A physical-analytical model for friction hysteretic contribution estimation between tyre tread and road asperities

Abstract

The numerical prediction of rubber friction properties is a great challenge from the modelling point of view. In many applications such as tyres, sealing systems, conveyor belts, the observed friction process arises from complex mechanisms occurring at the interface rubber/substrate [1]. During the sliding contact between two deformable bodies, the friction main contributions can be accountable in adhesive and hysteretic causes [2]. The adhesive contribution is related to the formation and breaking of the adhesive bridges in the real contact points inside the nominal contact region, instead the hysteretic contribution is related to the deformation cycles that result in energy losses due to the viscoelastic behaviour of the bodies. Due to these mechanisms, a frictional force is generated during the relative sliding between two bodies. As concerns the hysteretic contribution, previous studies [3] showed that even in the absence of adhesion in the contact region, the contact pressure is distributed in a non-symmetrical manner causing a force of resistance that opposes the motion. In this paper, a physical-analytical model is developed to calculate the friction hysteretic component of a tyre tread elementary volume in sliding contact with road asperities. In this study, the road macroscale is only considered. The shape of the asperity is modelled as the osculating sphere [4]. The model is based on the energy balance between the work done by the friction force component and the energy dissipated in the material due to hysteresis. The compound viscoelastic properties are defined in terms of storage and loss moduli by means D.M.A. experimental tests. The internal dissipated energy is evaluated considering the stress and strain field calculated by Hamilton formulation [5]. Finally, some consideration about further model improvements are made regarding the introduction of a complete road spectrum (PSD) and the material modelling by fractional derivative algorithms.