Rubber Composition–Properties Relationships during Tire Numerical Simulation and Design Optimization

Abstract

Numerical simulation based on finite element analysis is now widely used during the design optimization of tires, thereby drastically reducing the time investment in the design process and improving tire performance because it is obtained from the optimized solution. Rubber material models that are used in numerical calculations of stress–strain distributions are nonlinear and may include several parameters. The relations of these parameters with rubber formulations are usually unknown, so the designer has no information on whether the optimal set of parameters is reachable by the rubber technological possibilities. The aim of this work was to develop such relations. The most common approach to derive the equation of the state of rubber is based on the expansion of the strain energy in a series of invariants of the strain tensor. Here, we show that this approach has several drawbacks, one of which is problems that arise when trying to build on its basis the quantitative relations between the rubber composition and its properties. An alternative is to use a series expansion in orthogonal functions, thereby ensuring the linear independence of the coefficients of elasticity in evaluation of the experimental data and the possibility of constructing continuous maps of “the composition to the property.” In the case of orthogonal Legendre polynomials, the technique for constructing such maps is considered, and a set of empirical functions is proposed to adequately describe the dependence of the parameters of nonlinear elastic properties of general-purpose rubbers on the content of the main ingredients. The calculated sets of parameters were used in numerical tire simulations including static loading, footprint analysis, braking/acceleration, and cornering and also in design optimization procedures.

Analytical investigation on tire dynamics by rigid–elastic coupled tire model with nonlinear sidewall stiffness

“…The finite element method [6] is introduced to describe the structural [7] and material feature of tires in detail. The detailed tire model is suitable for tire design [8] and wear analysis [9], while the comprehensive computational model, the difficult obtained material parameters and extensive FEA oriented pre-processing limit the vehicle dynamics appliance of the finite element tire model and the finite element tire model is of some difficulty to satisfy the simulation of durability and ride comfort of vehicles.…”

“…According to different model methods of the flexible tread, FTEF tire model can be divided into continuous flexible tread tire model [7][8][9][10][11][12][13][14][15][16] and distributed mass tire model. Continuous flexible tread tire model, including onedimension flexible tread model (string, beam [13] model), two-dimension flexible tread model (ring [14] and plate [15] model) and three-dimension flexible tread model (shell [16] model) can be used to conduct the vibration analysis of high frequency and the simulation of geometrical, structural and mechanical non-linear feature, while the coupled feature between the space-domain deformation of flexible tread and the time-domain deformation increases the difficulty of the rolling characteristic analysis.…”