Page - 57 - in Maximum Tire-Road Friction Coefficient Estimation

3 Vehicle model mb mw cARB,jcS,j cT,z zb,i zi zR,i Figure 3.10.: Coordinates zR,i, zi and zb,i of quarter vehicle including the body spring S, the anti-roll barARB and the tireRwith its corresponding stiffnesses of axle j and wheel i; based on Hirschberg, [HW12, p.51]. the body springs are connected in parallel. However, unlike the body springs, where the applied forces depend on the spring deflections ∆zS,i = zb,i−zi, the total force of the ARB depends on the difference of the spring deflections between the left and right sides. In order not to have included the wheel’s vertical motion as additional degrees of freedom, a substitution for the roll motion of the chassis is assumed for the vertical tire load transfer, and cARB,j can be simplified treated as a scalar. The total stiffnesses of the axles ctot,j are then given by 1 ctot,j = 1 cT,z + 1 cS,j+cARB,j . (3.18) The percentage of the roll moment supported by each axle is given by pj= ctot,j∑ jctot,j ·100. (3.19) Thus, the tire load variation ∆Fz,φ,j due to lateral body accelerations bay is given by ∆Fz,φ,j=mb ·bay ·pj ·hCG tj (3.20) including the tracks tj of the front and the rear axles. Finally, the tire loads for the four 57