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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.

One of the elements of tire stiffness is sidewall stiffness. This stiffness, which influences tire vibration characteristics, is also an important design parameter for carrying the vehicle body. Tire is one of pressure vessels and inflation pressure is dominant in sidewall stiffness. Thus, tire sidewall stiffness is decided from the tension of inflation pressure and the structural dynamic, including the properties of the rubber material. To reveal the dynamic characteristics of tire sidewall stiffness, this study describes differences in stiffness due to inflation pressure. It can be expected that variation of inflation pressure is monitored from the axle vibration response during vehicle traveling in the future. That is because the relationship of the vibration characteristics and the inflation pressure of tire are derived by sidewall stiffness. First, we derive a formula for sidewall stiffness based on the structural dynamics of Akasaka's theory.

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 demand to reduce noise in the passenger cars is increasing. Tire vibration characteristics must be considered when studying road noise because of the strong interaction between tire vibration characteristics and interior car noise. Car manufacturers are keenly interested in studies on the prediction of NVH (Noise, Vibration and Harshness) performance, including viewing tires as substructure. Recently, studies have illustrated the effect that tire lateral bending mode have has on road noise, while most past studies of tire vibration focused on the circumference mode, which excited the vertical spindle force. Therefore, further study of tire lateral bending mode is necessary. Modeling of the tire lateral bending mode is described in this paper. First, lateral spindle force is measured under tire rolling conditions. Second, experimental modal analysis is performed to grasp tire lateral bending mode. Finally, a tire vibration model is built using the cylindrical shell theory.

Road noise is one of the main vehicle interior noises. To minimize this, it is necessary to reveal the vibration characteristics of a rolling tire. Tire vibration has complex behavior due to tire contact with the road and rolling. In an earlier study, we clarified the effect of contact patch restriction for tire vibration characteristics in the non-rolling condition using the tire dynamical model. However, mode shapes were identified with circumferential wave number. Therefore, it is difficult to clarify the effect for tire vibration in the contact and rolling condition. In this paper, we will apply the receptance method, which is used as an analysis of the rotating disc and gear pair for the tire model toward the tire vibration analysis in the contact and rolling condition. Furthermore, the validity of the approach using this method will be verified from comparison with the result of an earlier study.