Semi-Analytical Model for High-Speed Rotor Whirl Prediction: An Assumed Modes Formulation for an Axisymmetric Rotor With Non-Uniform Properties

Abstract

Most fully analytical treatments of rotor whirl are restricted to very simple rotor geometries, and have limited use while studying real-world rotors. Analysis of more complex rotors is routinely carried out in Finite Element software such as Ansys, but this is less effective at generating fundamental insights to inform the design process. This paper is motivated by the ongoing development of a Supercritical-CO2 turbine rotor, and illustrates a rotor model of intermediate complexity. Such a model, given the relative novelty of the turbine design task stemming from the very high rotational speeds required, will improve confidence in rotordynamic simulations and is expected to help with any future troubleshooting. The approach used is to consider the rotor’s rigidity and inertia to vary along its length as functions of spatial coordinate x, and obtain predictions of whirl speeds through a Lagrangian formulation with assumed modes. This method can accommodate axisymmetric rotors with variation in cross-section or material properties, or both. It is first demonstrated on a simple and analytically tractable rotor geometry. Then, it is applied to a simplified version of the turbine rotor, whose properties’ x-dependence is approximated by curves fit to a small number of datapoints obtained from simpler (non-rotordynamic) simulations.