Matteo Massaro

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.

Minimum time cornering: the effect of road surface and car transmission layout

This paper investigates the minimum time/limit handling car manoeuvring through nonlinear optimal control techniques. The resulting ‘optimal driver’ controls the car at its physical limits. The focus is on cornering: different road surfaces (dry and wet paved road, dirt and gravel off-road) and transmission layouts (rear-wheel-drive, front-wheel-drive and all-wheel-drive) are considered. Low-drift paved circuit-like manoeuvres and aggressive/high-drift even counter-steering rally like manoeuvres are found depending on terrain/layout combinations. The results shed a light on the optimality of limit handling techniques.

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.

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.

Advanced motorcycle virtual rider

The target of this work is the development of a motorcycle virtual rider model that plans a trajectory and follows it. The reference speed and trajectory are obtained by applying the optimal manoeuvre method (i.e. a nonlinear optimal control technique) to a basic model of the motorcycle. Then, the vehicle control and guidance are obtained using a PID architecture and the gains vary with speed. Separated loops for speed and lateral motion controls have been implemented, the lateral motion control is complex because of the motorcycle instability, whereas the longitudinal control is simpler. The characteristics of the PID control are illustrated and discussed in detail, some examples are given for a cornering manoeuvre first and then for a run in the Mugello circuit.

Numerical investigation of engine-to-slip dynamics for motorcycle traction control applications

This work discusses the motorcycle engine-to-slip dynamics which are strictly related to the traction control design. A street motorcycle is analysed by means of an advanced mathematical model which also includes the tyre flexibility and the transmission compliance. The effects of the following parameters on engine-to-slip dynamics are investigated: vehicle speed, engaged gear ratio, sprocket absorber flexibility and road properties. Guidelines for increasing the maximum achievable closed-loop bandwidth are given.

Electric rear axle torque vectoring for combined yaw stability and velocity control near the limit of handling

In this paper we propose a control architecture to stabilize a vehicle during cornering near the limit of lateral acceleration using the rear axle electric torque vectoring configuration of a hybrid vehicle. A vehicle model incorporating nonlinear tyre characteristics and coupling of tyre forces along longitudinal and lateral directions is used to calculate reference steady-state cornering conditions, as well as to design a linear controller with wheel slip ratio inputs. A backstepping controller then provides the necessary motor torques to achieve the wheel slip ratio requested by the linear controller. The controller provides stability of the lateral vehicle dynamics and regulates the longitudinal velocity to ensure feasibility of the reference trajectory.

Numerical and experimental investigation of passive rider effects on motorcycle weave

Despite the importance of rider passive response to the lateral dynamics of motorcycles, there is very little literature on the subject. Even more uncommon are works that consider rider passive steering impedance and its effect on motorcycle stability. Moreover, until this time, there have been no published studies on steering impedance that include correlation to on-road motorcycle stability testing. This paper explores these topics using an advanced motorcycle simulation model which includes rider torso and steering impedance values derived from experimental characterisation and anthropometric modelling. A novel method for quantitatively evaluating on-road stability is discussed and utilised to compare the simulation results to on-road weave stability testing for two different riders in the ‘hands-off’ and ‘hands-on’ the handlebars conditions. Good correlation is achieved between simulation and test indicating stability differences between riders and highlighting hands-off/on effects.

A nonlinear virtual rider for motorcycles

This work presents a virtual rider for the guidance of a nonlinear motorcycle model. The target motion is defined in terms of roll angle and speed. The virtual rider inputs are the steering torque, the rear-wheel driving/braking torque and front-wheel braking torque. The virtual rider capability is assessed by guiding the nonlinear motorcycle model in demanding manoeuvres with roll angles of 50° and longitudinal accelerations up to 0.8 g. Considerations on the effective preview distance used by the virtual rider are included.

Optimal control of motorsport differentials

Modern motorsport limited slip differentials (LSD) have evolved to become highly adjustable, allowing the torque bias that they generate to be tuned in the corner entry, apex and corner exit phases of typical on-track manoeuvres. The task of finding the optimal torque bias profile under such varied vehicle conditions is complex. This paper presents a nonlinear optimal control method which is used to find the minimum time optimal torque bias profile through a lane change manoeuvre. The results are compared to traditional open and fully locked differential strategies, in addition to considering related vehicle stability and agility metrics. An investigation into how the optimal torque bias profile changes with reduced track-tyre friction is also included in the analysis. The optimal LSD profile was shown to give a performance gain over its locked differential counterpart in key areas of the manoeuvre where a quick direction change is required. The methodology proposed can be used to find both optimal passive LSD characteristics and as the basis of a semi-active LSD control algorithm.