Matsubara, M., Tsujiuchi, N., Ise, T., and Kawamura, S., "Vibration Analysis of Rotating Tires Focused on Effect of Rotation Using a Three - Dimensional Flexible Ring Model," SAE Technical Paper 2017-01-1903, 2017.
The tire is one of the most important parts, which influence the noise, vibration, and harshness of the passenger cars. It is well known that effect of rotation influences tire vibration characteristics, and earlier studies presented formulas of tire vibration behavior. However, there are no studies of tire vibration including lateral vibration on effect of rotation. In this paper, we present new formulas of tire vibration on effect of rotation using a three-dimensional flexible ring model. The model consists of the cylindrical ring represents the tread and the springs represent the sidewall stiffness. The equation of motion of lateral, longitudinal, and radial vibration on the tread are derived based on the assumption of inextensional deformation. Many of the associated numerical parameters are identified from experimental tests. Unlike most studies of flexible ring models, which have mainly discussed radial and circumferential vibration, this study presents eigen functions concerning not only radial and circumferential but also lateral vibration using the three-dimensional flexible ring-based model. First, we developed a three-dimensional flexible ring tire model. The basic equations, including the effect of the initial tension resulting from rotation-induced centrifugal and Coriolis forces, were derived using the Lagrange equation. Second, we performed an experimental modal analysis of a non-rolling tire, in order to validate the model. Finally, the effect of rotation on lateral vibration was determined via numerical analysis. This analysis revealed that traveling wave modes occur at high rolling speeds. As a result, the vibration behavior including lateral vibration is described by a standing-wave mode in the static condition and a traveling-wave mode in the rolling condition.