• LuGre
• model
• tire
• friction
• vehicle dynamic
• simulations

Development of a tire model for vehicle simulations at low velocity, this model will replace the Pacejka one in condition of null or low velocity of the vehicle. The model was studied and developed in association with "Maserati S.p.A.". The model is based on the LuGre friction model and it is adapted in order to be use on Simulink models of existing vehicles. The purpose of this model is to find a solution to the numerical problem that the Pacejka model has at null velocity. Indeed, during the evaluation of the tire forces with the Pacejka model, if the vehicle velocity is zero it will be found a division by zero.
In the paper it will be explained the friction model used and the improvements applied to it for the simulations. It is explained how to evaluate the parameters of the model and there are also explained the limits and the advantages of the model. Next the model is applied to the longitudinal dynamic of the vehicle, and it is shown how to characterise the tire in this model. There are shown the results of some simulations of longitudinal dynamic which are done with the aid of car models supplied by the company. In the following section the model is adapted to the lateral dynamic of the vehicle and there are explained some changes in the model equations to prepare the model for the simulations. Another time, with the models supplied, some simulations are done, and the results are shown and analysed. At the end of the paper the longitudinal and lateral model are merged and with them some last simulations are done to verify the final model.