Reduction of Physical and Constraint Degrees of Freedom of Redundant Formulated Multibody Systems

Abstract

Commercial multibody system simulation (MBS) tools commonly use a redundant coordinate formulation as part of their modeling strategy. Such multibody systems subject to holonomic constraints result in secondorder dindex three differential algebraic equation (DAE) systems. Due to the redundant formulation and a priori estimation of possible flexible body coordinates, the model size increases rapidly with the number of bodies. Typically, a considerable number of constraint equations (and physical degreesoffreedom (DOF)) are not necessary for the structure's motion but are necessary for its stability like outofplane constraints (and DOFs) in case of pure inplane motion. We suggest a combination of both, physical DOF and constraint DOF reduction, based on proper orthogonal decomposition (POD) using DOFtype sensitive velocity snapshot matrices. After a brief introduction to the redundant multibody system, a modified flat Galerkin projection and its application to indexreduced systems in combination with POD are presented. The POD basis is then used as an identification tool pointing out reducible constraint equations. The methods are applied to one academic and one highdimensional practical example. Finally, it can be reported that for the numerical examples provided in this work, more than 90% of the physical DOFs and up to 60% of the constraint equations can be omitted. Detailed results of the numerical examples and a critical discussion conclude the paper.