Matsubara, M., Tsujiuchi, N., Koizumi, T., Ito, A. et al., "Natural Frequency Analysis of Tire Vibration Using a Thin Cylindrical Shell Model," SAE Technical Paper 2015-01-2198, 2015, doi:10.4271/2015-01-2198.
Early studies on the tire vibration characteristics of road noise focused on radial modes of vibration because these modes are dominant in vertical spindle force. However, recent studies of Noise, Vibration and Harshness (NVH) prediction have suggested that tire modeling not only of radial modes, but also of lateral vibration, including lateral translational and lateral bending modes, affect interior noise. Thus, it is important to construct tire dynamic models with few degrees of freedom for whole-vehicle analysis of NVH performance. Existing tire dynamics model can't express tire lateral vibrations.This paper presents a new approach for tire vibration analysis below 200Hz, and a formula for tire natural frequencies. First, a tire dynamic model is developed based on the thin cylindrical shell theory. Kinetic and potential energies are derived. Mode shape function is also derived by the assumption of inextensility in the neutral of the tread ring. The formulas of natural frequencies are derived from these relation expressions using Rayleigh's method. Second, impact tests for tires are performed for validation of the proposal theory. Results show that theoretical values of natural frequencies are close to the experimental data. Finally, the substructure's contributions to stiffness against natural frequencies are shown.