Bond Graph Formulation of Impact with Friction in Multibody Systems

Vjekoslav Damic, Maida Cohodar, and Drazen Damic


Bond Graph Modeling, Simulation, Impact, Friction


In the paper modeling of impact phenomena with friction appearing in multibody systems is formulated using bond graphs. The approach used is based on the impulse-momentum balance equations. Impact is recognized by testing value of relative distance between two colliding bodies. A switch element is used which sets effort or flow at interaction to be zero. Problem becomes more complicated when friction acting in tangential plane is included in analysis. Discontinuous dry friction model is used to predict sliding in tangential direction and the conditions under which the motion ceases. Mathematical model is pretty complicated and causalities change during impact and separations of the bodies. To solve problem the mathematical model is generated in form of differential algebraic equation (DAE) and solved using form of Backward Differentiation Formulae (BDF) that allow high impulses during the impact. Two numerical examples are considered in the paper. The first is slider crank mechanism which uses the friction model. To confirm the developed impact model with friction a flexible pendulum falling under the action of gravity and hitting the ground is analysed. Agreement of presented simulation results with that reported in literature and which were using different approaches proves the validity of proposed model.

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