Vittore Cossalter

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.

The Modal Analysis of a Motorcycle in Straight Running and on a Curve

The vibrational modes (generalized) of a two-wheel vehicle are studied in several trim configurations. The modal analysis is carried out on a 3D non-linear mathematical model, developed using the natural coordinates approach. A special procedure for evaluating the steady state solutions in straight running and on a curve is proposed. The paper presents detailed results of the modal analysis for a production sports motorcycle. Furthermore, the influence of speed and lateral (centripetal) acceleration on stability, shape and modal interactions (coupling) is highlighted. Finally, consistency between the first experimental tests and simulation results is shown.

On the use of natural coordinates in optimal synthesis of mechanisms

Abstract This paper deals with the use of natural coordinates for the synthesis of mechanisms using optimization methods. It will be shown that an approach based on this kind of coordinates has many interesting aspects. The modeling of a mechanism with natural coordinates, like any other multi-body system, is carried out by means of a system of algebraic constraint equations. These are complemented by additional equations describing the requirements of the mechanism. All types of requirements — paths, function generation, body guidance, correlation between members — may be given in this way, so that there is a unified method for treating any kind of synthesis. An interesting method is developed here for kinematic analysis of candidate mechanisms. According to this method, kinematic analysis is carried out in the sense that only constraint equations are satisfied exactly, while requirements are satisfied at best. This corresponds to finding the motion of the candidate mechanism that is ‘closest’ to established requirements. This method is then reduced to the solution of the Initial Value Problem (IVP) of a proper system of Ordinary Differential Equations (ODEs). Lastly, the design space (i.e., the space of the design parameters) also takes advantage of the natural coordinates approach. It is based on the initial values of the natural coordinates themselves rather than on link lengths. This avoids the need to assemble the mechanism in the initial position (and associated branching problems), gives more uniform spanning of the solution space, and guarantees that at least the starting configuration for the ODEs IVP exists and is known. Three examples are given: a four-bar linkage generating a straight path, the same type of linkage generating a square angle (both without correlation), and a six-link Stephenson’s mechanism producing a function with a dwell range.

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.

The influence of frame compliance and rider mobility on the scooter stability

This article investigates the effect of frame compliance and rider mobility on the scooter stability. Particular attention is given to the wobble mode, because it may easily become unstable in the vehicle speed range. This article includes a synthetic discussion of previous works, presents a new mathematical model, and discusses the results of both numerical and experimental analyses of the vehicle stability by varying the vehicle characteristics and motion conditions. The mathematical model describes the out-of-plane dynamics of the scooter and consists of a twelve-degree-freedom linear model. It describes the main scooter features and, in particular, includes the frame compliance, rider mobility, and an advanced tire model. The torsion and bending compliance of both the front fork and swingarm are modelled using lumped rotational springs; similarly, the rider mobility is described by means of two soft springs which connect the rider body to the chassis. The tire model describes in detail the carcass geometry and its compliance. The full scooter model is available on the website www.dinamoto.it and has been derived using ‘MBSymba’, which is a package for the symbolic modelling of multibody systems. The scooter stability has been investigated at both low and high speeds; in particular, the effect of vehicle compliance and rider mobility on the weave and wobble modes have been examined. Numerical simulations show that the bending flexibility of the front fork stabilizes wobble mode at high speed and has a contrary effect at low speed, whereas the torsion flexibility of the fork does not appear to have a remarkable influence; the bending flexibility of the swingarm slightly stabilizes the weave mode at very high speeds whereas the torsion flexibility of the swingarm has a contrary effect. The effect of rider mobility is to stabilize the weave mode at high speed and the wobble mode at low speed. Several experimental tests have been carried out in the same speed range and a good correlation between simulations and tests has been found. The variation of some important vehicle parameters has been investigated; in particular, tests were repeated for different values of the rear-frame inertia, the rear-chassis stiffness, the front-tire characteristics, the normal trail, and the steer inertia.

A simple numerical approach for optimum synthesis of a class of planar mechanisms

Abstract In this study a numerical method for optimum synthesis of planar mechanisms, generators of functions, paths and rigid motions, is presented. Design parameters have wide variability ranges, inside which first guesses, demanded by the iterative minimization procedure, can be chosen at random. Kinematic analysis is carried out by decomposition of the mechanism into Assur groups; mechanism assembly is managed by the construction of a proper penalty function. Optimization is carried out by using a non-derivative and a quasi-Newton method in series. Some optimum design examples are presented to illustrate the power of the method.

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.

Experimental Study of Motorcycle Transfer Functions for Evaluating Handling

Summary The transfer functions of a motorcycle, especially that between roll angle and steering torque, qualify input-output characteristics - that is, motion produced as a function of steering torque - and are closely related to ease of use and handling. This paper describes the measurement of the transfer functions of a typical sports motorcycle, resulting from data collected in slalom tests. These functions are then compared to analytical transfer functions derived from known models in the literature. The comparison shows fair to good agreement. Lastly, the formation of steering torque is analysed and the observed transfer functions are interpreted in this framework. It is shown that gyroscopic effects are mostly responsible for the lag between steering torque and roll angle, and that there is a velocity for which the various terms that combine to form steering torque cancel each other out, yielding a ‘maximum gain condition’ for torque to roll transfer function which drivers rated ‘good handling’.

Development and Validation of an Advanced Motorcycle Riding Simulator

This paper illustrates and discusses the main features of the motorcycle riding simulator designed and built at the University of Padua over recent years. The simulator has been developed for a variety of purposes: to develop and test electronic devices aimed at improving rider safety and vehicle performance (antilock braking systems, traction control systems, etc.), to investigate different design choices and parameter effects on vehicle dynamics, to train riders, and to study their behaviours in different scenarios (normal riding, dangerous situations, etc.). Within the simulator the rider sits on a motorcycle mock-up provided with all the inputs available on a real motorcycle (throttle, clutch, brakes, etc.). These controls are used as inputs for an advanced virtual motorcycle model which computes the real-time vehicle dynamics. With the aim of giving the rider a proper motion cue, a washout filter converts the motion of the virtual motorcycle into the proper motion of a five-degrees-of-freedom motorcycle mock-up. Finally the audiovisual cues are delivered with a 180° panel and 5.1 surround sound system. To validate the simulator, a specific protocol which includes both an objective evaluation and a subjective evaluation was designed and carried out. External devices such as advanced rider assistant systems, on-bike information systems, and human–machine interfaces can be easily integrated into the simulator by means of a standard controller area network.

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.