Dynamic analysis of bladed-rotor systems based on complex modal analysis theory

Abstract

This study presents a dynamic analysis approach for the modern bladed-rotary machines that are designed to be more flexible and sophisticated than ever and thus the conventional approaches might fail to ensure fair accuracy and reliability for the analysis. To this end, the general rotating blade-array model is first introduced in which the blade-group motions are described as (progressive and regressive) traveling waves with nodal diameters by using complex multi-blade coordinate representation. A generalized model for bladed-rotor systems is then developed by combining the rotating blade-array and the conventional rotor disk-shaft-bearing system models without loss of generality. Since this model is represented by a typical periodically time-varying linear system equation due to the general configuration of the rotating and stationary components, modulated coordinated transformation scheme is employed to describe the periodic system by an equivalent time-invariant, but infinite order, linear system equation. On the basis of the complex modal analysis theory, we obtain the complex modal solutions, i.e. modal frequency, modal damping, modal and adjoint vectors, of the general bladed-rotor system. As an analysis tool for the bladed-rotor system dynamics, seven representative directional frequency response matrices (dFRMs) are newly defined from the modal solutions. Each of the dFRMs separately characterize the bladed-rotor system dynamics depending upon the symmetric nature in the rotor and stator components: the four of the dFRMs describe the global system axisymmetry, anisotropy, asymmetry, and coupled asymmetry and anisotropy, similarly to the conventional dFRMs; whereas, the rest three dFRMs represent the blade-group symmetry, asymmetry, and coupled asymmetry to the system anisotropy. Lastly, the concept of infinity-norm is applied to the dFRMs, because of the difficulty in directly utilizing the dFRMs for the bladed-rotor system design and operation even t...