## Modelling of a rear axle Torque Vectoring Dual Clutch driveline for battery electric vehicles with verification in a virtual environment

Vehicle manufacturers depend on modelling and simulation in a virtual environment while developing new automotive systems, as it saves both time and costs. These models allow rapid changes to be made during the development of a system. As electrification gains momentum amongst vehicle manufacturers, consumers and the authorities, new transmission concepts are being explored. This report explores the method of physical and acausal modelling for building a simulatable model of one such concept namely, a rear axle Torque Vectoring Dual Clutch (TVDC) system for a battery electric vehicle. The TVDC model is also integrated with the complete vehicle model to conduct complete vehicle verification in a simulation environment. The objective is to model the system physically using the Modelica language and export it as a Functional Mock-up Unit into a virtual vehicle environment on IPG CarMaker. The model is then integrated with a control model and a full vehicle model. Modelling approaches using standard Modelica libraries and flat' or equation-based modelling are explored and compared. The model is then validated by running simulations on standard test tracks and observing the performance of the system. The torque vectoring function will be the main focus and the drive torques to the rear wheels from the TVDC driveline will be studied to ensure that they have the desired behaviour. The model is further validated by comparing the simulation results with measurement data from a test vehicle with the TVDC system installed, for the same test runs and ensuring that the same kind of control signals results in similar behaviour in drive torque distribution on the rear axle. Additionally, an open differential vehicle model is simulated to establish comparisons with the TVDC driveline in terms of power consumption and steering effort. The equation-based modelling approach was found to be more flexible in terms of modelling preconceived systems in contrast with library-based modelling that though easier, is restrictive in connecting certain component blocks together. On running the necessary simulations, it was concluded that the driveline model was robust in the sense that the system did not fail in simulations involving dynamic driving scenarios and long driving cycles such as the Göteborg City Cycle. The model demonstrated its ability to be controlled, by exhibiting the behaviour desired by the devised control strategy. Comparison with track measurement data from a test vehicle fitted with the TVDC driveline showed that the same kind of control signals in the simulation and measurements resulted in the same kind of torque distribution at the rear axle and this is a successful validation of the model's performance in steady-state driving scenarios. It was also concluded that information on the control strategy used in the test vehicle's driveline would be useful in validating the model performance further in dynamic driving situations. Comparison of the TVDC driveline model with the open differential model did not show a significant difference in energy consumption or steering effort. However since the focus was on modelling and model validation, no substantial conclusions were drawn as the control strategy used in the TVDC system was basic and was probably insufficient for the sake of comparison. It can be concluded that physical modelling in Modelica is a reliable way to develop driveline system models for simulation. This physical modelling method can be an effective early virtual development' tool for driveline concepts and as such is verified by the comparisons with real vehicle tests.