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Research Papers: Gas Turbines: Structures and Dynamics

# On Damping Entire Bladed Disks Through Dampers on Only a Few Blades

[+] Author and Article Information
Javier Avalos

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106javier.avalos@asu.edu

Marc P. Mignolet

Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106marc.mignolet@asu.edu

J. Eng. Gas Turbines Power 132(9), 092503 (Jun 07, 2010) (10 pages) doi:10.1115/1.3078792 History: Received September 11, 2008; Revised September 18, 2008; Published June 07, 2010; Online June 07, 2010

## Abstract

The focus of this paper is on demonstrating the potential to damp entire bladed disks using dampers on only a fraction of the blades. This problem is first considered without the presence of random mistuning, and it is demonstrated that a few dampers at optimized locations can lead to a significant reduction in the forced response of the entire bladed disk. Unfortunately, this optimum design may not be robust with respect to random mistuning and a notable fraction of the reduction in forced response obtained may disappear because of mistuning. To regain the reduction in forced response but with mistuning present, robustness to mistuning is enhanced by using intentional mistuning in addition to dampers. The intentional mistuning strategy selected here is the $A/B$ pattern mistuning in which the blades all belong to either type $A$ or $B$. An optimization effort is then performed to obtain the best combination of $A/B$ pattern and damper location to minimize the mistuned forced response of the disk. The addition of intentional mistuning in the system is shown to be very efficient, and the optimum bladed disk design does indeed exhibit a significant reduction in mistuned forced response as compared with the tuned system. These findings were obtained on both single-degree-of-freedom per blade-disk models and a reduced order model of a blisk.

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## Figures

Figure 3

Amplification factor of the maximum blade response in sweep as a function of the number of optimized dampers for different values of kC. P1 problem, r=4, and C/c=10.

Figure 4

(a) Amplification factor of the maximum blade response in sweep as a function of the damper constants, C/c, for different values of kC, and for one, two, and three dampers of optimized locations. P1 problem, r=4. (b) Same, zoomed.

Figure 5

95th percentile of the maximum blade response on the disk in sweep versus standard deviation of random mistuning. Tuned disk and optimal solution of P1 problem, three dampers, kC=10,000 N/m, and r=4.

Figure 6

95th percentile of the maximum blade response on the disk in sweep versus standard deviation of random mistuning. Single-degree-of-freedom model, kC=10,000 N/m, C/c=10, and optimization carried out at 1%. (a) r=4, intentional mistuning level=5%; (b) r=2, intentional mistuning level=5% (solid lines) and 3% (dash lines); (c) r=0–6, intentional mistuning level=5%; and (d) r=0–6, intentional mistuning level=3%.

Figure 1

Figure 2

Blisk example: (a) blisk view, (b) blade sector finite element mesh, and (c) natural frequencies and coupling indices versus nodal diameter plot

Figure 7

95th percentile of the maximum blade response on the disk in sweep versus standard deviation of random mistuning. Single-degree-of-freedom model, kC=5000 N/m, r=4, C/c=10, optimization carried out at 1%, and intentional mistuning level=5%.

Figure 8

95th percentile of the maximum blade response on the disk in sweep versus standard deviation of random mistuning. Single-degree-of-freedom model, kC=10,000 N/m, C/c=10, and optimization carried out at 1%. min-max optimization, worst case engine order at standard deviation of 1% (a) r=1 and 2, intentional mistuning level=5% and (b) r=3 and 4, intentional mistuning level=5%.

Figure 9

95th percentile of the maximum blade response on the disk in sweep versus standard deviation of random mistuning. Blisk model. C/c=10, optimization carried out at 1%, and intentional mistuning level=5%. (a) r=1 and (b) r=2. These figures also include the cases in Table 1.

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