The Lateral Dynamics of Motorcycles and Bicycles

The paper is a review of the state of knowledge and understanding of the steering behaviour of single-track vehicles, with the main accent on vehicle design, and vehicle design analysis and behaviour prediction.

The body of the paper consists of a chronological account of the steps which have been taken in establishing the current position. Scientific study of the motions of two-wheelers has been in progress for more than 100 years, but progress was slow and many conflicting conclusions were drawn until increasing understanding of tyre mechanics, systematic application of the laws of motion for systems of rigid bodies, digital computation and modern numerical methods, and improved mobile measurement, recording, and data processing capabilities allowed the pace to accelerate.

The current position, which is that a good understanding of the relationship between design and performance has been achieved, but that by no means have all the problems of significance been solved, is described at the end of the paper.     

The Dynamics of Single Track Vehicles

SUMMARY

The paper contains a brief review of the more subjective aspects of the steering behaviour of single track vehicles, a review of the more significant published work in the field, and an assessment of the current state of understanding and likely ways in which further progress can be made

Attention is drawn to the many areas of agreement between theory and practice and to some areas of disagreement. The greatest need now seems to be for the incorporation of more complex tyre models into vehicle handling models.     

Dynamics of Tracked Vehicles

SUMMARY

This paper provides a brief review of the state-of-the-art of tracked vehicle dynamics, including mobility over soft terrain, ride dynamics over rough surfaces and manoeuvrability. It is found that considerable progress has been made in the development of analytical frameworks for evaluating and predicting tracked vehicle mobility over soft terrain, taking into account the characteristics of terrain response to normal and shear loading. Certain computer simulation models for tracked vehicle mobility have been gaining increasingly wide acceptance by industry and governmental agencies in product development and in procurement. It is also found that most of the research on tracked vehicle ride dynamics and manoeuvrability is confined to operations on rigid surfaces. To achieve a realistic evaluation and prediction of the dynamic behaviour of tracked vehicles in the field, the key is to have a better understanding of terrain response to dynamic vehicular loading, including its dynamic stiffness and damping. Challenges that face vehicle dynamicists in this emerging field are identified.     

Off-Road Vehicle Dynamics

SUMMARY

Recent developments in off-road vehicle dynamics are reviewed. Progress on this topic and the application of new techniques to the particular problemsassociated with off-road operation tend to lag behind practices established for road vehicles.

The factor which limits further progress is the lack ofappropriate off-road tyre data, in particular, on vibrational and lateral force generation characteristics. Also, a long term study should be aimed at understanding the dynamic behaviour of tyres on yielding surfaces.     

A Review of Modelling Methods for Railway Vehicle Suspension Components

SUMMARY

The dynamic behaviour of railway vehicles has been the subject of study for over a century but the advances in computing technology in the last few years have led to a very rapid development in the use of numerical techniques for solving railway vehicle dynamics problems. As these techniques have developed, and have been applied to ever more complex problems, the modelling of the vehicle components has increased in importance. Mathematical models of railway vehicles may now include components such as swing links, air-springs, trailing arm suspensions, load sensitive friction dampers, rubber bushes with hysteresis etc, all of which require sophisticated modelling techniques to produce accurate results. This paper looks at the developments that have taken place in this area, the background to the need for sophisticated models, the improvements in accuracy that can result and some of the difficulties in applying these techniques to the modelling of real situations.     

Railway Vehicles with Perfect Curving Behaviour Which are Asymptotically Stable at Vanishing Speed

SUMMARY

Paper deals with the linear behaviour of a railway vehicle with any arbitrary number of wheelsets, body parts and connecting elements. A vehicle which has both perfect curving properties and asymptotical stability at vanishing speed, has to satisfy a twofold condition, indicated by Wickens in 1978. In the present paper this condition is derived in reliance upon the dimension theorem for linear mappings. How the investigation can be executed in practice, is shown for the case of a two-axled vehicle. At last the behaviour in a transition curve is discussed.     

Optimization for Vehicle Suspension I: Time Domain

SUMMARY

A numerical procedure for finding the optimum values of a number of parameters describing a model vehicle suspension has been studied. The vehicle has been modelled by dynamic systems of linear springs and dampers, and the goal is to obtain lower acceleration peaks at an elected design point in the vehicle.

The problem is stated as a mathematical programming problem which can be solved by means of the sequential linear programming technique. The procedure has been implemented for a four wheel independent suspension model capable of being subjected to road irregularities and to centrifugal and braking accelerations.     

Modelling Combined Ride and Handling Manœuvres for a Vehicle with Slow-Active Suspension

SUMMARY

The computer modelling of vehicle ride and handling has been widely reported, but often only one or other of these functions is considered. This is especially true in the design of active suspension controllers, where the effects that improvements in the performance of one aspect have on the other are often not presented. This paper initially describes a combined ride and handling model for a large executive saloon fitted with a slow-active suspension. Separately derived ride and roll control strategies are combined and the effects on both ride and handling considered for straight running and various handling man?uvres on rough roads. The results are compared to the original passively suspended vehicle and the effect of running each strategy separately.     

Autonomous Lateral Control of Vehicles in an Automated Highway System

SUMMARY

Lateral control of vehicles in IVHS requires the installation of on-board sensors as well as the installation of roadway hardware such as cables, magnets, etc. Existing control approaches in PATH require road curvature and vehicle lateral position (with respect to the center of the lane) information. Hence these approaches rely on roadway sensors to obtain relative lateral position. These methods will necessitate infrastructural changes to the highway.

This paper introduces the concept of autonomous lateral control or auto-tracking. The method allows us to use only line-of-sight sensor information to effect vehicle control. We present a detailed vehicle model. Controllers have been proposed to demonstrate the effectiveness of the proposed auto-tracking scheme. We also examine the possibilities of using this method for lane change purposes in an automated highway system.     

A Comparison between Four Computing Models of Different Complexity Describing the Steering Behavior of Two-axled Automobiles

SUMMARY

In this paper chassis controls for vehicle handling and active safety have been reviewed. In particular, we have observed the effectiveness and limit of 4WS and DYC. It is pointed out that DYC is more effective in vehicle motion with larger side-slip and/or higher lateral acceleration and taking the nonlinearity of tire and vehicle dynamics into consideration is essential for introducing the control law for the chassis controls and their integration/coordination. We wish to emphasize that there is a need to further propose control laws based on deeper observation and understanding on the tire and vehicle dynamics.     

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

SUMMARY

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.     

Validation of a MATLAB Railway Vehicle Simulation Using a Scale Roller Rig

SUMMARY

A 1/5 scale roller rig has been constructed for use in analysing the dynamic behaviour of railway vehicles. The roller rig includes a servo hydraulic system to allow a realistic input of track irregularities at the rollers and instrumentation is fitted to allow measurement of the position and acceleration of the bodies. This paper reports on the first stage in validating the behaviour of the roller rig using a relatively simple, linear computer model constructed in MATLAB. Initial results show good correlation between the behaviour seen on the roller rig and that predicted by the model.     

Driver-Vehicle-Lateraldynamics under Regular Driving Conditions

SUMMARY

In order to minimize accidents and achieve comfortable handling it is necessary to analyse the control behaviour of the driver-vehicle system and adapt the vehicle to the driver. However, most of the tests have shown, that under normal driving conditions the driver adapts himself to the vehicle, which is exactly the other way round as it was originally thought. In this paper it would be shown, how the driver adapts himself to the vehicle and which technical parameters may effect this adaptation.     

Comparison of All-Wheel Steerings in the System Driver-Vehicle

SUMMARY

Different load or tires and a drive on an ice-coated road can overcharge a driver to such an extend, that the result may be an accident. Therefore the aim of development is a self-acting compensation of the vehicle to different vehicle transfer behaviour (invariant vehicle behaviour).

The calculation of so called optimal characteristics shows, that only rear-wheel steering cannot realize this aim of development. Therefore an additional front-wheel angle, which is not influenced by the driver, is necessary. A transfer function can be calculated in order to get controlled steering of the rear wheels without the influence of load.

It is not possible to realize optimal characteristics, because the parameters of the vehicle are difficult to measure. Only an optimal diagnosis and control of driving condition realize a relief for the driver in every driving situation in order to avoid most of the accidents.

The often demanded sideslip angle compensation only worsens driving conditions on ice-coated roads. Therefore systems which identify the driving condition themselves have to be favoured in any case.     

A Modular Computer Model for the Design of Vehicle Dynamics Control Systems1

SUMMARY

This paper describes a multiport approach to computer-aided modeling of vehicle dynamics. The modeling approach produces models that are suitable for the interactive design and evaluation of complex control strategies. The vehicle model which can be used for ride and handling analysis, is built from modular components. The components are programmed using the syntax of the computer aided control system design (CACSD) program EASYS. Seven modeling components are used to create a three-dimensional vehicle dvnamics model. The model is flexible enoug-h to simulate any suspension design with revolute joints.

Each component of the model consists of a FORTRAN subroutine and a main calling module called a macro. To simplify the process of model building, the modeling components in the car model are designed to represent physical elements, such as the spring, damper, link or tire. To create a model, the components, which are represented by blocks, are interconnected through points, located on the blocks, called pons. These ports have been designed to simulate the location of the connection points between the physical elements, as observed in real systems. The construction of multibody models within a CACSD program offers the flexibility of simultaneous interactive simulation of the three-dimensional dvnamics and evaluation of the desien of the controls.

Although modeling of multibody systems using FORTRAN components has been pioneered by Chace, Haug and Orlandea; and bond graph modeling of multibody systems has been investigated by Bos, this approach is novel because:-

The model is included in the control system design program (EASYS). This arrangement allows the designer to exploit the advanced control design tools available in the program. Furthermore, this approach significantly reduces the computation time required for running the model after parameters modification.

The model is built from components that are interconnected by ports which represent the actual physical location of the connection points between the elements. The multiport approach simplifies the model building process for multibody systems. This simplification is achieved by reducing the model of a multibody system to a block diagram form.     

Random Response of Tractor-Semitrailer System

SUMMARY

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.     

Numerical Simulation of Vehicle Behavior during Straight Line Keeping on Undulating Road Surfaces

SUMMARY

Numerical design of vehicles having optimal straight line stability on undulating road surfaces requires an accurate vehicle model based on knowledge of the relevant phenomena. Therefore, vehicle behavior on undulating straight roads has been analyzed and modeled. Measurements on a flat road surface have shown that the dedicated vehicle model yields accurate simulation results of the steering response to medium steering wheel angle inputs. In addition, the model has been validated by measuring two vehicle responses during normal driving on an undulating straight road: viz. the responses to the small steering wheel angle input and to the input by the global inclination of the road surface.     

A book review of “Dynamik der Kraftfahrzeuge (German)”, Dynamics of Motor Vehicles by M. Mitschke,Springer-Verlag, 1972, 529 pp., 382 figs.

SUMMARY

The demands upon the dynamic behaviour of a vehicle can be stated as an optimization problem. The optimum solution is calculated using an iterative optimization algorithm. Scaling the problem by non-linear transformations reduces the number of iterations. Lagrange multipliers provide useful information about the sensitivity of the optimum with respect to changes of the constraints. The analysis of the dynamic behaviour is performed in the frequency domain. New structural variants are calculated using system synthesis. As an example, the engine, cab and wheel suspension systems of a tractor/semi-trailer have been optimized all together.