Page - 50 - in Maximum Tire-Road Friction Coefficient Estimation

3 Vehicle model 3.2. Selected vehicle model The investigation in Section 3.1 showed that damper and spring excitation caused by forces that act in the centre of gravity have little impact. As vertical movement caused by road induced excitation is eliminated, the degree of freedom in vertical direction for the chassis and each wheel can be omitted. In addition, since the influence of wheel kinematics andcomplianceproved tohave little impact for this investigation, suspension and wheel kinematics do not need to be considered. As the movement of the chassis relative to the tire is also not of interest, the rotational DOF of the chassis around xb and yb axis are omitted, cf. Figure 3.1. In summary, the assessment of the required model accuracy in Section 3.1 showed that the following investigated phenomena have to be considered in the selected vehicle model: • a non-linear steering ratio, • front and rear ARB stiffness (not zero), • vertical tire load variation, • transient lateral tire dynamics and • effective tire radii depending on the vertical tire load. In addition to a standard single-track model, such as the one proposed in [RS40], and the aforementioned phenomena, the wheel rotation of all four wheels and non-linear horizontal tire characteristics are considered. The model equations are now explained in the following sections. In the global coordinate system {Og,xg,yg,zg}, three degrees of freedom remain for the global position vector gy, which reads gy(t) =     xg yg ψ     . (3.2) In the vehicle-fixed coordinate system {Ob,xb,yb,zb}, 7 degrees of freedom remain for the generalised velocity vector bz, bz(t) = [ vx vy bωz ωfl ωfr ωrl ωrr ]T . (3.3) 50