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.     

Stabilization of High-Speed Railway Vehicles

The problems of critical speeds of railway vehicles with dry friction units determination are discussed. A new approach is used which extends the field of application of dynamic response linear analysis methods to vital nonlinear multibody systems. The special features concerning the influence of dry friction forces in the body supports on the trucks and parameters of horizontal constraints of wheelsets and truck frames on critical speed are indicated. It is shown that a significant rising of railway vehicle critical speeds can be reached by changing the structure of constraints between the body and the trucks.     

Non-Linear Dynamics of Railway Vehicles

The theoretical development of the lateral dynamics of railway vehicles has made rapid strides in recent years and many of the instabilities arising from the geometry of the wheel-rail interface and the forces acting in the contact area are now understood. In addition methods of analysis of curving and dynamic response to track irregularities have been developed and validated by experiment. This paper reviews the present status of equations of motion, limit cycle solutions for hunting oscillations and the relationship of stability to behaviour in curves.     

Stabilization of High-Speed Railway Vehicles

SUMMARY

The problems of critical speeds of railway vehicles with dry friction units determination are discussed. A new approach is used which extends the field of application of dynamic response linear analysis methods to vital nonlinear multibody systems. The special features concerning the influence of dry friction forces in the body supports on the trucks and parameters of horizontal constraints of wheelsets and truck frames on critical speed are indicated. It is shown that a significant rising of railway vehicle critical speeds can be reached by changing the structure of constraints between the body and the trucks.     

Recent Development in Active Steering of Railway Vehicles

Summary This paper presents the recent development on active steering for railway vehicles, and carries out a technical appraisal of different actuation schemes and control approaches. It brings together the latest research activities and findings for the full active steering techniques for rail vehicles with the solid-axle wheelsets, independently-rotating wheelsets and wheel-pairs without axles, but relevant work on passive and semi-active solutions is also briefly described. Potential benefits of the use of a combination of modern control technology and mechatronic approach are evaluated, and in particular solutions for the difficult design trade-off between the stability and the curving performance are presented. Various actuation configurations are discussed, and advantages and drawbacks of those schemes are investigated. The outline design using a number of control methods is analysed, and measurement requirement and state estimation techniques essential for implementation of the active steering schemes are also explored. In addition the issue of safety criticality is highlighted and a possible approach for developing fault-tolerant systems is proposed. Overall the paper provides an authoritative assessment of the major advances in actively-steered wheels and addresses outstanding critical issues.     

Stability and Riding Quality of Railway Vehicles

The so-called critical speed of a linearized railway vehicle is shown to be no useful measure for the stability of the system in practice. The important interaction between vehicle and track can be taken into account by the riding quality for a certain vehicle on every particular piece of track. The riding quality is determined by the accelerations transmitted to the payload, weighted according to comfort standards, and the relative displacements between wheel and rail. From the riding quality demands both for vehicle design and for maintenance of the track can be derived.     

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.     

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.     

History of Stability of Railway and Road Vehicles

Stability of running of vehicles is one of the important design criteria of railway and road vehicles. Railway vehicle stability is based on kinematics as well as contact mechanics. It reaches back to the 19th century and had its first hey-day with the work of Carter and Rocard on stability of locomotives. A rediscovery of their knowledge, which seemed to have been forgotten, was inevitable due to increased vehicle speeds since the early Fifties. — Though investigations on road vehicle stability only began approximately in 1930 with the treatment of the shimmy phenomenon, realistic solutions were available at the same time as for railway vehicles. Besides considering historical aspects we discuss in the paper links which exist between both approaches; open questions are described.     

History of Stability of Railway and Road Vehicles

Stability of running of vehicles is one of the important design criteria of railway and road vehicles. Railway vehicle stability is based on kinematics as well as contact mechanics. It reaches back to the 19th century and had its first hey-day with the work of Carter and Rocard on stability of locomotives. A rediscovery of their knowledge, which seemed to have been forgotten, was inevitable due to increased vehicle speeds since the early Fifties. — Though investigations on road vehicle stability only began approximately in 1930 with the treatment of the shimmy phenomenon, realistic solutions were available at the same time as for railway vehicles. Besides considering historical aspects we discuss in the paper links which exist between both approaches; open questions are described.     

Railway Vehicles With Generic Bogies Capable of Perfect Steering

SUMMARY

The general form of the equations of motion of a symmetric railway vehicle with two unsymmetric two-axle bogies is derived. The equations include a generic elastic stiffness matrix that describes the nature and configuration of the structural connections between the various components of the vehicle. This matrix satisfies the condition for perfect steering (without generating creep forces) on uniform curves and the necessary condition for dynamic stability derived in previous work. The paper shows the application of these basic conditions to a class of generic unsymmetric bogies. The analysis has as its objective the derivation of the simplest rather than the most general configuration that meets the conditions imposed. The results are related to past and current practice. It is shown that perfect steering, with stability at low speeds, can be achieved by means of passive suspension elements not employing linkages, and that it is possible to simplify existing steering arrangements.     

Railway Vehicles With Generic Bogies Capable of Perfect Steering

The general form of the equations of motion of a symmetric railway vehicle with two unsymmetric two-axle bogies is derived. The equations include a generic elastic stiffness matrix that describes the nature and configuration of the structural connections between the various components of the vehicle. This matrix satisfies the condition for perfect steering (without generating creep forces) on uniform curves and the necessary condition for dynamic stability derived in previous work. The paper shows the application of these basic conditions to a class of generic unsymmetric bogies. The analysis has as its objective the derivation of the simplest rather than the most general configuration that meets the conditions imposed. The results are related to past and current practice. It is shown that perfect steering, with stability at low speeds, can be achieved by means of passive suspension elements not employing linkages, and that it is possible to simplify existing steering arrangements.