Solid Element Rotordynamic Modeling of a Rotor on a Flexible Support Structure Utilizing Multiple-Input and Multiple-Output Support Transfer Functions

Abstract

The authors present an improved modeling approach to analyze the coupled rotor-support dynamics by modeling the rotor with solid finite elements (FEs) and utilizing multiple-input and multiple-output transfer functions (TFs) to represent the flexible support. A state-space model is then employed to perform general rotordynamic analyses. Transfer functions are used to simulate dynamic characteristics of the support structure, including cross-coupling between degrees-of-freedom. These TFs are derived by curve-fitting the frequency response functions of the support model at bearing locations. The impact of the polynomial degree of the TF on the response analysis is discussed, and a general rule is proposed to select an adequate polynomial degree. To validate the proposed approach, a comprehensive comparison between the complete solid FE rotor-support model (CSRSM) and the reduced state-space model (RSSM) is presented. Comparisons are made between natural frequencies, critical speeds, unbalance response, logarithmic decrement, and computation time. The results show that the RSSM provides a dynamically accurate approximation of the solid FE model in terms of rotordynamic analyses. Moreover, the computation time for the RSSM is reduced to less than 20% of the time required for the CSRSM. In addition, the modes up to 100,000 cpm are compared among the super-element, beam element, and RSSM. The results show that the RSSM is more accurate in predicting high-frequency modes than the other two approaches. Further, the proposed RSSM is useful for applications in vibration control and active magnetic bearing systems.