Stability of two-wheeled vehicles is influenced by the transient properties of tires, which are described in terms of the relaxation length, which is the distance that the vehicle travels before tire forces reach the steady state values. Relaxation length is often studied by means of rigid ring models, in which the belt of the tire is modeled as a rigid ring elastically connected to the rim and the contact patch is connected to the belt by means of residual springs. Actually these models are able to take into account the lateral and the diametrical modes of vibration of the rigid belt with respect to the rim and to represent in a simplified way the modes with belt deformation by means of the residual stiffness. Experimental tests are needed to find the parameters of the models and to validate results. This research focuses on the relaxation length of side-slip force and aims to improve knowledge in this field, since there is no consolidated method for deriving the parameters of rigid ring models and, especially in two-wheeled vehicles, the relevance of rigid belt and deformable belt modes is not well known. Experimental tests are performed on a rotating disk machine developed for testing tires of two-wheeled vehicles, two motorcycle and two scooter tires are considered. Transient properties are studied by carrying out tests with harmonic variations of side-slip angle, since in the frequency domain the relaxation length corresponds to a phase lag between the input and tire force. Phase lags are measured and relaxation lengths are identified for a wide range of inflation pressures. Then each tire is modally tested and natural frequencies, dampings and vibration modes are found, the stiffnesses associated to the lateral and diametrical modes are identified. Finally a comparison is made between the identified relaxation length and the prediction given by a model based on the identified tire modes. The relevance of deformable belt modes is analyzed and their influence on relaxation length is discussed.

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