Advanced slip ratio for ensuring numerical stability of low-speed driving simulation: Part II—lateral slip ratio

Abstract

A tire model is essential for vehicle dynamics simulations. The slip ratio of a tire model affects the stability of the simulation. The traditional slip ratio frequently causes numerical problems in low-speed driving simulations when the longitudinal speed approaches zero. To solve this phenomenon, many researchers have proposed various solutions by adding tuning parameters or defining the slip ratio through differential equations. However, these methods have the disadvantages of reducing the reliability of the tire model and increasing the computational complexity. In Part 1 of this paper, we proposed a method to calculate the advanced slip ratio without using tuning parameters or differential equations. This method guarantees the numerical stability of a simulation by limiting the time constant of the wheel dynamics model to be greater than the marginal time constant of the explicit integrator. In Part 1, just the longitudinal slip ratio was considered; thus, the problem of numerical instability of the slip ratio at low speed also occurs in the lateral direction. Therefore, in the second part of this study, the advanced slip ratio is extended to the lateral direction. Furthermore, the proposed method is applied to a bicycle model to verify its performance in a driving simulation. Finally, the simulation results are analyzed to verify the validity and stability of the advanced slip ratio in both directions.