Durability analysis and implementation of the floating frame of reference formulation

Abstract

The finite element floating frame of reference (FFR) formulation, implemented in most commercial multibody system (MBS) computer programs, is widely used in the durability analysis by a large number of industry sectors. In this paper, a single-degree of freedom system is used to derive a new analytical model from the general nonlinear FFR equations. The obtained new analytical model, which can serve as a benchmark example, is used to address fundamental issues related to the accurate, efficient, and general implementation of the FFR formulation, including the treatment of the algebraic joint constraint equations, fundamental difference between the FFR reference conditions and the structural mechanics boundary conditions, the choice of the deformation modes, handling redundant MBS constraints, effect of the MBS joints on the oscillation frequencies, and difference between fixed and moving boundary conditions. Structural mechanics boundary conditions eliminate degrees of freedom and define the system topology, while the FFR reference conditions eliminate coordinate redundancy and do not introduce any motion constraints. The paper shows analytically how the MBS joint constraint equations change the system oscillation frequencies, demonstrates the effect of using inappropriate set of reference conditions, proves there is no single set of reference conditions suited for all applications, and uses other FE methods to verify the results and support the conclusions drawn. The results obtained in this investigation show that improper selection of the reference conditions can lead to solution errors that exceed 100%, making such a solution completely unreliable in any durability investigation. General implementation of the FFR formulation will significantly contribute to increasing reliance on virtual testing, less reliance on building actual prototypes, better understanding of flexible body dynamics, and better communication between various computer-aided engineering groups.