Page - 56 - in Maximum Tire-Road Friction Coefficient Estimation

3 Vehicle model ∆Fz,φ,jFz,f Fz,r tj 1/2 tjlrlf bax COG hCG ∆Fz,φ,j COG bay Figure 3.9.: Simplifiedmodel for thedynamic tire loadvariationvalid for smallpitchand roll angles considering the forces induced by horizontal accelerations in the vehicle’s COG: a) longitudinal movement (braking, accelerating), b) lateral movement (cornering); graphic representation based on Hirschberg, [HW12, p.7]. due to bax read Fz,f = mb · lr ·g−hCG · bax lr+ lf and Fz,r = mb · lf ·g+hCG · bax lr+ lf , (3.17) see also Figure 3.9. Equation 3.17 includes the vehicle’s mass mb, the gravitational acceleration g and the position of the centre of gravity, i.e. its heighthCG, the distances to the front and the rear axle lf and lr and the track width tj of the j-th axle. In order to apportion the tire load to the four wheels, additional assumptions are necessary, since the vehicle is statically undetermined in the vertical direction with four wheels supporting the load. In the lateral direction, this can be done by considering the rolling torque induced by the lateral body acceleration bay, which is not equally supported by the frontandrear suspension. Theamounts supportedbyeachof the j axlesdependson the stiffnesses of the tires cT,z in the vertical direction, the anti-roll bars cARB,j and the springs cS,j. The tire and the body spring are connected in series, as shown in Figure 3.10. During cornering, the wheels on one axle travel in opposite directions, which leads to an increased rolling movement of the chassis. This movement is reduced with the ARB, which act as torsion springs between the right and left side of an axle. The ARB and 56