The Steering Characteristics of Multiple Axle Bogie Systems

Legislation limits the load that may be transferred to the roadway by the axies of a commercial vehicle and this has resulted in the development of multi axle bogies for both the tractor and trailer units of articulated vehicles and at the rear of rigid vehicles, some of these bogies contain self steering or articulation steered axles

Experience shows that the tyre wear characteristics of multi axle bogies may be unsatisfactory. The paper analyses the role of such bogies in the context of vehicle handling and shows how the lateral tyre forces vary between the axles. An hypotheses relating the forces in a steady state turn to wear is given. The analysis may also be applied to the general case of vehicle handling.     

半挂牵引车牵引座强度设计及整车稳定性分析

文章以半挂牵引车牵引座强度设计及整车稳定性分析为研究对象,首先对半挂牵引车牵引座工作原理进行了简单的介绍,随后对半挂牵引车牵引座强度设计优化进行了系统的探讨与分析,最后讨论了影响半挂牵引车整车稳定性因素,以供参考。     

Effects of multiple axles on the lateral dynamics of multi-articulated vehicles

This paper describes an analytical study of the lateral dynamics of multi-articulated vehicles with multiple axles. A linear planar model of vehicle dynamics is adopted for multiple-axle vehicle combinations with an optional number of trailers. Two tractor and double-trailer combinations are examined for their directional stability and response. Non-oscillatory stability and steering sensitivity in steady-state turning and lane changing are analysed using a stability factor of multiple-axle vehicle combinations. Off-tracking in the steady-state turning of multiple-axle vehicle combinations is also analysed. Numerical calculations for oscillatory stability, steering sensitivity, and off-tracking are presented for multiple-axle vehicle combinations.     

The Steering Characteristics of Multiple Axle Bogie Systems

SUMMARY

Legislation limits the load that may be transferred to the roadway by the axies of a commercial vehicle and this has resulted in the development of multi axle bogies for both the tractor and trailer units of articulated vehicles and at the rear of rigid vehicles, some of these bogies contain self steering or articulation steered axles

Experience shows that the tyre wear characteristics of multi axle bogies may be unsatisfactory. The paper analyses the role of such bogies in the context of vehicle handling and shows how the lateral tyre forces vary between the axles. An hypotheses relating the forces in a steady state turn to wear is given. The analysis may also be applied to the general case of vehicle handling.     

Active roll control for rollover prevention of heavy articulated vehicles with multiple-rollover-index minimisation

This paper presents the application of a nominal control design algorithm for rollover prevention of heavy articulated vehicles with active anti-roll-bar control. This proposed methodology is based on an extension of linear quadratic regulator control for ‘state derivative-induced (control coupled) output regulation’ problems. For heavy articulated vehicles with multiple axles, a performance index with multiple rollover indices is proposed. The proposed methodology allows us to compare the usefulness of various control configurations (i.e. actuators at different axles of the vehicle) based on the interaction of this control configuration with vehicle dynamics. Application of this methodology to a specific heavy articulated vehicle with a tractor semi-trailer shows that a single active anti-roll-bar system at the trailer unit gives better performance than multiple-axle actuators at tractor and trailer together with the single lane change manoeuvre as the external disturbance. Thus, the proposed methodology of this paper not only highlights the importance of the interactions between control and vehicle dynamics in rollover prevention problems but, in fact, proposes a novel technique to exploit the benefits of these interactions judiciously.     

Front-Rear Interaction of a Pitch-Plane Truck Model

Results from a previously reported experimental study on heavy articulated vehicles show that the choice of tractor unit strongly affects the dynamic tyre forces generated by the trailer axles, but the choice of trailer unit does not strongly affect the tyre forces generated by the tractor axles. These results have implications for assessing the road-friendliness of tractor and trailer units. The objectives of the work described in this paper are to understand the dynamic interaction between the tractor and trailer unit, and to identify the conditions for which strong interaction exists. A mathematical model with two degrees of freedom is used to simulate the pitch-plane dynamics of an articulated vehicle. Three idealized vehicles are investigated and three conditions for strong dynamic interaction are identified. It is thought that these conditions are likely to exist in a large proportion of heavy trucks.     

Implementation and validation of a three degrees of freedom steering-system model in a full vehicle model

This paper describes the coupling between a three degrees of freedom steering-system model and a multi-body truck model. The steering-system model includes the king-pin geometry to provide the correct feedback torque from the road to the steering-system. The steering-system model is combined with a validated tractor semi-trailer model. An instrumented tractor semi-trailer has been tested on a proving ground and the steering-wheel torque, pitman-arm angle, king-pin angles and drag-link force have been measured during steady-state cornering, a step steer input and a sinusoidal steering input. It is shown that the steering-system model is able to accurately predict the steering-wheel torque for all tests and the vehicle model is accurate for vehicle motions up to a frequency where the lateral acceleration gain is minimum. Even though the vehicle response is not accurate above this frequency, the steering-wheel torque is still represented accurately.     

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.     

A comprehensive study on the stability analysis of vehicle dynamics with pure/combined-slip tyre models

In this paper, a vehicle's lateral dynamic model is developed based on the pure and the combined-slip LuGre tyre models. Conventional vehicle's lateral dynamic methods derive handling models utilising linear tyres and pure-slip assumptions. The current article proposes a general lateral dynamic model, which takes the linear and nonlinear behaviours of the tyre into account using the pure and combined-slip assumptions separately. The developed methodology also incorporates various normal loads at each corner and provides a proper tyre–vehicle platform for control and estimation applications. Steady-state and transient LuGre models are also used in the model development and their responses are compared in different driving scenarios. Considering the fact that the vehicle dynamics is time-varying, the stability of the suggested time-varying model is investigated using an affine quadratic stability approach, and a novel approach to define the critical longitudinal speed is suggested and compared with that of conventional lateral stability methods. Simulations have been conducted and the results are used to validate the proposed method.     

A combined use of phase plane and handling diagram method to study the influence of tyre and vehicle characteristics on stability

This paper deals with in-curve vehicle lateral behaviour and is aimed to find out which vehicle physical characteristics affect significantly its stability. Two different analytical methods, one numerical (phase plane) and the other graphical (handling diagram) are discussed. The numerical model refers to the complete quadricycle, while the graphical one refers to a bicycle model. Both models take into account lateral load transfers and nonlinear Pacejka tyre–road interactions. The influence of centre of mass longitudinal position, tyre cornering stiffness and front/rear roll stiffness ratio on vehicle stability are analysed. The presented results are in good agreement with theoretical expectations about the above parameters influence, and show how some physical characteristics behave as saddle-node bifurcation parameters.     

A model of driver steering control incorporating the driver's sensing of steering torque

Steering feel, or steering torque feedback, is widely regarded as an important aspect of the handling quality of a vehicle. Despite this, there is little theoretical understanding of its role. This paper describes an initial attempt to model the role of steering torque feedback arising from lateral tyre forces. The path-following control of a nonlinear vehicle model is implemented using a time-varying model predictive controller. A series of Kalman filters are used to represent the driver's ability to generate estimates of the system states from noisy sensory measurements, including the steering torque. It is found that under constant road friction conditions, the steering torque feedback reduces path-following errors provided the friction is sufficiently high to prevent frequent saturation of the tyres. When the driver model is extended to allow identification of, and adaptation to, a varying friction condition, it is found that the steering torque assists in the accurate identification of the friction condition. The simulation results give insight into the role of steering torque feedback arising from lateral tyre forces. The paper concludes with recommendations for further work.     

半挂汽车列车直线行驶横向摆振研究

建立了双质心单轨半挂汽车列车数学模型,对某重型半挂汽车列车进行仿真,探讨了不同车速、不同装载条件及挂车轴距的变化对其直线行驶横向稳定性的影响。根据相似准则求得了某重型汽车列车模型,并对其进行了台架试验。试验结果与理论结果的对比分析表明,两误差较小,具有较好的一致性。     

Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents

For the first time, this paper investigates the application of the concept of Lyapunov exponents to the stability analysis of the nonlinear vehicle model in plane motion with two degrees of freedom. The nonlinearity of the model comes from the third-order polynomial expression between the lateral forces on the tyres and the tyre slip angles. Comprehensive studies on both system and structural stability analyses of the vehicle model are presented. The system stability analysis includes the stability, lateral stability region, and effects of driving conditions on the lateral stability region of the vehicle model in the state space. In the structural stability analysis, the ranges of driving conditions in which the stability of the vehicle model is guaranteed are given. Moreover, through examples, the largest Lyapunov exponent is suggested as an indicator of the convergence rate in which the disturbed vehicle model returns to its stable fixed point.     

Sliding mode-based lateral vehicle dynamics control using tyre force measurements

In this work, a lateral vehicle dynamics control based on tyre force measurements is proposed. Most of the lateral vehicle dynamics control schemes are based on yaw rate whereas tyre forces are the most important variables in vehicle dynamics as tyres are the only contact points between the vehicle and road. In the proposed method, active front steering is employed to uniformly distribute the required lateral force among the front left and right tyres. The force distribution is quantified through the tyre utilisation coefficients. In order to address the nonlinearities and uncertainties of the vehicle model, a gain scheduling sliding-mode control technique is used. In addition to stabilising the lateral dynamics, the proposed controller is able to maintain maximum lateral acceleration. The proposed method is tested and validated on a multi-body vehicle simulator.     

Kinematics of a smart variable caster mechanism for a vehicle steerable wheel

The lateral force of a tyre is a function of the sideslip and camber angles. The camber angle can provide a significant effect on the stability of a vehicle by increasing or adjusting the required lateral force to keep the vehicle on the road. To control the camber angle and hence, the lateral force of each tyre, we can use the caster angle of the wheel. We introduce a possible variable and controllable caster angle ? in order to adjust the camber angle when the sideslip angle cannot be changed. As long as the left and right wheels are steering together according to a kinematic condition, such as Ackerman, the sideslip angle of the inner wheel cannot be increased independently to alter the reduced lateral force because of weight transfer and reduction of the normal load F _z . A variable caster mechanism can adjust the caster angle of the wheels to achieve their top capacity and maximise the lateral force, when needed. Such a system would potentially increase the safety, stability, and maneuverability of the vehicles. Using the screw theory, this paper will examine the kinematics of a variable caster and present the required mathematical equation to calculate the camber angle as a function of suspension mechanism parameters and other relevant variables. Having a steered wheel about a tilted steering axis will change the position and orientation of the wheel with respect to the body of the car. This paper provides the required kinematics of such a suspension and extracts the equations in special practical situations. The analysis is for an ideal situation in which we substitute the tyre with its equivalent disc at the tyre plane.     

Lateral Tyre Force by a Milliken Test on a Flat Track Roadway Simulator

The lateral tyre force versus slip angle and vertical load is obtained through specific tests on the single tyre or with a theoretical-empirical analysis with physical models. This study is about the possibility to use a third way: Executing a particular handling test, known as Force-Moment test, using a Flat Track Roadway Simulator (the Fiat-Elasis MTS FTRS). The understanding and the project of vehicle handling is strongly based on the knowledge of lateral tyre force response [1, 2, 3, 7].     

Lateral Tyre Force by a Milliken Test on a Flat Track Roadway Simulator

The lateral tyre force versus slip angle and vertical load is obtained through specific tests on the single tyre or with a theoretical-empirical analysis with physical models. This study is about the possibility to use a third way: Executing a particular handling test, known as Force-Moment test, using a Flat Track Roadway Simulator (the Fiat-Elasis MTS FTRS). The understanding and the project of vehicle handling is strongly based on the knowledge of lateral tyre force response [1, 2, 3, 7].     

非满载液罐半挂汽车列车侧向耦合动力学模型

为方便液罐半挂汽车列车（Tractor Semi-trailer Tank Vehicle,TSTTV）罐-车整体的优化设计匹配,综合提高整车的侧倾稳定性、侧向动力学稳定性及操纵特性,基于Lagrange方法和椭圆规摆等效机械液体晃动模型建立TSTTV的整车侧向耦合动力学模型,其典型特征是实现罐内液体侧向晃动与车辆横摆运动、侧向运动、悬挂质量的侧倾运动及非线性侧向轮胎力的集成一体化建模,贯通液体晃动动力学与车辆侧向动力学稳定性之间的联系。通过开环正弦停滞转向输入操作响应对所建立的模型进行分析评价,考察车辆横摆角速度、质心侧偏角、侧倾角、侧向载荷转移率及液体晃动角等状态量在2种充液比（F_L=40%,80%）及2种罐体椭圆率（Δ=1.0,1.3）下的响应。研究结果表明：所建立的TSTTV模型可以实现液体侧向晃动作用下的车辆侧向耦合动力学仿真分析,能够反映充液比、罐体截面椭圆率等运输条件和罐体几何参数对整车侧倾稳定性、侧向动力学稳定性及操纵特性的影响;基于该模型可以针对液体介质、充液比及道路环境等运输条件因素的影响,研究以提高整车侧向动力学稳定性为目标的TSTTV灌-车整体的优化设计匹配问题,这对提升液罐车的设计性能、提高行驶的安全性和运输效率具有重要意义。     

基于LQR的重型半挂汽车列车稳定性控制策略

以半挂车的横摆角速度、侧向加速度、牵引车与半挂车的铰接角及铰接角速度为控制变量,建立了4自由度6轴重型半挂汽车列车的动力学参考模型,并应用ISO双移线工况对此模型进行验证。考虑到等速圆周稳态工况下行驶和地面附着系数等因素对汽车的限制,确定了控制变量横摆角速度和侧向加速度的参考值。采用基于线性二次型调节器(LQR)的最优控制策略及半挂汽车列车单侧制动方案,应用Trucksim软件对参考模型进行了鱼钩转向工况仿真分析。仿真结果表明:所提出的控制策略正确、有效,实现了提高半挂汽车列车稳定性的控制目标。     

Integrated chassis control for a three-axle electric bus with distributed driving motors and active rear steering system

This paper describes an integrated chassis control framework for a novel three-axle electric bus with active rear steering (ARS) axle and four motors at the middle and rear wheels. The proposed integrated framework consists of four parts: (1) an active speed limiting controller is designed for anti-body slip control and rollover prevention; (2) an ARS controller is designed for coordinating the tyre wear between the driving wheels; (3) an inter-axle torque distribution controller is designed for optimal torque distribution between the axles, considering anti-wheel slip and battery power limitations and (4) a data acquisition and estimation module for collecting the measured and estimated vehicle states. To verify the performances, a simulation platform is established in Trucksim software combined with Simulink. Three test cases are particularly designed to show the performances. The proposed algorithm is compared with a simple even control algorithm. The test results show satisfactory lateral stability and rollover prevention performances under severe steering conditions. The desired tyre wear coordinating performance is also realised, and the wheel slip ratios are restricted within stable region during intensive driving and emergency braking with complicated road conditions.