Abstract:
In the motorsport environment, where traction at one wheel is often compromised
due to high cornering accelerations, Limited Slip Differentials (LSD) offer significant
improvements in traction and vehicle stability. LSDs achieve these performance
benefits through the transfer of torque from the faster to slower rotating driving wheel.
In the majority of racing formulae, modern devices have evolved to become highly
adjustable, allowing this torque bias to alter both ultimate vehicle performance and
handling balance through specific corner entry, apex and corner exit phases.
This work investigates methods to optimise LSD setup parameters, both for minimum
lap time and desirable handling characteristics. The first stage of addressing this
objective involved the creation of a range of contemporary motorsport LSD models.
These included a plate or Salisbury type, a Viscous Coupling (VC) and a Viscous
Combined Plate (VCP). A differential test rig was developed to validate these models.
The parameter optimisation is addressed in two main parts. Firstly, a Quasi Steady
State (QSS) time optimal method is used to maximise the vehicle's GG acceleration
envelope using a direct, nonlinear program (NLP). A limitation of this approach
however, is that system transients are neglected. This is addressed through the
development of an alternative indirect, nonlinear optimal control (NOC) method. Both
methods were able to find LSD setup parameters which minimised lap time, providing
significant improvements over traditional open and locked devices. The NOC method
however, was able to give greater insight into how a locked device ultimately limits the
vehicle yaw response during quick direction changes.
The time optimal analysis was extended to investigate aspects of vehicle stability
and agility. These factors are known to have a major influence on driveability and
thus, how much of the theoretical performance limit the driver can extract. A more
unified GG diagram framework was implemented, to characterise both the vehicle's
acceleration limits, and how its stability and agility changes leading up to this limit.
The work has generated a number of novel contributions in this research field. Firstly,
the creation and validation of a range of state-of-the-art motorsport LSD models.
Secondly, the methodologies used to optimise LSD setup parameters, the results from
which, have themselves provided the basis of a novel, vehicle speed dependent LSD
device. Finally, a more practical and intuitive way to evaluate vehicle stability and
agility at different cornering phases. This has laid the foundations of a procedure
which not only maximises the vehicle's acceleration limits, but also allows its response
to be tailored to suit individual driver preferences.