Turbine bladed disks or blisks, which constitute critical components of most modern turbomachinery, are known for their complex vibratory behavior. The nonlinear dynamics observed in most operational regimes of blisk with contact interfaces are dominated by one of two typical contact behaviors. Frictional contacts are dominated by Coulomb friction forces, while intermittent contacts are characterized by multiple separation events. Other factors such as the dispersion in material or geometric properties across blades, known as mistuning, also affect the dynamics significantly. Presently, probabilistic analysis is the widely accepted design methodology to account for mistuning, which is unknown prior to manufacture. Thus, reduced order modeling of these blisks is essential as high fidelity models are prohibitively expensive for such simulations. This paper provides a technical discussion of dynamic modeling and reviews projection-based techniques used for creation of reduced models of blisks with contacts.

Reduced order models (ROMs) of turbine bladed disks (blisks) are essential to quickly yet accurately characterize vibration characteristics and effectively design for high cycle fatigue. Modeling blisks with contacting shrouds at adjacent blades is especially challenging due to friction damping and localized nonlinearities at the contact interfaces which can lead to complex stick–slip behavior. While well-known techniques such as the harmonic balance method (HBM) and Craig–Bampton component mode synthesis (CB-CMS) have generally been employed to generate ROMs in the past, they do not reduce degrees-of-freedom (DoFs) at the interfaces themselves. In this paper, we propose a novel method to obtain a set of reduction basis functions for the contact interface DoFs as well as the remaining DoFs called “adaptive microslip projection” (AMP). The method is based on analyzing a set of linear systems with specifically chosen boundary conditions on the contact interface. Simulated responses of full order baseline models and the novel ROMs under various conditions are studied. Results obtained from the ROMs compare very favorably with the baseline model. This study addresses the case of a shrouded blisk in microslip close to stick. The AMP procedure may be possibly applied to other systems with Coulomb friction contacts, but its accuracy and effectiveness will need to be evaluated separately.

In this study, a novel design for ring dampers is proposed, where the concept of tuned vibration absorbers is leveraged to substantially increase damper effectiveness while minimizing potential stresses near the blade root. Tuned absorbers have been used in the past to reduce the forced response amplitudes of both mechanical and civil structures. The absorber natural frequency is tuned to the targeted frequency of the host structure where it is attached. The vibration reduction mechanism relies on energy transfer from the host structure to the absorber. The novel design technique proposed here uses a vibration absorber approach to achieve energy transfer from the blisk to the damper, which leads to larger damper motion. This enables energy dissipation due to friction, reducing vibrations even in blade-dominated modes. An academic finite element model of a blisk with a ring damper is used to demonstrate the novel tuned damper concept and design technique. The geometric mistuning of the damper due to the presence of a gap in the ring structure is also taken into account. The results demonstrate the validity of the proposed tuned damper concept, showing a substantial vibration amplitude reduction compared to the linear baseline results, in which the damper is not tuned or absent.

Mistuning commonly refers to non-cyclically symmetric variations in such an otherwise cyclically-symmetric structure. Mistuning in a blisk due to variations in blade materials and geometry have been studied extensively and are known to have a significant impact on the forced response of blisks. However, mistuning can also arise due to variations at contact interfaces within a blisk with friction damping mechanisms such as under platform dampers or shrouds. Past literature analyzing the effect of this source of contact mistuning is limited, particularly by the use of lumped or single-node contacts at each sector to shorten analysis times. In this paper, we aim to better understand the specific effects of parameter variations across contact interfaces on an otherwise tuned blisk. A blisk with shroud to shroud contacts is considered. Accurate representation of microslip phenomena are incorporated in the analysis by modeling multiple localized node to node contact models at contact surfaces on each blisk sector. Contact stiffnesses which dictate the friction damping dynamics of the shrouds are chosen as the mistuning parameters. The harmonic balance method is used to solve for forced responses. We analyze cases with random patterns of contact stiffnesses in different microslip regimes in the proximity of different modal regions. Probabilistic analysis of nonlinear contact responses are carried out close to a linear region where comparatively high amplification factors are observed. Statistics are also developed for linear cases and compared with the nonlinear case to qualify the dependence of amplification factors of nonlinear forced responses on the level of microslip and on the variance of contact parameters.