Rotor Dynamic Modeling of Hydropower Rotors by 3D-Finite Element Analysis

Sammanfattning: By using the rotor dynamic capabilities of Simcenter Nastran Rotordynamics, an eigenvalue analysis of 3D-finite element models of the Jeffcott rotor and the overhung rotor were conducted and compared to the results with beam-based, lumped parameter models. The first two critical speeds of the Jeffcott rotor were estimated with variations of 3.9 and 6.4%. The first three critical speeds of the overhung rotor were estimated with 8.5, 6.7 and 6.5% variations, respectively. The Jeffcott rotor was also analysed with different element configurations: Solid elements, axisymmetric Fourier elements, beam/solids and all beam elements. The Fourier elements were the most appropriate option for axisymmetric rotors regarding computational time and accuracy. Tilting pad journal bearings were simulated and validated against data from Vattenfall's facilities in Älvkarleby, where a vertical rotor is connected to two four-pad tilting pad journal bearings. The bearing formulation was defined in a Fortran based subroutine, which acquires the rotor's speed and position to supply a bearing load vector in Simcenter Nastran's transient solver. The experimental rig was also modelled to include the rotor/stator interaction. The force and displacement orbits at the bearings were replicated adequately concerning experimental data, where a maximum deviation of 20.8% and 9.8% were observed for the forces in x and y-directions.  A 3D-finite element model and a beam based finite element model were compared for an actual hydropower unit, which aimed to investigate the mode extraction procedure and how high mass, elastic rotor components influence the system's dynamics. Consistent rotor modes were identified at frequencies within 15% deviation, where the maximum deviation occurred in the upper range frequency pairs. Convergence between the models was observed for the static, lower range frequencies when considering a rigid generator rotor in the 3D finite element model. The outcome is consistent with the model assumptions and underlines that the beam based model cannot capture specific contributions from elastic rotor components. 3D-finite element analysis is a viable option when considering non-axisymmetric and complex rotors. High mass, non-rigid components must be analysed  in this manner as their dynamic contributions may not be captured with other approaches. Intricate and non-rigid supporting structures are also suitable for 3D modelling to properly reflect the stator-rotor interaction. It is a delicate matter to pinpoint when these conditions occur, and modelling decisions must be therefore be substantiated by simulations and experimental validation.