Modelling flexible body systems: a bond graph component model approach

Recent developments in mechatronic systems, such as robotics and flexible manipulators, require a systematic, multidisciplinary approach to design. Bond graphs provide a general modelling paradigm that can be used in design of such multi-domain physical systems. Modelling the dynamics of flexible body systems has been the subject of active research over the last two decades. Model development is not simple when such systems undergo large translational and/or rotational displacements, and this has led to several modelling approaches. Bond graphs can be used successfully to design such systems. This paper treats slender deformable bodies as a collection of finite-element beams. Model development employs bond graphs based on a co-rotational formulation. This approach differs from others in that it uses a velocity formulation, instead of the more common positional formulation. The bond graph component model approach enables systematic creation of models of rigid and deformable multibody systems as a tree of component models, the leaves of which are the elementary components that represent the underlying physical processes. This facilitates building complex models of dynamic systems. The mathematical representation of this structure can be formulated as a system of differential-algebraic equations (DAEs) amenable to solution by readily available techniques. BondSim , an integrated modelling and simulation environment, facilitates this modelling process. A beam element model developed as a bond graph component is applied to the well-known spin-up manoeuvre of a flexible beam, a problem often used to test the validity of flexible-body models. The results show that a model developed using bond graphs is capable of predicting rather subtle centrifugal stiffening effects. Bond graphs thus provide a sound paradigm for developing mathematical models of such multi-domain, multibody systems.