On the Theory of Nonlinear Dynamics and its Applications in Vehicle Systems Dynamics

We present a brief outline of nonlinear dynamics and its applications to vehicle systems dynamics problems. The concept of a phase space is introduced in order to illustrate the dynamics of nonlinear systems in a way that is easy to perceive. Various equilibrium states are defined, and the important case of multiple equilibrium states and their dependence on a parameter is discussed. It is argued that the analysis of nonlinear dynamic problems always should start with an analysis of the equilibrium states of the full nonlinear problem whereby great care must be taken in the choice of the numerical solvers. When the equilibrium states are known certain linearizations around one chosen state may be applied carefully in order to facilitate or speed up the numerical solution of the dynamical problem. It is argued, however, that certain problems cannot be linearized. The applications of nonlinear dynamics in vehicle simulations is discussed, and it is argued that it is necessary to know the equilibrium states of the full nonlinear system before the simulation calculations are performed.     

On Lateral Dynamics of Vehicles Based on Nonlinear Characteristics of Tires

The problems of vehicle lateral dynamics based on nonlinear characteristics of tires are discussed in this paper. A new nonlinear perturbation model on the cornering behavior of the tire is constructed. The nonlinear influences of tires on the steady-state steering behavior, dynamic response and handling stability of vehicle are discussed, applying the approximate analytical methods for nonlinear vibration. An analytical criterion of stability is obtained. Some numerical examples are given.     

On Lateral Dynamics of Vehicles Based on Nonlinear Characteristics of Tires

The problems of vehicle lateral dynamics based on nonlinear characteristics of tires are discussed in this paper. A new nonlinear perturbation model on the cornering behavior of the tire is constructed. The nonlinear influences of tires on the steady-state steering behavior, dynamic response and handling stability of vehicle are discussed, applying the approximate analytical methods for nonlinear vibration. An analytical criterion of stability is obtained. Some numerical examples are given.     

Nonlinear dynamics and stability analysis of vehicle plane motions

In this article, the problems of dynamics and stability for vehicle planar motion systems have been investigated. By introducing a so-called joint-point locus approach, equilibria of the system and their associated stability properties are given geometrically. With this method, it is discovered that the difference between the front and the rear steering angles plays a key role in vehicle system dynamics and that the topological structure of the phase portrait and the types of bifurcations are different from those published previously. In particular, the vehicle system could still be stabilized even when pushed to work in a certain severely nonlinear region, by applying extremely large steering angles. However, it is worth noticing that the attractive domain of the stable equilibrium is very narrow. These developments might prove to be important in active steering control design. Numerical experiments are carried out to illustrate the potentials of the proposed techniques.     

Identification Methods for Vehicle System Dynamics

The paper presents a survey on parameter identification techniques for complex vehicle models. In order to cope with the complexity of the model, the information on the system available from the equations of motion has to be included in the identification process. Basic methods for the solution of this problem are shown. The application of the approach is demonstrated by identification of the vertical automobile dynamics. It is concluded that the presented techniques will become more important with increasing applications of theoretical modeling in vehicle system dynamics.     

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.     

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.     

Nonlinear dynamics and stability analysis of vehicle plane motions

In this article, the problems of dynamics and stability for vehicle planar motion systems have been investigated. By introducing a so-called joint-point locus approach, equilibria of the system and their associated stability properties are given geometrically. With this method, it is discovered that the difference between the front and the rear steering angles plays a key role in vehicle system dynamics and that the topological structure of the phase portrait and the types of bifurcations are different from those published previously. In particular, the vehicle system could still be stabilized even when pushed to work in a certain severely nonlinear region, by applying extremely large steering angles. However, it is worth noticing that the attractive domain of the stable equilibrium is very narrow. These developments might prove to be important in active steering control design. Numerical experiments are carried out to illustrate the potentials of the proposed techniques.     

Identification Methods for Vehicle System Dynamics

SUMMARY

The paper presents a survey on parameter identification techniques for complex vehicle models. In order to cope with the complexity of the model, the information on the system available from the equations of motion has to be included in the identification process. Basic methods for the solution of this problem are shown. The application of the approach is demonstrated by identification of the vertical automobile dynamics. It is concluded that the presented techniques will become more important with increasing applications of theoretical modeling in vehicle system dynamics.     

Crash analysis and dynamical behaviour of light road and rail vehicles

The main goal of crashworthiness is to ensure that vehicles are safer for occupants, cargo and other road or rail users. The crash analysis of vehicles involves structural impact and occupant biomechanics. The traditional approaches to crashworthiness not only do not take into account the full vehicle dynamics, but also uncouple the structural impact and the occupant biomechanics in the crash study. The most common strategy is to obtain an acceleration pulse from a vehicle structural impact analysis or experimental test, very often without taking into account the effect of suspensions in its dynamics, and afterwards feed this pulse into a rigid occupant compartment that contains models of passengers. Multibody dynamics is the most common methodology to build and analyse vehicle models for occupant biomechanics, vehicle dynamics and, with ever increasing popularity, structural crash analysis. In this work, the aspects of multibody modelling relevant to road and rail vehicles and to occupant biomechanical modelling are revised. Afterwards, it is shown how multibody models of vehicles and occupants are used in crash analysis. The more traditional aspects of vehicle dynamics are then introduced in the vehicle models in order to appraise their importance in the treatment of certain types of impact scenarios for which the crash outcome is sensitive to the relative orientation and alignment between vehicles. Through applications to the crashworthiness of road and of rail vehicles, selected problems are discussed and the need for coupled models of vehicle structures, suspension subsystems and occupants is emphasized.     

汽车动力传动系实时动力学仿真模型

将动力传动系视为刚体系统,建立适用于开发型驾驶模拟器的动力传动系4自由度实时动力学仿真模型,输入驾驶员的点火开关信号、油门踏板信号、离合器踏板信号及挡位信号,在一定的传动系各部件及驱动轮的运动状态下,传动系模型可向整车动力学模型输出驱动轮上的驱动力矩,从而完成车辆的实时动力学仿真,并进一步向驾驶模拟器输送整车的实时运动状态。仿真与动力性试验的对比结果表明,该模型不但具有实时性,而且可通过整车模型使开发型驾驶模拟器为驾驶员提供逼真的整车运动响应。     

Coupled lateral-longitudinal vehicle dynamics and control design with three-dimensional state portraits

The dynamics of vehicles with pneumatic tyres are well-known to be non-holonomic, nonlinear, and subject to state bounds in order to remain on defined roadways. As such, it can be challenging to apply many of the tools typically used to analyse nonlinear dynamics and synthesise control strategies. Furthermore, the use of traditional stability analyses is often insufficient for vehicle control design since adherence to the roadway geometry implies a constrained space that dictates stricter conditions on the states than provable stability. A two-state phase portrait approach has been used to analyse vehicle dynamics and provides an illustrative view of the state trajectories at constant speed. This paper extends the phase portrait to three states to represent the nonlinear vehicle dynamics with steering and longitudinal tyre force inputs and consideration of the longitudinal vehicle dynamics. The concept of a fixed point in the phase plane is extended to a stable curve and example controllers are examined and synthesised using the three-dimensional vector space.     

Aeroelastic Effects in Multibody Dynamics

To enable a realistic assessment of the aeroelastic phenomena of aircraft, a simultaneous application of computational fluid dynamics (CFD), computational structural mechanics and flight mechanics has to be performed. Each discipline has developed powerful specialized tools which have to be adapted for multidisciplinary applications. The combination of CFD and elastic multibody systems is well suited for the simulation of a range of aircraft applications, especially for aircraft ground dynamics. Approaches to a coupling of elastic multibody systems and computational fluid dynamics have been performed using close coupling, that is a modal approach, and loose coupling, that is by co-simulation. In the article the applied programs and the coupling methods are presented. Advantages and limits of using multibody simulation as compared to the direct use of FEA methods for the representation of structural dynamics are discussed. Results of coupled steady and unsteady simulations are presented. Finally, an approach to the aeroelastic trim problem is shown.     

Aeroelastic Effects in Multibody Dynamics

To enable a realistic assessment of the aeroelastic phenomena of aircraft, a simultaneous application of computational fluid dynamics (CFD), computational structural mechanics and flight mechanics has to be performed. Each discipline has developed powerful specialized tools which have to be adapted for multidisciplinary applications. The combination of CFD and elastic multibody systems is well suited for the simulation of a range of aircraft applications, especially for aircraft ground dynamics. Approaches to a coupling of elastic multibody systems and computational fluid dynamics have been performed using close coupling, that is a modal approach, and loose coupling, that is by co-simulation. In the article the applied programs and the coupling methods are presented. Advantages and limits of using multibody simulation as compared to the direct use of FEA methods for the representation of structural dynamics are discussed. Results of coupled steady and unsteady simulations are presented. Finally, an approach to the aeroelastic trim problem is shown.     

Vehicle Dynamics Estimation Using Kalman Filters

This paper deals with the application of stochastic state estimators in vehicle dynamics control. It is often unrealistic to assume that all vehicle states and the disturbances acting on it can be measured. System states that cannot be measured directly, can be estimated by a Kalman Filter. The idea of the Kalman filter is to implement a model of the real system in an on-board computer in parallel with the system itself. This paper will give 3 examples of this principle applied to automotive systems.     

Vehicle Dynamics Estimation Using Kalman Filters

This paper deals with the application of stochastic state estimators in vehicle dynamics control. It is often unrealistic to assume that all vehicle states and the disturbances acting on it can be measured. System states that cannot be measured directly, can be estimated by a Kalman Filter. The idea of the Kalman filter is to implement a model of the real system in an on-board computer in parallel with the system itself. This paper will give 3 examples of this principle applied to automotive systems.     

整车多体动力学模型的建立、验证及仿真分析

利用多体动力学方法建立了某轿车的整车非线性多体动力学模型,模型中考虑了前后悬架、转向系统的详细几何结构参数,以及连接处的橡胶衬套、阻尼器的非线性特性,轮胎采用M agic Formu la模型。对所建模型进行了多种试验验证,并分析了该样车的操纵稳定性等相关特性,仿真结果表明所建整车多体模型有较高的精度。     

A novel method for identifying inertial parameters of electric vehicles based on the dual H infinity filter

ABSTRACT

Accurate identification of vehicle inertial parameters is essential to the design of vehicle dynamics control systems. In this paper, a novel vehicle inertial parameter identification method based on the dual H infinity filter (DHIF) for electric vehicles (EVs) is proposed. The filter algorithm employs a nonlinear longitudinal vehicle model with three vehicle states. A hierarchical framework is engaged by the DHIF to estimate the vehicle states and inertial parameters concurrently. In order to minimise the disturbance of unknown noise, the vehicle states are estimated by using the linear H infinity filter (LHIF), while the nonlinear H infinity filter (NHIF) utilises the observed states to identify the vehicle inertial parameters. Finally, the proposed estimation method is verified and compared through the dSPACE based hardware-in-the-loop (HIL) simulation experiments. The results indicate that the DHIF-based estimation method is effective to identify the vehicle inertial parameters with high precision, remarkable robustness, and quick convergence.     

On Inverse Equations for Vehicle Dynamics

Instead of writing equations which when solved yield the response of a vehicle to an input such as the front wheel steer angle, one can often invert the equations so that a response quantity is specified as an input and a new set of equations is solved yielding the steer angle required as an output. Using these equations one can discover the input steer angle a driver would need to impose in order to accomplish a specific maneuver for various vehicles.

It is shown that there are many possible inverse equation sets and that the eigenvalues of the inverse equations are hard to interpret since they may have little to do with the vehicle parameters. The linear single-input single-output case is studied first to fix ideas using a simple example. For the bicycle model vehicle, it is shown that any vehicle may have unstable inverse equations depending upon the response quantity used. Extensions to nonlinear and multiple-input multiple output systems are discussed.     

Dynamics of Automated Guideway Transit Vehicle with Single-axle Bogies

Summary The steering type of a mechanical guidance system has been used for Automated Guideway Transit (AGT) system in Japan. Recently, the single-axle bogie system has developed for AGT vehicle and applied to Yurikamome 7200 type vehicle. This paper describes dynamic characteristics of AGT vehicle with single-axle bogies. Introducing a nonlinear, 15 degree-of-freedom dynamic model, a computer simulation study on the lateral motion of the AGT vehicle with single-axle bogies are carried out. In order to show the dynamic characteristics of the single-axle bogie clearly, it is compared to that of the AGT vehicle with conventional steering system. The simulation study with actual vehicle parameters shows that single-axle bogie has suitable characteristics for AGT system. The multi-body dynamics modeler, DADS, is used to build the dynamic model of AGT vehicle with single-axle bogies and this is used to demonstrate the vehicle motion in actual guideway. Obtained results are compared to that of the field test. It is shown that the vehicle dynamic response can be obtained in realistic situation by using multibody dynamics code, that is useful for designing both vehicle and guideway.