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In this paper, based on our previously preliminary out-of-plane tire model, a complete out-of-plane flexible tire model is further developed by considering the variation of dimension and parameter values among different slices of the tire model. This tire model is validated via various MSC ADAMS® FTire virtual cleat tests. Especially, the cleat tests with non-zero tire camber angles and non-symmetric cleat shapes, which can better capture the out-of-plane tire properties, are included. By comparing the predicted results of the proposed tire model with FTire for various cleat tests, it shows that the complete out-of-plane flexible ring tire model is better at fully representing the actual tire properties for some complicated cleat testing scenarios.

In this paper, a detailed three dimensional (3D) flexible ring tire model is first proposed which includes a rigid rim with thickness, different layers of discretized belt points and a number of massless tread blocks attached on the belt. The parameters of the proposed 3D tire model can be divided into in-plane parameters and out-of-plane parameters. In this paper, the relationship of the in-plane parameters between the 3D tire model and the 2D tire model is determined according to the connections among the tire components. Based on the determined relationship, it is shown that the 3D tire model can produce almost the same prediction results as the 2D tire model for the in-plane tire behaviors.

Vehicle tire performance is an important consideration for vehicle handling, stability, mobility, and ride comfort as well as durability. Significant efforts have been dedicated to tire modeling in the past, but there is still room to improve its accuracy. In this study, a detailed in-plane flexible ring tire model is proposed, where the tire belt is discretized, and each discrete belt segment is considered as a rigid body attached to a number of parallel tread blocks. The mass of each belt segment is accumulated at its geometric center. To test the proposed in-plane tire model, a full-vehicle model is integrated with the tire model for simulation under a special driving scenario: acceleration from rest for a few seconds, then deceleration for a few seconds on a flat-level road, and finally constant velocity on a rough road. The simulation results indicate that the tire model is able to generate tire/road contact patch forces that yield reasonable vehicle dynamic responses.

A tire may be one of the most critical and complex components in vehicle dynamics and road loads analyses because it serves as the only interface between the road surface and the vehicle. Extensive research and development activities about vehicle dynamics and tire models have been published in the past decades, but it is still not clear about the applications and parameter identification associated with all of these tire models. In this literature review study, various published tire models used for vehicle dynamics and road loads analyses are compared in terms of their modeling approaches, applications and parameters identification process and methodologies. It is hoped that the summary of this literature review work can help clarify and guide the future research and development direction about tire modeling.