The Floating Frame of Reference Formulation for Rotordynamics Applications: Limitations and Practical Solutions

The floating frame of reference formulation (FFRF) is one of the most widely used computational methods for modeling linearly elastic flexible multibody systems. It offers a convenient and computationally efficient approach, particularly the nodal-based framework. An advantage of the FFRF is its ability to directly utilize 3D models created with CAD software and meshed with finite element tools, making it an appealing alternative to beam-element models for studying rotating machinery. However, it is well known that FFRF is not suitable for rotordynamics applications because it fails to capture centrifugal stiffening. Centrifugal stiffening arises as rotating components, such as discs and blades, experience tensile forces that increase their natural frequencies, effectively enhancing structural stiffness. This study addresses limitations of FFRF for rotordynamic applications and presents a practical solution for incorporating centrifugal stiffening into the nodal-based FFRF for rotordynamics applications without relying on multiple floating frames or hyper-reduction techniques. Our approach introduces an additional stiffness term into the FFRF equations of motion, which we demonstrate is essential for achieving accurate rotordynamics simulations. The significant improvements achieved with our proposed approach compared to the conventional FFRF are demonstrated using two rotors with disks and one bladed rotor.