Simulation of Dynamic Gas Cavity Effects of a Tire under Operational Conditions

The authors are responsible for the development of a structural 3D shell based bead-to-bead model with sidewalls and belt that separately models all functional layers of a modern tire [4]. In this model, the inflation pressure is modeled as a uniform stress acting normal to the shell's inner face. The pressure can vary depending on the application: prescribed by the MBS-tool to align to a constant pressure specified for a vehicle or scenario, but it can also be modified dynamically to simulate e.g. a sudden pressure loss in a tire [1]. For many applications, this description of the inflation pressure as a time dependent quantity is sufficient. However, there are applications where it is needed to describe the inflation gas using a dynamic gas equation (Euler or Navier-Stokes). One such example is when the tire model is used in NVH (Noise-Vibration-Harshness) applications where the frequency range extends the 200 Hz range. For passenger car tires, a first mode of the inflation gas is at around 200-250. This mode couples with the tire structure and yields significant peaks in the spindle force spectrum, which have to be considered in the NVH assessment of a car. In this paper, we show the effect of modeling the inflation gas of a tire by an isentropic compressible Euler equation and couple it to the tire dynamics in the nonlinear transient application range. After motivation and validation of the overall model by comparison with respective measurements, we also describe how to derive a linear model from the overall transient tire model, that can then be used in linear FEM based NVH-tools. It can be observed that the tire rotation will yield a split in the cavity mode which increases with rotational velocity, an effect that can also be correctly predicted by the linearized model.