Author:

Keywords:

flexible multibody dynamics, interface reduction, static modes switching, global modal parameterization, body-level model reduction, system-level model reduction, real-tiem simulation

Abstract:

The ever-increasing trend to design machines and processes to befaster, more lightweight, more energy-efficient and more reliablecauses virtual prototyping to gain importance over physicalprototyping. Accurate numerical modeling techniques for flexiblemultibody systems are needed in the different stages of thedesign. Furthermore, numerical models are not only used in thedesign phase; certain applications rely on simulation results ofnumerical models computed in real-time. Real-time targets arecurrently only met for highly simplified multibody models.However, in industry a strong desire exists to extend real-timecapabilities to more advanced models.In model reduction, the evolution of the system state is decomposedin dominant and negligible motion patterns. In the currentstate-of-the-use in flexible multibody modeling mainly body-levelmodel reduction is used. Body-level model reduction refers tomodel reduction applied to the flexibility description ofindividual bodies, i.e. mechanism components. These reduced bodyflexibility models are then incorporated in the model equations ofthe overall system. In case of a multitude of possible loadingpoints on a flexible body, its reduced body flexibility model willbe of significant size, such that time integration of the overallmultibody model becomes expensive. A first goal of this researchis to develop and validate efficient modeling techniques for therepresentation of flexibility in multibody dynamics, especiallytargeting this flaw in the state-of-the-use.A first solution to this problem is interface reduction, in which component interaction is approximated by a limited set of interaction patterns.An alternative interface reduction scheme is proposed and the associated computational hurdles are solved. This offers the user an alternative to model intercomponent interaction, without the numerically introduced artificial stiffness of conventional techniques. In a numerical experiment the effect of this artificial stiffness is illustrated.However, accuracy requirements can impose the use of more detailed body flexibility models. Quite often, many DOFs can be loaded during simulation, but few are loaded simultaneously. The multitude of possibly loaded DOFs imposes an expensive body flexibility description, but at any moment in time only a low-dimensional part of this description contributes to the solution. An innovative methodology is proposed, called Static Modes Switching, which at every time step only includes the strictly needed deformation patterns, so that at every time step an accurate body flexibility description of minimal size is obtained. Considerable simulation speed gains are obtained with an acceptable loss of accuracy.A second goal of this research is to develop and validate system-level model reduction techniques which enable real-time simulation of flexible multibody systems.The presence of both differential and algebraic equations in the model equations, and the number of degrees of freedom needed to accurately represent flexibility prohibit real-time simulation of these systems. Most current model reduction techniques for non-linear systems project the model equations on a set of invariable motion patterns. Only by using configuration-dependent motion patterns, one can transform the model equations from a set of differential-algebraic equations into a set of ordinary differential equations, and achieve a maximal dimension reduction. This is done in Global Modal Parameterization (GMP), for which this research proposes a generalization. Global Modal Parameterization divides the computational load over an expensive preparation phase and a cheap simulation phase. This research focuses on applications where fast online simulation capabilities justify an expensive offline preparation, such as real-time applications.In a first step, modal motion patterns are used. The sources of approximation error of a GMP-description are investigated. The effect of the configuration space discretization coarseness on the different approximation error sources is illustrated. The trade-offs to be defined by the user to control these approximation errors are explained. It was observed that the eigenmodes with eigenfrequencies near or within the frequency range of the excitation should be included in the motion patterns for model reduction. Furthermore, additional motion patterns are required to compensate for the quasi-static contribution of the omitted eigenmodes.Mode veering and mode crossing cause abrupt changes in mode shapes. As a modal GMP approach is based on describing the motion by the contributions of these rapidly changing motion patterns, the degrees of freedom of a GMP-description can vary abruptly for moderate system changes. It is theoretically proven that this even results in singularities for mode veering.Although the individual eigenmodes vary abruptly, the vector space spanned by a pair of veering/crossing modes has limited variability.To exploit this, linear combinations of eigenmodes are proposed to generate smoothly varying motion patterns. This requires an automatic detection of mode veering. A numerical experiment shows that this is unfeasible for systems with multiple parameters defining the dynamics.As a second solution, Krylov subspaces are proposed for the motion patterns of the GMP model reduction. A Krylov subspace also spans the dominant dynamics near a chosen frequency, without singularities due to mode veering.The maximal variability with respect to the system configuration of the first Krylov vector is one order of magnitude lower than the first eigenmode. However, due to the recursive definition and the orthogonalization in the Arnoldi computational process, variability is propagated and amplified through the series of Krylov vectors. By omitting this orthogonalization step, this propagation and amplification of variability vanishes. However, a singularity-free GMP-simulation using Krylov seems to be infeasible.Finally, several future research tracks are proposed.