Tire/ Road Dynamic Contact; Study of Different Approaches to Modelling of a Tire

International audienceIn terms of safety and environment, reduction of the noise generated by tire vibrations on a road is very significant. In order to study the vibration properties of vehicle tires, various methods have been presented in literature. In most of these methods, the global structure of tires has been modelled as circular ring, orthotropic plate, periodic or full 3-dimensional models. A brief review of the characteristics of these models and comparison of their dynamic behaviour are the main purpose of the current study. The tire is supposed to be subjected to an excitation caused by contact of the tire and road. Study of vibrational responses demonstrates that the validity of each model is limited to a certain frequency range. To employ the circular ring and orthotropic plate models, first, we require to estimate some structural and material data associated to the nature of these models. To this end, the vibrational response of a 3D model is considered to determine some properties such as radial and tangential stiffnesses in circular ring model or bending, foundation stiffness, and tension in orthotropic plate model. Furthermore, the effect of inflation pressure on the dynamic behavior of the mentioned models is examined. For verification, the dynamical behaviour of a tire is studied experimentally. Application of the present study can be contemplated in the prediction of rolling noise and rolling resistance. A lot of research on the vibration properties of vehicle tires has been done during the last decades. In this purpose, one of the simplest methods is the model of rotating ring on the elastic foundation. Due to the completeness and simplicity, since the 1960s, this method has drawn the attractions of numerous researchers. Development of the method is pioneered by Clark [1], Tielking [2], and Bohm [3] who presented a method for calculating the dynamic behavior of a loaded pneumatic tire modeled as an elastically supported cylindrical shell. In these works, the tire sidewall effects were modeled by the radial springs. Pacejka [4] modeled the tire as a circular ring under pressure. By considering the circumferential springs for the elastic foundation, he developed models for the lateral vibration. The effect of structural damping on the study of dynamic response of the classical ring on the foundation for the first time was considered by Padovan [5] in 1976. Later, Potts et al. [6] studied the vibration of a rotating ring on an elastic foundation in terms of the material and geometric properties of the tire. In order to study the free vibration of a circular ring tire located on an elastic foundation, a finite element method was presented by Kung et al. [7] in 1987. Huang [8,9] studied the response of a rotating ring subjected to the harmonic and periodic loadings. In 2008, Wei [10] proposed an analytical approach to analyze the forced transient response of the tires modeled based on the ring on the elastic foundation. The next method to model the tire structure is the model of Timoshenko beam. In the recent decade, Pinnington and Briscoe [11] developed a one-dimensional wave model to describe the tire dynamics. The tire belt is represented as a tensioned Timoshenko beam in order to derive arbitrary sidewall impedance. The waves, which propagate along the tire, take shear and rotational effects into account. The validity of the circular ring models is limited to the frequency less than 400Hz, when the wavelength is large enough compared to the width of the tire