Analysis of normal and tangential restitution coefficients in car collisions based on finite element method

Abstract

In momentum-based impact models used in accident reconstructions, the restitution coefficient is a key role to determine impulses and delta-V accurately in car-to-car collisions. The restitution coefficients can be defined as the normal and the tangential direction in the contact plane, and the same value of the normal and tangential coefficients is employed in a two-dimensional PC-Crash model. Ishikawa (1993) proposed an impact model with the normal and tangential restitution coefficient, however, to the best of the author's knowledge, few studies have further investigated tangential restitution coefficients in detail. In this study, the normal and tangential restitution coefficients of the impact model were investigated based on the finite element (FE) analysis. FE simulations of angled barrier crashes with varying barrier angles as well as 16 car-to-car collisions were conducted. As the contact plane slides, the ratio of the tangential impulse to the normal impulse becomes the same value with the maximum friction coefficient. The tangential restitution coefficient is related to whether sliding occurs on the contact plane, and can be expressed as a function of the impulse ratio. The tangential restitution coefficient decreased with increasing the impulse ratio and is positive in non-sliding collisions and negative in sliding collisions. An approximate expression for the tangential restitution coefficient was formulated as a function of the generalized impulse ratio. The calculated impulses of the impact model with normal and tangential restitution coefficients were closer to the FE analysis than the PC-Crash model which uses a constant restitution coefficient of 0.1.