A practical rolling resistance simulation method for tires using a static finite element method is presented that fulfills three requirements: (1) easy input data preparation, (2) shorter computation time, and (3) adequate accuracy. The method implements a static deflection analysis first and the stress and strain thus obtained, together with the loss factors of the materials determined separately, are used to estimate the energy dissipation of a rolling tire. First, the stress and strain profiles of all element groups that have the same cross-sectional coordinates and are located along the circumferential direction are obtained. Second, hysteresis loops are computed by introducing a viscoelastic phase lag between the stress and strain profiles. The sum of the areas of the hysteresis loops is regarded as the dissipation energy density of the element group. The loss factors of the rubber materials are experimentally obtained and the effective loss tangents of the fiber-reinforced rubber are determined by the homogenization theory of dynamic viscoelasticity. The rolling resistance simulation of a passenger radial tire using this approach accurately captures the trends of an actual tire.

Since tires carry out many functions and many of them have tradeoffs, it is important to find the combination of design variables that satisfy well-balanced performance in conceptual design stage. To find a good design of tires is to solve the multi-objective design problems, i.e., inverse problems. However, due to the lack of suitable solution techniques, such problems are converted into a single-objective optimization problem before being solved. Therefore, it is difficult to find the Pareto solutions of multi-objective design problems of tires. Recently, multi-objective evolutionary algorithms have become popular in many fields to find the Pareto solutions. In this paper, we propose a design procedure to solve multi-objective design problems as the comprehensive solver of inverse problems. At first, a multi-objective genetic algorithm (MOGA) is employed to find the Pareto solutions of tire performance, which are in multi-dimensional space of objective functions. Response surface method is also used to evaluate objective functions in the optimization process and can reduce CPU time dramatically. In addition, a self-organizing map (SOM) proposed by Kohonen is used to map Pareto solutions from high-dimensional objective space onto two-dimensional space. Using SOM, design engineers see easily the Pareto solutions of tire performance and can find suitable design plans. The SOM can be considered as an inverse function that defines the relation between Pareto solutions and design variables. To demonstrate the procedure, tire tread design is conducted. The objective of design is to improve uneven wear and wear life for both the front tire and the rear tire of a passenger car. Wear performance is evaluated by finite element analysis (FEA). Response surface is obtained by the design of experiments and FEA. Using both MOGA and SOM, we obtain a map of Pareto solutions. We can find suitable design plans that satisfy well-balanced performance on the map called “multi-performance map.” It helps tire design engineers to make their decision in conceptual design stage.

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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