Tire vibration analysis of three-dimensional flexible ring with brush model under static contact conditions by using frequency-based substructuring

The use of a simplified physical model of the tire of road vehicles is an efficient and simultaneous method to study the specifications of the entire chassis, including the tire specifications. Therefore, it is important to develop a simplified physical model that can be used in the early design phase when detailed computer-aided design data are not available. In this study, a vibration analysis of tires in road contact is described using frequency-based substructuring in a three-dimensional elastic ring model of a tire that includes a brush model simulating the tread rubber. By modeling the brush as a contact spring between the tire and the road surface, the natural frequencies and mode shapes of the tire under load conditions can be calculated using point-coupled three-way contact spring constraints. The experimental results show that the natural frequency changes significantly with road contact and does not depend on the vertical load. The theoretical analysis also showed that the natural frequency does not change when the stiffness of the contact spring is large enough to limit the displacement of the road contact, which is consistent with the experimental results. Unlike previous studies, this method calculates the mode shape with road contact based on the mode shape without road contact; therefore, the required model parameters can be determined based on the experimental modal analysis for the free-free condition.