Fundamentals of vehicle–track coupled dynamics

This paper presents a framework to investigate the dynamics of overall vehicle–track systems with emphasis on theoretical modelling, numerical simulation and experimental validation. A three-dimensional vehicle–track coupled dynamics model is developed in which a typical railway passenger vehicle is modelled as a 35-degree-of-freedom multi-body system. A traditional ballasted track is modelled as two parallel continuous beams supported by a discrete-elastic foundation of three layers with sleepers and ballasts included. The non-ballasted slab track is modelled as two parallel continuous beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The vehicle subsystem and the track subsystem are coupled through a wheel–rail spatial coupling model that considers rail vibrations in vertical, lateral and torsional directions. Random track irregularities expressed by track spectra are considered as system excitations by means of a time–frequency transformation technique. A fast explicit integration method is applied to solve the large nonlinear equations of motion of the system in the time domain. A computer program named TTISIM is developed to predict the vertical and lateral dynamic responses of the vehicle–track coupled system. The theoretical model is validated by full-scale field experiments, including the speed-up test on the Beijing–Qinhuangdao line and the high-speed running test on the Qinhuangdao–Shenyang line. Differences in the dynamic responses analysed by the vehicle–track coupled dynamics and by the classical vehicle dynamics are ascertained in the case of vehicles passing through curved tracks.     

大跨径钢桥面铺装层车辆动响应影响因素分析

从耦合振动的角度出发,研究大跨径钢桥面铺装层在车辆随机动荷载作用下的响应机制.将汽车等效为2自由度5参数模型,考虑桥梁表面不平顺产生的随机激励,建立车-钢桥面铺装耦合振动分析模型.利用模态分析与时变系数常微分方程求解方法,分析钢桥面铺装在车辆随机动荷载作用下的动力响应分布规律.定义由铺装层竖向位移、拉应力和拉应变表示的动力放大系数,研究车速、桥面不平度、铺装层开裂损伤和粘结层滑移等对动力放大系数的影响.结果表明,路面不平度、粘结层滑移是影响动力放大系数的主要因素,在进行大跨径钢桥面铺装结构设计时可考虑动力放大系数为1.5.     

Unscented Kalman filter for vehicle state estimation

Vehicle dynamics control (VDC) systems require information about system variables, which cannot be directly measured, e.g. the wheel slip or the vehicle side-slip angle. This paper presents a new concept for the vehicle state estimation under the assumption that the vehicle is equipped with the standard VDC sensors. It is proposed to utilise an unscented Kalman filter for estimation purposes, since it is based on a numerically efficient nonlinear stochastic estimation technique. A planar two-track model is combined with the empiric Magic Formula in order to describe the vehicle and tyre behaviour. Moreover, an advanced vertical tyre load calculation method is developed that additionally considers the vertical tyre stiffness and increases the estimation accuracy. Experimental tests show good accuracy and robustness of the designed vehicle state estimation concept.     

冲击荷载下双参数粘弹性地基矩形板的振动分析

机场刚性道面是通过具有一定传荷能力的接缝,达到共同工作的目的,基于此建立了冲击荷载作用下双参数粘弹性地基上四边弹性嵌固矩形板的新型力学模型。利用变分原理、Laplace变换和互等功定理求解了该系统的位移解析解,计算了弹性地基和粘弹性地基上有限矩形板的动力响应,探讨了地基参数和弹性嵌固边界刚性系数对板的动态响应的影响。得到了冲击荷载下双参数粘弹性地基矩形板系统参数影响的动力特性规律。该研究结果可为路面结构的动力响应分析、板厚设计、参数识别和质量评价等提供理论依据。     

New tyre-road contact model for applications at low speed

Most of the tyre models have been developed for high speed, combined forces, etc., however, in certain tests it is necessary to know tyre behaviour at very low speed in order to evaluate different systems. So, during vehicle inspection and maintenance of the steering and brake system, by means of sideslip tester and roller brake tester respectively, the forces transmitted by the tyres are measured; all of these inspections are carried out at low speeds. Furthermore, usually, automobile vehicles run at low speeds during an important part of their operating life (less than 60 km/h), mainly during urban traffic, and in steady state conditions. Therefore, it is particularly interesting to develop an accurate model of the contact patch tyrepavement for low speeds without the complexity of models that cover a wide speed range but provide less precision at very low speeds. The dynamometer plate has proved to be an appropriate test equipment to characterise the tyre-pavement contact at low speed and the steering geometry and wheel alignment. It has the feature of being able to carry out tests with the tyre installed in the vehicle as in completely real conditions. The main aim of this research is to set up a contact model between tyre and pavement at very low speed based on the measurement of longitudinal and lateral forces. A test methodology that allows carrying out the experimental tests in a systematic and controlled way with the dynamometer plate has also been developed. From this model it will be possible to estimate the forces that tyres are capable of transmitting in different situations to act in the parameters which affect these forces and maximize them.     

基于无限长梁模型的车路振动耦合系统半解析解

针对无限长道路与车辆耦合系统响应计算复杂难题,考虑地基的弹性特性与道路不平度,建立基于无限长欧拉-伯努利梁模型的车路振动耦合系统。进而以车辆为参考点建立移动坐标系,提出通过积分变换推导耦合系统振动响应解析解的方法,并应用留数定理对其进行数值计算,获得车辆垂向位移、加速度、路面振动响应等系统响应的半解析解。与传统应用模态叠加法的有限长道路与车辆耦合响应相比,具有更高的计算效率与精度,系统参数化研究也证明了该半解析解的有效性。     

振荡剪切荷载下沥青非线性黏弹性研究综述

沥青作为一种典型的黏弹材料,其黏弹性与路用性能密切相关,20世纪研究者们就开始关注并研究沥青的黏弹性。全面表征复杂条件下沥青的黏弹性,对于准确评价沥青路用性能具有重要的意义。实际应用中,沥青路面不可避免承受小幅及大幅振荡剪切荷载,沥青线性黏弹性与非线性黏弹性的研究同等重要,仅研究沥青线性黏弹性会导致沥青路用性能评价不准确。目前,基于稳态蠕变试验的沥青非线性黏弹性研究已基本成熟,但车辆对路面的实际作用模式为振荡剪切荷载,针对振荡剪切荷载下沥青非线性黏弹性的研究尤为重要。大幅振荡剪切试验是材料非线性黏弹性测试的主要方法,已成功应用于胶体、悬浮液等领域,而关于大幅振荡剪切荷载下沥青非线性黏弹性的研究则刚刚起步。为促进沥青非线性黏弹性的研究,综述了国内外大幅振荡剪切荷载下沥青非线性黏弹性的测试方法、分析方法及本构模型,指出了现有大幅振荡剪切荷载下沥青非线性黏弹性研究存在的问题,提出了未来沥青非线性黏弹性研究的建议。研究可为沥青非线性黏弹参数的确定、路用性能的评价及预测提供理论依据,同时为其他黏弹材料的非线性黏弹性研究提供一定参考。     

考虑弹性支撑边界条件的电动汽车-路面系统机电耦合振动特性分析

轮毂电机驱动电动汽车的簧下质量大导致轮胎动载荷增加,并且电机电磁力和转矩波动对车轮造成电机激励,进一步加剧车轮振动引起垂向振动负效应的问题。鉴于此,考虑电机的电磁激励,建立了电动汽车-路面系统的机电耦合动力学模型,推导了弹性支撑边界条件下路面结构的模态频率和振型表达式,以及路面振动引起的二次激励。计算了简支与弹性支撑边界条件下的路面模态频率,根据频率分布进行了截断阶数选取,并分析了边界条件、电机激励和车速对路面响应的影响。在此基础上,研究了不同行驶速度、路基反应模量及路面不平顺幅值下,激励形式对汽车车身加速度、悬架动挠度和轮胎动载荷的影响。结果表明：路面不平顺幅值越小,弹性支撑对路面响应的影响越大,弹性支撑边界条件下的路面响应较小,电机激励会引起路面响应的增加;弹性支撑边界条件下,路面不平顺幅值和路基反应模量越小,考虑路面不平顺、路面二次激励和电机激励的三重综合激励对电动汽车响应的影响越大,激励形式对轮胎动载荷的影响最大,对车身加速度的影响次之,对悬架动挠度的影响最小;电机激励导致轮胎动载荷增加,对路面破坏和寿命产生的负效应不容忽视。所建电动汽车-路面系统机电耦合模型及研究思路可为电动汽车垂向动力学分析提供参考与理论支持。     

A novel global sensitivity analysis on the observation accuracy of the coupled vehicle model

ABSTRACT

This paper proposes a novel 2-step global sensitivity analysis algorithm to provide an in-depth sensitivity analysis of the vehicle parameters on the system responses. A 9 degree-of-freedom nonlinear vertical–lateral coupled vehicle model is developed, and 12 parameters along with 7 system responses are selected for the sensitivity analysis. In order to reduce the computational effort, the proposed 2-step algorithm calculates the elementary effects and selects 7 influential parameters from these 12, and then uses the Sobol' method to obtain the global sensitivity indexes of these influential parameters. An unscented Kalman filter is finally designed to show the effect and importance of the selected sensitive parameters on the observation accuracy. Simulations with different vehicle types, velocities and tyre models have verified that the proposed algorithm can accurately describe the relationship between the vehicle parameters and system responses, which is of directive significance to improve vehicle controller and observer performances.     

Sliding window method for vehicles moving on a long track

The rail is modelled as a simply supported beam in the vehicle–track coupled dynamics. The beam is formulated by a partial differential equation that is transformed into an ordinary differential equation by the method of mode superposition for numerical calculation. However, the size of the matrix that is formed by the mode-superposition method increases significantly with track length, which limits the calculation efficiency. Some methods have been developed to solve this calculation issue, but they diminish the merits of the vehicle–track coupled dynamics, which would systematically investigate the dynamics of a vehicle and a track from the entire vehicle–track system. A new method is developed to resolve this contradiction. First, a theory based on a sliding window is established to improve the computational stability with respect to the length and the window-movement ratio. Then, two methods, namely finite element method analysis and an analytical solution, are used to verify the accuracy of the new method, which is highly efficient when used in a vertical half-vehicle–track coupled model to calculate the vehicle response when the vehicle moves on a long track. The results of the vehicle response calculated with and without the sliding window show good consistency.     

A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations

A sliding-mode observer is designed to estimate the vehicle velocity with the measured vehicle acceleration, the wheel speeds and the braking torques. Based on the Burckhardt tyre model, the extended Kalman filter is designed to estimate the parameters of the Burckhardt model with the estimated vehicle velocity, the measured wheel speeds and the vehicle acceleration. According to the estimated parameters of the Burckhardt tyre model, the tyre/road friction coefficients and the optimal slip ratios are calculated. A vehicle adaptive sliding-mode control (SMC) algorithm is presented with the estimated vehicle velocity, the tyre/road friction coefficients and the optimal slip ratios. And the adjustment method of the sliding-mode gain factors is discussed. Based on the adaptive SMC algorithm, a vehicle's antilock braking system (ABS) control system model is built with the Simulink Toolbox. Under the single-road condition as well as the different road conditions, the performance of the vehicle ABS system is simulated with the vehicle velocity observer, the tyre/road friction coefficient estimator and the adaptive SMC algorithm. The results indicate that the estimated errors of the vehicle velocity and the tyre/road friction coefficients are acceptable and the vehicle ABS adaptive SMC algorithm is effective. So the proposed adaptive SMC algorithm can be used to control the vehicle ABS without the information of the vehicle velocity and the road conditions.     

离散元法的沥青路面车-路动力学响应分析

为了分析车辆荷载作用下沥青路面结构的细观状态力学响应，建立了二自由度1/4车辆模型与多层路基路面耦合离散元模型，通过各结构层单轴压缩应力-应变试验与相同工况试验数据比较，经迭代运算得到路面离散元模型各结构层细观参数，应用试验得到的沥青路面细观参数建立多层路基路面模型，在离散元模型的上表面设定一定不平度，在一定速度作用下，1/4车辆模型在路基路面离散元模型上表面匀速移动，从而求解车辆动荷载作用下沥青路面各结构位移、应力等细观受力状态。进而改变1/4车辆模型的车体悬架刚度、悬架阻尼系数、轮胎刚度，轮胎阻尼系数，从而获得在改变车辆参数作用下沥青路面内部的应力变化规律。研究结果表明：基于离散元理论不但可以求得沥青路面在车-路相互作用下各层的应力与变形，而且还可以求得沥青路面各结构层颗粒流的变化趋势，在车辆移动荷载作用下，随着路基路面深度增加，各结构层颗粒流竖直方向动态位移与应力响应依次减少，其中上基层颗粒流动位移比上面层颗粒流动位移减少25%，下面层颗粒流竖向应力约为上面层颗粒流竖向应力的50%，水平方向上颗粒流既有压应力又有拉应力，变化比较复杂，上面层颗粒流水平方向主要承受压应力，其余结构层主要承受拉应力；增加轮胎与悬架刚度系数对模型颗粒流水平方向拉应力影响较大，增加轮胎与悬架阻尼系数对垂直方向颗粒流压应力与水平方向拉应力影响较小。     

Velocity and normal tyre force estimation for heavy trucks based on vehicle dynamic simulation considering the road slope angle

A precise estimation of vehicle velocities can be valuable for improving the performance of the vehicle dynamics control (VDC) system and this estimation relies heavily upon the accuracy of longitudinal and lateral tyre force calculation governed by the prediction of normal tyre forces. This paper presents a computational method based on the unscented Kalman filter (UKF) method to estimate both longitudinal and lateral velocities and develops a novel quasi-stationary method to predict normal tyre forces of heavy trucks on a sloping road. The vehicle dynamic model is constructed with a planar dynamic model combined with the Pacejka tyre model. The novel quasi-stationary method for predicting normal tyre forces is able to characterise the typical chassis configuration of the heavy trucks. The validation is conducted through comparing the predicted results with those simulated by the TruckSim and it has a good agreement between these results without compromising the convergence speed and stability.     

Influence of tyre–road contact model on vehicle vibration response

The influence of the tyre–road contact model on the simulated vertical vibration response was analysed. Three contact models were compared: tyre–road point contact model, moving averaged profile and tyre-enveloping model. In total, 1600 real asphalt concrete and Portland cement concrete longitudinal road profiles were processed. The linear planar model of automobile with 12 degrees of freedom (DOF) was used. Five vibration responses as the measures of ride comfort, ride safety and dynamic load of cargo were investigated. The results were calculated as a function of vibration response, vehicle velocity, road quality and road surface type. The marked differences in the dynamic tyre forces and the negligible differences in the ride comfort quantities were observed among the tyre–road contact models. The seat acceleration response for three contact models and 331 DOF multibody model of the truck semi-trailer was compared with the measured response for a known profile of test section.     

移动荷载下粘弹地基上刚性道面板弯沉求解

文中以一种更符合机场刚性道面实际情况的力学计算模型——移动荷载作用下粘弹性地基上无限大弹性薄板系统来研究道面弯沉的求解。应用线性系统的叠加原理和坐标变换,建立求解系统的动力响应广义积分公式,把运动荷载问题转化为获取位移脉冲响应函数。利用拉普拉斯和汉克尔变换求板在瞬时点源荷载作用下的解,再结合广义积分得到道面板在移动荷载作用下的弯沉解析解。     

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.     

轮压荷载作用下钢桥面铺装层力学机理分析

该文以工程中采用的一种新型钢桥面铺装为背景,建立了钢桥面板及铺装的三维有限元模型,分析了在车轮水平荷载作用下,铺装层与钢桥面的界面应力分布规律及轮载最不利位置,所得结论对钢桥面铺装的设计具有参考价值。     

非洲法语区典型粒料基层沥青路面结构力学分析

运用ALIZE软件,对非洲法语区典型柔性粒料基层路面结构在车辆荷载作用下的力学响应及结构受力特征和超标准轴载对结构的影响进行分析.结果 表明:总体上各结构层应力集中度高,弯沉盆范围小,容易产生车辙及疲劳裂缝;结构整体模量较低,联轴对结构影响较小;增加沥青层厚度可快速降低基层、底基层以及土基等结构层顶面压应变值,有利于提...     

A planar quasi-static constraint mode tyre model

The fast-paced, iterative, vehicle design environment demands efficiency when simulating suspension loads. Towards that end, a computationally efficient, linear, planar, quasi-static tyre model is developed in this work that accurately predicts a tyre's lower frequency, reasonably large amplitude, nonlinear stiffness relationship. The axisymmetric, circumferentially isotropic, stiffness equation is discretised into segments, then parameterised by a single stiffness parameter and two shape parameters. The tyre's deformed shape is independent of the overall tyre stiffness and the forces acting on the tyre. Constraint modes capture enveloping and bridging properties and a recursive method yields the set of active constraints at the tyre–road interface. The nonlinear stiffness of a tyre is captured by enforcing unidirectional geometric boundary conditions. The model parameters are identified semi-empirically; simulated cleat test loads match experiments within 7% including nonlinear stiffness when simulating a flat plate test and a discontinuous stiffness when simulating a cleat test.