Reduced Order Models for Blade-To-Blade Damping Variability in Mistuned Blisks

Abstract

A novel reduced order modeling methodology to capture blade-to-blade variability in damping in blisks is presented. This new approach generalizes the concept of component mode mistuning (CMM), which was developed to capture stiffness and mass mistuning (and did not include variability in damping among the blades). This work focuses on modeling large variability in damping. Such variability is significant in many applications and particularly important for modeling damping coatings. Similar to the CMM based studies, structural damping is used to capture the damping effects due to the mechanical energy dissipation caused by internal friction within the blade material. The steady state harmonic responses of the blades are obtained using the novel reduced order modeling methodology and are validated by comparison with simulation results obtained using a full order model in ANSYS with a maximum amplitude error of 0.3%. It is observed that there is no strong correlation between the engine order of excitation and both the variation in the response from blade to blade and the blade amplification factors. The effects of damping mistuning are studied statistically through Monte Carlo simulations. For this purpose, the blisk model is subjected to multiple traveling wave excitations. The uncertainty in the various mechanisms responsible for dissipation of energy and the uncontrollability of these dissipation mechanisms makes it difficult to assign a reliable value for the loss factor of each blade. Hence, large variations (up to ±80%) in the structural damping coefficients of the blades are simulated.

Numerical Investigation of a Mistuned Academic Bladed Disk Dynamics With Blade/Casing Contact

“…4, provide insight on the sensitivity of A lin with respect to n d . A lin is maximal for n d = 6 and minimal for n d = 3, and does not vary monotonously with n d which is consistent with the literature [32]. The general shape of A lin with regards to n d is in good agreement with previous findings for the 12-blade model used in [33].…”

“…The linear amplification A lin variation with respect to n d is explained mostly in two ways in the literature: (1) the forcing frequency may correspond to a veering region [32,38] or, (2) the forcing frequency may excite closely spaced blade dominated modes, identified on the tuned system [33]. As underlined in the SAFE diagram, see Fig.…”

Numerical Investigation of an Academic Mistuned Bladed Disk Dynamics Accounting for Blade/Casing Contacts

“…The linear amplification A lin variation with respect to n d is explained mostly in two ways in the literature: (1) the forcing frequency may correspond to a veering region [22] or, (2) the forcing frequency may excite closely spaced blade dominated modes, identified on the tuned system [18]. As underlined in the SAFE diagram, see Fig.…”

Dynamic Modeling and Projection-Based Reduction Methods for Bladed Disks With Nonlinear Frictional and Intermittent Contact Interfaces

“…One of the more general techniques developed for mistuned blisk reduction based on CB-CMS is known as CMM [25][26][27]. CMM employs a substructuring approach where the change in the tuned system due to mistuning is treated as an additional component to the tuned system.…”

“…The effects of mistuning were studied widely, and a number of different ROMs were proposed for linear mistuned blisks. These include modifications of general linear reduction methods such as Craig-Bampton component mode synthesis (CB-CMS) [17][18][19][20][21][22], as well as more specialized techniques developed especially for blisks such as subset of normal modes (SNM) [23], fundamental model of mistuning (FMM) [24], component mode mistuning (CMM) [25][26][27], and asymptotic model of mistuning [28][29][30]. Alternatives for linear systems with parametric variations include parametric reduced order models [31,32].…”