2D Transient Thermal Analytical Solution of the Heat Build-Up in Cyclically Loaded Rubber Cylinder

Predicting the heat build-up in rubber under dynamic cyclic loading is still challenging due to its complexity. The simplest way to make such a prediction is to use numerical methods like the Finite Element Method (FEM), which is preferable especially for geometrically complex rubber components. However, for components with simple geometry, analytical methods may be more appropriate as they better reflect the physical background and allow an assessment of the accuracy of the FE methods through comparison. This paper deals with the detailed derivation of the analytical equations for predicting the heat generation from the heat equation in a rubber cylinder under dynamic cyclic loading. The work focuses exclusively on a thermal solution assuming known rubber material parameters and corresponding loading conditions of the cylinder. The results of the equations derived in this way are compared and discussed with the results of a Finite Element Analysis (FEA) in the radial and axial directions and in the time domain. The analytical expression represents a significant contribution to the effective prediction of the evolution of heat generation in rubber without meeting the requirements of the FEA implementation.