The purpose of the present study is to propose an analytical model for tires and to examine the mechanism of polygonal wear based on numerical results obtained using this model. Polygonal wear is an abnormal phenomenon that occurs in time-delay systems. A number of studies on polygonal wear of tires have been conducted. However, investigation of the growth process of polygonal wear is not sufficient because the surface shape of the tire changes constantly with wear. Therefore, a numerical simulation model that can examine transient behavior is necessary. In the present paper, we propose a tire model composed of mass points. The wheel is simulated as a rigid body, and the tire tread as a number of masses positioned around the circumference of the wheel. The tire masses are connected to points around the circumference of the wheel by rotational and translational Voigt elements, and the tire masses are connected by rotational and translational Voigt elements. The contact between the tire and the road surface is assumed to be elastic. Numerical simulations are carried out under several conditions using the proposed model. The distributions of the stress and the slip ratio are obtained, and the wear shapes of tires are examined using the proposed model. We show that polygonal wear occurs under certain conditions. Finally, a tire model that expresses these basic characteristics is proposed and its usefulness is demonstrated.

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