Sensitivity analysis of tyre characteristic parameters on ABS performance

Abstract

This study aims to provide quantitative insight into the sensitivity of tyre parameters on the performance of the anti-lock braking system (ABS) control algorithms. Unlike conventional sensitivity analysis methods, which depend on a few test cases, in this study, Magic Formula (MF) 6.1 tyre model is used to generate a comprehensive set of thousands of virtual tyres that encompasses all possible combinations of the four main longitudinal parameters. To broaden the scope of impact of this study, two ABS controllers – one based on wheel spin acceleration (literature version of Bosch ABS) and the other based on sliding mode control (SMC) are designed in MATALB-Simulink${}^{\circledR }$ and integrated with IPG Carmaker${}^{\circledR }$ to perform complete vehicle dynamics simulations. Straight-line ABS simulations are performed on dry asphalt road using both the controllers and each test-run is performed for five different set-point longitudinal slip ratios (${\lambda }_{ref}$). The results of the conditional variance-based sensitivity analysis consisting of 211,250 simulation tests indicate that the tyre peak friction coefficient and shape factor have significant contributions to ABS stopping distance. The sensitivity for stopping distance to tyre parameters varies amongst the controllers. While with Bosch algorithm parameter D almost completely controls the stopping distance, the sliding mode ABS is sensitive to parameters ${\lambda }_{ref}$, C and D. Tyre parameter interactions indicated by the factor $K=B\ast C\ast D$, though hard to visually interpret, is expounded using global sensitivity analysis metrics.

Keywords:

• Anti-lock braking system (ABS)
• conditional variance-based sensitivity analysis
• conditional mean
• Magic Formula (MF) tyre
• stopping distance (SD)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors thank JK Tyres and Industries Pvt Ltd., India, for financially supporting the project. RB / 1617 / EDD / 003 / HSSE / RKRI.