Dynamic Response of a Six-axle Locomotive to Random Track Inputs

SUMMARY

Spectral analysis techniques are employed to analyze the dynamic response of a six-axle locomotive on tangent track to vertical and lateral random track irregularities. The locomotive is represented by a thirty-nine (39) degrees of freedom model. A linear model is employed by considering small displacements, linear suspension elements and a linear theory for the wheel-rail interaction. Power spectral densities of displacements, velocities and accelerations and the statistical average frequencies of the system are obtained for each degree of freedom. Comparison of the calculated dominating frequencies with existing experimental values shows good agreement. The technique of spectral analysis is an effective tool for model validation, and for the determination of rail vehicle response to track irregularities. The probability functions for the response can be used as a measure for the ride quality of rail vehicles and for the study of fatigue damage of components.

     

High Speed Stability for Rail Vehicles Considering Varying Conicity and Creep Coefficients

SUMMARY

The critical or hunting speed of solid axle rail vehicles is known to be a strong function of primary suspension stiffness, wheel/rail profile geometry (conicity and gravitational stiffness), wheel/rail friction forces (creep coefficients), bogie/carbody inertia properties, and secondary suspension design. This paper deals with the problem of maximizing the critical speed through design of the primary and secondary suspension but with control only over the range of wheel/rail geometry and friction characteristics. For example, the conicity may varie from .05 to .3 and the linear creep coefficients from 25% to 100% of the predicted Kalker values.

It is shown that the maximum critical speed is greatly limited by the wheel/rail geometry and friction variations. It is also shown that, when lateral curving and ride quality are considered, the best design approach is to select an intermediate primary longitudinal stiffness, to limit the lowest value of conicity (e.g. to .1 or .2) by wheel profile redesign, increasing the secondary yaw damping value (yaw relaxation) and optimizing the primary and secondary lateral stiffness.     

High Speed Stability for Rail Vehicles Considering Varying Conicity and Creep Coefficients

The critical or hunting speed of solid axle rail vehicles is known to be a strong function of primary suspension stiffness, wheel/rail profile geometry (conicity and gravitational stiffness), wheel/rail friction forces (creep coefficients), bogie/carbody inertia properties, and secondary suspension design. This paper deals with the problem of maximizing the critical speed through design of the primary and secondary suspension but with control only over the range of wheel/rail geometry and friction characteristics. For example, the conicity may varie from .05 to .3 and the linear creep coefficients from 25% to 100% of the predicted Kalker values.

It is shown that the maximum critical speed is greatly limited by the wheel/rail geometry and friction variations. It is also shown that, when lateral curving and ride quality are considered, the best design approach is to select an intermediate primary longitudinal stiffness, to limit the lowest value of conicity (e.g. to .1 or .2) by wheel profile redesign, increasing the secondary yaw damping value (yaw relaxation) and optimizing the primary and secondary lateral stiffness.     

Dynamic Response of a Six-axle Locomotive to Random Track Inputs

Spectral analysis techniques are employed to analyze the dynamic response of a six-axle locomotive on tangent track to vertical and lateral random track irregularities. The locomotive is represented by a thirty-nine (39) degrees of freedom model. A linear model is employed by considering small displacements, linear suspension elements and a linear theory for the wheel-rail interaction. Power spectral densities of displacements, velocities and accelerations and the statistical average frequencies of the system are obtained for each degree of freedom. Comparison of the calculated dominating frequencies with existing experimental values shows good agreement. The technique of spectral analysis is an effective tool for model validation, and for the determination of rail vehicle response to track irregularities. The probability functions for the response can be used as a measure for the ride quality of rail vehicles and for the study of fatigue damage of components.     

Achieving anti-roll bar effect through air management in commercial vehicle pneumatic suspensions

ABSTRACT

This paper introduces the concept of managing air in commercial vehicle suspensions for reducing body roll. A conventional pneumatic suspension is re-designed to include higher-flow air hoses and dual levelling valves for improving the dynamic response of the suspension to the body roll, which commonly happens at relatively low frequencies. The improved air management allows air to get from the air tank to the airsprings quicker, and also changes the side-to-side suspension air pressure such that the suspension forces can more readily level the vehicle body, much in the same manner as an anti-roll bar (ARB). The results of a multi-domain simulation study in AMESim and TruckSim indicate that the proposed suspension configuration is capable of providing balanced airflow to the truck’s drive-axle suspensions, resulting in balanced suspension forces in response to single lane change and steady-state cornering steering maneuvers. The simulation results further indicate that a truck equipped with the reconfigured suspension experiences a uniform dynamic load sharing, smoother body motion (less roll angle), and improved handling and stability during steering maneuvers commonly occurring in commercial trucks during their intended use.     

Wheel slide protection control using a command map and Smith predictor for the pneumatic brake system of a railway vehicle

In railway vehicles, excessive sliding or wheel locking can occur while braking because of a temporarily degraded adhesion between the wheel and the rail caused by the contaminated or wet surface of the rail. It can damage the wheel tread and affect the performance of the brake system and the safety of the railway vehicle. To safeguard the wheelset from these phenomena, almost all railway vehicles are equipped with wheel slide protection (WSP) systems. In this study, a new WSP algorithm is proposed. The features of the proposed algorithm are the use of the target sliding speed, the determination of a command for WSP valves using command maps, and compensation for the time delay in pneumatic brake systems using the Smith predictor. The proposed WSP algorithm was verified using experiments with a hardware-in-the-loop simulation system including the hardware of the pneumatic brake system.     

Dynamics of Pneumatic Tire Vehicles with Connected Suspension Systems

SUMMARY

A vehicle model, with 10 degrees of freedom is used to investigate the skidding conditions of any wheel of the vehicle in motion. Equations for the load transfer and equations for the pneumatic tire spring and shock absorber are derived. Parameters such as gradual cornering, U-curve cornering, the wavy road surface of different wave lengths and cases of independent and connected suspension systems are inputs to the system. The tire calculated forces and their corresponding maximum resistance forces are the outputs of the systems. A connected suspension system is found to resist skidding better than the independent suspension system. The system is non-linear, and numerical solutions are obtained.     

An investigation of the effects of pneumatic actuator design on slip control for heavy vehicles

Progress in reducing actuator delays in pneumatic brake systems is opening the door for advanced anti-lock braking algorithms to be used on heavy goods vehicles. However, little has been published on slip controllers for air-braked heavy vehicles, or the effects of slow pneumatic actuation on their design and performance. This paper introduces a sliding mode slip controller for air-braked heavy vehicles. The effects of pneumatic actuator delays and flow rates on stopping performance and air (energy) consumption are presented through vehicle simulations. Finally, the simulations are validated with experiments using a hardware-in-the-loop rig. It is shown that for each wheel, pneumatic valves with delays smaller than 3 ms and orifice diameters around 8 mm provide the best performance.     

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.     

Tangential force variation due to the bogie direction reversal procedure

A range of tangential forces is generated within the contact patch when a wheelset moves on the rail. These forces are intensified when incorporating curved tracks and motored axle rail vehicles [Arrus, P., de Pater, A.D. and Meyers, P., 2002, The stationary motion of a one-axle vehicle along a circular curve with real rail and wheel profiles. Vehicle System Dynamics, 37(1), 29–58]. The wheelset is subject to flange contact if an unbalanced force remains in a curve towards the high rail gauge face. The resultant force in the transverse direction includes the lateral force, the radial force, and the creep forces in addition to the effect of the frequent wheelset displacement due to the kinematic oscillation [Iwnicki, S., 2003, Simulation of wheel–rail contact forces. Fatigue Fracture Engineering Material Structure, 26, 887–900]. This article has focused on a potential variation in some of the forces cited when the wheelset is subject to backward and forward movements. A severe wear rate observed within the wheel flange region in Iranian Railways was investigated by operating a test bogie on a curvaceous track. An obvious improvement in the wear rate and wear pattern of the wheels was attained when the second test bogie encountered a bogie direction reversal procedure. This enhancement is considered in this article from the force analysis standpoint.     

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.     

Rail Vehicles' Riding Quality and Comfort Related to Theoretical and Experimental Optimization Application to High Speed Trains

SUMMARY

The literature concerned with road damage caused by heavy commercial vehicles is reviewed. The main types of vehicle-generated road damage are described and the methods that can be used to analyse them are presented. Attention is given to the principal features of the response of road surfaces to vehicle loads and mathematical models that have been developed to predict road response. Also discussed are those vehicle features which, to a first approximation, can be studied without consideration of the dynamics of the vehicle, including axle and tyre configurations, tyre contact conditions and static load sharing in axle group suspensions. The main emphasis of the paper is on the dynamic tyre forces generated by heavy vehicles: their principal characteristics, their simulation and measurement, the effects of suspension design on the forces and the methods that can be used to estimate their influence on road damage. Some critical research needs are identified.     

Failure mode and effects analysis of dual levelling valve airspring suspensions on truck dynamics

Failure mode and effects analysis are performed for a dual levelling valve pneumatic suspension to determine the effect of suspension failure on tractor–semi-trailer dynamics, using a detailed model of suspension pneumatics coupled with a truck dynamic model. A key element of failure analysis in suspensions with one or two levelling valves is determining the effect on the vehicle body roll when one or more failures occur. The failure modes considered are mainly the suspension pneumatic components, including clogged levelling valve, bent control rod, disabled lever arm, and punctured or leaking connectors and pipes. The pneumatic suspension is modelled in AMESim, with critical parameters established through component testing. Upon validating the AMESim component model experimentally, the pneumatic suspension model is integrated into TruckSim for studying the consequences of suspension failure on truck dynamics. The simulation results indicate that the second levelling valve in a dual-valve arrangement brings a certain amount of failure redundancy to the system, in the sense that when one side fails, the other side can compensate for the failure. Equipping the trailer with dual levelling valves brings an additional stabilising effect to the vehicle in the event of tractor suspension failure.     

Effect of System Nonlinearities on Locomotive Bogie Hunting Stability

This paper presents the effect of system parameters on hunting of a rail vehicle with nonlinear yaw dampers and wheel-rail interface. This study is intended to complement earlier studies by True et al. where they investigated the effect of nonlinearities stemming from creep-creep force saturation and wheel/rail contact forces. The rail vehicle is represented by a two-axle truck (bogie) that includes the dynamics of the wheelsets and the truck frame. The numerical simulation results show that yaw damping can have a mixed effect on the hunting critical speed. In some ranges, increasing damping can actually lower the critical speed, unlike the results commonly obtained from a linear model. Flange contact nonlinearities can also have a significant effect on the hunting behavior. Large lateral stiffness of the rail can increase lateral force to vertical force (L/V) ratio during hunting. Increasing the gauge clearance, however, can have an opposite effect. The effect of a variety of other parameters, such as the primary suspension yaw and lateral stiffness, primary suspension lateral damping, wheelset mass, and truck frame mass, are summarized in a table.     

Optimization of curving performance of rail vehicles

The curving performance of a transit rail vehicle model with 21 degrees of freedom is optimized using a combination of multibody dynamics and a genetic algorithm (GA). The design optimization is to search for optimal design variables so that the noise or wear, arising from misalignment of the wheelsets with the track, is reduced to a minimum level during curve negotiations with flange contact forces guiding the rail vehicle. The objective function is a weighted combination of angle of attack on wheelsets and ratios of lateral to vertical forces on wheels. Using the combination of the GA and a multibody dynamics modelling program, A'GEM, the generation of governing equations of motion for complex nonlinear dynamic rail vehicle models and the search for global optimal design variables can be carried out automatically. To demonstrate the feasibility and efficacy of the proposed approach of using the combination of multibody dynamics and GAs, the numerical simulation results of the optimization are offered, the selected objective function is justified, and the sensitivity analysis of different design parameters and different design parameter sets on curving performance is performed. Numerical results show that compared with suspension and inertial parameter sets, the geometric parameter set has the most significant effect on curving performance.     

Optimization of curving performance of rail vehicles

The curving performance of a transit rail vehicle model with 21 degrees of freedom is optimized using a combination of multibody dynamics and a genetic algorithm (GA). The design optimization is to search for optimal design variables so that the noise or wear, arising from misalignment of the wheelsets with the track, is reduced to a minimum level during curve negotiations with flange contact forces guiding the rail vehicle. The objective function is a weighted combination of angle of attack on wheelsets and ratios of lateral to vertical forces on wheels. Using the combination of the GA and a multibody dynamics modelling program, A’GEM, the generation of governing equations of motion for complex nonlinear dynamic rail vehicle models and the search for global optimal design variables can be carried out automatically. To demonstrate the feasibility and efficacy of the proposed approach of using the combination of multibody dynamics and GAs, the numerical simulation results of the optimization are offered, the selected objective function is justified, and the sensitivity analysis of different design parameters and different design parameter sets on curving performance is performed. Numerical results show that compared with suspension and inertial parameter sets, the geometric parameter set has the most significant effect on curving performance.     

Robustness analysis of bogie suspension components Pareto optimised values

Bogie suspension system of high speed trains can significantly affect vehicle performance. Multiobjective optimisation problems are often formulated and solved to find the Pareto optimised values of the suspension components and improve cost efficiency in railway operations from different perspectives. Uncertainties in the design parameters of suspension system can negatively influence the dynamics behaviour of railway vehicles. In this regard, robustness analysis of a bogie dynamics response with respect to uncertainties in the suspension design parameters is considered. A one-car railway vehicle model with 50 degrees of freedom and wear/comfort Pareto optimised values of bogie suspension components is chosen for the analysis. Longitudinal and lateral primary stiffnesses, longitudinal and vertical secondary stiffnesses, as well as yaw damping are considered as five design parameters. The effects of parameter uncertainties on wear, ride comfort, track shift force, stability, and risk of derailment are studied by varying the design parameters around their respective Pareto optimised values according to a lognormal distribution with different coefficient of variations (COVs). The robustness analysis is carried out based on the maximum entropy concept. The multiplicative dimensional reduction method is utilised to simplify the calculation of fractional moments and improve the computational efficiency. The results showed that the dynamics response of the vehicle with wear/comfort Pareto optimised values of bogie suspension is robust against uncertainties in the design parameters and the probability of failure is small for parameter uncertainties with COV up to 0.1.     

气动翼板抑制悬索桥颤振的物理机理

从能量的角度研究气动翼板控制悬索桥颤振的物理机理。基于弯扭二模态耦合颤振系统,分别推导了气流由主梁和一对气动翼板输入系统的能量以及结构阻尼耗散能量的表达式。以某跨海方案桥为例进行了研究,结果表明：气动翼板能有效耗散气流由主梁输入系统的能量,桥梁颤振临界风速提高达30％。     

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.     

Wear/comfort Pareto optimisation of bogie suspension

Pareto optimisation of bogie suspension components is considered for a 50 degrees of freedom railway vehicle model to reduce wheel/rail contact wear and improve passenger ride comfort. Several operational scenarios including tracks with different curve radii ranging from very small radii up to straight tracks are considered for the analysis. In each case, the maximum admissible speed is applied to the vehicle. Design parameters are categorised into two levels and the wear/comfort Pareto optimisation is accordingly accomplished in a multistep manner to improve the computational efficiency. The genetic algorithm (GA) is employed to perform the multi-objective optimisation. Two suspension system configurations are considered, a symmetric and an asymmetric in which the primary or secondary suspension elements on the right- and left-hand sides of the vehicle are not the same. It is shown that the vehicle performance on curves can be significantly improved using the asymmetric suspension configuration. The Pareto-optimised values of the design parameters achieved here guarantee wear reduction and comfort improvement for railway vehicles and can also be utilised in developing the reference vehicle models for design of bogie active suspension systems.