Solid Element Rotordynamic Modeling of a Rotor on a Flexible Support Structure Utilizing MIMO Support Transfer Functions

The accurate modeling of a rotor system is essential for effective design and troubleshooting in rotating machinery. The beam-type finite element (FE) may be inadequate for modeling a rotor or support structure with complex shapes. In addition, the isolated support impedance methods may be inaccurate for modeling the support structure that has modes that are highly coupled between bearings and directions at the bearing locations. The solid FE method is a good replacement of the beam FE and support impedance approaches. However, a drawback for this method is the significant amount of computation time required to obtain accurate solutions due to the large number of nodes in the solid FE analysis. The authors present an improved approach to analyze the coupled rotor-support dynamics, by modeling the rotor with solid elements and utilizing transfer functions (TFs) to represent the flexible support. A state-space model is then employed to perform general rotordynamic analyses. The solid FE rotor model includes the gyroscopic effects and the asymmetric and cross-coupled stiffness coefficients of the bearing. A series of rational TFs are used to simulate dynamic characteristics of the support structure, including the cross-coupling between degrees of freedom (DOFs). These TFs are derived by curve-fitting the frequency response functions (FRFs) of the solid FE support model at the bearing locations. The impact of the polynomial degree of the TF on the unbalance response analysis is discussed, and a general rule is proposed to select an adequate polynomial degree. To validate the proposed modeling approach, a comprehensive comparison among the complete solid FE rotor-support model and the solid FE rotor model with the TFs representing the flexible support (the reduced state-space model) are presented. Comparisons are made between natural frequencies, critical speeds, unbalance response, logarithmic decrement (log dec), and computation time. The results of these comparisons show that the reduced state-space rotor-support model provides a dynamically accurate approximation of the solid FE rotor-support model in terms of general rotordynamic analyses. Moreover, the computation time for the proposed modeling approach is reduced to 2.5 minutes, compared to 14 minutes for the complete solid FE modeling. The reduction of the computation time may vary with different number of DOFs of the rotor model and the support structure model. In addition, the modes up to 100,000 cpm are compared among the beam rotor with the solid FE support model, the solid FE rotor with the super-element support model, and the reduced state-space model. The results show that the reduced state-space model is more accurate in predicting high-frequency modes than the beam rotor-support and super-element support models. Further, the proposed approach with the state-space model is useful for applications in vibration control and active magnetic bearing (AMB) systems.