Modification of the semi-Hertz wheel–rail contact method based on recalculating the virtual penetration value

ABSTRACT

Wheel–rail contact calculation is of vital importance in vehicle system dynamics. In the existing methods of wheel–rail contact calculation, the finite element method and Kalker’s CONTACT program, which are based on the complementary energy principle, are the two methods with accuracy recognised. However, because of its very slow calculation speed, it cannot meet the requirement of online calculation, so a variety of fast non-elliptic algorithms have been proposed. The semi-Hertz method, which is recognised for its great contributions to the fast wheel–rail contact calculation, is based on the concept of virtual penetration. The calculation of virtual penetration is crucial to evaluate the shape and normal pressure distribution of the contact patch. In practice, the virtual penetration is related to the curvature of the whole contact patch; however, the range of the contact patch is determined by the value of penetration. Such an interaction leads the calculation into a dead loop. In the semi-Hertz method, the penetration is calculated by the Hertz parameters of the initial contact point. Thus, the practical range of the method is limited. In this paper, a fast-iterative method for solving virtual penetration is proposed, and a reliable value of virtual penetration can be obtained under any lateral wheel–rail relative curvature variation with good stability and speed. The normal and tangential solutions are analysed with different methods in this paper.     

考虑层间接触状态的路面动力响应解析解及参数反演

为了对现有路面结构FWD检测技术的改进提供相关参考,并进一步完善路面结构质量评价体系,从轴对称动力平衡方程出发,应用Hankel-Laplace积分变换,推导了考虑路面材料横观各向同性特性和路面结构层间接触状态的路面结构力学响应解析解,结合传递矩阵法提出了一种路面结构力学响应快速计算方法,并通过与ABAQUS计算结果的...     

An inverse design method for rail grinding profiles

Inspired by the optimisation design method for restoration of worn wheel profiles, an inverse design method based on optimal rail grinding profiles is presented in this paper. To improve grinding quality, vehicle dynamic performance is chosen as the main criteria and rolling radii difference function is selected as the key factor (also main target function) determining dynamic performance. Grinding material to be removed is chosen as the auxiliary target aimed at extending rail service life. Besides that, wheel–rail contact distribution is also taken into consideration as an auxiliary target preventing stress concentration and fatigue growth. By introducing certain presuppositions, all the design targets will form an inverse design problem. This problem can be solved using hybrid discrete numerical methods. Considering different grinding requirements, two examples of grinding profile design for straight and curved track will be discussed. Results show that the presented method is efficient and effective. Practical implementation has been carried out at several grinding sites in China.     

Non-singular slip (NSS) method for longitudinal tire force calculations in a sudden braking simulation

In a dynamic vehicle simulation, longitudinal tire force is primarily based on the longitudinal slip (ratio). In the longitudinal slip formula, state variables are used in the denominator. This causes a divergence problem for numerical simulations of vehicle dynamics. To avoid this numerical singularity, a differential slip calculation method was developed for use in dynamic vehicle simulations. However, this method also causes a singularity when the wheel velocity approaches zero in a pure slip state, such as during sudden braking. In this paper, a new longitudinal slip calculation method, which can overcome singularities in all velocity conditions, is proposed. For this purpose, the Taylor series is adapted to the slip formula and the idea of virtual wheel rotation stiffness is introduced for the development of the slip equation. The physical phenomenon at the zero slip state is analyzed. Finally, the proposed slip formula is used to solve the numerical singularity problem, and the non-singular slip (NSS) calculation method is proposed. The proposed NSS method is applied to tire model performance test (TMPT) simulations to validate its performance.     

A Nonlinear Analysis of the Generic Types of Loss of Stability of the Steady State Motion of a Tractor-Semitrailer∗

SUMMARY

All different types of loss of stability which occur generically for a tractor semitrailer vehicle are studied when varying two parameters namely the speed V of the vehicle and the position d of the center of mass of the trailer. For a fixed value of d and varying V it turns out that only two cases either a divergence or a Hopf bifurcation can occur typically. By means of a nonlinear analysis the post-bifurcation behavior for both cases is treated showing that it is critical in both cases. This latter result means that the system is an imperfection sensitive one for which the calculation only of the linear stability limit, does not have very much practical meaning, because small perturbations of the system (changes of parameters) can lead to a drastic reduction of the critical speed. Our paper furthermore indicates how a nonlinear investigation of stability problems in vehicle dynamics with no restriction to the number of degrees of freedom of the system can be done in a straight forward manner.     

Optimization for Vehicle Suspension I: Time Domain

SUMMARY

A numerical procedure for finding the optimum values of a number of parameters describing a model vehicle suspension has been studied. The vehicle has been modelled by dynamic systems of linear springs and dampers, and the goal is to obtain lower acceleration peaks at an elected design point in the vehicle.

The problem is stated as a mathematical programming problem which can be solved by means of the sequential linear programming technique. The procedure has been implemented for a four wheel independent suspension model capable of being subjected to road irregularities and to centrifugal and braking accelerations.     

Dynamics of an isolated railway wheelset with conformal wheel–rail interactions

ABSTRACT

In multi-body dynamics, we model a non-conformal wheel/rail contact at one centre point since this contact is flat and Hertzian. However, the quasi-conformal contact requires more points since the contact is curved and non-Hertzian. The methodology in solving these points during dynamic simulations is the basis of this development. In this online effort, first, we present a general contact joint and the gutter search method of Pascal and Jourdan [The rigid-multi-Hertzian method as applied to conformal contacts. USA: ASME; 2007] in the context of a multi-body approach. Next, by adopting the non-iterative approach, a subset of these points with positive profile interpenetrations is selected to idealise one curved contact by a set of multi-Hertzian patches for which the Hertz normal contact solution is available. Finally, the feasibility of this multibody approach together with its implementation in two different codes is evaluated by simulating the motion of an isolated wheelset with realistic inertia. On tangent tracks, the wheelset with non-conformal pairing displays self-excited unstable oscillations while it displays a stable behaviour below a critical speed with conformal profiles. A further study reveals the net friction losses at multiple patches within the curved contact being the reason for the stable behavior.     

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.     

Stability Criteria for Automobile-Trailer Combinations

ABSTRACT

The characteristic equation for a simple automobile-trailer combination is analyzed, revealing the parameter groups which are important in determining the stability characteristics. Application of Routh's method results in separate criteria for oscillatory and non-oscillatory criteria which can be evaluated algebraically, and which can also be displayed graphically showing a region of stability on a two-dimensional plot. The stability region is bounded by limits of oscillatory and non-oscillatory stability, and the evaluation of a specific case corresponds to the location of a point relative to the boundaries.     

Safety of a railway wheelset – derailment simulation with increasing lateral force

The motivation for this research is to make a comparison between dynamic results of a free railway wheelset derailment and safety limits. For this purpose, a numerical simulation of a wheelset derailment submitted to increasing lateral force is used to compare with the safety limit, using different criteria. A simplified wheelset model is used to simulate derailments with different adhesion conditions. The contact force components, including the longitudinal and spin effects, are identified in a steady-state condition on the verge of a derailment. The contact force ratios are used in a three-dimensional (3D) analytical formula to calculate the safety limits. Simulation results obtained with two contact methods were compared with the published results and the safety limit was identified with the two criteria. Results confirm Nadal’s conservative aspect and show that safety 3D analytical formula presents slightly higher safety limits for lower friction coefficients and smaller limits for high friction, in comparison with the simulation results with Fastsim.     

Method for obtaining the wheel–rail contact location and its application to the normal problem calculation through ‘CONTACT’

This work presents a robust methodology for calculating inter-penetration areas between railway wheel and rail surfaces, the profiles of which are defined by a series of points. The method allows general three-dimensional displacements of the wheelset to be considered, and its characteristics make it especially suitable for dynamic simulations where the wheel–rail contact is assumed to be flexible. The technique is based on the discretisation of the geometries of the surfaces in contact, considering the wheel as a set of truncated cones and the rail as points. By means of this approach, it is possible to reduce the problem to the calculation of the intersections between cones and lines, the solution for which has a closed-form expression. The method has been used in conjunction with the CONTACT algorithm in order to solve the static normal contact problem when the lateral displacement of the wheelset, its yaw angle and the vertical force applied in the wheelset centroid are prescribed. The results consist of smooth functions when the dependent coordinates are represented as a function of the independent ones, lacking the jump discontinuities that are present when a rigid contact model is adopted. Example results are shown and assessed for the normal contact problem for different lateral and yaw positions of the wheelset on the track.     

The Application of Linear Optimal Control Theory to the Design of Active Automotive Suspensions

SUMMARY

Some linear stochastic control theory relevant to the design of active suspension systems subject to integrated or filtered white noise excitation is reviewed, and application of the theory to a particular problem is considered. The problem considered is the well known quarter car problem in which a control law which minimises a performance function representing passenger discomfort, suspension working space, and tyre load fluctuations is required. With full state feedback, the requirement for a formulation of the problem which leads to the system under consideration being observable and controllable is referred to, and it is shown how a well known coordinate transformation enables this requirement to be satisfied. With limited state (or output) feedback, problem formulations which will avoid potential numerical problems in deriving the optimal control are described. Example solutions are included in order to illustrate the methods.     

Sliding window method for vehicles moving on a long track

The rail is modelled as a simply supported beam in the vehicle–track coupled dynamics. The beam is formulated by a partial differential equation that is transformed into an ordinary differential equation by the method of mode superposition for numerical calculation. However, the size of the matrix that is formed by the mode-superposition method increases significantly with track length, which limits the calculation efficiency. Some methods have been developed to solve this calculation issue, but they diminish the merits of the vehicle–track coupled dynamics, which would systematically investigate the dynamics of a vehicle and a track from the entire vehicle–track system. A new method is developed to resolve this contradiction. First, a theory based on a sliding window is established to improve the computational stability with respect to the length and the window-movement ratio. Then, two methods, namely finite element method analysis and an analytical solution, are used to verify the accuracy of the new method, which is highly efficient when used in a vertical half-vehicle–track coupled model to calculate the vehicle response when the vehicle moves on a long track. The results of the vehicle response calculated with and without the sliding window show good consistency.     

基于FLAC3D的机场软基处理方法模拟研究

机场地基处理时,提高浅部土层地基强度、减少工后剩余沉降,控制地基不均匀沉降,确保机场工后安全运行,是地基处理设计应考虑的关键问题。为了保证营口机场工程地基处理的准确性,选择有代表性的试验区进行现场试验。根据典型试验区地基现场处理数据,基于FLAC3D对试验区强夯处理进行了数值模拟研究,并把H1,H2,H3不同试验区的地基处理方法得到的数据与数值模拟计算结果对比,评价各地基处理方法的优缺点,最终确定将H2试验区的地基处理方法用于营口机场全场（跑道、联络道、站坪）大范围软基处理。     

A robust non-Hertzian contact method for wheel–rail normal contact analysis

A modified Kik–Piotrowski (MKP) model is proposed in this paper for an accurate and robust calculation of wheel–rail normal contact problem. The presented method is able to consider the relationship between the elastic deformation of a line and the normal pressure distribution within the contact patch. A novel shape correction method is put forward to correctly describe the elastic deformation of the contact patch. Taking the results estimated by Kalker’s variational method and Kik–Piotrowski method as references, the proposed method is validated by three contact cases, including the assumed standardised non-Hertzian contact and the two-point contact, as well as the contact behaviours based on three actual wheel–rail profiles. The simulation results indicate that, compared with Kik–Piotrowski method, the proposed MKP method achieves better agreement with Kalker’s variational method. Moreover, the MKP method can avoid the abrupt change of wheel–rail normal force due to the sudden transfer of the contact point, which contributes to a better computational stability.     

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.     

路堤稳定安全系数取值探讨

介绍了在山区路堤稳定性分析方法和土性指标的采用以及安全系数取值上比较混乱,没有统一尺度的现状,通过对安全系数实际采用的情况、各规范间安全系数的比较、计算方法及土性指标对稳定性计算结果的影响等方面的分析,在推荐地基土采用固结快剪指标的简化毕肖普法的基础上,提出了路堤稳定安全系数的推荐值。通过研究得出:根据不同地基条件、不同分析工况,路堤稳定安全系数取值为1.20～1.45。     

Design and validation of a robust active trailer steering system for multi-trailer articulated heavy vehicles

ABSTRACT

Multi-trailer articulated heavy vehicles (MTAHVs) are increasingly used around the world due to their economic and environmental benefits. However, MTAHVs exhibit poor maneuverability and low lateral stability, which may lead to fatal traffic accidents. Given the safety risks, it is necessary to solve the steering and stability problems of MTAHVs before they are safely mass deployed on our roads. To this end, active trailer steering (ATS) based on the linear quadratic regulator (LQR) technique has been explored. The LQR-based ATS demonstrates improved maneuverability and enhanced lateral stability. In the ATS design, the vehicle and operating parameters are assumed constant. Thus, it is natural to question the robustness of the ATS in presence of vehicle and operating parameter uncertainties. To address the problem, this paper proposes a robust ATS system. The robust ATS controller is designed using a linear matrix inequality (LMI) based LQR method. In the design, both vehicle and steering actuator parameter uncertainties are considered; to enhance the robustness of the ATS, the weighting matrices of the proposed controller are optimized. The robust controller is applied to an A-Train Double, one type of MTAHV. The effectiveness of the robust ATS is demonstrated using numerical and hardware-in-the-loop real-time simulations.     

桥梁冲击系数理论研究和应用进展

为推动桥梁冲击系数理论和应用研究的进一步深入开展,从计算方法、理论与数值模拟、现场试验与测试3个方面系统梳理国内外公路、城市和铁路桥梁工程领域冲击系数(或动力系数)的研究进展,并探讨其不足和发展趋势.计算方法方面,从桥梁冲击系数的定义出发,详细阐述典型国家最新规范冲击系数表达式;理论与数值模拟方面,分析了车辆参数、桥梁...