-road friction force from the top layer, is estimated with the inverse quadratic interpolation method. The tire-road friction controller of the extended anti-lock braking system (Ext-ABS) is designed through use of the nonlinear sliding mode control method. Simulation results indicate that acceptable modifications to changes in road surface conditions and adequate stability can be expected from the proposed control strategy.     

基于四轮轮边驱动电动车的路面附着系数估算方法

路面附着系数是影响车辆行驶安全性的重要因素,利用轮边驱动电动汽车驱动力矩可以对路面利用附着系数进行观测。当观测到μ-λ曲线接近于峰值点时,将该时刻的轮胎利用附着系数作为路面峰值附着系数,并根据识别的路面峰值附着系数进行驱动防滑控制。该方法能够有效防止轮胎滑转,提高车辆行驶稳定性。