Out-of-plane vibrations and relaxation length of the tyres for single-track vehicles

The properties of tyres have a large influence on the stability of single-track vehicles. This paper focuses on the characterization of the dynamic properties of tyres. In the first section of the paper, modal analysis of the tyres is presented. Two motorcycle tyres and four scooter tyres are modally tested in order to measure the natural frequencies and the damping coefficients of the first typical modes of vibration. Tests are carried out for seven different inflation pressures in order to study how the pressure affects the properties of the tyres. The modal stiffnesses and the damping coefficients are identified for each mode of vibration. The second section of the paper focuses on the characterization of the transient properties of the tyres according to a ring model, in which the tyre tread is a ring connected to the rim with a series of springs and dampers. A comparison between a first-order model, which takes into account only the modal stiffnesses, and a second-order model, which considers also the self-aligning torques and the modal damping coefficients, is made. A prediction of the relaxation length according to the first-order model is presented. The relaxation length is calculated considering the term due to the measured contact patch, the terms due to the stiffnesses of the lateral and camber modes and the residual stiffness term, which accounts for the modes with ring deflection. In the last section, the predicted relaxation lengths are compared with those measured by means of a tester machine.