SINGULARLY PERTURBED BOND GRAPH MODELS FOR SIMULATION OF MULTIBODY SYSTEMS

This paper develops a bond graph-based formalism for modeling multibod y systems in a singularly perturbed formulation. As opposed to classic al multibody modeling methods, the singularly perturbed formulation is explicit, which makes it suitable for modular simulation. Kinematic j oints that couple rigid bodies are described by a set of differential equations with an order of magnitude smaller time scale than that of t he system. Singularly perturbed models of joints can be used to invest igate nonlinear properties of joints, such as clearance and friction. The main restriction of this approach is that the simulation may need to be computed using 64 bits precision because of the two-time scale n ature of the solution. The formalism is based on developing bond graph models of art elementary set of graphical velocity-based constraint f unctions. This set can be used to construct bond graphs of any type of mechanical joint. Here, this set is used to develop bond graphs of se veral joints used in multibody systems and spatial mechanisms. Complex models of multibody systems may now be built by graphically concatena ting bond graphs of rigid bodies and bond graphs of joints. The dynami c equations of the system are automatically generated from the resulti ng bond graph model. The dynamic equation derived from the bond graph are in explicit state space form, ready for numerical integration, and exclude the computationally intensive terms that arise from accelerat ion analysis.