Development of a generalised equivalent estimation approach for multi-axle vehicle handling dynamics

This paper devotes analytical effort in developing the 2M equivalent approach to analyse both the effect of vehicle body roll and n-axle handling on vehicle dynamics. The 1M equivalent vehicle 2DOF equation including an equivalent roll effect was derived from the conventional two-axle 3DOF vehicle model. And the 1M equivalent dynamics concepts were calculated to evaluate the steady-state steering, frequency characteristics, and root locus of the two-axle vehicle with only the effect of body roll. This 1M equivalent approach is extended to a three-axle 3DOF model to derive similar 1M equivalent mathematical identities including an equivalent roll effect. The 1M equivalent wheelbases and stability factor with the effect of the third axle or body roll, and 2M equivalent wheelbase and stability factor including both the effect of body roll and the third-axle handling were derived to evaluate the steady-state steering, frequency characteristics, and root locus of the three-axle vehicle. By using the recursive method, the generalised 1M equivalent wheelbase and stability factor with the effect of n-axle handling and 2M equivalent generalised wheelbase and stability factor including both the effect of body roll and n-axle handling were derived to evaluate the steady-state steering, frequency characteristics, and root locus of the n-axle vehicle. The 2M equivalent approach and developed generalised mathematical handling concepts were validated to be useful and could serve as an important tool for estimating both the effect of vehicle body roll and n-axle handling on multi-axle vehicle dynamics.     

Generalised multi-axle vehicle handling

The familiar two-axle bicycle model and associated basic concepts of vehicle handling are reviewed and used to introduce minor changes in convention from the literature. The two-axle model is extended to a three-axle vehicle to illustrate the effectiveness of the notation combined with a simplifying mathematical identity found in the two-axle vehicle literature. A generalised model is then developed that produces dynamic equations of motion by inspection for a vehicle with an arbitrary number of steerable and non-steerable axles. Furthermore, the vehicle dynamic concepts of understeer and wheelbase are generalised and can be directly computed for various arbitrary vehicle configurations.     

Vehicle dynamics control using an active third-axle system

This paper introduces the active third-axle system as an innovative vehicle dynamic control method. This method can be applicable for different kinds of three-axle vehicles such as buses, trucks, or even three-axle passenger cars. In this system, an actuator on the middle axle actively applies an independent force on the suspension to improve the handling characteristics, and hence, its technology is similar to slow-active suspension systems. This system can change the inherent vehicle dynamic characteristics, such as under/over steering behaviour, in the linear handling region, as well as vehicle stability in the nonlinear, limit handling region. In this paper, our main focus is to show the potential capabilities of this method in enhancing vehicle dynamic performance. For this purpose, as the first step, the proposed method in both linear and nonlinear vehicle handling regions is studied mathematically. Next, a comprehensive, nonlinear, 10 degrees of freedom vehicle model with a fuzzy control strategy is used to evaluate the effectiveness of this system. The dynamic behaviour of a vehicle, when either uncontrolled or equipped with the active third axle is then compared. Simulation results show that this active system can be considered as an innovative method for vehicle dynamic control.     

A comparative study of equivalent modelling for multi-axle vehicle

In this paper, equivalent modelling methods of a multi-axle vehicle are presented and compared. Firstly, for the sake of comparison, a single-track model of a three-axle and a two-axle vehicle is developed, and then existing equivalent modelling derivations are presented and discussed. Next, the proposed model-based dynamic equivalence of force/moment at the centre of gravity (CG) is introduced and optimised. It represents the approximately equivalent steady-state and transient response of the yaw rate and side slip angle, which allows different cornering stiffness on the central and rear axle. Finally, to demonstrate how the proposed method is advantageous to the other equivalent models available in the literature, different simulation cases are compared in the dimension of time-domain, eigenvalues characteristics and frequency-domain. Furthermore, the proposed method is extended to any multi-axle vehicle configurations and a general expression is formulated.     

High fidelity quasi steady-state aerodynamic model effects on race vehicle performance predictions using multi-body simulation

We described in this paper the development of a high fidelity vehicle aerodynamic model to fit wind tunnel test data over a wide range of vehicle orientations. We also present a comparison between the effects of this proposed model and a conventional quasi steady-state aerodynamic model on race vehicle simulation results. This is done by implementing both of these models independently in multi-body quasi steady-state simulations to determine the effects of the high fidelity aerodynamic model on race vehicle performance metrics. The quasi steady state vehicle simulation is developed with a multi-body NASCAR Truck vehicle model, and simulations are conducted for three different types of NASCAR race tracks, a short track, a one and a half mile intermediate track, and a higher speed, two mile intermediate race track. For each track simulation, the effects of the aerodynamic model on handling, maximum corner speed, and drive force metrics are analysed. The accuracy of the high-fidelity model is shown to reduce the aerodynamic model error relative to the conventional aerodynamic model, and the increased accuracy of the high fidelity aerodynamic model is found to have realisable effects on the performance metric predictions on the intermediate tracks resulting from the quasi steady-state simulation.     

Kinematic and dynamic analysis of a heavy truck with individual front suspension

The main focus of this work is on the characteristics of a commercial vehicle with individual front suspension (IFS). Both kinematic and dynamic properties of the vehicle are investigated through simulations and analytical expressions. Moreover, employing the model of the tractor semitrailer combination, the study presents the results of comparison between the trucks with IFS and rigid front axle with respect to comfort and handling. This is done by analysing the responses of the vehicles to different road and steering inputs. The obtained results show enhanced comfort and steering feeling for the truck with IFS.     

汽车操纵稳定性主客观评价数据的一种处理方法

汽车操纵稳定性主客观评价之间的相关性分析是汽车技术的重要课题。提出了汽车操纵稳定性主客观评价数据的一种处理方法．通过回归分析筛选客观参数，运用BP神经网络建立相关性模型，验证结果说明了该方法的可行性。     

不同转向模式的多轴转向车辆性能分析

为解决重型车辆转向时的低速机动性和高速稳定性的问题,提出了多轴动态转向技术,并以三轴车辆为研究对象进行分析。首先建立多轴转向的二自由度车辆模型以及运动微分方程,为提高车辆的稳定性,以零质心侧偏角为目标,推导各轴间的转角比例系数及有关的状态空间矩阵、传递函数,使用MATLAB软件对不同转向模式下的操纵稳定性进行了稳态响应、瞬态响应以及频域响应的仿真。通过分析比较,说明采用多轴动态转向技术,车辆在转向时具有低速机动性高、高速稳定性好的特点。     

双前桥转向系统瞬时转动中心理论分析及二轴转角的确定

建立了双前桥转向系统瞬时转动中心的数学模型,进行了理论分析和数学公式推导,得出了转动中心位置的一般公式以及一轴、二轴转角关系式。以某车型为例讨论了二轴转角、偏移和转动半径分别在不同双后轴距离处以及一轴不同转角条件下的变化规律。结果表明,瞬时转动中心不在后二轴中心线上,而是相对后二轴中心向后偏移,且偏移量随后二轴轴距增大而增大;前一轴转角对于瞬时转动中心的影响不大。转向半径随着后二轴轴距增大而增大;当一轴转角较小时,转向半径变化很大,当一轴转角最大时转向半径达到最小。     

Lane-keeping benefits of practical rear axle steer

The classic two-degree-of-freedom yaw-plane or ‘bicycle’ vehicle model is augmented with two additional states to describe lane-keeping behaviour and further augmented with an additional control input to steer the rear axle. A simple driver model is hypothesised where the driver closes a loop on a projected lateral lane position. The driver can select the preview distance to compensate driver/vehicle dynamics, consistent with the ‘cross-over’ model found in the literature. A rear axle steer control law is found to be a function of the front axle steering input and vehicle speed that exhibits stability similar to a positive-real system, while at the same time improving the ability of the driver/vehicle system to track a complex curved lane and improving steady-state manoeuvrability. The theoretically derived control law bears similarity to practical embodiments allowing a deeper understanding of the functional value of steering a rear axle.     

Handling and safety enhancement of race cars using active aerodynamic systems

A methodology is presented in this work that employs the active inverted wings to enhance the road holding by increasing the downward force on the tyres. In the proposed active system, the angles of attack of the vehicle's wings are adjusted by using a real-time controller to increase the road holding and hence improve the vehicle handling. The handling of the race car and safety of the driver are two important concerns in the design of race cars. The handling of a vehicle depends on the dynamic capabilities of the vehicle and also the pneumatic tyres’ limitations. The vehicle side-slip angle, as a measure of the vehicle dynamic safety, should be narrowed into an acceptable range. This paper demonstrates that active inverted wings can provide noteworthy dynamic capabilities and enhance the safety features of race cars. Detailed analytical study and formulations of the race car nonlinear model with the airfoils are presented. Computer simulations are carried out to evaluate the performance of the proposed active aerodynamic system.     

转向横拉杆弹性对车辆操纵稳定性的影响研究

为了研究转向横拉杆的弹性对车辆操纵稳定性的影响,利用ADAMS软件建立了某轿车的多体动力学模型并进行了操纵稳定性的仿真分析。对于操纵稳定性的稳态特性,采用了ISO4138标准,在车辆行驶100 km/h下的固定圆周转向规程来进行评价;对于瞬态操纵稳定性特性,则采用ISO7401标准中方向盘扫频输入的响应特性来进行评价。仿真结果表明,转向横拉杆的弹性与轿车操纵稳定性的不足有很大关系,如果弹性横拉杆刚性过大,则需要1个较大的转向传动比以弥补其不足转向特性。因此,在汽车设计开发中,必须将转向横拉杆的弹性特性和转向传动比综合平衡考虑,两需要很好的匹配才能保证其具有良好的操纵稳定性。     

Comparison of various double-lane change manoeuvre specifications

One of the commonly used performance measures to quantify a vehicle's handling transient dynamics is the maximum forward speed (MFS) while passing a certain specified double-lane change (DLC) manoeuvre without violating the boundary and tyre lift-off. The MFS is directly associated with the minimum curvature radius (MCR) of the vehicle centre of gravity (CG) trajectory controlled by the driver during the manoeuvre. The MCR is further affected by the vehicle dimensions to meet the boundary condition. In this study, a single heavy vehicle CG trajectory is assumed to be a combination of three straight lines and two third-order spline curves. A heavy vehicle multi-body system model established with ADAMS/Car is correlated with test data for step-steer and constant radius cornering events, and then the model is used to demonstrate that the assumptions considered in the formulation applied in this paper are valid for this specific vehicle category. The MCRs of four heavy vehicles are maximised among all the possible choices of the vehicle CG trajectory during each of five specific DLC manoeuvres, including North Atlantic Treaty Organization (Allied Vehicle Testing Publication 03-160W), International Organization for Standardization (ISO) 3888-1, ISO 3888-2, Consumer Union Short Course and Test Operations Procedure 2-2-609. The maximised MCR (MMCR), considered as the best possible choice of vehicle CG trajectories, is further solved as a function of the vehicle width and length. The results will show the sensitivity of the MMCR to the vehicle length and width, thus the impact on the vehicle transient handling dynamics. Finally, the comparison of five DLC specifications may help users to correlate a vehicle's MFS from one specification to others.     

主动悬架最优控制整车模型的研究

以一个车辆的整车模型为研究对象，通过利用轴距预瞄信息，应用最优控制理论设计了一个车辆的悬架控制策略，通过模拟和仿真的结果，验证了该模型和算法的可行性，并分析了轴距预瞄控制对于改进车辆性能的能力，检验了所建立的整车模型。     

Roll- and pitch-plane-coupled hydro-pneumatic suspension. Part 2: dynamic response analyses

In the first part of this study, the potential performance benefits of fluidically coupled passive suspensions were demonstrated through analyses of suspension properties, design flexibility and feasibility. In this second part of the study, the dynamic responses of a vehicle equipped with different configurations of fluidically coupled hydro-pneumatic suspension systems are investigated for more comprehensive assessments of the coupled suspension concepts. A generalised 14 degree-of-freedom nonlinear vehicle model is developed and validated to evaluate vehicle ride and handling dynamic responses and suspension anti-roll and anti-pitch characteristics under various road excitations and steering/braking manoeuvres. The dynamic responses of the vehicle model with the coupled suspension are compared with those of the unconnected suspensions to demonstrate the performance potential of the fluidic couplings. The dynamic responses together with the suspension properties suggest that the full-vehicle-coupled hydro-pneumatic suspension could offer considerable potential in realising enhanced ride and handling performance, as well as improved anti-roll and anti-pitch properties in a very flexible and energy-saving manner.     

Roll and pitch independently tuned interconnected suspension: modelling and dynamic analysis

In this paper, a roll and pitch independently tuned hydraulically interconnected passive suspension is presented. Due to decoupling of vibration modes and the improved lateral and longitudinal stability, the stiffness of individual suspension spring can be reduced for improving ride comfort and road grip. A generalised 14 degree-of-freedom nonlinear vehicle model with anti-roll bars is established to investigate the vehicle ride and handling dynamic responses. The nonlinear fluidic model of the hydraulically interconnected suspension is developed and integrated with the full vehicle model to investigate the anti-roll and anti-pitch characteristics. Time domain analysis of the vehicle model with the proposed suspension is conducted under different road excitations and steering/braking manoeuvres. The dynamic responses are compared with conventional suspensions to demonstrate the potential of enhanced ride and handling performance. The results illustrate the model-decoupling property of the hydraulically interconnected system. The anti-roll and anti-pitch performance could be tuned independently by the interconnected systems. With the improved anti-roll and anti-pitch characteristics, the bounce stiffness and ride damping can be optimised for better ride comfort and tyre grip.     

The handling surface: a new perspective in vehicle dynamics

The problem of describing the understeer–oversteer behaviour of a general vehicle, such as one with locked differential or tandem rear axle, is addressed taking a new perspective. The well-known handling diagram and the associated classical understeer gradient may be inadequate, mainly because they are no longer unique. The new concept of handling surface and a new definition of understeer gradient, which is indeed the gradient of the handling surface and hence a vector, are presented. It is also shown how the new concepts relate to and generalize the classical ones. Finally, a procedure for the experimental measure of the new understeer gradient is outlined.     

汽车操纵稳定性虚拟仿真的研究

应用现代虚拟现实技术，把汽车操纵稳定性研究传统的数字仿真变成为具有“真实场景”的虚拟仿真，还研制了用于汽车操纵动力学仿真的虚拟场景自动生成软件。结合汽车操纵动力学仿真数学模型和相关软件，建立了一个具有真实视觉感的、实时的汽车操纵动态虚拟仿真系统。文中给出了实例。     

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。