Page - 55 - in Maximum Tire-Road Friction Coefficient Estimation

3 Vehicle model withrx,iandry,ibeingthe lateraland longitudinaldistances fromthevehicle-fixedorigin Ob to the i-thwheel’s centreC. The last four rowsofqdescribe theangularmomentums of the four wheels. The applied forces are shown in Figure 3.8. For the wheel i, the applied forces read Oi ∑ Mc,i=MD,i−Fi,x ·rS,i−MR,i. (3.15) Theangularmomentumsof thewheels includethedrivingorbrakingtorqueMD,i,which is an input for the simulation, and the longitudinal tire forceFx,iwith its leverarm, the static tire radius rS,i. The rolling resistanceMR,i reads MR,i=Fz,i ·fr,i ·rS,i (3.16) with the rolling resistance coefficient fr,i and the tire load Fz,i. The tire-dependent parameter fr,i is given in Appendix D. r S,i β r M R,i M D,i F x,i Figure 3.8.: Kinetic quantities for wheel i showing the driving and braking torqueMD,i, the rolling resistance torqueMR,i and the longitudinal tire forceFx,i, based on Eichberger, [Eic11, p.149]; graphic depiction modified from Hirschberg, [HW12, p.33]. 3.2.2. Vertical tire load variation Horizontal accelerations in the chassis’ centre of gravity produce forces that are sup- portedbythe suspension (e.g. the tires, the springs, theanti-roll barsandthedampers). When considering static effects only, the influences of the damper and damping effects of the tires are omitted. Additionally, the following considerations apply only on even roads. The static tire load due to the weight distribution is superposed by the forces necessary to support the longitudinal body accelerations bax during braking and accel- erating. Thus, the tire loads for the front and the rear axles including tire load variation 55