Polynomial tire model
Nonlinear relation between tire lateral force and slip angle expressed by a third order polinomial equation. This model is used by several authors [1] [2] [3].
Contents
Sintax
Fy = TireModel.Characteristic(alpha)
TireModel.PlotTire()
Arguments
The following table describes the input arguments:
| alpha | Tire slip angle [rad] |
Outputs
| Fy | Tire lateral force [N] |
Description
Model equation:
\[ F_y = k_1 \alpha - k_2\alpha^3 \]
where \(F_y\) is the lateral force and \(\alpha\) is the tire slip angle. \(k_1\) and \(k_2\) are the model coefficients.
Hypothesis
- Nonlinear tire model
- Valid up to the maximal lateral force (Tire saturation).
References
[1] JOHNSON, D.; HUSTON, J. Nonlinear lateral stability analysis of road vehicles using Liapunov's second method. SAE Technical Paper, SAE International, 1984.
[2] SADRI, S.; WU, C. Stability analysis of a nonlinear vehicle model in plane motion using the concept of lyapunov exponents. Vehicle System Dynamics, Taylor & Francis, v. 51, n. 6, p.906-924, 2013.
[3] SAMSUNDAR, J.; HUSTON, J. C. Estimating lateral stability region of a nonlinear 2 degree-of-freedom vehicle. SAE Technical Paper, 1998.