In-Plane Modal Characteristics of Tire: An Improved Flexible Ring Model with Damping and Contact Effects

As tire is the only part of contact between a vehicle and the road, the dynamic response property of a tire under different loads is of great importance to fully understand the tire performance. Simplifying a tire as a ring-shaped structure is a promising method to simulate the dynamic performance of tires. In this study, a flexible ring model that considers the contact characteristics was developed to investigate the in-plane vibrations of a static passenger car tire. The proposed method integrates three key steps in the improved modeling method: the structural modeling of the tire, the implementation of the tire contact boundary condition and the grounded modeling of tire vibration. In this method, the proposed ring model is applied to calculate the radial frequency response functions of the tire under different vertical loads up to 250 Hz with low computational cost. The structural and damping parameters of the analytical model are determined using the genetic algorithm method. The accuracy of the radial modal parameters of the free tire—including natural frequency, damping ratio, and frequency response function—as well as the vertical stiffness calculated by the contact model, is validated by experimental modal analysis and tire stiffness tests, respectively. The in-plane mode of the grounded tire in the analytical approach is verified by a finite element model. The results show that the in-plane vibration behavior of the tire can be efficiently evaluated using the proposed analytical method. Furthermore, the influences of vertical loading and inflation pressure on the natural frequencies and dynamic responses of the grounded tire were investigated. It indicates that this improved ring model offers many application scenarios and extension possibilities compared to the classical tire ring model in the analysis of tire in-plane vibrations.