Validation of Railway Vehicle Lateral Dynamics Models

SUMMARY

The general form of the railway vehicle lateral dynamic predictions seems to have been proven. If wheels are coned, rails are of uniform cross-section, and suspensions are linear, then good predictions can be obtained. If wheels are not coned, and rail sections vary, but the suspension is relatively linear, as in modern vehicles, it is still possible to obtain good predictions of critical speed for flexible suspensions. The situation with “stiff” vehicles remains unproven. In each case dynamic response calculations will be only as good as the knowledge of the track input including the rolling line term. The validity of making calculations to predict critical speeds of very non-linear vehicles has not yet been convincingly demonstrated. Validation experiments for the more difficult case of time history representation suggest the possibility of correct prediction for easily comprehensible vehicles, but even this requires an enormous amount of supportive experimental work.     

Steering and Dynamic Stability of Railway Vehicles

For railway vehicles having coned wheels mounted on solid axles there is a conflict between dynamic stability and steering ability

It is shown that the stiffness and kinematic properties of all possible interwheelset connections are characterised by two properties describing the distortional characteristics of the vehicle in plan. Within this framework, the various possibilities for steered wheelsets are considered, and several past and current proposals are reviewed. Using the linear approach to dynamic stabibty and curve negotation the performance of existing and newly proposed configurations is discussed

For any symmetric, two-axle vehicle it is shown that for perfect steering on a curve there should be zero bending stiffness between the wheelsets. It is further shown that if the bending stiffness is zero, the vehicle lacks dynamic stability as the critical speed of instability, is zero. In this case, the vehicle undergoes a steering oscillation which occurs at the kinematic frequency of a single wheelset and which is a motion in which pure rolling occurs

Similar results are obtained with vehicles with three or more axles if adjacent axles are connected by shear structures. However, it is shown that it is possible to satisfy both the requirements of perfect steering and a non-zero critical speed if the vehicle has zero bending stiffness and if, in addition to adjacent wheelsets being connected in shear, at least one pair of non-adjacent axles are connected by a shear structure.     

Steering and Dynamic Stability of Railway Vehicles

SUMMARY

For railway vehicles having coned wheels mounted on solid axles there is a conflict between dynamic stability and steering ability

It is shown that the stiffness and kinematic properties of all possible interwheelset connections are characterised by two properties describing the distortional characteristics of the vehicle in plan. Within this framework, the various possibilities for steered wheelsets are considered, and several past and current proposals are reviewed. Using the linear approach to dynamic stabibty and curve negotation the performance of existing and newly proposed configurations is discussed

For any symmetric, two-axle vehicle it is shown that for perfect steering on a curve there should be zero bending stiffness between the wheelsets. It is further shown that if the bending stiffness is zero, the vehicle lacks dynamic stability as the critical speed of instability, is zero. In this case, the vehicle undergoes a steering oscillation which occurs at the kinematic frequency of a single wheelset and which is a motion in which pure rolling occurs

Similar results are obtained with vehicles with three or more axles if adjacent axles are connected by shear structures. However, it is shown that it is possible to satisfy both the requirements of perfect steering and a non-zero critical speed if the vehicle has zero bending stiffness and if, in addition to adjacent wheelsets being connected in shear, at least one pair of non-adjacent axles are connected by a shear structure.     

Flutter and Divergence Instabilities in Systems of Railway Wheelsets with Semi-rigid Articulation

For railway vehicles having coned wheels mounted on solid axles there is, in general, a conflict between stability of lateral deviations from the motion along the track and ability to steer round curves. However, certain configurations of three-axle vehicle can satisfy the requirement of perfect curving and for certain values of the system parameters are dynamically stable. In the case where three wheelsets have semi-rigid articulation and either the distribution of conicity amongst the wheelsets or the position of the articulation joint are varied, it is shown that both flutter and divergence instabilities can occur at low speeds, in contrast to the more common dynamic instabilities of other forms of railway vehicle which are driven by the inertia forces.     

Static and Dynamic Stability of a Class of Three-Axle Railway Vehicles Possessing Perfect Steering

For railway vehicles having coned wheels mounted on solid axles there is, in general, a conflict between stability of lateral deviations from the motion along the track and ability to steer round curves. However, the three-axle vehicle with zero bending stiffness and with shear elasticity between all wheelsets can satisfy the requirement of perfect steering and for a range of values of equivalent conicity possesses both static and dynamic stability. The static and dynamic stability of the most general form of symmetric three-axle vehicle is investigated, and stability criteria derived.     

Nonlinear Design Approach to Four-Wheel-Steering Systems Using Neural Networks

Four-wheel-steering (4WS) systems have been studied and developed with remarkable success from the viewpoint of vehicle dynamics. Most of the control methods require a linearized bicycle model of the actual vehicle system which is however strongly influenced by tire nonlinearity. This paper proposes a new method to design the 4WS system taking into account the nonlinear characteristics of tires and suspensions. For this purpose integration of artificial neural network and linear control theory is introduced for the identification and control of a nonlinear vehicle model structured using a software for multi-body dynamic analysis (ADAMS). This model takes into account the nonlinear characteristics of actual vehicles with tires modeled by “magic formula“. The results of computer simulations show that the proposed nonlinear approach is efficient in improving the handling and stability of vehicles.     

Static and Dynamic Stability of Unsymmetric Two-Axle Railway Vehicles Possessing Perfect Steering

For railway vehicles having coned wheels mounted on solid axles, there is a conflict between the stability of lateral deviations from the motion along the track and the ability to steer round curves. A general theory is developed for the two-axle vehicle in which there is a lack of symmetry, fore-and-aft, both of the interwheelset structure and of the equivalent conicities of the wheelsets. It is shown that whilst parameters can be selected which provide static and dynamic stability and perfect steering for both directions of motion, there is a lightly damped mode of oscillation for any practical configuration and the significance of this is discussed.     

The Static Stability of Articulated Commercial Vehicles

This review of the state of the art emphasizes recent results that have been obtained in extending conventionalanalysis techniques to the treatment of “Highway Trains”, that is, to heavy trucks that have multiple articulation points and employ suspensions with multiple axles. Equations of motion applicable to the equilibrium turning performances of articulated vehicles are examined with respect to using analysis techniques involving steering gains, understeer gradients, effective wheel-bases, handling diagrams, and critical speeds. These examinations provide the basis for in sights into simplified approaches for understanding the steady turning mechanics of articulated, multi-axle vehicles riding on pneumatic tires.     

Determining the Characteristics of Helical Springs for Application in Suspensions of Railway Vehicles

This study concerns the theoretical calculation of the characteristics of helical springs used, particularly, for the primary and secondary suspensions of railway vehicles: the static characteristics will be determined by an exact method where as the dynamic characteristics will be determined with the help of an approximate method whose precision is, however, sufficient to make a valid evaluation of the dynamic behavior of the vehicles themselves.

The first part of the study is presented here, while a second part will appear in the next issue of “Vehicle System Dynamics”.     

Development of a new analytical model for a railway vehicle equipped with independently rotating wheels

The urban tram introduced recently has a low-floor structure for the convenience of passengers getting on and off. To adjust the low-floor level and improve performance on curves, most low-floor trams have IRWs (independently rotating wheels) with no central axle between the two wheels. Eliminating the central axle, however, creates several inherent problems, such as insufficient guiding force and excessive wear. To analyze these problems, a new analytical model is described in this paper to describe the dynamic characteristics of IRWs more precisely. This analytical model is developed to consider the effects of longitudinal creep in particular, which have been ignored in conventional analytical models of IRWs. In addition, a running stability analysis based on the newly developed analytical model is conducted to compare the critical speeds of IRW-axle vehicles and rigid-axle vehicles. The dynamic characteristics of an initial disturbance are compared to verify that the analytical model is effective in expressing the dynamic characteristics of IRWs.     

Optimal Performance of Variable Component Suspensions

Most vehicle suspension systems use fixed passive components that offer a compromise in performance between sprung mass isolation, suspension travel, and tireroad contact force. Recently, systems with discretely adjustable dampers and air springs been added to production vehicles. Active and semi-active damping concepts for vehicle suspensions have also been studied theoretically and with physical prototypes. This paper examines the optimal performance comparisons of variable component suspensions, including active damping and full-state feedback, for “quartercar” heave models. Two and three dimensional optimizations are computed using performance indicators to find the component parameters (control gains) that provide “optimal” performance for statistically described roadway inputs. The effects of performance weighting and feedback configuration are examined. Active damping is shown to be mainly important for vehicle isolation. A passive vehicle suspension can control suspension travel and tire contact force nearly as well as a full state feedback control strategy.     

Wheel slip control with torque blending using linear and nonlinear model predictive control

Modern hybrid electric vehicles employ electric braking to recuperate energy during deceleration. However, currently anti-lock braking system (ABS) functionality is delivered solely by friction brakes. Hence regenerative braking is typically deactivated at a low deceleration threshold in case high slip develops at the wheels and ABS activation is required. If blending of friction and electric braking can be achieved during ABS events, there would be no need to impose conservative thresholds for deactivation of regenerative braking and the recuperation capacity of the vehicle would increase significantly. In addition, electric actuators are typically significantly faster responding and would deliver better control of wheel slip than friction brakes. In this work we present a control strategy for ABS on a fully electric vehicle with each wheel independently driven by an electric machine and friction brake independently applied at each wheel. In particular we develop linear and nonlinear model predictive control strategies for optimal performance and enforcement of critical control and state constraints. The capability for real-time implementation of these controllers is assessed and their performance is validated in high fidelity simulation.     

A Computational Procedure for Non-Linear Dynamic Analysis of Vehicles

In the research and design of vehicles, the accurate simulation of their dynamic behaviour is often of interest. Therefore, on the one hand, the non-linear properties of suspensions and tyres may not be neglected. On the other hand, the application of large mechanical models is necessary in order to get correct information about the local dynamic behaviour of critical parts or elements of vehicles. With regard to these requirements, in this paper, a special computational procedure is presented for the non-linear dynamic analysis of vehicles using large finite element models. Correctness, in comparison to COSMOS/M commercial finite element program, and applicability of the presented procedure is shown by the use of a bus finite element model containing 2214 degrees of freedom.     

大跨径钢管混凝土拱桥的动力性能改造

移动车辆荷载是公路桥梁所承担的主要荷载形式，桥梁性能与服役寿命除依赖于其静力性能外，更依赖于结构在车辆荷载作用下的动力工作性能。钢管混凝土拱桥具有自重轻、强度大、抗变形能力强等优点，但若结构中各构件的组成、刚度、连接方式、布置形式不合理，虽然各项静力指标满足要求，也可能给结构带来严重的动力工作性能问题．结合黑龙江省哈同公路依兰牡丹江大桥的工程实例，针对该桥动力工作性能不足的问题，提出了对其动力性能进行改造的方法。经过改造后桥梁结构的动力工作性能有了很大程度的提高，保证了桥梁的安全性和使用性。     

Road disturbance estimation for the optimal preview control of an active suspension systems based on tracked vehicle model

This research investigates stochastic estimation of a look-ahead sensor scheme using the optimal preview control for an active suspension system of a full tracked vehicle (FTV). In this scheme, wheel disturbance input to the front wheels are estimated using the dynamic equations of the system. The estimated road disturbance input at the front wheels are utilized as preview information for the control of subsequently following wheels of FTV. The design of optimal preview control is used as a classical linear quadratic Gaussian problem by combining dynamics of the original system and estimation of previewed road inputs. The effectiveness of the preview controller is evaluated by comparing the estimated information with the measured information for different road profiles, where Kalman filter is used for the state-variables estimation of the FTV. This research also considers the reduced order estimation using commonly available sensors in order to decrease the number of sensors and measurements. The simulation results’ using an active suspension system with different preview information shows that the proposed system can be beneficial for the improvement of ride comfort of tracked vehicles without using any specialized sensors for preview information calculation.     

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.     

Computer-Aided Analysis of Urban Railway Vehicles

SUMMARY

Computer-aided dynamic simulations are usually employed when designing modern urban railway vehicles. Even if the modeling procedure is similar to the one used for trains, specific features have to be taken into account for tramways: they are designed for low speeds (less than 80 km/h) and narrow curves (less than 20 m of radius). Moreover, in order to improve accessibility, low floor designs have been developed (the floor lying at about 300 mm above the rails level). The simulation procedure has therefore to take account of the occurence of multiple wheel/rail contacts or the modelization of independent wheels. A specific software well adapted to the computer-aided design of urban railway vehicles has been developed by the Faculte Polytechnique de Mons. It performs the following classical analyses:

lateral linearization, modal analysis and root locii plots;

vertical linearization and comfort prediction;

non-linear time simulation in straight track (limit cycles) and in curve (derailment study)

parametric analyses

The vehicle model is formed by combination of bodies ( or flexible bodies, rotating bodies like wheelsets or independent wheels) and interconnection elements ( spring and damper elements). Contact between rails and wheels is treated as a part of the rotating bodies. A residual formulation has been preferred. When combined with the use of a complete iteration matrix, this formulation is well adapted to the treatment of stiff differential equations. It is based on a fast determination of the residues of the dynamic equations combined with the calculation of the iteration matrix through a numerical derivation procedure. The advantages of the approach are discussed. The model of a partial low floor vehicle with wheelsets and independent wheels is described.     

机械差速器耦合轮对轨道车辆导向性能分析

目前对称样式的差速器广泛应用于旋转车轮轨道车辆中,左右车轮差速控制的装置,成为时下研究的一个热点问题。研究学者在动力学的基础上对机械差速耦合轮对运行车辆的影响建立了模型进行分析,其中包含刚性的车轮和独立旋转的车轮,通过模型分析对比研究了机械差速耦合轮对车辆直线和曲线行驶导向性能的研究。研究发现,机械差速耦合装置独立旋转的车轮在车轮在复位对中有着积极的影响,对独立车轮导向能力差有了很好的解决办法。和刚性车轮进行比较,机械差速在通过性能上有着更好的安全性和导向性能。在城市轨道交通领域有着很好的应用。文章通过讨论车轮导向的原理,研究了机械差速耦合装置对轨道交通车辆导向性能的影响。     

Influence of compliance for an elastokinematic model of a proposed rear suspension

The research is carried out to improve passenger’s comfort to increase the vehicles stability in dynamic conditions. The literature available in the automotive engineering considers different topics for studying suspensions. An example represents mechanisms structure and analysis (synthesis, kinematics, and dynamics) under various operating conditions. These aspects have been approached before analytically, numerical. The current paper studies the influence of the lateral force on the contact patch of the wheel and the corresponding variations of vehicle stability parameters, such as camber angle and wheel rear track. The study is performed for a newer innovative rear suspensions mechanism which does not have a wheel track and camber angle variation, relative to the chassis, when the suspension components was considered rigid. A numerical solution is obtained through a virtual model on several commercial codes: MSC Adams, Patran, Nastran. Concerning the analysed parametes, their variation increases as the applied force is increased. Moreover, the largest variation corresponds to the case were elastic bushings and deformable links are considered.     

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.