Analytical Solution for the Stresses Arising in +/− Angle Ply Belts of Radial Tires

Abstract

Abstract Stresses arising in the belts of radial ply tires, particularly those at the belt edge, are known to be critical to tire durability. Belt edge stresses are commonly calculated using finite element (FE) methods that provide estimates of the levels but do not necessarily give significant insight into the underlying mechanics. In contrast, analytical models can provide physical insight into the mechanisms affecting tire durability but are currently incomplete due to the challenges faced in obtaining closed-form mathematical solutions. Nevertheless, analytical solutions remain important to tire design and development because they can expose the entire design space, show the mathematical relationships between the variables, and allow rapid parameter studies. This work develops an analytical description of the belt deformations and stresses, particularly at the belt edge. The formulation captures all the first-order mechanics pertinent to finite width, antisymmetric +/− angle belt packages present in radial tires. It incorporates interply shear stresses already recognized in the literature and adds to that a new mechanism controlling the interaction of the plies via a Poisson effect. The analytical model is validated by comparison to FE simulations and is also contrasted with a classical analytical model in the literature. The design space for the belt composite is then explored by parameter variation. Finally, since all these solutions depend on homogenization of the belt layers, the analytical solution is compared to a FE model of discrete cables embedded in rubber to explore the accuracy of the homogenization step.