Abstract
The knowledge gained from the analysis of the transient brush theory may be effectively used to derive simplified, pragmatic tyre models to be used in vehicle dynamics simulations. Two different formulations have been proposed in the literature. The first is the so-called single contact point. It consists of a simple class of models, which usually find good agreement with experimental data and are based on a rather intuitive approximation. However, they systematically neglect the dynamics of the bristles inside the contact patch. The second formulation presented in this chapter is the two-regime approach, which also captures the transient effect due to the bristles. It relies on more sophisticated mathematical tools, and, albeit being relatively easy to implement, rarely admit closed-form representations. The two different models are compared together against the exact description introduced in Chap. 4.
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Notes
- 1.
Basically, the interior of the friction circle is an invariant set for \(\boldsymbol{F}_{\boldsymbol{t}}(t)\) [15]. This result may be easily generalised to any model in which the sigma surfaces are are given as \(\hat{\boldsymbol{\sigma }}(\boldsymbol{F}_{\boldsymbol{t}})=f(F_{\boldsymbol{t}})\boldsymbol{F}_{\boldsymbol{t}}\), where \(f(\cdot )\) is a scalar positive function, and the matrix of the enhanced stiffness \(\mathbf {C}_{\boldsymbol{\sigma }}^\prime \) is symmetric and positive definite.
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Romano, L. (2022). Theories of Transient Generation of Tyre Forces and Moment. In: Advanced Brush Tyre Modelling. SpringerBriefs in Applied Sciences and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-98435-9_6
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DOI: https://doi.org/10.1007/978-3-030-98435-9_6
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