A Simple Method of Handling Thermomechanical Coupling for Temperature Computation in a Rolling Tire

Abstract The thermomechanical analysis of a pneumatic tire is a highly complex process due to the effects of temperature on both the mechanical state and the viscoelastic energy dissipation in the tire. This coupled thermomechanical behavior typically requires that rolling tire temperatures be determined iteratively. As a result, a steady-state analysis involves updating the temperature dependent elastic and viscoelastic properties as the solution proceeds. The process is further complicated in a non-steady-state analysis where material properties need to be updated at multiple intervals in time. A simplified method is proposed. First, the sensitivity of the tire elastic response of the tire to changes in material stiffness is characterized using the “deformation index”. Then, using a commercial finite element program and an appropriate user subroutine, heat generation is expressed as a function of the local temperature using a simple algebraic expression involving the temperature dependent material properties and the deformation indices. Temperatures are computed using the finite element program with the coupling information contained in the user subroutine. The result is a simplified method for a fully coupled thermomechanical analysis of a tire for steady-state and transient thermal analysis. The accuracy and the simplicity of the method are demonstrated using a small “tire-like” model. The simplified method is compared to the fully coupled iterative method for a steady-state thermal solution.