A theoretical three-dimensional ring based model for tire high-order bending vibration

Abstract Tire vibration includes not only radial vibration, but also lateral vibration. The lateral vibration always plays an important role to vehicle Noise, Vibration and Harshness (NVH), especially high-order lateral bending vibration. In this paper, a new theoretical three-dimensional ring based model and related new displacement function were both developed for tire radial and lateral vibrations, especially for tire high-order bending vibration. The proposed model considers the detailed features of the 3D ring such as the ring thickness, the shear strain in lateral-tangential plane and lateral normal strain, tangential and lateral pre-stress induced by inflation. The new displacement function in Dual Flourier series was developed for the tire model, which can in particular describe the belt bending vibrations in transverse direction. Either of the proposed model and displacement function is indispensable to compute high-order modes of the belt. The proposed model was verified with the conducted physical experiments. The proposed model costs less than 5 s to compute the natural frequencies of tire. The results show that the tire vibration modes from 300 Hz to 500 Hz could be predicted quite well as well as that below 300 Hz. The model is an efficient and effective tool to investigate the dynamic characteristics of tire.