The unification of acceleration envelope and driveability concepts

Abstract

This work aims to study which level of detail should be preserved in the multibody modelling of a racing car in order to obtain reliable results without excessive model complexity. Three multibody models have been developed and compared through optimal control simulations. The models differ from each other for the order of dynamics comprised: starting from a 14 degrees of freedom (dof) car which includes chassis and wheels motion, a 10 dof model model is obtained by neglecting the wheels hop dynamics, finally a 7 dof model is derived by completely eliminating the suspension motion. Optimal control problem simulations, including parametric analyses varying the center of mass position and suspensions stiffness, have been executed on a full lap on the International circuit of Adria. Simulations results show that the 10 dof model gives almost the same results of the 14 dof one, while significantly reducing the computing time. On the contrary, the basic 7 dof model highlights remarkable differences in both the parametric analysis, suggesting the dynamics has been over-simplified.

Minimum time optimal control simulation of a GP2 race car

“…The model developed here abandons the QSS tyre load simplification since it has been showed that it negatively influences simulations outcomes. 18 Moreover, suspension kinematics are taken into consideration because they have a relevant influence on vehicle performance. 24,25 A car model that includes this features leads to a relatively complex lap time OCP, that may be very difficult to solve.…”

“…Indeed such terms are related to small inertial forces (less than 0 . 1 times the inertial force related to z ·· as ) that do not play an important role in time simulations. 18 On the contrary, the terms related to the ratio between variables in u as and z as are required to take into account the anti-lift, anti-squat or scrub behaviour of the suspension and are relevant even in determining the stationary trim of the suspension or of the vehicle. 24,25…”

“…The minimum time problem is here formulated as an indirect OCP with the same approach described in previous works, 18,33 so it will be described only briefly; the reader can refer to those works for further information. The OCP allows to find the vehicle control inputs u = { j u , j y } that drive the vehicle from the starting grid line s = 0 and t ( 0 ) = 0 to the finish one s = L in the minimum time T = t ( L ) , while satisfying a set of both equality and inequality constraints.…”

“…Indeed in the QSS tyre load car models, the four suspensions dof together with three of the chassis dof (pitch, roll and vertical displacement) can be neglected. A recent work 18 showed that the QSS tyre loads are a coarse approximation when using to optimise some car parameters. In such work, a car model endowed with suspensions (similar to the one in Kelly 9 ) has been used for a full lap simulation on the Adria International Raceway circuit.…”

Lap time simulation and design optimisation of a brushed DC electric motorcycle for the Isle of Man TT Zero Challenge

“…The minimum time problem is formulated here as an optimal control problem with the same approach presented in [26], [25], [24], and will be briefly summarized here. The Optimal Control Problem (OCP) consists in finding the vehicle control inputs u s that drive the vehicle from the starting grid line s 0 to the end s f of the TT course in the minimum time, while satisfying a set of differential equality and algebraic inequality constraints.…”