41.2.3.1. Normal Force of Tire

The normal force of a road on a tire at the contact patch is generated the direction of z-axial in the contact coordinates.

(41.26)\[{{F}_{z}}=\min \left( 0.0,\text{ }\left\{ \text{ }{{\text{F}}_{\text{zk}}}+{{F}_{zc}}\text{ } \right\} \right)\]
where,
\({{F}_{zk}}\) is the normal force due to tire vertical stiffness.
\({{F}_{zc}}\) is the normal force due to tire vertical damping.

\({{F}_{zk}}=-K\times \delta\), and

\(K\) : Vertical tire stiffness
\(\delta\) : Penetration (tire deflection)

\({{{F}'}_{zc}}=-2.0\times \sqrt{M\times \left| K \right|}\times C\times \dot{\delta }\)

\(M\): Mass of tire
\(C\): Vertical damping ratio
../_images/image04722.png

Figure 41.12 Step function \(\lambda\)

\({{F}_{zc}}=\lambda \times {{{F}'}_{zc}}\)

\(\lambda\) is the step function of penetration.

\(Max\delta =0.01*{{r}_{2}}\)

\({{r}_{2}}\) is the carcass radius of toroidal tire.