On issues of elastic–rigid coupling in finite element modeling of high-speed machines

Modeling high-speed, flexible mechanism systems through the finite element method has long been the subject of intensified research. It is recognized that the important characteristics encountered in analysis of high-speed machinery are so-called coupling effects between elastic and rigid-body motions. However, it remains to be seen whether widely published formulations based on the finite element technique have correctly accounted for the elastic-rigid coupling. The intent of this paper is to bring this crucial issue to the attention of research communities, with the appropriate formulation presented. This study shows that the past formulations have some extra and therefore non-existent coupling terms that in fact lead to cancellation in the net coupling effect, thus unknowingly and improperly losing the coupling effects originally expedted in finite element modeling of high-speed machines. The originality of this work lies in its demonstration of correctly accounting for the coupling effects in deriving the governing equations for high-speed, flexible mechanism systems.