Efficient predictions of the vibratory response of mistuned bladed disks by reduced order modeling.

Nominally, a bladed disk assembly (single stage of a turbomachinery rotor) is a rotationally periodic structure. The dynamics of the bladed disk may then be analyzed based on one fundamental diskblade sector. In practice, however, there are inevitably small differences among the structural properties of individual blades that destroy cyclicity and thus require full assembly modeling. These structural irregularities, commonly referred to as mistuning, may stem from manufacturing tolerances, material imperfections, or operational wear. Mistuning is known to have a potentially dramatic effect on the vibratory behavior of the rotor, since it can lead to spatial localization of the vibration energy. As a result, certain blades may experience forced response amplitudes and stresses that are substantially larger than those predicted by an analysis of the nominal design. To address this problem, this dissertation focuses on the development of reduced order modeling techniques that can predict efficiently and accurately the effects of mistuning on the vibratory response of turbomachinery rotors. This dissertation first reviews an existing technique representing the state-of-the-art at the outset of this research effort. An extension of this technique to rotors with shrouded blades is presented, with emphasis on a novel approach to shrouded blade mistuning. Next, the standard Craig-Bampton component mode synthesis (CMS) method is re-formulated specifically for mistuned bladed disks with a cyclic disk component. A non-CMS modal analysis approach is also considered, in which individual blade mistuning is projected onto a truncated set of cyclic system modes. The two latter methods are merged into a secondary modal analysis reduction technique (SMART). In this method, a secondary modal analysis is performed on a primary CMS model, and only the system modes of interest are retained. Blade mistuning is introduced in the primary CMS modal coordinates and then projected onto the secondary modal coordinates. Furthermore, important effects of stage-to-stage structural coupling are investigated, leading to a SMART formulation for mistuned multi-stage rotors. Finally, recent findings concerning the numerical stability and modal convergence of CMS-based techniques are presented, leading to the formulation of a hybrid CMS method with promising characteristics. The developed techniques enable comprehensive dynamic analyses of randomly mistuned bladed disks. Furthermore, they allow reliable statistical assessments of mistuning sensitivity to be included as an integral part of the turbomachinery rotor design process.Ph.D.Applied SciencesMechanical engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128733/2/3000922.pd