Order-Tuned Vibration Absorbers for Cyclic Rotating Flexible Structures

Abstract

This paper investigates the use of order-tuned absorbers to attenuate vibrations of flexible blades in a bladed disk assembly subjected to engine order excitation. The blades are modeled by a cyclic chain of N oscillators, and a single vibration absorber is fitted to each blade. These absorbers exploit the centrifugal field arising from rotation so that they are tuned to a given order of rotation, rather than to a fixed frequency. A standard change of coordinates based on the cyclic symmetry of the system essentially decouples the governing equations of motion, yielding a closed form solution for the steady-state response of the overall system. These results show that optimal reduction of blade vibrations is achieved by tuning the absorbers to the excitation order n, but that the resulting system is highly sensitive to small perturbations. Intentional detuning (meaning that the absorbers are slightly over- or under-tuned relative to n) can be implemented to improve the robustness of the design. It is shown that by slightly undertuning the absorbers there are no system resonances near the excitation order of interest and that the resulting system is robust to mistuning (i.e., small random uncertainties in the system parameters) of the absorbers and/or blades. These results offer a basic understanding of the dynamics of a bladed disk assembly fitted with order-tuned vibration absorbers, and serve as a first step to the investigation of more realistic models, where, for example, imperfections and nonlinear effects are considered, and multi-DOF and general-path absorbers are employed.

Modal properties and stability of centrifugal pendulum vibration absorber systems with equally spaced, identical absorbers

“…(42). These vectors resemble the eigenvectors of circulant system matrices derived for cyclic systems [23]. They provide an orthogonal basis of the null space of A and are a complete set of solutions of Eq.…”

Vibration absorbers for a rotating flexible structure with cyclic symmetry: nonlinear path design

“…where the phase difference among adjacent sectors is built into the transformation defined by (20) via the interblade phase angles φ i . Since g(v, v, v) = 0 (resp.…”

“…2.3 of [2] in the context of engine order excitation.) Depending on the value of n relative to N , (20) can capture backward TW (BTW), forward TW (FTW), and standing wave (SW) responses [2]. It is noted from the onset, however, that there could be a multitude of other response types and that the averaged models to be developed based on (20) are general enough to capture them.…”

“…Depending on the value of n relative to N , (20) can capture backward TW (BTW), forward TW (FTW), and standing wave (SW) responses [2]. It is noted from the onset, however, that there could be a multitude of other response types and that the averaged models to be developed based on (20) are general enough to capture them. However, the desired and most basic response is that of a traveling wave, the existence, stability and bifurcation of which forms the main focus of this work.…”

“…These absorbers, which essentially consist of masses that move along prescribed paths relative to the structure [6], have the advantage that they remain tuned over all rotation speeds. Order-tuned absorbers have been widely studied and employed for reducing torsional vibrations in rotating systems [7][8][9][10][11][12][13][14][15][16][17], and more recently they have been proposed for reducing flexural vibrations in rotating systems [2,5,6,[18][19][20][21]. Recent studies have also included impacting dynamics of single flexible elements with absorbers, which will occur if loading becomes large [6,19].…”