Advanced slip ratio for ensuring numerical stability of low-speed driving simulation. Part I: Longitudinal slip ratio. (July 2019) - Jung, Samuel; Kim, Tae-Yun; Yoo, Wan-Suk
The slip ratio, which is the ratio of the slip speed to the driving speed, is an essential input in tire models for vehicle-driving analysis. At a driving speed of zero, because the denominator of the slip ratio is zero, singularity is crucial for stable numerical analysis for examining the low-speed dynamic behavior of vehicles. A lagged slip ratio is widely adopted in most commercial software to prevent such failures, but this causes oscillation and requires a tuning parameter. Moreover, it increases the computational complexity because differential equations are employed to define the slip. To overcome this, researchers proposed a modified slip ratio without a differential equation; however, a tuning parameter was still required. Herein, we propose an advanced slip-ratio calculation method that allows stable simulation without the use of a differential equation or tuning parameter in the explicit integration. The accuracy and stability of the proposed slip ratio were verified against other methods via braking simulation. The proposed method showed very stable results compared to conventional methods and did not fail even with explicit integration. Furthermore, in the case of implicit integration, it prevented step-size reduction.