Non-steady state modelling of wheel–rail contact problem

Among all the algorithms to solve the wheel–rail contact problem, Kalker's FastSim has become the most useful computation tool since it combines a low computational cost and enough precision for most of the typical railway dynamics problems. However, some types of dynamic problems require the use of a non-steady state analysis. Alonso and Giménez developed a non-stationary method based on FastSim, which provides both, sufficiently accurate results and a low computational cost. However, it presents some limitations; the method is developed for one time-dependent creepage and its accuracy for varying normal forces has not been checked. This article presents the required changes in order to deal with both problems and compares its results with those given by Kalker's Variational Method for rolling contact.     

Kalker's algorithm Fastsim solves tangential contact problems with slip-dependent friction and friction anisotropy

This paper presents two extensions of Kalker's algorithm Fastsim of the simplified theory of rolling contact. The first extension is for solving tangential contact problems with the coefficient of friction depending on slip velocity. Two friction laws have been considered: with and without recuperation of the static friction. According to the tribological hypothesis for metallic bodies shear failure, the friction law without recuperation of static friction is more suitable for wheel and rail than the other one. Sample results present local quantities inside the contact area (division to slip and adhesion, traction) as well as global ones (creep forces as functions of creepages and rolling velocity). For the coefficient of friction diminishing with slip, the creep forces decay after reaching the maximum and they depend on the rolling velocity. The second extension is for solving tangential contact problems with friction anisotropy characterised by a convex set of the permissible tangential tractions. The effect of the anisotropy has been shown on examples of rolling without spin and in the presence of pure spin for the elliptical set. The friction anisotropy influences tangential tractions and creep forces. Sample results present local and global quantities. Both extensions have been described with the same language of formulation and they may be merged into one, joint algorithm.     

考虑摩擦滑移的普通板式橡胶支座剪切性能研究

普通板式橡胶支座作为中国量大面广的公路钢筋混凝土梁桥结构体系中的重要支承构件,其力学性能对局部和整体结构的刚度分布和受力变形特点具有一定的影响,甚至影响服役公路桥梁结构的安全性和适应性。因此,针对桥梁服役过程中该类支座普遍存在的滑移、脱空等典型病害特征,研究其不同受力状态下的剪切性能。考虑支座界面接触方式、几何尺寸等参数,设计并进行了6个普通板式橡胶支座的剪切性能试验。对不同参数影响下支座的损伤破坏模式、剪应变-剪应力曲线、支座有效剪切应变及抗剪刚度等参数进行对比分析。进一步应用有限元数值模拟方法,对摩擦滑移下的支座剪切性能进行参数分析,并将其有限元分析结果与普通板式橡胶支座的剪切性能试验结果进行对比。研究结果表明,支座上、下表面的接触摩擦条件可明显影响支座的水平侧移和抗侧力。对于界面摩擦因数较小的情况,卸载后支座摩擦滑动位移不能完全恢复,随着循环加载次数的增加,摩擦滑动位移增幅增大,且支座界面摩擦滑移可降低支座有效剪切变形和抗剪刚度的发挥。0.5,0.7,1.0等效剪切变形下支座的抗剪刚度试验结果、模拟结果与理论计算结果对比表明,试验结果与模拟结果吻合较好,而既有抗剪刚度理论计算结果偏大,且未考虑支座界面摩擦滑移、脱空的影响。因此,在进行实际桥梁结构的力学性能计算时,应考虑不同受力阶段支座力学性能指标的取值。     

Dynamic Friction Models for Road/Tire Longitudinal Interaction

Summary In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.     

Dynamic Friction Models for Road/Tire Longitudinal Interaction

Summary In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.     

Tangential problem solution for non-elliptical contact areas with the FastSim algorithm

This article deals with the application of the FastSim algorithm to the solution of the tangential contact problem for non-elliptical contact areas. At first, the causes creating problems for the solution of non-hertzian contact areas with this algorithm shall be analyzed. Then, different currently existing methods shall be studied, analyzing their accuracy characteristics and computational cost to determine whether or not they are appropriate to use in dynamic simulations. Finally, a new strategy shall be proposed that, in the opinion of the authors, offers good characteristics of precision and computational cost.     

Tangential problem solution for non-elliptical contact areas with the FastSim algorithm

This article deals with the application of the FastSim algorithm to the solution of the tangential contact problem for non-elliptical contact areas. At first, the causes creating problems for the solution of non-hertzian contact areas with this algorithm shall be analyzed. Then, different currently existing methods shall be studied, analyzing their accuracy characteristics and computational cost to determine whether or not they are appropriate to use in dynamic simulations. Finally, a new strategy shall be proposed that, in the opinion of the authors, offers good characteristics of precision and computational cost.     

Nonlinear tire-road friction control based on tire model parameter identification

A hierarchical control structure is a more suitable structural scheme for integrated chassis control. Generally, this type of structure has two main functions. The upper layer manages global control and force allocation, while the bottom layer allocates realized forces with 4 independent local tire controllers. The way to properly allocate these target forces poses a difficult task for the bottom layer. There are two key problems that require attention: obtaining the nonlinear time-varying coefficient of friction between the tire and different road surfaces and accurately tracking the desired forces from the upper layer. This paper mainly focuses on longitudinal tire-road friction allocation and control strategies that are based on the antilock braking system (ABS). Although it is difficult to precisely measure longitudinal tire-road friction forces for frequently changing road surface conditions, they can be estimated with a real-time measurement of brake force and angular acceleration at the wheels. The Magic Formula model is proposed as the reference model, and its key parameters are identified online using a constrained hybrid genetic algorithm to describe the evolution of tire-road friction with respect to the wheel slip. The desired wheel slip, with respect to the reference tire-road friction force from the top layer, is estimated with the inverse quadratic interpolation method. The tire-road friction controller of the extended anti-lock braking system (Ext-ABS) is designed through use of the nonlinear sliding mode control method. Simulation results indicate that acceptable modifications to changes in road surface conditions and adequate stability can be expected from the proposed control strategy.     

3D brush model to predict longitudinal tyre characteristics

A 3D tyre brush model, which aims to predict the longitudinal tyre characteristic under steady-state conditions by modelling the occurring physical effects in the tyre–road contact patch, is presented. The model includes an analytical method to describe the tyre footprint geometry, the pressure distribution, the slip due to the lateral tyre contour, the slip due to braking or traction and the longitudinal as well as the lateral shear stresses on a flattened tyre. The presented development tool offers a method to investigate different rubber friction data (caused by different tread compounds and/or surface textures) and to analyse its influence on longitudinal tyre characteristics. The tyre design is fixed (same casing, dimension and pattern). The results include the shear stresses as well as the different sliding velocities in the contact patch for different slip conditions. The model was developed for a standard summer pattern design and a standard tyre dimension (205/55R16). It can also be adapted to other tread designs and tyre dimensions. To offer a good comparability between model results and test bench measurements, the surface curvature of an internal test rig is considered.     

三塔悬索桥中塔主缆与鞍座间抗滑移试验研究

泰州长江公路大桥的初步设计中提出三塔悬索桥设计方案,为了研究特定工况下中塔主缆在鞍座内的滑移情况,江苏省长江公路大桥指挥部主持开展了主缆与中主鞍座间抗滑移试验研究。我国和美国、日本都曾开展过主缆与鞍座鞍槽间摩擦机理分析的试验,由于试验及试验模拟的差异等,试验结果离散性较大。本试验采用与实桥直径相同的镀锌钢丝和具有相同曲率、结构尺寸以及表面处理的鞍槽,力求全面模拟各束股与束股之间、钢丝之间、束股与鞍槽间的真实的接触特征,采用与实桥基本相同的接触挤压应力,以期能较为真实地反映三塔悬索桥中塔主缆在鞍座间的抗滑移情况。     

Re-adhesion control for a railway single wheelset test rig based on the behaviour of the traction motor

A method for detecting wheel slip/slide and re-adhesion control of AC traction motors in railway applications is presented in this paper. This enables a better utilisation of available adhesion and could also reduce wheel wear by reducing high creep values. With this method, the wheel–rail (roller) creepage, creep force and friction coefficient can be indirectly detected and estimated by measuring the voltage, current and speed of the AC traction motor and using an extended Kalman filter. The re-adhesion controller is designed to regulate the motor torque command according to the maximum available adhesion based on the estimated results. Simulations under different friction coefficients are carried out to test the proposed method.     

Estimation of the tyre–road maximum friction coefficient and slip slope based on a novel tyre model

In this article, a new approach to estimate the vehicle tyre forces, tyre–road maximum friction coefficient, and slip slope is presented. Contrary to the majority of the previous work on this subject, a new tyre model for the estimation of the tyre–road interface characterisation is proposed. First, the tyre model is built and compared with those of Pacejka, Dugoff, and one other tyre model. Then, based on a vehicle model that uses four degrees of freedom, an extended Kalman filter (EKF) method is designed to estimate the vehicle motion and tyre forces. The shortcomings of force estimation are discussed in this article. Based on the proposed tyre model and the improved force measurements, another EKF is implemented to estimate the tyre model parameters, including the maximum friction coefficient, slip slope, etc. The tyre forces are accurately obtained simultaneously. Finally, very promising results have been achieved for pure acceleration/braking for varying road conditions, both in pure steering and combined manoeuvre simulations.     

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.     

Dynamic simulation of railway vehicles: wheel/rail contact analysis

The multibody simulation of railway vehicle dynamics needs a reliable and efficient method to evaluate the contact points between wheel and rail, because their positions have a considerable influence on the direction and intensity of the contact forces. In this work, an innovative semi-analytic procedure for the detection of the wheel/rail contact points (named the DIFF method) is presented. This method considers the wheel and the rail as two surfaces whose analytic expressions are known and is based on the idea that in the contact points the difference between the surfaces has local minima and is equivalent to solving an algebraic two-dimensional system. The original problem can be reduced analytically to a simple scalar equation that can be easily solved numerically (since the problem dimension is one, even elementary non-iterative algorithms can be efficient).     

Shear forces in the contact patch of a braked-racing tyre

This article identifies tyre modelling features that are fundamental to the accurate simulation of the shear forces in the contact patch of a steady-rolling, slipping and cambered racing tyre. The features investigated include contact patch shape, contact pressure distribution, carcass flexibility, rolling radius (RR) variations and friction coefficient. Using a previously described physical tyre model of modular nature, validated for static conditions, the influence of each feature on the shear forces generated is examined under different running conditions, including normal loads of 1500, 3000 and 4500 N, camber angles of 0° and?3°, and longitudinal slip ratios from 0 to?20%. Special attention is paid to heavy braking, in which context the aligning moment is of great interest in terms of its connection with the limit-handling feel. The results of the simulations reveal that true representations of the contact patch shape, carcass flexibility and lateral RR variation are essential for an accurate prediction of the distribution and the magnitude of the shear forces generated at the tread–road interface of the cambered tyre. Independent of the camber angle, the contact pressure distribution primarily influences the shear force distribution and the slip characteristics around the peak longitudinal force. At low brake-slip ratios, the friction coefficient affects the shear forces in terms of their distribution, while, at medium to high-slip ratios, the force magnitude is significantly affected. On the one hand, these findings help in the creation of efficient yet accurate tyre models. On the other hand, the research results allow improved understanding of how individual tyre components affect the generation of shear forces in the contact patch of a rolling and slipping tyre.     

Estimation of maximum road friction coefficient based on Lyapunov method

With the real time and accurate information of motor torque and rotation speed of the four-in-wheel-motordrive electric vehicles, a slip based algorithm for estimating maximum road friction coefficient is designed using Lyapunov stability theory. Modified Burckhardt tire model is used to describe longitudinal slip property of the tire. By introducing a new state variable, a nonlinear estimator is proposed to estimate the longitudinal tire force and the maximum road friction coefficient simultaneously. With the appropriate selection of estimation gain, the convergence of the estimation error of the tire longitudinal force and maximum road friction coefficient is proved through Lyapunov stability analysis. In addition, the error is exponentially stable near the origin. Finally the method is validated with Carsim-Simulink co-simulation and real vehicle tests under multi working conditions in acceleration situation which demonstrate high computational efficiency and accuracy of this method.     

预压弹簧摩擦片式防滑差速器的优化设计

针对某款SUV后驱动桥的轮间预压弹簧摩擦片式防滑差速器结构,在综合考虑各种附着系数道路行驶的条件下,提出了预压弹簧摩擦片式防滑差速器的优化设计数学模型,应用混合离散变量组合型法(MDCP)对所给出的实例进行优化,并对优化的结果进行了分析。     

悬索桥主缆与索鞍间滑移行为及力学特征试验

为明确主缆与索鞍间的滑移机理,给相关理论研究提供必要基础,开展了试验研究以揭示主缆在不平衡力作用下的滑移行为及力学特征。制定了以两端张拉丝股模拟主缆平衡状态、以单侧顶推索鞍模拟主缆偏载状态的加载方案,并设计了相应的试验模型及测试方法;考虑索股侧面摩擦及试验索股数目的影响,开展了共8种工况的试验测试,利用实测数据对索力发展特征、索股滑移行为、滑移时变效应及名义摩擦因数变化规律等关键问题进行了系统研究。结果表明：顶推索鞍初期所产生的不平衡力在索股间平均分配,随着不平衡力增大,索股相继滑移且滑移后基本维持其索力差不变;索股均已滑移后的缆力差的发展具有单向性,但残余缆力差相对较小;索股位移发展包括弹性变形、局部蠕动和滑移3个典型阶段;主缆滑移时变效应有限,即主缆滑移后仍具备较可靠的稳载能力;名义摩擦因数随索股相继滑移而增加的同时会引起较突出的索力不均匀性问题,故在主缆抗滑措施研究中尚需对该问题予以重视;侧面摩擦是索股分批滑移及索股数目对试验结果产生影响的根本原因,鉴于侧面摩擦显著的抗滑贡献,对其继续深入研究并充分应用具有重要意义;建议多塔悬索桥主缆与索鞍间的摩擦因数取值可放宽至0.2。     

防抱制动系统控制算法的仿真研究

本文用要平面法分析了目前汽车上广泛使用的Ｐ１Ｒ３逻辑控制算法在不同条件下的收敛性，因这种算法只能使车轮的滑移率在μ－Ｓ曲线的峰值点变化，故采用逻辑控制的ＡＢＳ系统不能充分发挥它的最佳效能，本文进一步通过仿真研究了基于滑移率Ｓ的控制算法，并根据逻辑控制和滑移率控制的缺陷，提出了基于路面附着系数μ的控制算法，在理想状态下的证实了所提算法的有效性。