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

What is it about?

The paper “Out-of-plane vibrations and relaxation lengths of single-track vehicles” is composed of two main sections. In the first section of the paper, the vibrations of the tire that occur in the direction perpendicular to the vertical plane of the tire (the out-of-plane vibrations) are presented. The modes of vibrations of the tire are described by means of natural frequencies, damping coefficients and modes shapes, which have been identified by means of an impulsive modal analysis technique. The tires have been excited by means of an impulsive hammer impact and the acceleration has been measured in six points of the tire by means of a tri-axial accelerometer. Starting from an estimation of the mass of the tire that takes part to the vibration (based on Pacejka rules of thumb), equivalent modal stiffnesses have been identified for each mode of vibration. The second section of the paper focuses on the characterization of the transient properties of the tire, expressed in terms of relaxation length. For modest frequencies of side-slip excitation (below 5-10 Hz in motorcycle tires), the tire can be modeled as a first order system, characterized by a time lag. When the vehicle travels with constant forward speed V, the time lag corresponds to a travelled distance which is defined as relaxation length. The most common model used for describing transient properties of tires is a rigid ring model, in which the tire tread is a ring connected to the rim with a series of springs and dampers. A prediction of the relaxation length, carried out employing modal analysis results, is presented: the relaxation length is calculated considering the term due to the measured contact patch, the terms due to the modal stiffnesses of the lateral and camber modes and a residual stiffness term, which accounts for the modes with ring deflection. In a further section of the paper, the predicted relaxation lengths are compared with those measured by means of the specific tester machine of the University of Padova.

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Why is it important?

The uniqueness of the paper consists in three important aspects. First, in the framework of this research six different tires have been analyzed (one set of motorcycle tires and two set of scooter tires), therefore a wide range of different applications and construction technologies have been taken into account. The tires of the first set have radial structure and are suited to high performance motorcycles, the tires of the second set have diagonal structure and are suited to high wheel scooters and the tires of the third set are diagonal and suited to scooters. Second, the measurements have been carried out for seven different inflation pressures, including both lower and higher values than the nominal inflation pressure of the tires, therefore the effect of inflation pressure on tires transient properties have been studied as well. Third, the method proposed in this paper allows the identification of tires relaxation length employing data obtained by means of modal analysis, which is a simpler, faster and cheaper technique if compared with a fully-equipped specific machine for the measurement of tires properties.

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