Application of the Generalized Impulse-Momentum Balance Equations to Impacts with Friction in Planar Flexible Multibody Dynamics

摘要

Most formulations on normal impacts of rigid multibody systems use the momentum balance equations. Newton's hypothesis is usually employed, where the restitution coefficient is defined by the relative normal velocities of the impacting bodies before and after the collision. When friction is present in the impact, the process becomes more complicated. Different impact modes are possible: sliding, sticking or reverse sliding. The variables in the momentum balance equations are the changes in the velocity and the two components of the impulse, one in the normal direction to the common tangent of the contact surfaces and other in the tangent direction. To solve the equations two additional conditions are needed, one comes from the Coulomb law, and the other from the definition of the restitution coefficient. The use of the Newton hypothesis leads to wrong results. Therefore, it is necessary to use the Poisson hypothesis. The restitution coefficient is defined through the normal impulses of the compression and restitution periods. In this paper a formulation of impacts with friction of planar flexible multibody systems is presented. The floating frame of reference formulation is used to model the flexible bodies. The normal and tangential impulses in the contact point are calculated by a computational algorithm based on the graphics techniques developed by Routh.