A novel brush-model with flexible carcass for transient interactions

Analytical results in transient brush tyre models: theory for large camber angles and classic solutions with limited friction

“…On the other hand, despite their simplistic nature, the so called brush models [1][2][3][4][5][6] represent a solid basis for a basilar understanding of the tyre dynamics, being only grounded on physical assumptions which allow for a straightforward interpretation of the tyre-road interaction. In the brush theory, the tyre, modelled as a rigid body, is equipped with bristles which deform in longitudinal and lateral direction inside the contact patch.…”

“…More specifically, the pressure distribution q z ðx; sÞ is supposed not to be influenced by friction-related phenomena. 6 To simplify the analysis, with some abuse of notation, the vectors in the reduced Euclidean space R 2 are considered in the following, since the contact between the tyre and the road always takes place on the plane P.…”

Brush tyre models for large camber angles and steering speeds

“…The micro-sliding speed v st (x, t) reads, in vector form, Pacejka [2], Guiggiani [21], Limebeer and Massaro [23], Romano et al [24], Romano et al [52]…”

“…The previous analysis shows that, for sufficiently large values of ε ψ and ϕ, the global solution u t (ξ , s) is nonlinear in the slip and spin parameters and also every component of the tangential displacement depends on both σ x and σ y . Thus, we need to ascertain that Equations (24) and (27) are equivalent to the linear expressions predicted by classic 1DM for small values of ε ψ and ϕ. These formulae can be found in many books, although here we refer explicitly to the notation used in [52].…”

“…On the other hand, brush models [1,2,[21][22][23][24] represent a more naive but still insightful approach when it comes to a pure physical description of the tyre. They are derived from a simplified version of the classic theory of contact mechanics [25][26][27][28][29][30][31], are grounded on few assumptions, and are still accurate enough to reflect the main variations in tyre characteristics due to different operative conditions.…”