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.     

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.     

Forced Steering of Rail Vehicles: Stability and Curving Mechanics

SUMMARY

A forced steering rail vehicle employs linkages between.the carbody and wheelsets to force a more radial wheelset alignment. It is shown that the curve negotiation capability of forced steering trucks is significantly improved over conventional and self steering radial trucks. Parametric curves are presented showing angle-of-attack and lateral flange force as a function of steering gain parameters and truck bending stiffness. It is also shown that the forced steering concept can produce kinematic instability and severely reduced critical speeds for low conicities and creep coefficients. Analytic expressions are derived that illustrate how these kinematic instabilities can be avoided.     

Forced Steering of Rail Vehicles: Stability and Curving Mechanics

A forced steering rail vehicle employs linkages between.the carbody and wheelsets to force a more radial wheelset alignment. It is shown that the curve negotiation capability of forced steering trucks is significantly improved over conventional and self steering radial trucks. Parametric curves are presented showing angle-of-attack and lateral flange force as a function of steering gain parameters and truck bending stiffness. It is also shown that the forced steering concept can produce kinematic instability and severely reduced critical speeds for low conicities and creep coefficients. Analytic expressions are derived that illustrate how these kinematic instabilities can be avoided.     

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.     

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.     

Independent Suspension, Self Steered Axle, and 4WS for Busses

The dynamic behavior of commercial vehicles fitted with differentr types of suspension mechanisms and steering devices is investigated in this paper. Six vehicle models have been constructed: 2WS-SA is a standard two wheel steering bus with solid axles; 2WS-DW is a 2WSA vehicle with independent double wishbone suspension in front and rear axles; SSA-SA is a 2WS system with solid axles, the rear one being mounted on a self steered mechanism; SSA-DW is a vehicle with independent double wishbone suspension in the front axle, and a solid self steered rear axle; 4WS-SA has four wheel steering with solid axles; and 4WS-DW is a 4WS vehicle with independent double wishbone suspension in front and rear axles. The dynamic response of these models has been assessed in terms of lateral acceleration, yaw velocity, tire forces, tire force reserves, and slip angles. The expected advantages of a 4WS system (higher acceleration rates and lower slip angles) will be corroborated but, at the same time, it will be shown that they are obtained at the cost of lower force reserves. Self steered mechanisms produce smaller body slip angles, but it will be shown that they give rise to larger yaw velocity overshootings. The particular independent suspension analyzed does not show significant improvements with respect to the solid axle counterpart.     

Automotive Stability and Handling Dynamics in Cornering and Braking Maneuvers

SUMMARY

Automotive steering behaviour is classified for steady-state cornering and the definitions of over-/understeer and stability/instability are well known. In this paper it is intended to apply these definitions to combined cornering and braking maneuvers i.e. to extend the criteria to quasi-steady-state conditions. This way of investigation was chosen because it gives a clear idea of the typical handling behaviour. Furthermore, the vehicle behaviour is analyzed using the cornering stiffness of the axles and front/rear cornering stiffness ratio because this is always of primary significance. The following contribution is based on a theoretical analysis considering the most important non-linear vehicle properties.

The paper deals with two groups of vehicles: single vehicles (passenger cars) and combinations (passenger car/caravan and tractor/semitrailer). In the case of combinations the effect of trailers on the towing vehicles is examined. So, careful attention is paid to the coupling forces, which alter the wheel loads and influence steerability and stability.     

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.     

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.     

The Steering Characteristics of Multiple Axle Bogie Systems

SUMMARY

Legislation limits the load that may be transferred to the roadway by the axies of a commercial vehicle and this has resulted in the development of multi axle bogies for both the tractor and trailer units of articulated vehicles and at the rear of rigid vehicles, some of these bogies contain self steering or articulation steered axles

Experience shows that the tyre wear characteristics of multi axle bogies may be unsatisfactory. The paper analyses the role of such bogies in the context of vehicle handling and shows how the lateral tyre forces vary between the axles. An hypotheses relating the forces in a steady state turn to wear is given. The analysis may also be applied to the general case of vehicle handling.     

Analysis of Influence of Design Parameters on Steered Wheels Shimmy of Heavy Vehicles

SUMMARY

In choosing the steering system parameters the tendency is towards the minimization of kinematic errors that appear during turning. For that developed procedures exist that take into account also the influence of kinematic of the suspension system on kinematic parameters of vehicle turning. Besides that, maintenance tests have shown, that increased deflections of the suspension system lead to increased wear of tires of steered wheels. In this paper, a method is developed for minimization of steered wheel shimmy and its wear also during the straight-line drive of heavy vehicles. The procedure can also be used in the phase of designing the heavy vehicles.     

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.     

A simplified model for evaluating tire wear during conceptual design

In the field of vehicle dynamics, commercial software can aid the designer during the conceptual and detailed design phases. Simulations using these tools can quickly provide specific design metrics, such as yaw and lateral velocity, for standard maneuvers. However, it remains challenging to correlate these metrics with empirical quantities that depend on many external parameters and design specifications. This scenario is the case with tire wear, which depends on the frictional work developed by the tire-road contact. In this study, an approach is proposed to estimate the tire-road friction during steady-state longitudinal and cornering maneuvers. Using this approach, a qualitative formula for tire wear evaluation is developed, and conceptual design analyses of cornering maneuvers are performed using simplified vehicle models. The influence of some design parameters such as cornering stiffness, the distance between the axles, and the steer angle ratio between the steering axles for vehicles with two steering axles is evaluated. The proposed methodology allows the designer to predict tire wear using simplified vehicle models during the conceptual design phase.     

Robust hierarchical controller with conditional integrator based on small gain theorem for reference trajectory tracking of autonomous vehicles

ABSTRACT

A robust trajectory tracking controller is designed for autonomous vehicles based on a hierarchical architecture to make the autonomous vehicle track a given reference trajectory. The controller consists of two sub controllers: kinematic controller and dynamic controller. Based on the kinematics of tracking reference trajectory, a desired yaw rate is calculated by kinematic controller to make the lateral deviation global asymptotic stable. Then, steering wheel angle is calculated by a vehicle dynamic controller to make the vehicle yaw rate converge to the desired value and make the vehicle dynamic stable. Conditional integration method is used in the sub controllers. This method guarantees global asymptotic stability of tracking reference values and considers the uncertainty of parameters and constraints of desired yaw rate and actuators. Then based on small-gain theorem, the condition of the finite-gain L stability is given to the hierarchical controller to ensure the interconnected sub systems stable and prevent the amplification of system disturbance. Finally, the effectiveness and robustness of the controller are validated by real vehicle experiments.     

Stability Criteria for Articulated Railway Vehicles Possessing Perfect Steering

SUMMARY

The general form of the equations o f motion o f multi-body articulated railway vehicles are used to establish the conditions which the elastic stiffness matrix, which describes the nature and configuration o f the suspension elements connecting the various bodies, must satisfy in order to achieve both perfect steering on circular curves and dynamic stability. The resulting criteria are then used to discuss the properties of various multi-axle configurations which are either typical of current practice or possibilities for future designs.     

Hybrid Laboratory Test Method for Anti-Lock Systems

SUMMARY

Railway vehicles with steered axles possess some unique dynamic characteristics. This paper reviews the reasons for the differences between these and more conventional vehicles and examines the results of analysis demonstrating the sensitivity of the phenomena to various mass, stiffness and geometric parameters. The implications which these results carry are discussed in terms of their design importance and their effect upon the performance boundaries of steel-wheeled rail vehicles. This review shows that a profound understanding of steered axle railway vehicles is developing and that this leads to the conclusion that a wide range of applications can benefit from their use.     

Modal Controllers for Active Steering of Railway Vehicles with Solid Axle Wheelsets

This paper presents the development of a modal control strategy for the active steering of solid axle railway vehicles and reveals benefits of actively stabilising the wheelsets of a railway vehicle. A modal decomposition is applied to a 2-axle railway vehicle to de-couple its body lateral and yaw motions and hence to allow more detailed analysis of the vehicle behaviour and more robust design of active controllers. Independent controllers for the two motions are developed based on the two de-coupled modes. Parameter variations such as creep coefficients and wheelset conicity are taken into account in the design process to guarantee a robust design. The study shows that, compared to a passive vehicle, the vehicles with actively steered wheelsets not only perform much better on a curved track, but also improve the ride quality on straight track. Computer simulations are used in the study to verify the development of the controllers and assess the system performance with the control scheme proposed.     

商用车双转向桥中间杆系优化设计

商用车双转向桥包含两个独立的转向梯形机构,它们之间的运动是通过中间杆系来传递的.在设计双转向桥转向系统时,为了避免转向桥轮胎异常磨损,需要两个转向桥的车轮转角协调变化.提出了一种对现有双转向桥中间杆系优化设计的方法,可协调车辆第一、第二转向桥的转角关系,避免了横向滑移导致的双前桥车轮转向时造成的轮胎异常磨损.     

Modal Controllers for Active Steering of Railway Vehicles with Solid Axle Wheelsets

This paper presents the development of a modal control strategy for the active steering of solid axle railway vehicles and reveals benefits of actively stabilising the wheelsets of a railway vehicle. A modal decomposition is applied to a 2-axle railway vehicle to de-couple its body lateral and yaw motions and hence to allow more detailed analysis of the vehicle behaviour and more robust design of active controllers. Independent controllers for the two motions are developed based on the two de-coupled modes. Parameter variations such as creep coefficients and wheelset conicity are taken into account in the design process to guarantee a robust design. The study shows that, compared to a passive vehicle, the vehicles with actively steered wheelsets not only perform much better on a curved track, but also improve the ride quality on straight track. Computer simulations are used in the study to verify the development of the controllers and assess the system performance with the control scheme proposed.