Super-element global modal parameterization for efficient inclusion of highly nonlinear components in multibody simulation

Abstract

Over the last decades, higher and higher accuracy is expected from flexible multibody models. Accurate flexibility descriptions and detailed contact algorithms have been mostly developed with this aim. In practice, linearized models are often used at the expense of severe accuracy loss in order to improve simulation times. Several multibody packages have also been developed for the simulation of nonlinear components, but these typically lead to elevated simulation times. Alternatively, a cosimulation with a nonlinear finite element package can be performed, but this leads to very inefficient schemes. In order to allow a generic introduction of nonlinear components in multibody simulation packages, this paper introduces a novel nonlinear model reduction technique for nonlinear components, namely the Super-element Global Modal Parameterization (SE-GMP). The approach is aimed at reducing complex models of nonlinear components, while still taking the important nonlinear effects into account, in order to create a relatively simple model which can easily be coupled with other components in a multibody model. The proposed approach is based on the GMP formulation which is a nonlinear system level model reduction technique for (flexible) multibody systems. This work discusses the reduction procedure and different choices for the reduction space. Moreover, a strong focus is put on an appropriate choice of coordinates in order to allow for a convenient interfacing with multibody descriptions. Finally, the approach is demonstrated by the simulation of a slider-crank mechanism with a nonlinearly deforming crank.

On the dynamic analysis of rotating shafts using nonlinear superelement and absolute nodal coordinate formulations

“…This is due to the nonlinear relationship between global and local frame coordinates. To reduce this nonlinearity, a generalised modal reduction method based on the absolute coordinate formulation (ACF) with a constant mass matrix was proposed in Pechstein et al 23 and Naets and Desmet 24 There, FFRF-based and ACF-based superelements were compared, and it was concluded that the ACF-based element is more efficient and accurate. It was even found that in some cases, the results given by the FFRF-based superelement were not dependable.…”

Online state and input force estimation for multibody models employing extended Kalman filtering

“…Only the forceelements which are acting on the relative rigid DOFs θ i are considered as internal forces. The reduced internal forces F q i int are also obtained by projecting the unreduced (nonlinear) internal forces F x int onto the reduced DOFs, similar to the process described in [28]:…”

Global modes for the reduction of flexible multibody systems

“…In [24,25] a component-level reduction method based on an enhanced Craig-Bampton method is described. The other way around, the system-level based formulations employ a global reduction of rigid and elastic components [7,22,32,34]. Recently, the component mode synthesis (CMS) techniques have been employed to condense all the elastic coordinates, thereby obtaining an equivalent rigid-body model [19].…”