Application of LCP Contact Formulation on Mechanical Systems With Nonrigid Coupled Unilateral Contact Points Illustrated With a Simple Model of a Windscreen Wiper

Abstract

Technical applications with unilateral contact are often modeled as multiple coupled discrete mass points. The transition between contact states is often described by transforming the contact formulation into a linear complementary problem (LCP). In case of compliant materials such as rubber, the LCP can be simplified so that no algorithm is needed to solve the equation system. Thus, computational effort can be reduced considerably. In this paper a windscreen wiper lip is modeled as a simple mechanical system with unilateral contact points. The system consists of masses which are coupled by linear springs and dampers. The masses can come into contact with a rigid surface. The equations of motion are derived and transformed into an LCP. The modeling of the coupled, compliant system leads to a simplification of the equation system. Therefore, it can be solved line by line as single independent scalar LCP’s. Also at the transition from separation to contact, when an impact occurs, the contact points can be considered individually. It will be shown, that the coupling can be neglected during the infinitesimal small time of impact. The LCP formulation in combination with simple models of compliant structures therefore yields an effective method for treating multibody systems or discretized continua with several unilateral contact points.