Page - 133 - in Maximum Tire-Road Friction Coefficient Estimation

B. Tire model TMsimple and tire dynamics This section provides additional information about the tire model presented in Section 3.3. This includes the relationship between the TMsimple parametersK,B andA and physically describable tire characteristics, as well as an approach to calculate the time function τy for lateral tire dynamics. B.1. Parameter relationships between static tire model Within the tire model TMsimple, the parametersK,B andA show a dependence on parameters thatcanbedescribedbyphysical relations. Thethree influencingparameters are the peak valueYmax, the saturation valueY∞ and the initial stiffnessdY0, which are shown in Figure B.1 for a constant tire load. The required TMsimple parameters read K = Ymax, B = pi−arcsin ( Y∞ Ymax ) , (B.1) A = 1 dY0 ·K ·B with Y∞≤Ymax. To include the dependence of the tire forces on the friction potential, the extension Slip quantity X Ymax dY 0 Y Figure B.1.: Physicalrelationof lateral tireparametersandthe lateral tirecharacteristics in TMsimple for a constant tire loadFz, [Hir09a].