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Research Papers

On Nonlinear Forced Vibration of Shrouded Turbine Blades

[+] Author and Article Information
J. Szwedowicz

Thermal Machinery Laboratory, ABB Turbo Systems Ltd., Bruggerstreet 71a, CH-5401 Baden, Switzerlandszwedowicz@ch.abb.com

R. Visser

Faculty of Mechanical Engineering, University of Twente, 7500 AE Enschede, The Netherlands

W. Sextro

Institute of Mechanics, Graz University of Technology, Kopernikusgasse 24/III, A-8010 Graz, Austria

P. A. Masserey

TSDMH Department, ALSTOM (Switzerland) Ltd., Brown Boveri Street 7, CH-5401 Baden, Switzerland

FVV—Forschungsvereinigung Verbrennungskraftmaschinen (Research Association of Combustion Machines) TURBO-04-1037, Szwedowicz et al. (22).

The Abbott-Firestone curve (30) determines the rough surface as a function of the height distribution, which can be linearized by the five-parameter model (31).

J. Turbomach 130(1), 011002 (Dec 14, 2007) (9 pages) doi:10.1115/1.2218889 History: Received February 27, 2004; Revised March 09, 2006; Published December 14, 2007

Numerical predictions of the forced vibration of a disk assembly including frictional effects between the shrouds are presented concerning engineering needs for the blade design process. Assuming a tuned disk assembly, numerical static, free, and then forced vibration analyses of a shrouded turbine blade measured in the spin pit are performed systematically. For the excitation forces of an air jet evaluated from the fairly linear behavior of the experimental blade resonance peaks, the reliability of the proposed approach is validated through the very close agreement of the computed and measured resonant peaks. These resonant peaks demonstrate either a fairly linear behavior or a nonlinear one like the jump effect of blade resonance amplitudes, or elastic impacts between the shrouds. Also, the damping performance for different contact configurations between the shrouds is numerically analyzed. These numerical results indicate that the shrouds generate higher frictional damping for small angles (030deg) between the circumferential direction and the normal vector to the contact surface.

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References

Figures

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Figure 1

FE model of the analyzed shrouded turbine blade with the imposed two cyclic constraints, which are separated from the frictional contact kinematic restraints

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Figure 2

Numerical and experimental (only the first mode) eigenfrequencies of the shrouded blade for the contact area obtained from the nonlinear static calculations for the sticking (μ=∞) and slipping (μ=0.4) contact conditions between the shrouds

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Figure 3

Geometry of the nominal contact interface in the simulation (19) with the equivalent contact stiffness (kt,kn) between points OR and OL (Fig. 6) and a contact grid η×ζ (a dashed mesh)

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Figure 4

Results of the transient SDOF responses for damping ratios of (a) ξ=0.02%; (b) ξ=0.1%; (c) ξ=0.2%

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Figure 5

The Campbell diagram of the shrouded blade (Fig. 6) measured in the spin pit using air jet excitation and zoom of single resonance response curve used for the damping evaluation

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Figure 6

Equivalent excitation force F=(Fx2+Fy2)1∕2 simulating the air jet excitation in the spin pit measurement

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Figure 7

Dispersion curves calculated for nonlinear (contour plot) and linear contact behavior (circular symbols) which are related to the measured resonance frequencies (crosses)

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Figure 8

The measured and computed resonance response curves demonstrating fairly linear behavior of the shrouded turbine blade at a rotational speed of 491∕s

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Figure 9

The measured and computed resonance response curves of the shrouded turbine blade at a rotational speed of 57.11∕s showing the nonlinear jump effect of the blade amplitude

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Figure 10

The numerical and experimental resonance response curves with chattering effects (elastic impacts) between the shrouds at a rotational speed of 491∕s

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Figure 11

Analyzed shroud configurations for finding the best damping performance: (a) the slant contact configuration; (b) the zig-zag contact configuration; (c) the FE model of the shrouded blade

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Figure 12

For a rotational speed of 501∕s resulting static normal contact forces and effective contact area of both shrouded blades with a stagger angle of 0deg

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Figure 13

For a rotational speed of 501∕s nodal diameter diagrams of 60 blades with a stagger angle of 0deg coupled by (a) slant shroud and (b) zigzag shroud

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Figure 14

For an excitation force of 10N effective damping ratio concerning a friction coefficient of 0.4 and a contact roughness of 0.8μm

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