Modelling vibrations on deformed rolling tyres—a modal approach

This paper examines an approach to model the vibrations of a deformed rolling tyre at low frequencies (below 500 Hz). The starting point for this approach is a finite element (FE) model of the tyre and the aim is to calculate the dynamic response of a rolling tyre including the details of its complex build up. This allows to relate the tyre design parameters to its vibro-acoustic properties. In this context, a modal approximation based on the eigenvalues and eigenvectors extracted from the detailed FE model of the tyre seems a computationally efficient possibility. In the proposed approach the natural frequencies and modeshapes of a deformed tyre are calculated in a standard FE package using the full (nonlinear) FE model. Subsequently, this modal base is transformed to determine the response of the rotating tyre in a fixed (Eulerian) reference frame. Furthermore, this approach makes it possible to define a receptance matrix for the rotating tyre. Results from relatively simple tyre models show that the effects of rotation are modelled correctly and are in accordance with results from literature.