Longitudinal Tire Dynamics Model for Transient Braking Analysis: ANCF-LuGre Tire Model

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Abstract
In this investigation, the flexible tire model based on the absolute nodal coordinate formulation (ANCF) is integrated with LuGre tire friction model for evaluation of the longitudinal tire dynamics under severe braking scenarios. The ANCF-LuGre tire model developed allows for considering the nonlinear coupling between the dynamic structural deformation of the tire and its transient tire force distribution in the contact patch using general multibody dynamics computer algorithms. To this end, the contact patch obtained by the ANCF elastic ring tire model is discretized into small strips and the state of friction at each strip is defined by the differential equation associated with the discretized LuGre friction parameters. The normal contact pressure distribution predicted by the ANCF elastic ring elements that are in contact with the road surface are mapped onto the LuGre strips in the contact patch to evaluate the tangential tire force distribution and then the tire forces evaluated at LuGre strips are fed back to the generalized tangential contact forces of the ANCF elastic ring tire model. By doing so, the structural deformation of the ANCF elastic ring tire model is dynamically coupled with the LuGre tire friction in the final form of the governing equations. Furthermore, the systematic and automated parameter identification procedure for the LuGre tire force model is developed. It is shown that use of the proposed procedure with the modified friction curve proposed for wet road conditions leads to accurate prediction of the LuGre model parameters for measured tire force characteristics under various loading and speed conditions. Several numerical examples are presented in order to demonstrate the use of the in-plane ANCF-LuGre tire model for the longitudinal transient dynamics of tires under severe braking scenarios.

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