The chatter of racing motorcycles

The chatter of motorcycles appears during braking and consists of a vibration of the rear and front unsprung masses at a frequency in the range of 17-22 Hz depending on the motorcycle. This vibration could be very strong and acceleration of the unsprung masses can reach 5-10 g. The chatter is an auto-excited vibration and this fact explains why it appears suddenly when the mechanism of auto-excitation is generated. This paper presents the chatter phenomenon both from an experimental and a numerical point of view. First, the chatter is defined on the basis of some experimental data from racing motorcycles and from the comments of some racing teams technicians. Then, chatter is analysed in different motion conditions and for different braking styles by means of linear and non-linear simulations of the motorcycle dynamics. A physical interpretation of the phenomenon is also proposed.     

A General Method for the Evaluation of Vehicle Manoeuvrability with Special Emphasis on Motorcycles

This paper presents a novel approach to the assessment of the manoeuvrability of vehicles which is not based on the simulation of open-loop manoeuvres, nor does it rely on the modelling of the driver as a control system. Instead, the essence of the method is the solution of a two-point optimal control boundary value problem, in which a vehicle, subject to physical constraints like tyre adherence and road borders, among others, is required to go between given initial and final positions as fast as possible. The control inputs - i.e., the driver's actions - that make the vehicle move between the two states in the most efficient way are found as a part of the solution procedure and represent the actions of a sort of ideal, perfect driver . The resulting motion is called the optimal manoeuvre and, besides being the most efficient way that the given vehicle has for travelling between the two points according to the chosen optimal criterion, may be taken as a reference for meaningful comparisons with other vehicles. The value of the penalty function, used to define the optimal condition occurring at the optimal manoeuvre, may be taken as a measure of manoeuvrability or handling. With this approach the manoeuvrability properties are established as intrinsic to the vehicle, being defined with respect to an ideal perfect driver. Some possible forms of the penalty function, which means slightly different concepts of manoeuvrability and handling, are discussed. In the end, the case of motorcycles and some examples of optimal manoeuvres are given.     

Dynamic Properties of Motorcycle and Scooter Tires: Measurement and Comparison

Summary Results of an experimental research program dealing with motorcycle and scooter tires are presented. Experimental tests were carried out by means of a rotating disk test machine, which is particularly suited to test tires in the presence of large camber angles. First, the capabilities of the rotating disk machine are discussed and results are compared with the ones obtained by means of other test machines. Then the properties of several motorcycle and scooter tires are presented and compared. The advantage of presenting results in terms of camber and sideslip stiffness is highlighted. The effect of tire working conditions (inflation pressure, load and temperature) is analyzed. Finally the measurement of tire torques is discussed and some results dealing with self-aligning, twisting and rolling resistance torques are presented.     

Steady Turning of Two-Wheeled Vehicles

When driving along a circular path, the driver of a motorcycle controls the vehicle mainly by means of steering torque. If low steering torque is necessary, the driver feels that the vehicle is manoeuvrable. In this paper, a mathematical model concerning steering torque is developed; it takes into account the actual kinematic behaviour of the vehicle and the properties of motorcycle tyres. Tyre forces act at the contact points of toroidal tyres, which are calculated according to kinematic analysis. Non-linear equations are solved using an iterative approach. Several numerical results are presented, and the influence of tyre properties and some geometrical and inertial properties of the vehicle on steering torque are discussed.     

The effect of the inflation pressure of tyres on motorcycle weave stability: experiments and simulation

Increasing the stability of a motorcycle requires an understanding of the optimal conditions of the tyre. The inflation pressure is one of the main parameters that directly affects the tyre properties, which in turn influences motorcycle stability and safety. This paper focuses on the effect of the inflation pressure of the tested tyres on motorcycle weave stability. Experimental data are collected from tests carried out in straight running at constant speed. The data analysis is based on stochastic subspace identification methods. Simulations are performed using an advanced motorcycle multi-body code with parameters measured from the tested vehicle. Finally, the comparison between simulations and experimental tests is discussed. The research results show an agreement between experimental tests and simulations where weave stability increases with inflation pressure for the specified range of tyre pressure.     

A Motorcycle Multi-Body Model for Real Time Simulations Based on the Natural Coordinates Approach

This paper presents an eleven degrees of freedom, non-linear, multi-body dynamics model of a motorcycle. Front and rear chassis, steering system, suspensions and tires are the main features of the model. An original tire model was developed, which takes into account the geometric shape of tires and the elastic deformation of tire carcasses. This model also describes the dynamic behavior of tires in a way similar to relaxation models. Equations of motion stem from the natural coordinates approach. First, each rigid body is described with a set of fully cartesian coordinates. Then, links between the bodies are obtained by means of algebraic equations. This makes it possible to obtain simple equations of motion, even though the coordinates are redundant. The model was implemented in a Fortran code, named FastBike . In order to test the code, both simulated and real slalom and lane change maneuvers were carried out. A very good agreement between the numerical simulations and experimental test was found. The comparison of FastBike 's performance with those of some commercial software shows that first is much faster than others. In particular, real time simulations can be carried out using FastBike and it can be employed on a motorcycle simulator.     

Elaboration and quantitative assessment of manoeuvrability for motorcycle lane change

The desire to quantitatively assess vehicle manoeuvrability and handling has led to the development of various expressions, or metrics, which typically relate system input to system output. With regard to motorcycle manoeuvrability, a notable example of such a measure, or metric, is the Koch index [Koch, J., 1978, Experimentelle und Analytische Untersuchungen des Motorraad-Fahrer Systems. Dissertation, Berlin.]. This article describes the development of a new metric applied to lane change (LC) tests and coined 'LC roll index'. This metric takes into account the peak-to-peak values of the rider-input steering torque divided by the peak-to-peak roll rate response of the vehicle and normalizes this quantity by the forward velocity. In addition to this new metric, an analytical expression is developed, which in many cases summarizes a motorcycle's LC performance in a single, terse, analytical term. Experimental results are presented for three vastly different motorcycles: a scooter, a street, and a touring motorcycle performing variations of the LC manoeuvre. Numerous test runs for each vehicle are analysed and the results are summarized along with those presented in the recent literature. Finally, simulation results are presented to highlight the correlation between the proposed indices and handling.     

Frequency-domain method for evaluating the ride comfort of a motorcycle

In many European towns, the demand for fast and efficient mobility is frequently satisfied by means of two-wheeled vehicles. The improvement of comfort of two-wheeled vehicles used by tired and busy workers can increase safety in ground transport. Nowadays, multibody codes make it possible to predict the ride comfort of two-wheeled vehicles by means of time-domain or frequency-domain simulations. Comfort indices can be developed by post-processing the results of numerical simulations. This task is difficult, because the indices should depend on vehicle characteristics and should be independent of road quality and vehicle speed. Poor quality roads may generate nonlinear effects. Speed influences the trim of the vehicle and the wheelbase filtering, which takes place because the same road unevenness excites the front and rear wheel with a time delay which depends on the vehicle's speed.

In this paper, the comfort of two-wheeled vehicles is studied by means of a frequency-domain approach. The wheelbase filtering is averaged considering typical missions of the vehicle. The missions are journeys with a forward speed that assumes different values according to a probability density function. Indices of comfort are calculated taking into account the human sensitivity. The examples show that the proposed comfort indices depend on suspensions' characteristics and, hence, are useful design tools. Finally, some time-domain calculations are carried out to give emphasis to nonlinear effects and to show the limits of the frequency-domain analysis.     

Optimum Suspension Design for Motorcycle Braking

A mathematical model for the in-plane dynamic analysis of motorcycles is presented and the performance during an emergency braking manoeuvre is analysed. The effects of braking torque amplitude and time constant are discussed and the problems of lock-up and loss of contact of the rear wheel are highlighted. The suspensions' vibrations during braking are analysed by means of modal analysis. An optimisation method is developed in order to find the braking torque and the suspension parameters that minimise the stopping distance. The method takes the complete dynamic behaviour of the vehicle during braking into account and is based on a non-derivative minimisation algorithm. Several results are presented that show the possibility of shortening the stopping distance by optimum design of one or both of the suspensions.