Tire Rolling Loss Computation with the Finite Element Method

Abstract

Abstract This paper describes a process for the prediction of rolling resistance in tires. A new Directional Incremental Hysteresis (DIH) theory describing the hysteretic behavior of carbon black filled rubber is presented. The steps required to implement the DIH theory in a material model, within a Finite Element (FE) model, and to predict tire rolling resistance are described. The material model using the DIH theory is a strain-based model which includes an incremental formulation to deal with nonsinusoidal cycles within tires. The material model is also enhanced by a directional formulation which is active in situations where the strain tensor has a substantial change in direction with minimal change in magnitude. The hysteresis material model is developed only for the rubber compounds of the tire. While there is no direct contribution of cord hysteresis to predicted rolling loss, the structural effects of the cord on the rubber stress-strain behavior are included and will contribute to the tire rolling loss by affecting the stress-strain cycle of the rubber. Experimental work used to determine the parameters of the material model for specific compounds is outlined. Some example DIH parameters are listed by compound application. The DIH theory within the Finite Element method is then used to predict rolling resistance for a specific tire design. The results are compared to experimental data taken using SAE J-1269. The value of the tire rolling resistance is predicted within a few percent. In addition, the sensitivities of the tire to changes in load and inflation pressure are predicted and they are found to compare favorably to the experimental results. The DIH theory is implemented within a quasi-static FE model, and was not intended for use in dynamic applications such as the prediction of standing wave phenomena. While the quasi-static FE model used in this study can predict deformed shapes, stress distributions, and temperatures, there is presently no coupling between the thermal and mechanical models.