Boundary control for improving limiting performance in a new seatbelt model: A technique proposal

Abstract

Abstract Seatbelt has been recognized as the most effective means to prevent occupant in car against being ejected out and sustaining injury caused by the impact with interior. Improving its limiting performance, such as reducing torso forward displacement and limiting force applied by seatbelt webbing, is still well worth studying. In this paper, we employ in-plane motion models that a torso impacts against the mid-span of webbing for study. On the basis of conventional seatbelt model, we put forward a new model that its two outer ends are qualified to be able to move forwards and rearwards. Studying from the standpoint of longitudinal propagations of in-webbing transverse waves, we first introduce a displacement function superposed at origin by a wave propagating inwards from boundary and a wave propagating outwards which both arrive at the origin at the same time; then analyse the properties required for a class of the functions with adjustable parameters to be competent; finally solve the inwards-propagating and the outwards-propagating waves via the function inversely, and give the corresponding boundary displacement signal that needs to be input. Theoretically, the results show that this control technique can simultaneously reduce torso maximum displacement, maximum force, rebound velocity against backrest and the duration of interaction with seatbelt webbing, especially in the case with bigger ratio of torso mass to webbing mass and smaller product of initial angle of straightened webbing, wave speed and the reciprocal of impact velocity, which is apt to cause bigger maximum forward displacement and moderate maximum force. The results also show that shortening lag time of the control input benefits the comprehensive reductions of the criteria.