A comprehensive analytical model for pneumatic tires

Abstract

This study presents a comprehensive analytical tire model for both vehicle dynamic simulation and tire design. The model is composed of two parts--modeling of the contact mechanism and determination of the tire forces/moments. A static circular beam model is introduced for the contact mechanism, in which a tire is modeled with three compliance components--6-DOF spring/damper elements for the sidewall and the internal pressure, a flexible circular beam for the belt layers, and a series of radial springs for the tread. This contact model can estimate the 2-D contact shape and the contact pressure distributions for even or uneven road surfaces. The tire forces and moments are represented with the deformation of the tread elements. Two different methods are introduced to estimate deformations of tread elements---direct measuring method and integrating deformation rate method. In the former, the deformations of tread elements are directly measured by monitoring their displacements. In the latter, a tread deformation is obtained by integrating the slip velocity over the contacting time. By employing a rigid ring concept, the transient characteristics of the tire can also be examined in low frequency ranges. The ideas that are presented in this study are verified with a set of measurement data. For example, the tire forces/moments for various driving conditions such as combined slip conditions as well as pure lateral and longitudinal slip conditions. Also, the simulation results of 2-D contact pressure distributions are given for straight running and severe slip angle conditions.