Parameterized reduced order modeling of misaligned stacked disks rotor assemblies

Abstract

Light and flexible rotating parts of modern turbine engines operating at supercritical speeds necessitate application of more accurate but rather computationally expensive 3D FE modeling techniques. Stacked disks misalignment due to manufacturing variability in the geometry of individual components constitutes a particularly important aspect to be included in the analysis because of its impact on system dynamics. A new parametric model order reduction algorithm is presented to achieve this goal at affordable computational costs. It is shown that the disks misalignment leads to significant changes in nominal system properties that manifest themselves as additional blocks coupling neighboring spatial harmonics in Fourier space. Consequently, the misalignment effects can no longer be accurately modeled as equivalent forces applied to a nominal unperturbed system. The fact that the mode shapes become heavily distorted by extra harmonic content renders the nominal modal projection based methods inaccurate and thus numerically ineffective in the context of repeated analysis of multiple misalignment realizations. The significant numerical bottleneck is removed by employing an orthogonal projection onto the subspace spanned by first few Fourier harmonic basis vectors. The projected highly sparse systems are shown to accurately approximate the specific misalignment effects, to be inexpensive to solve using direct sparse methods and easy to parameterize with a small set of measurable eccentricity and tilt angle parameters. Selected numerical examples on an industrial scale model are presented to illustrate the accuracy and efficiency of the algorithm implementation.

Numerical Study on the Critical Frequency Response of Jet Engine Rotors for Blade-Off Conditions against Bird Strike

“…For asymmetric structures, 3D finite element modeling is often employed to capture a true picture of their kinematic behavior. Despite such advancements in the computing strength, a large number of sophisticated 3D models still face complicated computational issues [13].…”

Model Reduction Methods for Rotor Dynamic Analysis: A Survey and Review

“…Other methods such as Krylov-based methods have been applied to structural systems for FEA analysis [73] but are not commonly found in the literature nor are they normally employed in rotor systems. Another small subclass of reduction not as common to rotor dynamics, Parametric Model Order Reduction as presented by Baur et al [74], Panzer et al [75], and Daniel et al [76] for nonrotor dynamic applications and by Ganine [77] for modeling of misaligned stacked disks rotor assemblies, is based on the orthogonal projection of system equations to Fourier basis vectors corresponding to lower harmonics of the system. Common reduction methods found for developing controllers for rotor dynamic systems are balanced truncation/realization [11,[78][79][80][81], Structure preserving transformations (SPT) [59], System Equivalent Reduction Expansion Process (SEREP), and modified SEREP [5].…”

The Vibration of a Transversely Cracked Rotor Supported by Anisotropic Journal Bearings with Speed-Dependent Characteristic

“…As the crack damage is hard to detect in the early stage, it has become severe threats to the operation safety of equipment and attracts the attentions of many researchers. In order to develop effective techniques for detecting the crack damages, a large number of investigations have been published to analyze the nonlinear dynamics of cracked rotors and to gain insights into the dynamic response characteristics [1][2][3].…”

“…The only at the degrees of freedom (DOFs) of the bearing nodes. Then, the governing equations of motion of the two rotating parts in the rotating frame are obtained independently, so that the DOFs of nodes on the connecting and the crack surfaces exist in both the two equations, which can be expressed as ( ) (1) where superscript "p" is a label representing different parts; In the second step, the two independent governing equations are synthesized to form that of the whole cracked shaft. The vectors ( ) p u are firstly reorganized as ( )…”