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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 very well defined in the literature by Refs [1, 2]. 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 an 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 hightech 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).

During the design phase of a rotor system, the identification of whirl type carries much significance. Forward whirl (FW) critical speeds reveal themselves by harmonic peaks during spin-up. Backward whirl (BW) modes are dynamically quiet, but produce cyclic stresses and therefore contribute to material fatigue. The realization, that FW and BW can occur simultaneously in so-called mixed whirl (MW) modes, demands greater investigative scrutiny from the design team. While pure FW or BW modes can be identified by one pair of proximity probes at any single rotor location, many measurements along the rotor axis are needed to either rule out or confirm MW. Since there are practical and economic limits to the number of measurement locations and experiments, the purpose of this paper is to deliver guiding analytic insight. The proposed approach is to overcome experimental limitations by using a finite element (FE) model of the rotor system, compute its nodal whirl distributions from each of its complex-valued eigenvectors, and map the resulting whirl quantities back onto all FE grids. This delivers insightful surface and volume diagnostics to augment experimental rotor validation. Exercising this technique on simplified example models reveals unexpected insight in that FW and BW modes influence one another and become mixed across a greater rotor speed range than anticipated. Therefore, MW turns from an elusive phenomenon into a common occurrence throughout the Campbell diagram, to a point where it becomes increasingly challenging to discern pure FW and BW mode shapes — particularly, at higher modal frequencies. The most surprising and truly unexpected conclusion of this work is that all of the FW/BW pairs considered here do not intersect but veer upon closer investigation. And, as FW transforms into BW and vice versa during the veering transition in the Campbell diagram, their stability maps and root loci accentuate this shift by indicating that stability is traded between them. A mode’s ability to transition from one whirl type to another is significant from the practical design and simulation perspectives, in that engineering responsibility is shared between accurate predictions and appropriate design. As shown in this work, both numerical and eigenvector-based tracking algorithms favor intersection over veering at low rotor speed resolution and can produce believable but incorrect answers.

The exploration of new aero-engine configurations drives unseen and complex dynamic behavior which can only be captured accurately with enhanced modeling techniques. In an earlier publication, it was established that it is possible to analyze large engine models using high-fidelity two-dimensional (2D) axisymmetric harmonic and three-dimensional (3D) shell and solid elements. This finding stands in contrast to the relatively crude one-dimensional (1D) model simplifications that were introduced several decades ago. While motivated by limited computing power and easily obtained gyroscopic terms, these models are still common in the industry today. In spite of staggering advances in computation, however, said enhanced finite element rotor models are still considered to be quite large. When transitioning from the traditional 1D to the fully 3D rotor model, for example, one encounters an increase in model size of three orders of magnitude. This motivates the use of model reduction techniques such as the External Superelement (SE) which is obtained by component mode synthesis (CMS). The External SE represents a structural component by its physical attachment points, strategically selected interior grid points, and a linear combination of its dynamic modes. Its advantages are reduced computational cost, the ability to solve very large problems, the protection of intellectual property, and the enablement of a modular model description that promotes parallel processing as well as the utilization of high performance computing (HPC). In this paper, the analysis of a realistic aircraft engine is presented in which its rotating structures are modeled with high-fidelity 3D solid/shell elements. The dynamics of the engine assembly are solved using modal analysis and External SE technology with the goals to reduce wall time and improve efficiency. A detailed comparison of wall time is presented to quantify the associated performance gain.