Frequency loci veering due to deformation in rotating tyres

This paper shows that the eigenfrequencies of a deformed tyre exhibit a mutual repulsion behaviour if the rotation velocity is increased. This phenomenon is known as frequency loci veering and is induced by the a-periodicity resulting from the tyre deformation due to the weight of the car. The corresponding eigenmodes interact in the transition zones and finally interchange. This is not the case for the undeformed tyre, where it is well known that rotation splits the eigenfrequencies around the eigenfrequencies of the non-rotating tyre. The change in eigenfrequencies is linearly related to the rotation velocity and is determined by the circumferential wavenumber and tyre radius only. For the undeformed tyre no modal interaction occurs as a consequence of rotation. Furthermore, modal interaction increases as tyre load increases and decreases as material damping increases. In previous work a methodology to model tyre vibrations has been developed, exploiting a modal base determined in a standard FE package and including rotational effects by a coordinate transformation. Major advantages of this approach are that the complex build-up of a tyre is retained and that the large (nonlinear) deformations and small (linear) vibrations are treated separately. In the present paper, the effects of deformation on the eigenfrequencies of a rotation tyre are examined using this methodology.