Tractor-Semitrailer Dynamics: Design of the Fifth Wheel∗

SUMMARY

The nonlinear equations of motion are derived for a tractor-semitrailer truck where both the itractor and the semitrailer yaw, pitch, roll, and translate. Special emphasis is placed on the constraints imposed by the fifth wheel on the vehicle motion. In particular, the effects of two proposed fifth wheel design changes on the jackknifing behavior of a vehicle in a turning, braking maneuver are studied. The results demonstrate that the tendency of the vehicle to jackknife can be reduced with a geometric modification of the fifth wheel.     

基于RTK五轮仪研制的汽车运动性能试验研究

利用GPS载波相位RTK技术研制成了汽车道路试验RTK五轮仪。应用该五轮仪进行了汽车的直线和曲线运动性能测试,结果表明可以更精确测取汽车运动性能参数,实现基于动态轨迹测量的汽车运动性能试验评价。     

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.     

Nonlinear optimal integrated vehicle control using individual braking torque and steering angle with on-line control allocation by using state-dependent Riccati equation technique

This paper proposes the solution of state-dependent Riccati equation as a nonlinear optimal regulator to stabilise the motion dynamics of the vehicle model subjected to sudden disturbance inputs in the lateral direction. The proposed nonlinear regulator coordinates individually actuated wheel braking torque and steering wheel angle simultaneously in an optimal manner. Performance criteria are satisfied by solving the Riccati equation based on the given cost function subjected to the nonlinear vehicle dynamics. On-line control allocation in terms of optimal brake torque distribution enhanced by optimal wheel steering angle input is achieved. Furthermore, the proposed optimal nonlinear regulator is an active fault-tolerant control system against partial by-wire actuator failures while guaranteeing stability with good performance due to its capability to allocate the individual control inputs in an optimal way. The main aim is to stabilise the motion dynamics of the vehicle model during short-term emergency situations along the desired straight trajectory manageable by average drivers and to provide vehicle stability and handling predictability through the interaction of individual wheel braking and steering actuators. Simulation results are used to illustrate the effectiveness of the proposed methodology.     

智能汽车自动紧急转向避撞的跟踪控制方法对比研究

为了提高智能汽车的主动安全性,提出3种不同的自动紧急转向避撞跟踪控制方法。首先建立汽车避撞简化模型,对制动、转向及两者相结合的3种不同避撞方式进行对比分析。其次,为深入研究汽车避撞过程中的实际响应,建立包含转向、制动及悬架3个子系统耦合特性的底盘18自由度统一动力学模型,并进行相关试验验证。随后构建智能汽车自动紧急转向避撞控制框架,对五次多项式参考路径和七次多项式参考路径的横摆角速度和横摆角加速度进行对比分析。接着以线性2自由度转向动力学模型为参考对象,对最优控制四轮转向、最优控制前轮转向、前馈与反馈控制相结合的前轮转向3种不同的跟踪控制系统分别进行设计。最后,以汽车底盘18自由度统一动力学模型为研究对象,对上述3种避撞控制系统进行仿真试验对比分析。研究结果表明：与制动避撞相比而言,转向避撞所需的纵向距离有较大降低,随着车速的增加和路面附着系数的越低,效果越明显;七次多项式参考路径比五次多项式参考路径的避撞过渡过程更为平缓,当实际车速与控制器所用车速不一致时,前者避撞性能表现更优;最优四轮转向控制系统在高、低2种不同附着路面都具有较好的避撞效果,最优前轮转向控制系统次之,而前馈与反馈相结合的前轮转向控制系统在低附着路面上则表现出严重的失稳。     

Numerical investigation on effect of the relative motion of stock/switch rails on the load transfer distribution along the switch panel in high-speed railway turnout

In railway turnout, the stock rail and switch rail are separated to enable the vehicle changing among the tracks, and they are provided with different rail resilience level on the baseplate. Therefore, there will be vertical relative motion between stock/switch rails under the wheel loads, and the relative motion will affect consequentially the wheel–rail contact conditions. A method is developed to investigate the effect of the relative motion of stock/switch rails on the load transfer distribution along the switch panel in high-speed railway turnout. First, the rigid wheel–rail contact points of stock/switch rails are calculated based on the trace line method, and then the contact status is determined by the presented equations, finally, the distribution of wheel–rail contact forces of stock/switch rails is obtained based on the continuity of interface displacements and forces which using an approximate surface deformation method. Some parametric studies have been performed, such as the lateral displacement of wheel set, the vertical contact forces, the wheel profiles and the vertical stiffness of rail pad. The results of the parametric study are presented and discussed.     

Yaw rate and side-slip control considering vehicle longitudinal dynamics

Most conventional vehicle stability controllers operate on the basis of many simplifying assumptions, such as a small steering wheel angle, constant longitudinal velocity and a small side-slip angle. This paper presents a new approach for controlling the yaw rate and side-slip of a vehicle without neglecting its longitudinal dynamics and without making simplifying assumptions about its motion. A sliding-mode controller is used to develop a differential braking controller for tracking a desired vehicle yaw rate for a given steering wheel angle, while keeping the vehicle’s side-slip angle as small as possible. The trade-off that exists between yaw rate and side-slip control is described. Conventional and proposed algorithms are presented, and the effectiveness of the proposed controller is investigated using a seven-degree-of-freedom vehicle dynamics model. The simulation results demonstrate that the proposed controller is more effective than the conventional one.     

Lateral handling improvement with dynamic curvature control for an independent rear wheel drive EV

The integrated longitudinal and lateral dynamic motion control is important for four wheel independent drive (4WID) electric vehicles. Under critical driving conditions, direct yaw moment control (DYC) has been proved as effective for vehicle handling stability and maneuverability by implementing optimized torque distribution of each wheel, especially with independent wheel drive electric vehicles. The intended vehicle path upon driver steering input is heavily depending on the instantaneous vehicle speed, body side slip and yaw rate of a vehicle, which can directly affect the steering effort of driver. In this paper, we propose a dynamic curvature controller (DCC) by applying a the dynamic curvature of the path, derived from vehicle dynamic state variables; yaw rate, side slip angle, and speed of a vehicle. The proposed controller, combined with DYC and wheel longitudinal slip control, is to utilize the dynamic curvature as a target control parameter for a feedback, avoiding estimating the vehicle side-slip angle. The effectiveness of the proposed controller, in view of stability and improved handling, has been validated with numerical simulations and a series of experiments during cornering engaging a disturbance torque driven by two rear independent in-wheel motors of a 4WD micro electric vehicle.     

不同整体式转向梯形机构分析方法的对比研究

介绍了一种整体式转向梯形机构的空间运动学分析方法，并利用该方法计算了某轻型货车的前轴内、外轮转角关系，计算结果与实测的该车前轴内、外轮转角关系曲线吻合较好。应用不同的整体式转向梯形机构的平面分析方法对同一辆货车进行了分析，对所得分析结果与试验结果进行比较，结果表明我国目前采用较多的汽车设计教材中介绍的转向梯形分析方法误差较大。     

双横臂独立悬架ADAMS建模及运动特性分析

利用ADAMS建立了某轻型车完整的双横臂独立悬架运动学仿真模型,为反映车辆的真实行驶工况,对左、右车轮测试平台分别创建了随机激励。通过仿真分析,揭示了运动特性参数在悬架运动过程中的变化规律,并对原导向机构存在的问题进行了优化计算。结果表明,前轮定位参数在优化前、后的变化量较小,均在设计要求的范围内;轮距和前轮侧向滑移量的变化较大,优化后二者都在理想的范围内变动,达到了预期优化目标。     

Advanced emergency braking under split friction conditions and the influence of a destabilising steering wheel torque

The steering system in most heavy trucks is such that it causes a destabilising steering wheel torque when braking on split friction, that is, different friction levels on the two sides of the vehicle. Moreover, advanced emergency braking systems are now mandatory in most heavy trucks, making vehicle-induced split friction braking possible. This imposes higher demands on understanding how the destabilising steering wheel torque affects the driver, which is the focus here. Firstly, an experiment has been carried out involving 24 subjects all driving a truck where automatic split friction braking was emulated. Secondly, an existing driver–vehicle model has been adapted and implemented to improve understanding of the observed outcome. A common conclusion drawn, after analysing results, is that the destabilising steering wheel torque only has a small effect on the motion of the vehicle. The underlying reason is a relatively slow ramp up of the disturbance in comparison to the observed cognitive delay amongst subjects; also the magnitude is low and initially suppressed by passive driver properties.     

Computational model for analyzing the kinematics and compliance characteristics of a commercial vehicle’s front suspension system

This paper develops a computational model that can analyze the kinematics and compliance characteristics of the front suspension of a commercial vehicle. This computational model is called the flexible multi-body dynamic model because it is developed by interfacing the finite element model of the multi-leaf spring with the dynamic model of the front suspension. In this paper, the bump mode and roll mode tests are performed with a suspension parameter measuring device (SPMD). An excitation load for creating the bump mode and roll mode motion is applied on the left and right tires slowly in in-phase and out-of-phase modes. In the test, wheel rate, toe angle change, caster angle change, and camber angle change, which together represent the wheel alignment, are measured along with the longitudinal and lateral wheel center loci which together represent the wheel center trajectory change. The reliability of the developed computational model is verified by comparing the simulation results with the SPMD test results. The developed flexible multi-body computational model will provide useful information on kinematics and compliance characteristics in the earliest stages of the commercial vehicle design process.     

汽车轮重动态检测中的单片机

介绍了89C51单片机应用于动态称重时检测车辆轮重的系统设计和实践。运用该单片机的指令系统和中断功能,给出了一种可靠的车速测量方法,实现了89C51单片机和PC机之间的串行通信。     

Development of multiaxial wheel hub dynamometer

This article introduces a development of a dynamometer, the Multiaxial Wheel Hub Dynamometer. It is capable of making the measurement of the three force components and three moment components that are produced by the tires on the vehicle in motion. The features of this dynamometer are high frequency-response, high performance, and easy operation. It can be attached to the wheel hub and allows the measurement to be made while the vehicle is actually driven. It produces precise real time data leading up to the exact analysis of vehicle dynamics.     

Vibrations Generated by Rail Vehicles: A Mathematical Model in the Frequency Domain

Movement of railway vehicles generates mechanical vibrations of a wide range of frequency. Depending on track materials, dissipation in form of viscous and hysteretic damping is present, and stiffness depends on strain-rate. In a previous paper (Castellani et al., 1998), a mathematical model to describe track materials has been developed in the frequency domain. The present paper applies this model, and attempts an analytical formulation of vehicle-track and soil interaction in the frequency domain. Rail vibrations during the passage of a vehicle are generated by three families of forces: a) the weight of the moving vehicle, b) the inertial reaction of the vehicle under the effect of corrugations over an undeformable rail, and, c) the vehicle inertial forces due to displacements of the rail. The first two groups of forces do not depend on the rail displacement, and the related mathematical formulation is a simple problem of forces at a mobile point of application. Formulation of the vehicle inertial forces, related to the rail vibration, requires reference to the acceleration of the rail, as seen by an observer in motion with the vehicle itself. Moreover, it is necessary to express the equilibrium equation of two dynamic systems, the vehicle and the track, at a the movable point of contact. There is no straight numerical procedure to solve this equation in the frequency domain. In the paper two theoretical propositions (Fryba, 1988; Grassie et al., 1982) are revisited with reference to the effect of the transit of a single wheel. Fryba infers that, in the absence of corrugations, the forces c) are null. Grassie et al. (1982) present a mathematical formulation of the interaction between wheel and rail, at mobile point of contact. At each position, the interaction force is of impulsive type. They presume that for a corrugation of harmonic type, of wavelength ?, the wheel is subject to a harmonic motion, of the frequency f = V/?, where V is the wheel velocity. All other frequency components, due to the impulse, are disregarded. Both these assumptions are shown to be inconsistent from a theoretical point of view, however they suggest suitable approaches to the solution.     

Vergleich einiger Rechen- und Messergebnisse zum Fahrverhalten von Sattelzügen

In this paper some results of theoretical and experimental investigations on the dynamic directional properties of heavy tractor-semitrailer vehicles are presented.

A nonlinear digital computer model was developed on which the theoretical system analysis is based. This model takes account of the nonUnear tire properties and the friction couple of the fifth wheel. A combination of numerical computation methods (Runge-Kutta and Newton-Raphson techniques) is used for the digital computer simulation.

Full scale road tests with articulated vehicles of 38 ton total weight were conducted for experimental validation of the used theoretical model. As input signals to the vehicle, predetermined steering wheel angle functions were used. The system output signals corresponding to these input functions were measured and stored.

A comparison of the obtained theoretical and experimental results shows a very good qualitative agreement and hence leads to the conclusion that the developed theoretical model can give consistent estimates of the basic dynamic vehicle properties.     

Roll Dynamics of Commercial Vehicles

An analytical model is developed here for studying the roll dynamics of commercial vehicles. Large displacements and rotations are accounted for in this nonlinear model so that it can be used for the study of roll dynamics well beyond the limits of wheel lift-off. The model is used to illustrate some of the dynamic phenomena in vehicle rollover, especially the interactive coupling between the roll and the vertical modes of motion. The influence of suspension backlash on rollover resistance is demonstrated, and the phenomenon of roll motion resonance is illustrated to suggest new means for evaluating vehicle rollover sensitivity.     

汽车电子转向技术发展与展望

汽车电子转向系统是一种全新概念的转向系统，其取消了转向盘和转向车之间的机械连接，通过软件协调它们之间的运动关系，可以实现一系列传统转向系统无法实现的特殊功能。它可以实现传动比的任意设置，并对随车速变化的参数进行补偿。并且可以和ABS、汽车动力学控制、防碰撞、单个车轮转向、轨道跟踪、自动侧向导航等功能相结合，实现对汽车的整体控制。综述了国外汽车电子转向技术的研究现状，介绍了电子转向系统的结构及性能特点，阐述了电子转向系统的关键技术、主要问题及解决方法，并展望了电子转向系统的发展趋势。     

Analytical Wheel Models for Ride Dynamic Simulation of Off-road Tracked Vehicles

This paper outlines various analytical approaches of varying complexities to model the wheel in the ride dynamic formulation of off-road tracked vehicles. In addition to a proposed model, four analytical models available in the literature are compared to study their effectiveness in modeling the wheel/track-terrain interaction for ride dynamic evaluation of typical high mobility tracked vehicles. The ride dynamic model used in this study describes the bounce-pitch plane motion of an armoured personnel carrier (Ml 13 APC) traversing over an arbitrary rigid terrain profile at constant speed. The ride dynamic response of the tracked vehicle is evaluated with different wheel models, and compared against field-measured ride data. The relative performance of different wheel models are assessed based on the accuracy of response prediction and associated computational time. The proposed wheel model is found to perform very well in comparison, and is equally applicable for the case of wheeled vehicles.     

车辆纵振路面谱研究

为了解决车辆路面纵剪力对路面损伤的评价、车辆纵振平顺性的描述等难题，提出了车辆纵振路面谱这一概念。路面不平造成了车辆垂向和纵向的振动，使它与垂向路面谱共同产生。定义了车辆纵振路面谱的数学表达方法，设计了用五轮仪测量纵振路面谱的试验，对青－黄调整公路某段进行了实测。经数据回归分析，该路段垂向路面谱对应的路面级别为C级偏优，纵振路面谱为B级偏优。