Rotordynamic Analysis of a Rotor-Disk System Including a Synchronously Reduced Modal Truncation Method

Abstract

There are many published works on rotordynamics which detail the types of analyses that are carried out: critical speeds, stability assessment, and forced response. The purpose of this paper is to present a more complete analysis of an existing, academic rotor/bearing model, taken from a textbook, more like it would be carried out in an industrial setting. The advantage is that all parameters of the rotor model are well known so that there are minimal uncertainties. However, some published papers on rotordynamics, as discussed in this work, present an incomplete analysis. For example, they may report the calculated critical speeds but leave out the critical speed plot and mode shapes in favor of the Campbell diagram. They may model a Bernoulli Euler beam model of the shaft and neglect the additional terms in the Timoshenko beam model. These papers may show some unbalance response plots for one disk in the model but not report on the amplification factor. This paper gives a much more complete rotordynamics analysis of this common rotor/bearing model than other works. The full undamped rotor analysis is presented, including critical speeds, critical speed map, and undamped mode shapes. The stability analysis presents the full set of eigenvalues including both forward and backward modes as well as the complex mode shapes. The differences between the Bernoulli Euler beam model and the full Timoshenko beam model are shown for this rotor. Full unbalance response plots, in the horizontal and vertical directions, are presented as well as the response along the semi-major axis. The unbalance response plots have calculated amplitudes, phase angles and amplification factors. In addition to the standard rotordynamic analyses, a synchronously reduced modal truncation method is presented. This method is better suited to automation, when compared to most truncation methods that require significant intervention by the analyst. The maximum error was on the order of 0.01%. It is hoped that future publications will present the more complete analysis shown for this rotor/bearing system.