Modeling of Hybrid Electric Vehicle's Driveline and its components: current techniques and practical F1 example

The introduction focuses on the vehicle’s driveability problems, which can be different between Hybrid Electric Vehicle (HEV) configuration and a traditional Internal Combustion Engine (ICE)-based vehicle. All the possible the unwanted dynamics that can affect the driveline are presented, defining their typical vibration frequencies. The first part of this thesis treats every component which can be included in a complete modelling of the driveline: clutch, shaft, gearbox, differential, backlash, wheel, tyre and driving resistance. The first models to be considered are the simpler and linear ones. Then, to achieve more precision in the model behaviour, the non-linear and more sophisticated ones are explained and evaluated. Some of the models presented in precedent chapters are put together to obtain a complete driveline model. Each one of those can reproduce one or more unwanted behaviours. For every additional factor considered in the driveline, the real profiles are fitted with increasing precision by the simulations. The second part of this thesis goes through the modelling of a driveline similar to the Formula One's car of Scuderia Ferrari. The models are of increasing details: the first presents a low complexity and computation time, indeed it has only compliant driveshafts. The last reaches a high level of detail and a higher needed computation time. The relative modelling importance of the driveline components is evaluated. What is highlighted is that the driveshaft is the first element that has to be considered as compliant, for its high deformations due to the higher applied torque of the whole line of transmission. Furthermore the tyre model is of central importance; with its inclusion the simulation changed drastically: being the tyre the most flexible element of the driveline, it dramatically damps down the oscillation associated with shuffle (i.e. the principal negative factor of driveability). When the backlash is modelled, the vehicle’s jerk (time derivative of the acceleration) has a worse behaviour on the driveability point of view. This is introduced without compromising the linearity of the model: it is reproduced with 2 different LTI State Space models, which run alternatively on the basis of the backlash status. The final thesis' chapter adds other relevant details for an high fidelity model suitable for precise simulations: the clutch includes the possibility to detach its discs, hence a simulation of a standing start and subsequent gear shifting can be done; the gearbox includes the changing of the gear number, so to vary inertias and transmission speed ratio in function of the engaged gear; the tyre model also is changed to a non-linear one: it implements Pacejka's magic formula and the concept of relaxation length for high speeds. In case of speeds lower than 5 km/h another reproduction of tyre is introduced: the brush type LuGre model. The driveline part (without the wheel) is also converted into a state space format, with the alternative running of 32 different LTI state space models. The simulation, compared with precedent simpler models, shows the key factor which is the tyre model, the linear approximations can induce slight differences of the jerk profiles. This is the final product of this thesis' work, which is further developed and will be included in an official HiL Ferrari's simulator, for precise evaluations of the Formula One car's driveline dynamical behaviour.