Flexible Natural Coordinates Formulation (FNCF): Towards Simpler Equations of Motion for Flexible Multibody Models

The research presented within this work deals with rigid and flexible multibody modeling, with the focus on the latter. Such modeling is encountered in mechatronic system models ranging from a car suspension to an industrial weaving loom. The complexity of moving flexible components in terms of varying boundary conditions and varying inertial forces make it a challenging research field. The typical formulations used for this type of models are quite complex and are usually formulated with Differential-Algebraic Equations (DAEs) as opposed to Partial Differential Equations (PDEs) or even Ordinary Differential Equations (ODEs). Algebraic equations are the result of not making a kinematic relation explicit; whether that is due to the model not readily allowing it (e.g. closed loops) or due to required modeling choices (e.g. Euler parameters). The first contribution of this research is the development of the Flexible Natural Coordinates Formulation (FNCF). The Floating Frame of Reference (FFR) can be seen as a direct extension of the Cartesian Coordinates (CC) formulation from rigid to flexible multibody. No similar extension exists for the Natural Coordinates (NC) formulation. The FNCF approach fills this gap in the state of the art by offering a formulation that yields the same equation structure as the NC formulation, but for flexible multibody models. Whereas most flexible multibody formulations focus on obtaining equations of motion in as little degrees of freedom as possible, FNCF results in equations of motion in a lot of degrees of freedom, roughly 10 times as much as FFR, but with the added benefit of yielding much simpler equations in terms of polynomial complexity. This is a beneficial property when looking at using a flexible multibody model in applications such as state estimation, the adjoint variable method, and structural optimization. By FNCF having more but simpler equations, it is difficult to compare the computational efficiency with other flexible multibody formulations as it is highly dependent on the specific implementation. The computational effort shifts from the model evaluation to the equation solving, which means that it is much faster to optimize the code for an FNCF implementation than any other formulation as the optimization should be sought in the equation solving, which is usually done by an external library that is already very optimized. The second contribution of this research is the development of the MultiBody Research Code (MBRC). This is a software tool capable of performing system-level rigid and flexible multibody simulations and is developed as a tool for researchers to easily test out new component formulations and to easily define new connection elements between components. The MBRC is written in Matlab allowing it to be easily used by mechanical engineers that require a research tool for multibody modeling.

Jaar van publicatie:2022

Toegankelijkheid:Open