The hysteresis of rubber materials due to deformation and viscoelasticity is the main reason for the heat build-up (HBU) and rolling resistance (RR) of the rolling tire. It is important to realize the high precision prediction of HBU and RR of tire for the optimal design of high-performance fuel-saving tire. In this work, a thermo-mechanical coupling method based on Endurica and Abaqus co-simulation was used to predict the steady-state temperature distribution and RR of three finite element models (Lagrangian-Eulerian model, Lagrangian model, and Plane Strain model) of the solid tires under different loads and rotating speeds. The simulation results were compared with the experimental results. The Kraus self-heating model was utilized in the thermo-mechanical coupling method, which realized the quantitative relationship between the dynamic loss modulus of rubber and the loading conditions (temperature, strain, and strain rate). Special attention was paid to the determination of the material parameters in the Kraus self-heating model. The comparison between simulation results and experimental results shows that the Lagrangian model had the highest prediction accuracy, and the average prediction errors of the steady-state surface temperature and RR under three loading conditions were 3.4% and 7.9%, respectively. The Lagrangian-Eulerian model came in the second with average errors of 9.7% and 11.1%, respectively. The Plane Strain model had the worst prediction accuracy, with the average errors of 21.4% and 44.6%, respectively. In terms of the simulation time, the Plane Strain model had the lowest cost, and the average calculation time was 1143 s. The Lagrangian-Eulerian model took the second place, with an average calculation time of 2621 s. The Lagrangian model had the highest computation cost, with an average time of 5597 s. The comparison between the simulation results and the experimental results verified the effectiveness of the thermo-mechanical coupling analysis method. The methods of three finite element models of the solid tires in this work can provide some reference for the optimization design of elastomeric components (Lagrangian model), pneumatic tires (Lagrangian-Eulerian model), and non-pneumatic tires (Plane Strain model).
Keywords: Lagrangian–Eulerian model; heat build-up; rolling resistance; thermo-mechanical; viscoelastic.