Page - 101 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

B.2. Non-linear Tyre Model with itsnorm‖s‖= √ s2x+s 2 y. If thenormof thegeneralizedslip‖s‖onlyacts in the lon- gitudinal or lateral direction, the contact forceswF ′ x andwF ′ y will occur, see fig. B.2(b). These pure longitudinal or lateral forces are combined using the interpolation ‖wF‖= 1 2 [ wF ′ x+wF ′ y+ ( wF ′ x−wF ′y ) cos ( 2β′ )] , (B.13) where β′ = arctan ( sy sx ) , see fig. B.2(b). The cos(2β′) function is used to obtain a continuous interpolation with a horizontal tangent at wF ′ x and wF ′ y. The resulting tyre force in the tyre coordinate system in thewx andwy directions reads wF=‖wF‖ [ cos(β′) sin(β′) ] . (B.14) All the calculations up to now were done using the nominal wheel loads wFz,nom. For other wheel loadswFz, the parameters described in B.2(a) are modified using the expres- sions Fmax(wFz) =a1 wFz Fz,nom +a2 ( wFz Fz,nom )2 , dF0(wFz) = b1 wFz Fz,nom +b2 ( wFz Fz,nom )2 and F∞(wFz) = c1 wFz Fz,nom +c2 ( wFz Fz,nom )2 , (B.15) with a1 = 2Fmax− 1 2 Fmax,2 a2 = 1 2 Fmax,2−Fmax, b1 = 2dF0− 1 2 dF0,2 b2 = 1 2 dF0,2−dF0 and c1 = 2F∞− 1 2 F∞,2 c2 = 1 2 F∞,2−F∞. (B.16) The parametersFmax, dF0 andF∞ describe the tyre characteristics at a wheel load of Fz,nom, and the parameters Fmax,2, dF0,2 and F∞,2 at 2Fz,nom. Table C.5 shows the tyre data used. 101