Model reduction and dynamic matrices extraction from state-space representation applied to rotating machines

Abstract

Model reduction is a relevant subject within the field of rotordynamics since low order models are fundamental for control strategies design and implementation, health monitoring, behavior prediction, Fault Detection and Identification (FDI) and stochastic analyses. In this context, this article proposes a complete review of three widely used reduction methods: static or Guyan technique, the System Equivalent Reduction Expansion Process (SEREP) and the modified SEREP. Regarding SEREP, a new approach is presented in which right and left eigenvectors from the undamped original system (with mass and stiffness matrices not symmetric) are used to transform all original system dynamic matrices. To modified SEREP (that contemplates all original system characteristics, including frequency dependent damping and gyroscopic effect) an extraction from the reduced state-space representation is achieved to build rotor and bearings reduced dynamic matrices with physical interpretability. A set of practical recommendations is presented, highlighting key aspects to increase reduction success chances. The methods are applied to two different rotors and results show satisfactory agreement between reduced and complete model responses when analyzing Frequency Response Functions (FRFs) and Campbell diagrams. The computational costs of processing each reduced model and running common rotordynamic analyses with reduced and complete models are compared.