Theoretical formulation of tire Gough stiffness based on the high order shear composite beam

Tire is a kind of rubber-cord reinforced composite structure. Gough stiffness derived by using a beam model is a parameter of tire which is related to the transverse deflections and wear of tires. In the present study, the theoretical explanation of Gough stiffness was proposed to analyze the lateral bending deformation of the tire under different belt angles. By revising the Fiala tire model, the tire was simplified as composite beam on elastic foundation. The sidewall and tire tread pattern blocks were treated as an elastic foundation. The belt and tire body were simplified as a composite beam. Considering the high order shear deformation theory and the anisotropy of the cord-rubber material, the equilibrium equations were derived by using the principle of virtual work. The deformations under the transverse load with small deflections were derived for the first time. To verify the accuracy of the model, the theoretical results were compared with the results of finite element analysis, and the good agreement could be found. The effect of length, height, thickness and modulus of cord and rubber were analyzed. It is indicated that if the length-height ratio of the equivalent beam is unchanged, the corresponding belt angle of the maximum value of Gough stiffness will not be changed. According to maximum Gough stiffness, the optimal belt angle of the tire with different high width ratio was obtained. The results also agree with those results of the actual tire structure. The proposed model can provide theoretical direction for the structure and durability design of tires.