Finite Element Analysis of Bent Rotors
Authors: Juethner Konrad , Rose Ted , Kumar J. S. , Cao Jianming , Savela Gregory M. , Zuck Chris J. , Mathuria Parag H. 
Published: September 2022

Abstract
The rotating components of a gas turbine engine are typically designed around a perfectly straight centerline. In spite of advanced manufacturing technology and the conviction of the human eye, straightness is virtually impossible to achieve during manufacturing and assembly. High-tech metrology can quantify ever so slight centerline deviations along the unconstrained rotor assembly which are called bends. Related phenomena are rotor bow and thermal bow, the latter of which is normally due to asymmetric cooling after engine shutdown. Yet, bent and bowed rotors differ from one another in that bends are permanent deviations from the centerline of the unconstrained rotor, whereas rotor bow is temporary, typically elastic, and observed in the mounted, and, therefore, constrained rotor assembly. Greater complexity is introduced with the realization that a bent rotor can additionally be subject to rotor bow. The presence of bends leads to force and moment distributions along the rotating structure that can have significant dynamic implications for even very small bends. In opposition to unbalance loads, which increase with rotor speed, the rotating excitation of a bent rotor remains constant. The equations of motion (EOM) of a bent rotor are well defined in the literature. However, the analysis is usually confined to simplified cases where said centerline deviations at the bearing supports are zero. For realistic rotor applications, this is not the case and additional static analysis is required to obtain the proper dynamic load distribution along the rotor. In this paper, the finite element method (FEM) is used to analyze bent rotors within an MSC NASTRAN v2021 work-flow that can address rotor models of any complexity. The proposed approach can also account for static, compliant, and greatly featured support structures that communicate with the rotor model via its common, and potentially misaligned, bearing supports. Angular and lateral offsets are explored in three different scenarios of two rotor configurations: scenarios 1 and 2 introduce a simply bent rotor, along which synchronous force and moment distributions are computed (due to its intrinsic deviations) to subsequently excite the bent rotor dynamically. While scenario 1 requires an initial static analysis with enforced displacements to accomplish this task, the equivalent dynamic excitation of scenario 2 can be computed directly due to perfect bearing alignment. In scenario 3, the complexity of the rotor bend is increased to four angular kinks and four lateral offsets to suggest the deployment of this method in combination with high-tech metrology equipment that can produce a large number of such measurements via automated probing or scanning technologies. In a final step, the bent rotor is augmented with unbalances and compared to its nominal counterpart to deliver the motivation for this method and its value to the turbomachinery community. All results of scenarios 1, 2, and 3 are verified against an experimentally validated transfer matrix method (TMM).