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.     

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.     

Smoothing dry friction damping by dither generated in rolling contact of wheel and rail and its influence on ride dynamics of freight wagons

Friction dampers of mechanical systems are frequently exposed to medium-frequency (M-F) dither generated in the surrounding environment. A dithered system of technical importance is the railway freight wagon with friction dampers in the primary suspension developing two-dimensional friction, where dither is generated by the rolling contact of wheel and rail. This paper presents some results of the investigation of the influence of dither on dry friction damping. This influence has been studied experimentally and theoretically, and the parameters of dither influencing dry friction damping have been indicated. An experimental set-up has been designed that allows investigating friction damping in the presence of dither. The experiments have shown that friction damping in the presence of the M-F dither behaves like viscous damping. This means that dither smoothes dry friction as far as damping is concerned. To investigate this phenomenon theoretically, a rheological model of dry friction has been proposed that is applicable to one- and two-dimensional friction. In the latter case, the model takes into account friction anisotropy. According to performed numerical simulations of freight wagon motion, with dither supplied to the model through measured vertical accelerations of axle boxes, smoothing dry friction by dither strongly influences ride dynamics of the wagon with friction dampers in the primary suspension. Smoothing dry friction by dither should be accounted for in numerical simulations of motion of vehicles with friction dampers in the primary suspension by employing a proper model of the two-dimensional friction and application of realistic dither generated by rolling contact.     

车辆气动力展向相关性传递函数及其对桥上运动车辆响应的影响

为研究运动车辆气动力的展向相关性对桥上运动车辆响应的影响,在分析运动车辆顺风向和竖向脉动风速谱的基础上,发展出一种新型的运动车辆脉动风速相干函数形式,推导出与顺风向和竖向脉动风速对应的运动车辆气动力的展向相关性传递函数,并根据“余弦规则”得到作用在运动车辆上的抖振力谱。通过建立列车-轨道-桥梁多体系统耦合振动仿真模型,以单节列车在典型的高速铁路桥梁上行驶为例,对比不同车速、不同风速与不同地表类型时,运动车辆气动力的传递函数对桥上运动车辆响应的影响。研究结果表明：当考虑上述传递函数时,车辆响应的均方根均有不同程度的降低,其中对车体横向和竖向加速度均方根的影响最为显著;当车速为40 m·s^-1时,在考虑与不考虑传递函数情况下,车体横向加速度均方根的相对误差高达40.6%,车体竖向加速度均方根的相对误差也高达36.6%;随着车速的提高,各车辆响应均方根的相对误差均逐渐变小;随着风速的提高,轮重减载率和轮轨垂向力均方根的相对误差均逐渐变大,而车体竖向Sperling指标和轮轨横向力均方根的相对误差却先增加后减小;从A类地表类型到D类地表类型,车体加速度均方根以及车体Sperling指标的相对误差均逐渐增大,而轮轨力均方根、脱轨系数均方根、轮重减载率均方根的相对误差均先增大后减小。     

Modelling,simulation and applications of longitudinal train dynamics

ABSTRACT

Significant developments in longitudinal train simulation and an overview of the approaches to train models and modelling vehicle force inputs are firstly presented. The most important modelling task, that of the wagon connection, consisting of energy absorption devices such as draft gears and buffers, draw gear stiffness, coupler slack and structural stiffness is then presented. Detailed attention is given to the modelling approaches for friction wedge damped and polymer draft gears. A significant issue in longitudinal train dynamics is the modelling and calculation of the input forces – the co-dimensional problem. The need to push traction performances higher has led to research and improvement in the accuracy of traction modelling which is discussed. A co-simulation method that combines longitudinal train simulation, locomotive traction control and locomotive vehicle dynamics is presented. The modelling of other forces, braking propulsion resistance, curve drag and grade forces are also discussed. As extensions to conventional longitudinal train dynamics, lateral forces and coupler impacts are examined in regards to interaction with wagon lateral and vertical dynamics. Various applications of longitudinal train dynamics are then presented. As an alternative to the tradition single wagon mass approach to longitudinal train dynamics, an example incorporating fully detailed wagon dynamics is presented for a crash analysis problem. Further applications of starting traction, air braking, distributed power, energy analysis and tippler operation are also presented.     

Semi-active suspension systems for railway vehicles using magnetorheological dampers. Part II: simulation and analysis

In this paper, the semi-active suspension system for railway vehicles based on the controlled (MR) fluid dampers is investigated, and compared with the passive on and passive off suspension systems. The lateral, yaw, and roll accelerations of the car body, trucks, and wheelsets of a full-scale railway vehicle integrated with four MR dampers in the secondary suspension systems, which are in the closed and open loops respectively, are simulated under the random and periodical track irregularities using the established governing equations of the railway vehicle and the modelled track irregularities in Part I of this paper. The simulation results indicate that (1) the semi-active controlled MR damper-based suspension system for railway vehicles is effective and beneficial as compared with the passive on and passive off modes, and (2) while the car body accelerations of the railway vehicle integrated with semi-active controlled MR dampers can be significantly reduced relative to the passive on and passive off ones, the accelerations of the trucks and wheelsets could be increased to some extent. However, the increase in the accelerations of the trucks and wheelsets is insignificant.     

Dynamics of railway wagons subjected to braking torques on defective tracks

It is well known that track defects cause profound effects to the dynamics of railway wagons; normally such problems are examined for cases of wagons running at a constant speed. Brake/traction torques affect the speed profile due to the wheel–rail contact characteristics but most of the wagon–track interaction models do not explicitly consider them in simulation. The authors have recently published a model for the dynamics of wagons subject to braking/traction torques on a perfect track by explicitly considering the pitch degree of freedom for wheelsets. The model is extended for cases of lateral and vertical track geometry defects and worn railhead and wheel profiles. This paper presents the results of the analyses carried out using the model extended to the dynamics of wagons containing less ideal wheel profiles running on tracks with geometry defects and worn rails.     

Semi-active H∞ control of high-speed railway vehicle suspension with magnetorheological dampers

In this paper, semi-active H∞ control with magnetorheological (MR) dampers for railway vehicle suspension systems to improve the lateral ride quality is investigated. The proposed semi-active controller is composed of a H∞ controller as the system controller and an adaptive neuro-fuzzy inference system (ANFIS) inverse MR damper model as the damper controller. First, a 17-degree-of-freedom model for a full-scale railway vehicle is developed and the random track irregularities are modelled. Then a modified Bouc–Wen model is built to characterise the forward dynamic characteristics of the MR damper and an inverse MR damper model is built with the ANFIS technique. Furthermore, a H∞ controller composed of a yaw motion controller and a rolling pendulum motion (lateral motion+roll motion) controller is established. By integrating the H∞ controller with the ANFIS inverse model, a semi-active H∞ controller for the railway vehicle is finally proposed. Simulation results indicate that the proposed semi-active suspension system possesses better attenuation ability for the vibrations of the car body than the passive suspension system.     

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.     

Multibody dynamics modelling of the freight train bogie system

Previous work in the railway technology laboratory at Virginia Polytechnic Institute and State University (Virginia Tech) focused on better capturing the dynamics of the friction wedge, modelled using three-dimensional rigid body dynamics with unilateral contact conditions. The current study extends the previous work to a half-bogie model treated as an application of multibody dynamics with unilateral contact to model the friction wedge interactions with the bolster and the sideframe. The half-bogie model was derived using MATLAB and functions as a three dimensional, dynamic, and multibody dynamics model comprised of four rigid bodies: a bolster, two friction wedges, and a sideframe assembly. This expanded model allows each wedge four degrees of freedom: vertical displacement, longitudinal displacement (between the bolster and sideframe), pitch (rotation around the lateral axis), and yaw (rotation around the vertical axis). The bolster and the sideframe are constrained to have only the vertical degree of freedom. The geometry of these bodies can be adjusted for various simulation scenarios. The bolster can be initialised with a pre-defined yaw (rotation around the vertical axis) and the sideframe may be initialised with a pre-defined pitch/toe (rotation around the lateral axis). The results of the multibody dynamics in half-bogie model simulation are shown in comparison with results from NUCARS^®, an industry standard in train-modelling software, for similar inputs.     

An Investigation into Stick-Slip Vibrations on Vehicle/Track Systems

A model for the numerical simulation of vehicle/track interaction and stick-slip vibration is presented. A finite element model is developed to calculate vertical contact forces. These forces are then coupled through the contact patch into a non-linear time-domain model by which the stick-slip vibration behaviour of a wheel-rail system is analysed. The investigation suggests that stick-slip vibration may occur if a vehicle which has a maligned or an initial 'wind-up' wheeiset meets a vertical irregularity or contaminants on the track.     

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.

     

An Investigation into Stick-Slip Vibrations on Vehicle/Track Systems

SUMMARY

A model for the numerical simulation of vehicle/track interaction and stick-slip vibration is presented. A finite element model is developed to calculate vertical contact forces. These forces are then coupled through the contact patch into a non-linear time-domain model by which the stick-slip vibration behaviour of a wheel-rail system is analysed. The investigation suggests that stick-slip vibration may occur if a vehicle which has a maligned or an initial ‘wind-up’ wheeiset meets a vertical irregularity or contaminants on the track.     

The stability and mechanical characteristics of heavy haul couplers with restoring bumpstop

To investigate the stability and mechanical characteristics of a type of heavy haul coupler with restoring bumpstop, the geometry and force states of couplers were analysed at different yaw angles and the longitudinal forces. The structural characteristics of this coupler were summarised. To aid in the investigation, 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 and lateral forces were tested in order to investigate the effect of relevant parameters on the locomotive's wheelset lateral forces. The results show that only when the bumpstop force exceeds half of the coupler longitudinal compression force, can the follower be rotated and the yaw angle of the coupler increase. The bumpstop preload is the most important stabilising factor. The coupler lateral force is constant when the coupler longitudinal force is smaller than the critical values of 2000, 1400 and 1150 kN at coupler free angles of 7°, 8° and 9°, respectively, for operation on straight track. The coupler free angle and the locomotive's lateral clearance of the secondary stopper are important in decreasing the wheelset lateral forces of the locomotive. It is advised that a smaller locomotive's secondary lateral suspension stiffness, a free clearance of 35 mm and an elastic clearance of 15 mm from the secondary lateral stopper be selected. If the coupler's free angle is less than the self-stabilising angle which is 5.5° for operation on straight track, the coupler is stable no matter how great the longitudinal force is. The wheelset lateral forces are allowed at the coupler longitudinal force of 2500 kN when the free angle is 6°. These studies establish meaningful improvements for the stability of couplers and match the heavy haul locomotive with its suspension parameters.     

汽车转向与悬架系统的集成控制研究

在建立了汽车转向与悬架系统的综合模型的基础上,运用一种具有扩展的调节器结构LQG控制方法,设计了 主动悬架控制器,实现对车身横摆角速度、车身垂直加速度、车身侧倾角和俯仰角的集成控制,从而显著提高汽车的 平顺性、操纵稳定性和安全性。     

Direct tire force generation algorithm based on non-iterative nonlinear inverse tire model

The function of vehicle dynamics control system is adjusting the yaw moment, the longitudinal force and lateral force of a vehicle body through several chassis systems, such as brakes, steering and suspension. Individual systems such as ESC, AFS and 4WD can be used to achieve desired performance by controlling actuator variables. However, integrated chassis control systems that have multiple objectives may not simply achieve the desired performance by controlling the actuators directly. Usually those systems determine the required tire forces in an upper level controller and a lower level controller regulates the tire forces through the actuators. The tire force is controlled in a recursive way based on vehicle state measurement, which may not be sufficient for fast response. For immediate force tracking, we introduce a direct tire force generation method that uses a nonlinear inverse tire model, a pseudo-inverse model of vehicle dynamics and the relationship between longitudinal force and brake pressure.     

Simulation of Bending-Torsional-Lateral Vibrations of the Railway Wheelset-Track System in the Medium Frequency Range

In the present paper, the dynamic interaction between a wheelset of a high-speed-train car and a railway track is considered with the help of a discrete-continuous mechanical model. This model enables us to investigate the bending-torsional-axial vibrations of the wheelset coupled with the vertical and lateral vibrations of the track through the wheel-rail contact forces. The results of numerical simulations performed for the wheelset motion both on straight and curved tracks demonstrate qualitative similarities of the corresponding dynamic responses of the system and essential quantitative differences of the respective amplitude and average values. Particularly severe interaction between the wheelset and the track is observed in the form of periodic resonances caused by parametric excitation from the track.     

基于ADAMS/Car弹性运动学对整车分析的影响

ADAMS软件提供了柔性体模块,可真实地模拟物体的运动,文章以某轿车为研究对象,利用ADAMS仿真软件建立了带有弹性下控制臂悬架的整车模型。选择开环转向事件里的转向阶跃输入进行仿真分析,在后处理中对横摆角速度、车速、侧向加速度和纵向加速度进行分析。结果表明,柔性体悬架模型比多刚体悬架模型对车身的横摆角速度、侧向加速度、纵向加速度以及速度等具有更好的抑制作用,有利于提高汽车操纵稳定性。     

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.     

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.