The Dynamics of a Railway Freight Wagon Wheelset With Dry Friction Damping

Summary We investigate the dynamics of a simple model of a wheelset that supports one end of a railway freight wagon by springs with linear characteristics and dry friction dampers. The wagon runs on an ideal, straight and level track with constant speed. The lateral dynamics in dependence on the speed is examined. We have included stick-slip and hysteresis in our model of the dry friction and assume that Coulomb's law holds during the slip phase. It is found that the action of dry friction completely changes the bifurcation diagram, and that the longitudinal component of the dry friction damping forces destabilizes the wagon.     

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.     

Alternative friction models for braking train dynamics

Braking dynamics plays an essential role in ensuring the comfort and running safety of trains. Due to the complexity of the phenomena involved and the presence of dry friction, studies have been carried out by numerical methods using smoothening. Based on the non-smooth dynamics framework, in the present paper, an efficient and comprehensive alternative model is defined. Set-valued friction of Coulomb's law type is accounted for and motion equations are formulated as a differential inclusion. Some of the fundamental issues of contact dynamics are briefly reviewed. Static friction forces which arise in buffers are computed in a very intuitive and efficient manner, using an original method involving generalised inverses of matrices. The corresponding algorithm is described. Numerical integration is done by an event-driven algorithm. Indeterminate system configurations can be appropriately handled. The number of vehicles on which tests have been carried out ranged from 5 to 50. Comparison with the smoothening method reveals significant differences. Computational efficiency is dramatically improved. Computation speed can rise by a few orders of magnitude. Specific phenomena such as stick–slip or persistent longitudinal forces can be evidenced. Computed values of the system states differ substantially. In addition to this, any wagon connection model can be embedded.     

A review of dynamics modelling of friction wedge suspensions

Three-piece bogies with friction wedge suspensions are the most widely used bogies in heavy haul trains. Fiction wedge suspensions play a key role in these wagon systems. This article reviews current techniques in dynamic modelling of friction wedge suspension with various motivations: to improve dynamic models of friction wedge suspensions so as to improve general wagon dynamics simulations; to seek better friction wedge suspension models for wagon stability assessments in complex train systems; to improve the modelling of other friction devices, such as friction draft gear. Relevant theories and friction wedge suspension models developed by using commercial simulation packages and in-house simulation packages are reviewed.     

An integrated draft gear model with the consideration of wagon body structural characteristics

With the increase of railway wagon axle load and the growth of marshalling quantity, the problem caused by impact and vibration of vehicles is increasingly serious, which leads to the damage of vehicle structures and the components. In order to improve the reliability of longitudinal connection model for vehicle impact tests, a new railway wagon longitudinal connection model was developed to simulate and analyse vehicle impact tests. The new model is based on characteristics of longitudinal force transmission for vehicles and parts. In this model, carbodies and bogies were simplified to a particle system that can vibrate in the longitudinal direction, which corresponded to a stiffness-damping vibration system. The model consists of three sub-models, that is, coupler and draft gear sub-model, centre plate sub-model and carbody structure sub-model. Compared with conventional draft gear models, the new model was proposed with geometrical and mechanical relations of friction draft gears considered and with behaviours of sticking, sliding and impact between centre plate and centre bowl added. Besides, virtual springs between discrete carbodies were built to describe the structural deformation of carbody. A computation program for longitudinal dynamics based on vehicle impact tests was accomplished to simulate. Comparisons and analyses regarding the train dynamics outputs and vehicle impact tests were conducted. Simulation results indicate that the new wagon longitudinal connection model can provide a practical application environment for wagons, and the outputs of vehicle impact tests agree with those of field tests. The new model can also be used to study on longitudinal vibrations of different vehicles, of carbody and bogie, and of carbody itself.     

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.     

Dynamics of railway wagons subjected to braking/traction torque

Braking or traction torque is regarded as an important source of wheelset skid and a potential source of derailment risk that adversely affects the safety levels of train operations; therefore, this research examines the effect of braking/traction torque to the longitudinal and lateral dynamics of wagons. This paper reports how train operations safety could be adversely affected due to various braking strategies. Sensitivity of wagon dynamics to braking severity is illustrated through numerical examples. The influence of wheel/rail interface friction coefficient and the effects of two types of track geometry defects on wheel unloading ratio and wagon pitch are also discussed in the paper.     

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.     

Implementing a GPU-based numerical algorithm for modelling dynamics of a high-speed train

This paper discusses the initiative of implementing a GPU-based numerical algorithm for studying various phenomena associated with dynamics of a high-speed railway transport. The proposed numerical algorithm for calculating a critical speed of the bogie is based on the first Lyapunov number. Numerical algorithm is validated by analytical results, derived for a simple model. A dynamic model of a carriage connected to a new dual-wheelset flexible bogie is studied for linear and dry friction damping. Numerical results obtained by CPU, MPU and GPU approaches are compared and appropriateness of these methods is discussed.     

Analysis of the nonlinear dynamics of a 2–axle freight wagon in curves

This paper deals with the study of the nonlinear dynamic behaviour of 2-axle freight wagons in curves, considering the case of one single wagon (neglecting inter-car coupling forces) and of multiple wagons interacting through the buffers and the couplers. A multi-body model of a single wagon and of a three-car assembly is introduced, paying particular attention to the nonlinear and nonsmooth modelling of the suspensions and of the inter-car coupling elements. Using this model, a numerical analysis of the steady-state solution reached after the negotiation of curve transition is presented and bifurcations are identified for some particular values of the curve radius. For the single car case, it is shown that depending on the curve radius and the vehicle speed the carbody may experience severe periodic oscillations at speeds lying in the operating range of the vehicle. For the car-assembly case, it is shown that the coupling forces exchanged by the wagons significantly affect their dynamics in a curve, reducing the amplitude of vibration.     

Longitudinal train dynamics: an overview

This paper discusses the evolution of longitudinal train dynamics (LTD) simulations, which covers numerical solvers, vehicle connection systems, air brake systems, wagon dumper systems and locomotives, resistance forces and gravitational components, vehicle in-train instabilities, and computing schemes. A number of potential research topics are suggested, such as modelling of friction, polymer, and transition characteristics for vehicle connection simulations, studies of wagon dumping operations, proper modelling of vehicle in-train instabilities, and computing schemes for LTD simulations. Evidence shows that LTD simulations have evolved with computing capabilities. Currently, advanced component models that directly describe the working principles of the operation of air brake systems, vehicle connection systems, and traction systems are available. Parallel computing is a good solution to combine and simulate all these advanced models. Parallel computing can also be used to conduct three-dimensional long train dynamics simulations.     

Dynamic model for the wheel–rail contact friction

Accurately estimating the coefficient of friction (CoF) is essential in modelling railroad dynamics, reducing maintenance costs, and increasing safety in rail operations. The typical assumption of a constant CoF is widely used in theoretical studies; however, it has been noticed that the CoF is not constant, but rather depends on various dynamic parameters and instantaneous conditions. In this paper, we present a newly developed three-dimensional nonlinear CoF model for the dry rail condition and test the CoF variation using this model with estimated dynamic parameters. The wheel–rail is modelled as a mass–spring–damper system to simulate the basic wheel–rail dynamics. Although relatively simple, this model is considered sufficient for the purpose of this study. Simulations are performed at a train speed of 20 m/s using rail roughness as an excitation source. The model captures the CoF extremes and illustrates its nonlinear behaviour and instantaneous dependence on several structural and dynamic parameters.     

Effect of the combined centre of gravity on the running safety of freight wagons

ABSTRACT

This paper presents an analysis of loaded freight wagon dynamics in curve alignments. We investigate the effects of the combined centre of gravity (CCOG) on the running safety of freight wagons and examine proper position of the CCOG. A simple wagon-rail model is implemented using the multibody dynamics software ADAMS/Rail. The simulation model is operated on curve tracks with various radii and velocities and the curving performances are evaluated. The results indicate that the CCOG can be located within a flexible and accurate range. The longitudinal offset is good for the curving performance and the permissible lateral offset should be assessed based on the curve radius and cant deficiency.     

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.     

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.     

Optimal torque coordinating control of the launching with twin clutches simultaneously involved for dry dual-clutch transmission

As for the self-developed six-speed dry dual-clutch transmission (DCT), the optimal torque-coordinated control strategy between engine and dual clutches is proposed to resolve the problem of launching with twin clutches simultaneously involved based on the minimum value principle. Focusing on the sliding friction phase of the launching process, dynamics equations of dry DCT with two intermediate shafts are firstly established, and then the optimal transmitting torque variation rate and the driven plate's rotating speed of dual clutches are deduced by using the minimum value principle, in which the jerk intensity and friction work are taken as the performance indexes, and the terminal constraints of state variables are determined according to the driver's launching intention. Besides, the separating conditions of non-target gear clutch and the torque distributing relations of twin clutches are derived from the launching control targets that guarantee the approximately equal friction extent of two clutches and no power cycle. After the synchronisation of driving and driven plates of on-coming clutch, the output torque of engine is smoothly switched to the driver's demand level. Furthermore, launching the simulation model of the dry DCT vehicle is set up on the Matlab/Simulink platform. Simulation results indicate that the proposed launching control strategy not only can effectively reflect the driver's intention and extend the life span of twin clutches, but also obtain an excellent launching quality. Finally, the torque control laws of two clutches obtained through the simulation are transformed into clutch position control laws for the future realisation in the real car, and the closed-loop position controls of twin clutches in the launching process are conducted on the test bench with two sets of clutch actuator, obtaining preferable tracking effects.     

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.     

基于GT-Suite的活塞环-缸套摩擦特性研究

以活塞环-缸套为研究对象,利用GT-Suite软件建立了活塞环-缸套摩擦模型,将摩擦、润滑和动力学三者耦合起来,同时考虑了活塞环和缸套的扭曲变形、接触表面粗糙度等因素,计算分析标定工况下活塞环-缸套的油膜厚度、油压分布、摩擦力和摩擦功耗。着重分析了不同润滑油温和不同转速条件下第一环油膜厚度和摩擦功耗,结果表明:第一道活塞环处润滑效果差、摩擦功耗高;随着油温升高,油膜厚度显著减少,同时摩擦功耗显著减少,综合考虑润滑和摩擦功耗,发现油温在80~90℃时摩擦特性较为理想;随着转速提高,油膜厚度增加,同时摩擦功耗增加,转速对油膜厚度影响较小,对摩擦功耗有显著影响。     

Limit braking of a high-performance motorcycle

A mathematical-model-based study of the limit braking of a high-performance motorcycle and rider is described. Front and rear brakes are operable independently. A dry road and high friction are presumed, such that full braking of the front wheel would lead to an overturn or ‘stoppie’ in colloquial parlance. Effective braking needs to maintain some loading on the rear wheel. A planar but otherwise detailed system model is set up and braking strategies for front and rear are devised. Parameters of the braking control schemes are derived with the help of an optimisation process, minimising the final speed in braking from high speed over a fixed time interval. Simulation results are examined critically and the strategy is developed until efficient use of the friction available is made. The nature of optimal braking events is demonstrated. The influences of slipper-clutch torque setting and the rear-tyre target load chosen are shown.     

基于有限元的活塞组摩擦产热计算分析

基于有限元方法建立了活塞组摩擦产热计算模型,通过发动机工作过程的计算得到了活塞组摩擦产热计算所需的运动学和动力学边界。以某12缸增压柴油机为研究对象,计算得到了标定工况下其活塞组瞬时摩擦力及瞬时摩擦产热功率随曲轴转角的变化,活塞组平均摩擦产热总功率及其在活塞环、活塞裙部、气缸套的分配,以及活塞组摩擦产热所导致的活塞组、气缸套温升情况,计算分析了转速和负荷对活塞组摩擦产热的影响。