SOUND RADIATION FROM A ROLLING TYRE
Paper in proceedings, 2011
By combining an advanced linear tyre model based on Wave Guide Finite Elements with a state of the art non-linear and transient contact model it is possible to simulate a tyre rolling on a rough surface. The surface is characterised by roughness scans in parallel tracks along the rolling direction. As output one obtains the time varying contact forces. Based on these contact forces the post-processing allows for calculating for instance the vibrations of the tyre structure, the input power through the contact into the tyre (which represents the rolling resistance) or the forces at the hub.
Today there is still a lack of understanding how different tyre design parameters influence these rolling resistance and ore tyre/road noise generation. This lack of understanding is a clear hinder for the development of low noise tyre with low rolling resistance. Therefore the intention of this paper is to contribute to the clarification of this question by investigating which parts of the tyre vibration (expressed as modes and/or waves) are responsible for the sound radiation during rolling?
From simple analysis of wave speed on tyre-like structures such as rings or plates, it was rather soon understood that the radiation efficiency of most of the free waves is too low to explain the radiated sound power from rolling tyres. The only exceptions are waves with mainly in-plane motion. However due to the curvature of the tyre structure there is a strong coupling between in-plane motion and out of plane motion. Kim and Bolton  suggested that these fast waves are potential significant radiators at higher frequencies. However these waves are difficult to excite.
In the paper a slick tyre rolling on an ISO and a rough surface is simulated. Based on the calculated contact forces in the time domain the amplitudes of the modes excited during rolling are determined as function of frequency. A boundary element model is then applied to predict the sound pressure level on a reference surface around a tyre placed on rigid ground as function of the modal composition of the tyre vibrations. By taking into account different modes when calculating the vibrational field as input into the boundary element calculations, it is possible to identify individual modes or groups of modes of special relevance for the radiated sound power. The results show that mainly low-order modes with relative low amplitudes but high radiation efficiency in the frequency range between 800 and 1200 Hz are responsible for the radiated sound power at these frequencies, while those modes which are most strongly excited in that frequency range during rolling are irrelevant for the radiated sound power. This fact is in good agreement with earlier hypothesis suggested in . It is also very essential when focusing on the design of quieter tyres.
 Y.J. Kim, J.S. Bolton: Modelling tyre treadband vibration. Internoise, The Hague, 4 (2001).
 F. Wullens, W. Kropp: Wave content of the vibration field of a rolling tyre. Acta Acustica united with Acustica 93, 4(2007) 48-56.