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.     

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.     

A Qualitative Analysis of the Dynamics of Self-Steering Locomotive Trucks

The primary purpose of this study is to provide a qualitative analysis of the dynamics of the self-steering trucks that are commonly used for freight locomotives - namely, EMD's Radial Truck and GE's Steerable Truck - on improving curving performance and increasing adhesion in curves. Although there exists a number of anecdotal statements on the ability of steerable trucks to reduce curving forces and increase adhesion in curves, to the best of our knowledge, there exists no study that provides a qualitative or quantitative analysis of these features of steerable trucks. Two aspects of locomotive trucks are essential for their ability to deliver small curving forces and high adhesion in curves. First, the ability to allow the axles to yaw sufficiently relative to the truck frames, such that they can hold a small angle of attack with the rail. Second, providing sufficiently large longitudinal stiffness between the end axles and the axles and truck frame, to accommodate high adhesions. An equivalent stiffness analysis is used to show that the two steerable trucks that are considered for this study are far superior to conventional, three-axle, straight trucks in providing both a smaller angle of attack and a higher longitudinal stiffness for better curving and adhesion characteristics. The qualitative analysis of this study agrees with the experience the railroads have had with their self-steering trucks. The findings of this study indicate that self-steering trucks can result in lower lateral forces, accommodate tighter curves, and deliver higher adhesion in curves; without lowering the critical hunting speed of the locomotive. The results further show that the steering mechanism stiffness can have a large effect on the lateral, longitudinal, and yaw stiffness between the end axles; therefore, significantly lowering curving forces, and increasing adhesion and critical hunting speed of the truck.     

A Qualitative Analysis of the Dynamics of Self-Steering Locomotive Trucks

The primary purpose of this study is to provide a qualitative analysis of the dynamics of the self-steering trucks that are commonly used for freight locomotives – namely, EMD's Radial Truck and GE's Steerable Truck – on improving curving performance and increasing adhesion in curves. Although there exists a number of anecdotal statements on the ability of steerable trucks to reduce curving forces and increase adhesion in curves, to the best of our knowledge, there exists no study that provides a qualitative or quantitative analysis of these features of steerable trucks. Two aspects of locomotive trucks are essential for their ability to deliver small curving forces and high adhesion in curves. First, the ability to allow the axles to yaw sufficiently relative to the truck frames, such that they can hold a small angle of attack with the rail. Second, providing sufficiently large longitudinal stiffness between the end axles and the axles and truck frame, to accommodate high adhesions. An equivalent stiffness analysis is used to show that the two steerable trucks that are considered for this study are far superior to conventional, three-axle, straight trucks in providing both a smaller angle of attack and a higher longitudinal stiffness for better curving and adhesion characteristics. The qualitative analysis of this study agrees with the experience the railroads have had with their self-steering trucks. The findings of this study indicate that self-steering trucks can result in lower lateral forces, accommodate tighter curves, and deliver higher adhesion in curves; without lowering the critical hunting speed of the locomotive. The results further show that the steering mechanism stiffness can have a large effect on the lateral, longitudinal, and yaw stiffness between the end axles; therefore, significantly lowering curving forces, and increasing adhesion and critical hunting speed of the truck.     

Stability enhancement of a high-speed train bogie using active mass inertial actuators

In this study, a method regarding frame lateral vibration control based on the state feedback of an additional oscillator is proposed, so as to improve the bogie hunting stability. The multi-objective optimisation method (MOOP), with two objective functions of the stability index and control effort, is solved by the NSGA-II algorithm to obtain the feedback gains. The frame lateral vibration control can effectively improve the bogie hunting stability according to the linear and non-linear analysis of a high-speed train bogie, in which a fault of the yaw damper and time delay in the control system are considered. The effect of the oscillator suspension parameters and time delay on the system stability and robustness are analysed. The results show that the damped vibration frequency of the oscillator should be equal to the bogie hunting frequency, but a harder oscillator suspension can be used to improve the hunting critical speed margin of the bogie control system. However, just as how the feeding the frame states back directly, a hard oscillator suspension will lead to instability in the control system at a certain time delay. Therefore, the improvement of bogie hunting stability and reduction of control system stability must be considered when optimising the oscillator parameters. For the 350?km/h train bogie covered in this study, the optimal mass, natural frequency and damping ratio of the additional oscillator are acquired.     

The stability mechanism and its application to heavy-haul couplers with arc surface contact

To investigate the stability mechanism of a type of heavy-haul coupler with arc surface contact, the force states of coupler were analysed at different yaw angles according to the friction circle theory and the structural characteristics of this coupler were summarised. A multi-body dynamics model with four heavy-haul locomotives and three detailed couplers was established to simulate the process of emergency braking. In addition, the coupler yaw instability was tested in order to investigate the effect of relevant parameters on the coupler stability. The results show that this coupler exhibits the self-stabilisation and less lateral force at a small yaw angle. The yaw angle of force line is less than the actual coupler yaw angle which reduces the lateral force and the critical instability. An increase in the friction coefficient of the arc contact surfaces can improve the stability of couplers. The friction coefficient needs to be increased with the increase in the maximum coupler longitudinal compressive force. The stability of couplers is significantly enhanced by increasing the secondary suspension stiffness and reducing the clearance of the lateral stopper of the locomotives. When the maximum coupler compressive force reaches 2500 kN, the required friction coefficient reduces from 0.6 to 0.35, which notably lowers the derailment risk caused by the coupler. The critical instability angle of the coupler mainly depends on the arc contact friction coefficient. When the friction coefficient is 0.3, the critical instability angle was 4–4.5°. The simulation results are consistent with the locomotive line tests. These studies establish meaningful improvements for the stability of couplers and match the heavy-haul locomotive with its suspension parameters.     

A linear complementarity method for the solution of vertical vehicle–track interaction

A new method is proposed for the solution of the vertical vehicle–track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel–rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel–rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel–rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle–track interaction including a separation between wheel and rail.     

Investigation of the effects of sleeper-passing impacts on the high-speed train

The sleeper-passing impact has always been considered negligible in normal conditions, while the experimental data obtained from a High-speed train in a cold weather expressed significant sleeper-passing impacts on the axle box, bogie frame and car body. Therefore, in this study, a vertical coupled vehicle/track dynamic model was developed to investigate the sleeper-passing impacts and its effects on the dynamic performance of the high-speed train. In the model, the dynamic model of vehicle is established with 10 degrees of freedom. The track model is formulated with two rails supported on the discrete supports through the finite element method. The contact forces between the wheel and rail are estimated using the non-linear Hertz contact theory. The parametric studies are conducted to analyse effects of both the vehicle speeds and the discrete support stiffness on the sleeper-passing impacts. The results show that the sleeper-passing impacts become extremely significant with the increased support stiffness of track, especially when the frequencies of sleeper-passing impacts approach to the resonance frequencies of wheel/track system. The damping of primary suspension can effectively lower the magnitude of impacts in the resonance speed ranges, but has little effect on other speed ranges. Finally, a more comprehensively coupled vehicle/track dynamic model integrating with a flexible wheel set is developed to discuss the sleeper-passing-induced flexible vibration of wheel set.     

轻型商用车悬架匹配

为优化某轻卡乘坐舒适性,首先对悬架系统的刚度、阻尼匹配过程进行了分析总结,给出了悬架刚度、阻尼的匹配流程。然后针对某些受开发周期及资源限制,无法进行实车调校及精确仿真的车型给出了基于理论计算及统计数据的悬架阻尼匹配方法。从阻尼比选择,各速度段阻尼比分布,双向比分布等方面分析,总结了方便、快速,且实车验证切实有效的悬架系统阻尼匹配方法。     

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.     

Effect of curved track support failure on vehicle derailment

In order to investigate the effect of curved track support failure on railway vehicle derailment, a coupled vehicle–track dynamic model is put forward. In the model, the vehicle and the structure under rails are, respectively, modelled as a multi-body system, and the rail is modelled with a Timoshenko beam rested on the discrete sleepers. The lateral, vertical, and torsional deformations of the beam are taken into account. The model also considers the effect of the discrete support by sleepers on the coupling dynamics of the vehicle and track. The sleepers are assumed to move backward at a constant speed to simulate the vehicle running along the track at the same speed. In the calculation of the coupled vehicle and track dynamics, the normal forces of the wheels/rails are calculated using the Hertzian contact theory and their creep forces are determined with the nonlinear creep theory by Shen et al [Z.Y. Shen, J.K. Hedrick, and J.A. Elkins, A comparison of alternative creep-force models for rail vehicle dynamic analysis, Proceedings of the 8th IAVSD Symposium, Cambridge, MA, 1984, pp. 591–605]. The motion equations of the vehicle/track are solved by means of an explicit integration method. The failure of the components of the curved track is simulated by changing the track stiffness and damping along the track. The cases where zero to six supports of the curved rails fail are considered. The transient derailment coefficients are calculated. They are, respectively, the ratio of the wheel/rail lateral force to the vertical force and the wheel load reduction. The contact points of the wheels/rails are in detail analysed and used to evaluate the risk of the vehicle derailment. Also, the present work investigates the effect of friction coefficient, axle load and vehicle speed on the derailments under the condition of track failure. The numerical results obtained indicate that the failure of track supports has a great influence on the whole vehicle running safety.     

用于公路车-桥系统振动分析的精细化轮胎模型

为了解决当前公路车桥耦合振动模型中轮胎模型过于简化、车轮-路面接触力与桥梁响应计算结果不够精确的问题,提出了一种精细化轮胎模型.首先基于车辆橡胶轮胎的几何、力学特征,建立了径向弹簧力学模型并进行了理论推导;然后考虑轮胎与路面接触面的刚度分布特征和高速状况下轮胎的惯性力,提出了轮胎接触面分布刚度的计算方法,保证了轮胎接触...     

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.     

油气弹簧非线性特性对车辆平顺性的影响分析

推导并建立了某工程车辆油气弹簧的非线性刚度和阻尼特性的数学模型，并将其导入到车辆模型中。根据汽车悬架质量分配特点．将汽车简化为两自由度的舣质量振动系统，对此两自由度模型的车轮加速度、车身加速度和悬架动行程进行了仿真从仿真结果可以看出，非线性油气弹簧能很好地衰减由路面传递来的振动。分析了刚度和阻尼的变化对车辆平顺性的影响。     

Sliding mode-based lateral vehicle dynamics control using tyre force measurements

In this work, a lateral vehicle dynamics control based on tyre force measurements is proposed. Most of the lateral vehicle dynamics control schemes are based on yaw rate whereas tyre forces are the most important variables in vehicle dynamics as tyres are the only contact points between the vehicle and road. In the proposed method, active front steering is employed to uniformly distribute the required lateral force among the front left and right tyres. The force distribution is quantified through the tyre utilisation coefficients. In order to address the nonlinearities and uncertainties of the vehicle model, a gain scheduling sliding-mode control technique is used. In addition to stabilising the lateral dynamics, the proposed controller is able to maintain maximum lateral acceleration. The proposed method is tested and validated on a multi-body vehicle simulator.     

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.     

High Speed Stability and Curving Performance of Longitudinally Unsymmetric Trucks with Semi-active Control

The possibility of improving both the dynamic stability and curving performance of railway trucks through the use of semi-active control is discussed. According to the direction of vehicle motion, the truck parameters are switched in a longitudinally asymmetric manner. Using a method of evaluation proposed here, the stability of trucks having the same steering ability was examined using linear models. A truck equipped with independently rotating wheels on the trailing axle and with unsymmetric primary suspension has the best performance. A realistic method of achieving this is proposed: using harder primary longitudinal stiffness on the trailing axle and using a primary yaw damper only on the leading, allows bidirectional operation by changing the damping force.     

Active lateral secondary suspension with H ∞ control to improve ride comfort: simulations on a full-scale model

In this study, a full-scale rail vehicle model is used to investigate how lateral ride comfort is influenced by implementing the H _∞ and sky-hook damping control strategies. Simulations show that significant ride comfort improvements can be achieved on straight track with both control strategies compared with a passive system. In curves, it is beneficial to add a carbody centring Hold-Off Device (HOD) to reduce large spring deflections and hence to minimise the risk of bumpstop contact. In curve transitions, the relative lateral displacement between carbody and bogie is reduced by the concept of H _∞ control in combination with the HOD. However, the corresponding concept with sky-hook damping degrades the effect of the carbody centring function. Moreover, it is shown that lateral and yaw mode separation is a way to further improve the performance of the studied control strategies.     

The effect of spring pads in the secondary suspension of railway vehicles on bogie yaw resistance

This paper deals with properties of bogie yaw resistance of an electric locomotive with secondary suspension consisting of flexi-coil springs supplemented with tilting spring pads. Transversal stiffness of a sample of a spring/pad assembly was measured on a dynamic test stand of the University of Pardubice (Czech Republic) and the results were applied into a multi-body model of the locomotive created in the simulation tool ‘SJKV’. On the basis of the simulation results, a detailed analysis of the bogie yaw resistance was performed in order to explain the effect in dynamic behaviour of the locomotive when the moment against bogie rotation (and therefore the distribution of guiding forces on individual wheels, as well) is influenced with the vehicle speed in a certain curve. Results of this analysis show that the application of suspension elements with strongly directionally dependent transversal stiffness into the secondary suspension can just lead to a dependency of the bogie yaw resistance on cant deficiency, i.e. on the vehicle speed in curve. This fact has wide consequences on the vehicle dynamics (especially on the guiding behaviour of the vehicle in curves) and it also points out that the current method of evaluation of the bogie yaw resistance according to relevant standards, which is related with assessment of the quasistatic safety of a railway vehicle against derailment, is not objective enough.     

Fuzzy Logic Active and Semi-Active Control of Off-Road Vehicle Suspensions

For off-road vehicles, minimizing the absorbed power is the main objective of suspension control. The primary cause of increase in the absorbed power in off-road vehicles driven at high speeds on harsh courses is the exhaustion of the suspension travel. Fuzzy-logic approach to active and semi-active off-road vehicle suspension control, with the goal of improving the speed of the vehicle over rough terrains are developed. The ride metric used for quantifying improvements is the absorbed power of the sprung mass. Particular attention is paid to the proper modeling of the suspension using both the full kinematic constraints and the more convenient two degree of freedom linear model of the quarter vehicle suspension. The nonlinearities due to the kinematic constraints on motion are accounted for by modifying the stiffness and damping coefficients of the suspension spring and dashpot in the linear model. The control laws are developed using the less complex model and demonstrated in the fully constrained environment. Nonlinearities of the suspension, including tire stiffness/damping and bumpstops are included at all stages of controller development.