Digital archive of theses discussed at the University of Pisa


Thesis etd-11102004-232552

Thesis type
Tesi di laurea vecchio ordinamento
Simonetti, Michele
email address
Thesis title
Modelling of the steering moment in race cars for real-time simulator
Course of study
relatore Guiggiani, Massimo
relatore Vries, Edwin de
relatore Forasassi, Giuseppe
  • matlab
  • sospensione
  • veicolo
  • sterzo
Graduation session start date
Release date
This report describes the progress of my final thesis for the “Università degli Studi di Pisa”. The research I have been working on is made in cooperation with the “Delft University of Technology” (the Netherlands), within the “Socrates” project 2003-2004.
A TUDelft associated company called “Racing Interaction” has developed a high end force feedback steering wheel dedicated to the race cars. To utilize the full capabilities of this advanced hardware and to make drivers aware of the differences between main market game consoles and this professional force feedback steer, the force description (the real time model that calculates the steering moment) needs to be developed. The steering wheel force feedback in fact, carries relevant information regarding the instantaneous dynamics of the vehicle. This information, related to the speed and trajectory curvature, is used by drivers performing their steering task to reinforce the visual information from the simulator.
In order to model the steering moment, a full vehicle model of a “Formula Student” racing car is then developed.
The choice of the Formula Student car has been made because of it synthesizes the main features of a race car (starting from the suspension geometry and tunings), and also because of the easy way to collect datas from the TUDelft Formula Student Team.
Different literature sources have been investigated to determine the require level of complexity of the model, measured by the number of model degrees of freedom. Many authors affirm that the transient vehicle properties are mainly determined by the transient tyre model [7]. The influence of the body roll, pitch and bounce motion on the transient vehicle dynamics can be neglected (it is expected to be small due to the high suspension stiffness) and the load transfer accounted for quasi statically.
This suggests that a vehicle model concerning in-plane dynamics with an accurate tyre model (TUDelft is famous around the world for the “Magic Formula” tyre model) should be precise enough to simulate the vehicle behaviour. Unfortunately, since the beginning analysis, it came out that a model concerning in-plane dynamics was not sufficient to fully describe the steering moment. The steering moment is the result of the force transfer from tyre contact patch to the steering wheel, passing trough the suspension and steering system geometry. During the vehicle motion the suspension experiences a certain travel due to the roll, pitch and bounce vehicle motion that affects the forces transfer from tyre contact patch to steering wheel. In order to investigate their effects on the forces transfer, this leads to include in the analysis a suspension model and to add the relative degrees of freedom to the vehicle model together with the roll, pitch and bounce vehicle motions.
A three dimensional analysis is then developed and the resulting vehicle model is a two mass model with 15 degrees of freedom (6 Dof vehicle body, 4 Dof suspensions travel, 4 Dof wheels rotation, 1 Dof rack displacement).
Due to its influence on the steering moment calculation, the suspension kinematics has been carefully analyzed and described by the developed suspension model.
Datas from measurements have been used to identify the tyres characteristic curves described by the “Magic Formula” tyre model and to validate the vehicle lateral dynamics for different j-turn, lane-change and small track driving.
With the validated vehicle model, different manoeuvres have been simulated in Matlab environment and the steering moment has been calculated.