A 9-DOF Tractor-Semitrailer Dynamic Handling Model for Advanced Chassis Control Studies

Summary This paper describes a flexible and modular 9-degrees-of-freedom nonlinear dynamic handling model for a tractor-semitrailer combination vehicle. The equations of motion are derived from the fundamental equations of dynamics in Euler's formulation, with the use of general computer-algebra software. The primary aim of the model is simulation of handling scenarios with active yaw control, using unilateral braking. However, it may also prove useful in other areas of tractor-semitrailer handling analysis or hardware-in-the-loop simulations. The model is formulated as a state-space model that may be implemented in standard simulation environments. A Simulink implementation is presented, and simulation results are compared with experiments to validate the model.     

Optimal Control of the Tractor-Semitrailer Truck

This paper is concerned with the braking performance and the handling behavior of the tractor-semitrailer truck under optimal braking. Optimal control theory is used in order to deal with the problem and a combination of the steepest descent method and the Davidon Fletcher Powell method is used to solve it numerically. Results for some chosen braking maneuvers are obtained for a nonlinear truck model which has 14 degrees of freedom. These results show that, for the chosen maneuvers an idealized anti-skid braking is close to being optimal in the sense defined in this paper. Implementation of an idealized anti-skid braking on the tractor-semitrailer truck, however, may be not desirable.     

Optimal Control of the Tractor-Semitrailer Truck

SUMMARY

This paper is concerned with the braking performance and the handling behavior of the tractor-semitrailer truck under optimal braking. Optimal control theory is used in order to deal with the problem and a combination of the steepest descent method and the Davidon Fletcher Powell method is used to solve it numerically. Results for some chosen braking maneuvers are obtained for a nonlinear truck model which has 14 degrees of freedom. These results show that, for the chosen maneuvers an idealized anti-skid braking is close to being optimal in the sense defined in this paper. Implementation of an idealized anti-skid braking on the tractor-semitrailer truck, however, may be not desirable.     

应用虚拟样机技术进行半挂汽车列车制动动力学分析

将虚拟仿真软件ADAMS应用到半挂汽车列车制动动力学研究中，建立了半挂汽车列车整车26自由度（DOF）动力学模型，对半挂汽车列车直线制动及转弯制动进干亍了仿真分析。通过仿真分析发现，在车辆无ABS转弯制动时，即使按照理想抱死顺序实施制动，半挂车也会出现瞬态“甩尾”的危险工况。     

Anti-Skid Braking of a Tractor-Semitrailer Truck

This paper describes a study of anti-skid braking and the effects of such braking on the handling behavior and braking performance of a tractor-semitrailer truck. The truck, represented by a digital computer model having fourteen degrees of freedom, is taken to be in a cornering maneuver that involves braking and driver steering. Conventional braking or one of three types of anti-skid braking is used in the maneuver. The results show that the effects of anti-skid braking on the handling behavior and braking performance of the truck are beneficial. The results also show that the behavior of the wheels and the handling behavior and braking performance of the truck depend on the type of anti-skid braking used.     

Anti-Skid Braking of a Tractor-Semitrailer Truck

ABSTRACT

This paper describes a study of anti-skid braking and the effects of such braking on the handling behavior and braking performance of a tractor-semitrailer truck. The truck, represented by a digital computer model having fourteen degrees of freedom, is taken to be in a cornering maneuver that involves braking and driver steering. Conventional braking or one of three types of anti-skid braking is used in the maneuver. The results show that the effects of anti-skid braking on the handling behavior and braking performance of the truck are beneficial. The results also show that the behavior of the wheels and the handling behavior and braking performance of the truck depend on the type of anti-skid braking used.     

转向盘转角阶跃输入下半挂汽车列车操纵稳定性仿真分析

基于包括任意载荷分布的非线性轮胎模型在内的半挂汽车列车整车模型,应用汽车列车动力学仿真软件Arc Sim,分析了半挂汽车列车在转向盘转角阶跃输入时的转向特性。通过在不同车速、不同结构参数等条件下的仿真计算,揭示了半挂汽车列车的转向特性与车速、结构参数之间的内在联系,给出了半挂汽车列车转向特性在这些条件下的表现特征,为半挂汽车列车操纵稳定性分析提供了参考和借鉴。     

基于主动制动的半挂汽车列车横摆稳定性控制

为研究半挂汽车列车在高速大转向等极限操作工况下的横摆稳定性控制问题,建立了14自由度的半挂汽车列车非线性仿真模型;提出了牵引车与半挂车独立直接横摆力矩控制的横摆稳定性控制方案,通过牵引车和半挂车车轮的合理选择和主动制动实现横摆控制;以跟踪参考模型的稳态横摆响应为目标,设计了PI横摆稳定性控制器,对牵引车和半挂车分别设计了目标制动车轮的选择决策规则。单移线操作仿真结果表明,基于主动制动的横摆力矩控制可有效改善极限工况下半挂汽车列车的横摆稳定性,牵引车与半挂车进行独立横摆控制可以减小制动车轮选择决策的复杂性,而获得较好的控制效果。     

Berechnung des extremen Lenk- und Bremsverhaltens von Sattelkraftfahrzeugen

Simulation of Steering and Braking Behaviour of Tractor-Semitrailer Vehicles in Extreme Situations

This paper deals with the simulation of the behaviour of tractor-semitrailer vehicles at braking on wet, slippery road surface. The nonlinear model used for the computation enables to simulate extreme situations at wheel locking and swerving

The instabilities during braking such as jackknifing and trailer swing as well as non steerability are investigated. Straightline braking shows the influence of cornering on the behaviour during braking in a turn.     

半挂汽车列车闭环非线性系统行驶稳定性分析

对半挂汽车列车行驶稳定性的闭环非线性系统进行了研究,建立了半挂汽车列车三自由度非线性模型。以单点预瞄驾驶员模型与半挂汽车列车三自由度非线性模型的耦合系统为研究对象,应用李雅普诺夫一次近似定理,在线性范围内分析了系统参数的特征根轨迹,并在线性范围内分析了驾驶员预瞄时间和轮胎侧偏刚度对临界车速的影响。     

Tractor-Semitrailer Dynamics: Design of the Fifth Wheel*

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.     

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.     

Berechnung des extremen Lenk- und Bremsverhaltens von Sattelkraftfahrzeugen

SUMMARY

Simulation of Steering and Braking Behaviour of Tractor-Semitrailer Vehicles in Extreme Situations

This paper deals with the simulation of the behaviour of tractor-semitrailer vehicles at braking on wet, slippery road surface. The nonlinear model used for the computation enables to simulate extreme situations at wheel locking and swerving

The instabilities during braking such as jackknifing and trailer swing as well as non steerability are investigated. Straightline braking shows the influence of cornering on the behaviour during braking in a turn.     

Stability Bounds of a Tractor-Semitrailer

The dynamic stability of a tractor-semitrailer is presented here on a qualitative basis. In a four-dimensional space, equilibrium states of the system are discovered which lead to suitable initial conditions for numerical integration of the system equations. The intergal solutions define the stable and the unstable regions in the state-space, and thereby reveal the system behavior. A simple example concerning the effect of a front tire blowout illustrates how the theory can expose the vehicle motion under external perturbations.     

Random Response of Tractor-Semitrailer System

This work describes an analytical study of the dynamic behaviour of a tractor-semitrailer vehicle. A digital computer simulation was used to describe the longitudinal, vertical, and pitching motions of the vehicle travelling over a stationary random road surface. A man-seat model was also incorporated into the simulation. Vehicle response to road irregularities has been studied by assuming two different roads for loaded and unloaded cases.

Numerical results are presented for vehicle, showing system eigenvalues, power spectral densities and root mean square values of the linear and angular accelerations and displacements. Vehicle acceleration response is compared with the ISO riding comfort standard. All results for the loaded and unloaded cases and for smooth and rough roads indicated that an uncomfortable ride would result from vehicle response.     

Design of an Active Unilateral Brake Control System for Five-Axle Tractor-Semitrailer Based on Sensitivity Analysis

This paper presents the results of a parametric sensitivity analysis of a five-axle tractor-semitrailer vehicle combination using 3-DOF linear yaw/plane model. The first order logarithmic sensitivity functions are derived with respect to several vehicle design parameters. For stabilization of the vehicle's directional behaviour a fairly new control concept called “Active Unilateral Braking Control (AUBC)” acting on the tractor rear wheel's in order to produce a stabilizing yaw torque is investigated. The AUBC system improves not only the directional stability, but also affects the roll dynamics of the vehicle. The sensitivity of the controlled vehicle system with linear quadratic controller (LQR) is also examined, a robust controller design procedure is proposed as a result of the sensitivity analysis. The robustness of this controller in the presence of both internal (including parametric uncertainties, non-linear dynamics) and external disturbances (such as road irregularities and side wind) allows its implementation with confidence with a non-linear vehicle model. The applicability of this control system to a non-linear vehicle model is tested using a 34 DOF, non-linear vehicle model of the tractor-semitrailer combination.     

Process Save Reduction by Macro Joint Approach: The Key to Real Time and Efficient Vehicle Simulation

Applying a non-linear model reduction method to the tire suspension system of road vehicles enables an automatic transfer of complex offline simulation vehicle models to a mathematical model, which fits the real time simulation requirements. The basic assumption, that high frequent inner suspension dynamics are not relevant to handling manoeuvres, converts the differential algebraic equation system (DAE) of suspensions with kinematical closed loops into pure elasto-kinematical linkage equations. The equations of motions can be represented as an ordinary differential equation system (ODE) and considerable simulation time reductions are obtained for the off-line simulation and real time simulation is enabled. This so-called macro joint approach is an alternative modelling method to the well-known look-up table representation of suspension kinematics but it keeps the parameterisation of the original suspension model and is suitable to parameterised real time MBS models. With a second step the dynamics, caused by compliance in the suspension bushings, are reduced to their quasi-static behaviour. The consideration of these quasi-elasticity has nearly no influence on the necessary simulation time. This contribution shows the theoretical background and demonstrates the advantage of the macro joint model reduction approach on a typical vehicle example.     

Process Save Reduction by Macro Joint Approach: The Key to Real Time and Efficient Vehicle Simulation

Applying a non-linear model reduction method to the tire suspension system of road vehicles enables an automatic transfer of complex offline simulation vehicle models to a mathematical model, which fits the real time simulation requirements. The basic assumption, that high frequent inner suspension dynamics are not relevant to handling manoeuvres, converts the differential algebraic equation system (DAE) of suspensions with kinematical closed loops into pure elasto-kinematical linkage equations. The equations of motions can be represented as an ordinary differential equation system (ODE) and considerable simulation time reductions are obtained for the off-line simulation and real time simulation is enabled. This so-called macro joint approach is an alternative modelling method to the well-known look-up table representation of suspension kinematics but it keeps the parameterisation of the original suspension model and is suitable to parameterised real time MBS models. With a second step the dynamics, caused by compliance in the suspension bushings, are reduced to their quasi-static behaviour. The consideration of these quasi-elasticity has nearly no influence on the necessary simulation time. This contribution shows the theoretical background and demonstrates the advantage of the macro joint model reduction approach on a typical vehicle example.