Page - 18 - in Maximum Tire-Road Friction Coefficient Estimation

2 Estimation of the friction potential Concerning tire rubber physics, the conditions of both rolling and sliding of the tire contact patch on the road surface have to be taken into account simultaneously. The friction effects for pure sliding of rubber provide a basis for understanding the complex friction characteristics, see Section 2.1.2. For a rolling tire, geometric and kinematic effects also have to be considered, see Section 2.1.2. 2.1.1. Rubber physics Rubber friction, which depends on the internal friction in the rubber material, shows viscous and elastic behaviour, [Pop09]. Pure elastic behaviour is described by Hooke’s Law, which gives a linear relation between stress and strain. Ideal elastic materials accumulate deformation energy and deliver it completely when unloaded, while ideal viscous materials transform all deformation energy into thermal energy. For materials with ideal viscous behaviour, the complex shear modulus for Newtonian fluids describes the relation between shear stress and shear velocity. For visco-elastic materials such as rubber, thedeformationenergy ispartially storedandpartiallydissipated, [Bac96,p.13]. Effects such as the temperature dependence on rubber friction as well as its dependence of the velocity in the contact surface correlate with the complex shear modulus, [Pop09]. Friction components of sliding rubber The friction force for sliding rubber is composed of the force components caused by ad- hesion,hysteresis, viscosityandcohesion; as summarized inBachmann, [Bac96,p.16-24]. All components do not necessarily have to be present at the same time. v S F F Hysteresis v S F F Adhesion dF hn Figure 2.1.: Main friction mechanisms adhesion (left) and hysteresis (right) based on Schramm with the resulting friction forceFF, which is pointed in the oppo- sitedirectionoftheslidingvelocityvS, andtheelementdFhnofthehysteresis force projected to the plane of motion, [SHB10]. 18