Model Reduction Methods for Rotor Dynamic Analysis: A Survey and Review

Abstract

The focus of this literature survey and review is model reduction methods and their application to rotor dynamic systems. Rotor dynamic systems require careful consideration in their dynamic models as they include unsymmetric stiffness, localized nonproportional damping, and frequency-dependent gyroscopic effects. The literature reviewed originates from both controls and mechanical systems analysis and has been previously applied to rotor systems. This survey discusses the previous literature reviews on model reduction, reduction methods applied to rotor systems, the current state of these reduction methods in rotor dynamics, and the ability of the literature to reduce the complexities of large order rotor dynamic systems but allow accurate solutions.

On the dynamic analysis of rotating shafts using nonlinear superelement and absolute nodal coordinate formulations

“…It is for these reasons that many authors have utilised model reduction techniques. 10,11 One of these is the substructure method, which makes it possible to reduce an FE model by projecting it onto component modes. Originally, the substructure method (or modal reduction technique) was used to analyse linear dynamics problems such as modal analysis and time integration, 12,13 while later researchers 14,15 came to use the technique in the context of multibody dynamics.…”

Optimal control of reduced-order finite element models of rotor-bearing-support systems

“…However, many rotor systems have geometry which is not adequate to be modeled by beam elements. Therefore, combined beam-shell, 2D axisymmetric, and cyclic elements have been used [1]. Eventually, 3D solid elements have been used to model rotors which are not adequate to be modeled with all the aforementioned elements.…”

“…This is conducted through so-called model reduction (sometimes also called condensation). Many model reduction techniques have been proposed [1]. For the purpose of control of rotordynamic systems, Guyan reduction [2][3][4][5][6][7][8], modal analysis (MA) [9][10][11], component mode synthesis (CMS) [12][13][14][15], balanced truncation (BT) [16][17][18], structure preserving transformations (SPT) [19], system equivalent reduction expansion process (SEREP) [20][21][22], and modified SEREP [23] have been proposed.…”

Gas-Expanded Lubricants for Increased Energy Efficiency and Control in Rotating Machinery

“…Upon processing the performance data from the TEHD bearing model, rotor models were developed for the machines being studied: an eight-stage gas reinjection compressor documented in Barrett [95] and a steam turbine-generator system documented in Wagner [96]. A schematic of the compressor rotor finite element model is shown in Figure 3.1.…”