Page - 53 - in Maximum Tire-Road Friction Coefficient Estimation

3 Vehicle model Thegyroscopicandcentrifugal forcesaregivenbyk=mb· [ −bωz ·vy bωz ·vx 0 0 0 0 0 ]T , and the applied forces q, which read q=                b ∑ Fx b ∑ Fy Ob ∑ Mz Ofl ∑ MC,fl Ofr ∑ MC,fr Orl ∑ MC,rl Orr ∑ MC,rr                , (3.8) with the sum of all applied forces b ∑ Fx and b ∑ Fy acting on the vehicle in the longi- tudinal and lateral directions, the sum of the momentsOb ∑ Mz on the vehicle’s chassis around the zb axis and the sums of the wheel momentsOi ∑ MC,i around the yi axis. 3.2.1. Applied forces The vector of applied forcesq in Equation 3.6 contains different forces, which are shown in Figure 3.7 and explained in this section. The first two rows of q contain the applied forces for the linear momentum in longitudinal and lateral direction, which read b ∑ Fx = ∑ i bFx,i−FA−FW,x−mb ·g ·sinβr, (3.9) b ∑ Fy = ∑ i bFy,i−FW,y. (3.10) The applied forces include the horizontal tire forces bFi,x and bFi,y for each tire i in the bodycoordinatesystemOb, as showninFigure3.7, theaerodynamic forceFA, additional wind forcesFW,x andFW,y and the climbing resistancemg ·g ·sinβr, which contains the slopeβr. With the tire model in Section 3.3, the horizontal tire forcesFx,i andFy,i are calculated in the i-th wheel’s coordinate systemOi and, for the front wheels, have to be transformed by     b Fi,x bFi,y 0     =Tbi ·     i Fi,x iFi,y 0     . (3.11) 53