A Versatile Flat Track Tire Testing Machine

Summary A flat track tire testing machine developed by the IMMa group is described. It permits the simulation and study of the dynamic behavior of a great variety of tires under controllable and repetitive highly dynamic realistic working conditions in the laboratory for a diversity of vehicles, from motorcycles to light trucks. The machine incorporates: – a hydraulically operated tire support and loading system with wide operating ranges; – a computer controlled brake system to simulate braking maneuvers with ABS systems; – a complete sensorial system; – a data acquisition and control system continually monitoring and acting on the experimental variables, i.e., tire and belt speed, longitudinal slip, slip and camber angles, tire pressure, tire normal force, etc. As an application example, results are presented that adjust the parameter of the magic formula for a standard 175/70 R14 passenger vehicle tire. Accurate mathematical tire models are recognized as essential for the prediction of vehicle dynamic performances using simulation tools.     

轮胎附着极限下差动制动对汽车横摆力矩的影响

本文以纵滑－侧偏联合工况的稳态轮胎模型为基础，分析了汽车极限转向条件下制动作用于不同车轮时对汽车横摆力矩的影响，并通过整车动力学仿真进行了验证，研究结果为利用差动制动控制提高汽车的高速操纵稳定性提供了动力学依据。     

轮胎动力学特性仿真分析研究

分析了各种常用轮胎模型的特点与应用范围,根据汽车操纵动力学研究的需求,在Matlab环境下运用魔术公式建立了轮胎动力学模型,并对汽车轮胎力与纵向滑移率,纵向力、侧向力及回正力矩与纵向滑移率、侧偏角、外倾角、垂直载荷的关系等轮胎特性进行了仿真分析,实验结果表明,魔术公式轮胎动力学模型可以较好地模拟轮胎的动力学特性,适用于车辆动力学研究领域。     

Non-singular slip (NSS) method for longitudinal tire force calculations in a sudden braking simulation

In a dynamic vehicle simulation, longitudinal tire force is primarily based on the longitudinal slip (ratio). In the longitudinal slip formula, state variables are used in the denominator. This causes a divergence problem for numerical simulations of vehicle dynamics. To avoid this numerical singularity, a differential slip calculation method was developed for use in dynamic vehicle simulations. However, this method also causes a singularity when the wheel velocity approaches zero in a pure slip state, such as during sudden braking. In this paper, a new longitudinal slip calculation method, which can overcome singularities in all velocity conditions, is proposed. For this purpose, the Taylor series is adapted to the slip formula and the idea of virtual wheel rotation stiffness is introduced for the development of the slip equation. The physical phenomenon at the zero slip state is analyzed. Finally, the proposed slip formula is used to solve the numerical singularity problem, and the non-singular slip (NSS) calculation method is proposed. The proposed NSS method is applied to tire model performance test (TMPT) simulations to validate its performance.     

Tire wear estimation based on nonlinear lateral dynamic of multi-axle steering vehicle

This paper presents a novel nonlinear dynamic model of a multi-axle steering vehicle to estimate the lateral wear amount of tires. Firstly, a 3DOF nonlinear vehicle dynamic model is developed, including dynamic models of the hydropneumatic suspension, tire, steering system and toe angle. The tire lateral wear model is then built and integrated into the developed vehicle model. Based on the comparison of experimental and simulation results, the nonlinear model is proved to be better than a linear model for the tire wear calculation. In addition, the effects of different initial toe angles on tire wear are analyzed. As simulation results shown, the impact of the dynamic toe angle on the tire wear is significant. The tire wear amount will be much larger than that caused by normal wear if the initial toe angle increases to 1° - 1.5°. The results also suggest that the proposed nonlinear model is of great importance in the design and optimazation of vehicle parameters in order to reduce the tire wear.     

集成化仿真系统在气制动TCS控制器开发中的应用

利用Simulink/xPC实时仿真软硬件环境,设计了集成化TCS仿真软硬件系统。建立了包括整车、动力传动系、制动器、轮胎、路面的动力学模型,应用离线仿真、快速原型仿真和ECU在环仿真等方法开发了气制动TCS控制器控制逻辑。经实车试验表明,系统能有效控制驱动轮的打滑趋势,提高汽车加速性能,改善发动机的工作条件。     

Independent Suspension, Self Steered Axle, and 4WS for Busses

The dynamic behavior of commercial vehicles fitted with differentr types of suspension mechanisms and steering devices is investigated in this paper. Six vehicle models have been constructed: 2WS-SA is a standard two wheel steering bus with solid axles; 2WS-DW is a 2WSA vehicle with independent double wishbone suspension in front and rear axles; SSA-SA is a 2WS system with solid axles, the rear one being mounted on a self steered mechanism; SSA-DW is a vehicle with independent double wishbone suspension in the front axle, and a solid self steered rear axle; 4WS-SA has four wheel steering with solid axles; and 4WS-DW is a 4WS vehicle with independent double wishbone suspension in front and rear axles. The dynamic response of these models has been assessed in terms of lateral acceleration, yaw velocity, tire forces, tire force reserves, and slip angles. The expected advantages of a 4WS system (higher acceleration rates and lower slip angles) will be corroborated but, at the same time, it will be shown that they are obtained at the cost of lower force reserves. Self steered mechanisms produce smaller body slip angles, but it will be shown that they give rise to larger yaw velocity overshootings. The particular independent suspension analyzed does not show significant improvements with respect to the solid axle counterpart.     

汽车防抱死制动系统的自抗扰控制研究

汽车防抱死制动系统（Anti-lock Braking System,ABS）的作用是确保汽车制动时行驶方向的稳定性、可靠性,但是目前仍存在非线性、时变性以及参数不确定性等问题。为保证汽车制动行驶过程中的操纵稳定性和安全性,进一步实现各工况下防抱死制动系统的优化控制,以影响整车稳定的变量滑移率为研究对象,分析所设计策略的控制效果。搭建汽车动力学模型、制动系统模型、轮胎模型和滑移率模型等主要模型,设计基于滑移率的ABS二阶非线性自抗扰控制器。运用MATLAB/Simulink软件对基于自抗扰控制（Active Disturbance Rejection Control,ADRC）的ABS制动过程和基于模糊PID控制的ABS制动过程进行仿真,对比研究最佳滑移率、载荷、水泥-冰对接路面、扰动等对制动过程中的轮速、车速以及滑移率等动态性征反映的稳定性和抗扰能力的影响,同时研究其对最终制动距离和最终制动时间反映的制动性能的影响。最后,将自抗扰控制器和模糊PID控制器装配于试验车辆的ABS,进行水泥路面和冰-水泥对接路面制动过程的实车试验。研究结果表明：基于二阶非线性自抗扰控制算法的ABS制动的最终制动距离和最终制动时间更短、制动效果更优,制动过程中的轮速、车速和滑移率在响应速度、稳定性和抗扰能力等方面均更佳;试验结果与仿真结果吻合,证明了仿真模型及其仿真结果的可行性和正确性。     

Longitudinal Tire Dynamics

SUMMARY

This article begins with a brief review of the traditional concept of lateral relaxation length. The review illustrates that this concept yields a useful approximation which can be used with semi-empirical tire models which assume lateral forces are a function of steady-state slip angles. The article then presents an analogous derivation for longitudinal slip. Like its lateral counterpart, the derivation yields an approximation for transient longitudinal slip which can be used with tire models which assume longitudinal forces are a function of steady-state longitudinal slip. It is shown that, like the relaxation-length-based lateral slip angle, this formulation for longitudinal slip yields the ability to compute shear forces at the tire/road interface for either high or low speed applications, a necessary feature of simulations which support human in the loop driving simulation. Like traditional kinematically-based longitudinal slip, the transient formulation presented here is coupled with the wheel spin equation, and it shares the characteristic that it is very stiff compared to the equations of vehicle motion. This characteristic is a challenge impeding the real-time calculations required for driving simulation. The paper shows that local linearization of the wheel spin equations coupled with analytical solutions of the transient longitudinal slip formulation provide the basis for both insight into the longitudinal dynamics of the tire and for integrating the model in real-time.     

Analytical Tire Models for Dynamic Vehicle Simulation

Four basic tire models suitable for dynamic vehicle simulation are formulated. The models are compared through a six-degree-of-freedom nonlinear simulation of a cargo truck crossing rough ground. Guidelines are developed for the selection of an optimum tire model for a given dynamic vehicle simulation.     

Integrated Control of Active Rear Wheel Steering and Direct Yaw Moment Control

SUMMARY

An integrated control system of active rear wheel steering (4WS) and direct yaw moment control (DYC) is presented in this paper. Because of the tire nonlinearity that is mainly due to the saturation of cornering forces, vehicle handling performance is improved but limited to a certain extent only by steering control. Direct yaw moment control using braking and/or driving forces is effective not only in linear but also nonlinear ranges of tire friction circle. The proposed control system is a model matching controller which makes the vehicle follow the desired dynamic model by the state feedback of both yaw rate and side slip angle. Various computer simulations are carried out and show that vehicle handling performance is much improved by the integrated control system.     

Longitudinal Tire Dynamics

This article begins with a brief review of the traditional concept of lateral relaxation length. The review illustrates that this concept yields a useful approximation which can be used with semi-empirical tire models which assume lateral forces are a function of steady-state slip angles. The article then presents an analogous derivation for longitudinal slip. Like its lateral counterpart, the derivation yields an approximation for transient longitudinal slip which can be used with tire models which assume longitudinal forces are a function of steady-state longitudinal slip. It is shown that, like the relaxation-length-based lateral slip angle, this formulation for longitudinal slip yields the ability to compute shear forces at the tire/road interface for either high or low speed applications, a necessary feature of simulations which support human in the loop driving simulation. Like traditional kinematically-based longitudinal slip, the transient formulation presented here is coupled with the wheel spin equation, and it shares the characteristic that it is very stiff compared to the equations of vehicle motion. This characteristic is a challenge impeding the real-time calculations required for driving simulation. The paper shows that local linearization of the wheel spin equations coupled with analytical solutions of the transient longitudinal slip formulation provide the basis for both insight into the longitudinal dynamics of the tire and for integrating the model in real-time.     

基于虚拟样机技术的扭杆悬架汽车平顺性仿真

运用面向整车系统的数字化虚拟样机技术和大型机械系统动力学仿真软件ADAMS建立了包括前后悬架、轮胎、转向系统及整车的多体动力学模型。用Visual Basic编制路面生成文件，生成不同等级的随机路面。对整车进行了随机输入平顺性仿真分析，把仿真数据输入编制的平顺性仿真程序中，发现结果满足国家规定的汽车平顺性评价标准。     

Nonlinear Dynamics of Vehicle Traction

Summary The purpose of this study is to understand the nonlinear dynamics of longitudinal ground vehicle traction. Specifically, single-wheel models of rubber-tired automobiles under straight-ahead braking and acceleration conditions are investigated in detail. Customarily, the forward vehicle speed and the rotational rate of the tire/wheel are taken as dynamic states. This paper motivates an alternative formulation in which wheel slip, a dimensionless measure of the difference between the vehicle speed and the circumferential speed of the tire relative to the wheel center, replaces the angular velocity of the tire/wheel as a dynamic state. This formulation offers new insight into the dynamic behavior of vehicle traction. The unique features of the modeling approach allow one to capture the full range of dynamic responses of the single-wheel traction models in a relatively simple geometric manner. The models developed here may also be useful for developing and implementing anti-lock brake and traction control control schemes.     

New Model of Tire Overturning Moment Characteristics and Analysis of Their Influence on Vehicle Rollover Behavior

A newly developed tire model for the Overturning Moment (OTM) characteristics and the analysis of the influence of OTM on vehicle rollover behavior are presented. The new OTM model was developed based on the so-called Magic Formula tire model. The concept of the new model involves identifying the difference between the simple model and the measurements to the newly defined functions. It was seen that the new model agrees very well with the measured data over a wide range of tire vertical loads, slip angles and camber angles. The influence of tire OTM on the vehicle rollover behavior was also investigated by using a full vehicle simulation in which a rather large steering angle was input. The results obtained from the vehicle simulation with three different tire models (model without OTM, simple model and new model) were compared with the experimental results. It was found that the calculated result obtained with the new OTM model agreed best with the experiment.     

New Model of Tire Overturning Moment Characteristics and Analysis of Their Influence on Vehicle Rollover Behavior

A newly developed tire model for the Overturning Moment (OTM) characteristics and the analysis of the influence of OTM on vehicle rollover behavior are presented. The new OTM model was developed based on the so-called Magic Formula tire model. The concept of the new model involves identifying the difference between the simple model and the measurements to the newly defined functions. It was seen that the new model agrees very well with the measured data over a wide range of tire vertical loads, slip angles and camber angles. The influence of tire OTM on the vehicle rollover behavior was also investigated by using a full vehicle simulation in which a rather large steering angle was input. The results obtained from the vehicle simulation with three different tire models (model without OTM, simple model and new model) were compared with the experimental results. It was found that the calculated result obtained with the new OTM model agreed best with the experiment.     

用于不平路面车辆动力学仿真的轮胎模型综述

介绍了轮胎在不平路面的动力学特性。在回顾不平路面轮胎动力学模型发展的基础上，以近期的研究工作为重点，对用于不平路面车辆动力学仿真的轮胎模型进行了较为系统的介绍。概要地阐述了各种轮胎模型的建模理论、方法，并进行了分析和评述。最后，总结了不平路面轮胎力学建模的核心问题及发展方向，对不平路面车辆动力学仿真选择合适的轮胎模型给出了建议。     

Nonlinear Dynamics of Vehicle Traction

Summary The purpose of this study is to understand the nonlinear dynamics of longitudinal ground vehicle traction. Specifically, single-wheel models of rubber-tired automobiles under straight-ahead braking and acceleration conditions are investigated in detail. Customarily, the forward vehicle speed and the rotational rate of the tire/wheel are taken as dynamic states. This paper motivates an alternative formulation in which wheel slip, a dimensionless measure of the difference between the vehicle speed and the circumferential speed of the tire relative to the wheel center, replaces the angular velocity of the tire/wheel as a dynamic state. This formulation offers new insight into the dynamic behavior of vehicle traction. The unique features of the modeling approach allow one to capture the full range of dynamic responses of the single-wheel traction models in a relatively simple geometric manner. The models developed here may also be useful for developing and implementing anti-lock brake and traction control control schemes.     

基于动态目标调整的汽车全轮纵向力分配的研究

针对现有汽车稳定性控制系统中,汽车全轮纵向力分配算法在极端工况下出现轮胎力饱和.导致滑移率控制器过多介入而出现控制振荡和对控制目标的调整不合理等问题,提出了一种新的主动动态目标调整的全轮纵向力分配算法.该算法在极端工况下,根据车辆运动状态和路面附着状态,对直接横摆力矩控制目标M_(xd)和纵向驱动/制动力控制目标F_(xd)进行主动动态的调节.仿真结果表明,采用该算法解决了现有全轮纵向力分配算法的上述问题.     

轮胎动态模型的阻尼和对滚动阻力及动态响应影响的分析

在综合了一些文献研究结果的基础上,基于轮胎模态参数模型,给出了不同阻尼环节对滚动阻力及轮胎以不同速度滚越障碍物的动态响应的模拟结果,并部分地与试验结果进行对比,说明具有结构阻尼环节的轮胎模型,对于两者的模拟均给出了更好的定量结果。