R. S. Sharp

THE STABILITY AND CONTROL OF MOTORCYCLES

Mathematical models of a motorcycle and rider dependent on three alternative assumptions concerning the tyre behaviour are developed. Stability characteristics deduced from them are compared, and m...

Shear force development by pneumatic tyres in steady state conditions: a review of modelling aspects

SUMMARY Modelling of the generation of shear forces by pneumatic tyres under steady state conditions is reviewed. The review is placed in a practical context, through reference to the uses to which models may be put by the vehicle dynamicist and the tyre designer. It will be of interest also to the student of rolling contact problems. The subject is divided into sections, covering physically founded models which require computation for their solution, physically based models which are sufficiently simplified to allow analytical solutions and formula based, empirical models. The classes are more nearly continuous than this strict division would imply, since approximations in obtaining analytical solutions may be made, empirical correction factors may be applied to analytical results and formula based methods may take into account tyre mechanical principles. Such matters are discussed in the relevant sections. Attention is given to the important matter of choosing model parameters to best represent the beha...

Road Vehicle Suspension System Design - a review

SUMMARY Based mainly on English language literature, information relating to the design of automobile suspension systems for ride comfort and control of wheel load variations for frequencies below body structure resonances is reviewed. The information is interpreted in the context of vehicles which travel through a wide speed range on roads of markedly differing quality, which do so carrying different loads and which are required to possess good handling qualities. Sections are devoted to describing road surfaces, modelling vehicles and setting up performance criteria, and to passive, active, semi-active and slow-active system types. Methods for deriving active system control laws are outlined. Strengths and weaknesses of the various systems are identified and their relative performance capabilities and equipment requirements are discussed. Attention is given to adaptation of the suspension or control system parameters to changing conditions. Remaining research needs are considered.

Stability, Control and Steering Responses of Motorcycles

Following on from the author’s reviews of the stability and control of motorcycles in 1978 and 1985, the paper treats the earlier material in tutorial fashion and adds more recent information. Fixed and free control properties are compared and it is concluded essential to the operation of a motorcycle that the steering system is free. Motorcycles typically possess lightly damped oscillatory modes and the properties of these modes are discussed. Small perturbations from straight line motion and from cornering equilibrium states are treated. Steering control by handlebar torque and by rider upper body lean torque are compared. The behaviour of the rider as an extension of the structure of the machine and as a controller is also discussed. Theoretical analysis, experimental measurements and general experience are linked as far as possible. More recent years have seen a strong movement towards the use of structurally efficient frames for large motorcycles, in particular, and multibody dynamics software for handling analysis. Theoretical predictions can be extended in ways hardly possible before automated multibody analysis became available. The state of the art is illustrated with a description of a contemporary motorcycle / rider model and some results which are derived from it. Directions for future work are indicated.

Bicycles, motorcycles, and models

The development of bicycles and motorcycles since the first patented running machine, or draisine, in 1817 is described. Bicycle modeling and control were also discussed. These models include: derivatives or simplifications of Whipples bicycle dynamics model in which the lateral motion constraints at the road contact are nonholonomic, requiring special techniques to form correct equations of motion; and the Timoshenko-Young model in which the steer angle and speed completely determine the lateral motion of the base point of an inverted pendulum that represents the vehicles roll dynamics

The Application of Linear Optimal Control Theory to the Design of Active Automotive Suspensions

SUMMARY Some linear stochastic control theory relevant to the design of active suspension systems subject to integrated or filtered white noise excitation is reviewed, and application of the theory to a particular problem is considered. The problem considered is the well known quarter car problem in which a control law which minimises a performance function representing passenger discomfort, suspension working space, and tyre load fluctuations is required. With full state feedback, the requirement for a formulation of the problem which leads to the system under consideration being observable and controllable is referred to, and it is shown how a well known coordinate transformation enables this requirement to be satisfied. With limited state (or output) feedback, problem formulations which will avoid potential numerical problems in deriving the optimal control are described. Example solutions are included in order to illustrate the methods.

A Motorcycle Model for Stability and Control Analysis

The observed dynamic behaviourof motorcycles suggests that interesting andsignificant motions occur that are not currentlyunderstood. The most elaborate modelling exercisecompleted so far has produced results that needconfirmation and extension. The construction of thesemodels necessitates the use of automated methods andone such modelling methodology is described. Theautomated model building platform that was used hereis AutoSim. This code was used to generate a varietyof linear and nonlinear models in symbolic form. Therelatively complex geometry of the steering system andthe front tyre force system is discussed in detail anda new method of checking the self-consistency of themodel is described and exploited. Sample results inthe form of root-locus plots for small perturbationsfrom straight running and cornering equilibrium statesare presented. These are used to reproduce importantfindings from the literature. Conclusions are drawnon the basis of the results presented.

Mechanical Steering Compensators for High- Performance Motorcycles

This paper introduces the idea of using mechanical steering compensators to improve the dynamic behavior of high-performance motorcycles. These compensators are seen as possible replacements for a conventional steering damper and comprise networks of springs, dampers, and a less familiar component called the inerter. The inerter was recently introduced to allow the synthesis of arbitrary passive mechanical impedances, and finds a potential application in the present work. The design and synthesis of these compensation systems make use of the analogy between passive electrical and mechanical networks. This analogy is reviewed alongside the links between passivity, positive reality, and network synthesis. Compensator design methods that are based on classical Bode-Nyquist frequency-response ideas are presented. Initial designs are subsequently optimized using a sequential quadratic programing algorithm. This optimization process ensures improved performance over the machine’s entire operating regime. The investigation is developed from an analysis of specific mechanical networks to the class of all biquadratic positive real functions. This aspect of the research is directed to answering the question: “What is the best possible system performance achievable using any simple passive mechanical network compensator?” The study makes use of computer simulations, which exploit a state-of-the-art motorcycle model whose parameter set is based on a Suzuki GSX-R1000 sports machine. The results show that, compared to a conventional steering damper, it is possible to obtain significant improvements in the dynamic properties of the primary oscillatory modes, known as “wobble” and “weave.” DOI: 10.1115/1.2198547

MINIMUM TIME MANOEUVRING: THE SIGNIFICANCE OF YAW INERTIA

A formal method for the evaluation of the minimum time vehicle manoeuvre is described. The problem is treated as one of Optimal Control and is solved using a direct transcription method. The resulting Non Linear Programming problem is solved using a Sequential Quadratic Programming (SQP) algorithm for constrained minimisation of a multivariable function. The optimisation program is used to investigate the effect of the yaw moment of inertia on vehicle performance in a double lane change manoeuvre. The method is shown to have excellent capabilities to predict the vehicle maximum performance in transient conditions and to perform sensitivity analysis. The influence of yaw inertia on the minimum manoeuvre time is found to be surprisingly small. The extension of the method to larger problems, e.g., lap time simulation, is also discussed.

The Influence of Structural Flexibilities on the Straight-running Stability of Motorcycles

SUMMARY A new tyre model for studies of motorcycle lateral dynamics, and three new motorcycle models, each incorporating a different form of structural compliance, are developed. The tyre model is based on “taut string” ideas, and includes consideration of tread width and longitudinal tread rubber distortion and tread mass effects, and normal load variation. Parameter values appropriate to a typical motorcycle tyre are employed. The motorcycle models are for small lateral perturbations from straight running at constant speed, and include (a) lateral compliance of the front wheel in the front forks, (b) torsional compliance of the front forks, and (c) torsional compliance in the rear frame at the steering head about an axis perpendicular to the steering axis. Results in the form of eigenvalues, indicating modal damping properties and natural frequencies are presented for each model. The properties of four large production machines for a range of forward speeds, and the practicable range of stiffnesses are ...