Dynamic simulation of the inflation gas of a tire under operational conditions

In this work, we are describing the coupling of an already existing tire model with a quasi-1D flow model to describe the inflation gas cavity fluctuations in a simple physical way. Since the gas cavity fluctuations are due to excitations - produced by transient tire deformations based on the interaction with the road surface - the gas model must be built to fully account for the tire shape variation. Thus, we derive the 1D Euler equations in a torus having a time and spatial dependent cross section area. The equations are discretized with a finite difference spatial discretization and integrated by an extended Lax-Wendroff scheme, which can handle source terms. The coupling between the mechanical response and the inflation gas model is done in the following way: The transient shape of the tire appears as a source term in the Euler equations. The local gas cavity fluctuations on the other act on the tire structure and on the rim, both of which produce entries into the resulting spindle forces. We are showing results for the overall non-linear model for transient simulations (cleat runs) and are comparing the results with and without dynamic gas cavity model and with measurements. Finally, we are showing how the overall model can be linearized around a steady state. With the resulting linear model, a modal analysis can be performed and we identify the so called 'cavity mode' and its dependence on rotational velocity.