Modeling underplatform dampers for turbine blades: a refined approach in the frequency domain

Abstract

Friction damping is one of the most exploited systems of passive control of the vibration of mechanical systems. In order to mitigate vibration of turbine blades, friction dampers are commonly included in the bladed disk design. A common type of blade-to-blade friction dampers are the so-called underplatform dampers (UPDs); these are metal devices placed under the blade platforms and held in contact with them by the centrifugal force acting during rotation. The effectiveness of UPDs to dissipate energy by friction and reduce vibration amplitude depends mostly on the damper geometry and material and on the static loads pressing the damper against the blade platforms. The common procedure used to estimate the static loads acting on UPDs consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to compute the static pressure distribution over the damper/blade interfaces, assuming that it does not change when vibration occurs. In this paper a coupled approach is proposed. The static and the dynamic displacements of blade and UPD are coupled together during the forced response calculation. Both the primary structure (the bladed disk) and the secondary structure (the damper) are modeled by finite elements and linked together by contact elements, allowing for stick, slip and lift off states, placed between each pair of contact nodes, by using a refined version of the state-of-the-art friction contact model. In order to model accurately the blade/damper contact with a large number of contact nodes without increasing proportionally the size of the set of nonlinear equations to be solved, damper and blade dynamics are modeled by linear superposition of a truncated series of normal modes. The proposed method is applied to a bladed disk under cyclic symmetric boundary conditions in order to show the capabilities of the method compared to the classical decoupled approaches.

Keywords

Bladed disks friction damping harmonic balance method nonlinear dynamics passive control

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References

Allara

(2009) A model for the characterization of friction contacts in turbine blades. Journal of Sound and Vibration. 320(3): 527–544.

Cardona

Lerusse

Geradin

(1998) Fast Fourier nonlinear vibration analysis. Computational Mechanics. 22: 128–142.

Chan

TFC

Keller

(1982) Arc-length continuation and multi-grid techniques for nonlinear elliptic eigenvalue problems. SIAM Journal on Scientific and Statistical Computing. 3(2): 173–194.

Cigeroglu

Menq

(2007) A microslip friction model with normal load variation induced by normal motion. Nonlinear Dynamics. 50(3): 609–626.

Cigeroglu E, An N and Menq CH (2009) Forced response prediction of constrained and unconstrained structures coupled through frictional contacts. Journal of Engineering for Gas Turbines and Power 131(2): 022505 (11 pages).

Filippi

Akay

Gola

(2004) Measurement of tangential contact hysteresis during microslip. Journal of Tribology. 126: 482–489.

Firrone CM, Botto D and Gola MM (2006) Modelling a friction damper: analysis of the experimental data and comparison with numerical results. In Proceedings of 8th Biennial Conference on Engineering Systems, Design and Analysis (ESDA), Torino, Italy, July 4–7. ESDA2006–95605.

Firrone CM, Zucca S and Gola MM (2009) Effect of static/dynamic coupling on the forced response of turbine bladed disks with underplatform dampers. In Proceedings of the ASME Turbo Expo 2009: Power for Land, Sea and Air, Orlando, FL, July 8–12. GT2009–59905.

Griffin

(1980) Friction damping of resonant stresses in gas turbine engine airfoils. Journal of Engineering for Power. 102: 329–333.

10.

Griffin JH and Menq CH (1991) Friction damping of circular motion and its implications to vibration control. Journal of Vibration and Acoustics 113(2): 225 (5 pages).

11.

Menq

Yang

(1998) Non-linear spring resistance and friction damping of frictional constraint having two-dimensional motion. Journal of Sound and Vibration. 217(1): 127–143.

12.

Panning

Sextro

Popp

(2003) Spatial dynamics of tuned and mistuned bladed disks with cylindrical and wedge-shaped friction dampers. International Journal of Rotating Machinery. 9(3): 219–228.

13.

Panning L, Popp K, Sextro W, Goetting F, Kayser A and Wolter I (2004) Asymmetrical underplatform dampers in gas turbine bladings: theory and application. In Proceedings of ASME Turbo Expo 2004, Vienna, Austria, 14–17 June 2004, GT2004–53316.

14.

Petrov

(2004) A method for use of cyclic symmetry properties in analysis of nonlinear multiharmonic vibrations of bladed disks. Journal of Turbomachinery. 126(1): 175–183.

15.

Petrov EP (2007) Explicit finite element models of friction dampers in forced response analysis of bladed discs. In Proceedings of ASME Turbo Expo 2007, Montreal, Canada, May 14–17. GT2007–27980.

16.

Petrov

Ewins

(2003) Analytical formulation of friction interface elements for analysis of nonlinear multiharmonic vibrations of bladed discs. Journal of Turbomachinery. 125: 364–371.

17.

Petrov

Ewins

(2007) Advanced modeling of underplatform friction dampers for analysis of bladed disk vibration. Journal of Turbomachinery. 129(1): 143–150.

18.

Sanliturk

Ewins

(1996) Modelling two-dimensional friction contact and its application using harmonic balance method. Journal of Sound and Vibration. 193(2): 511–523.

19.

Sanliturk

Ewins

Stanbridge

(2001) Underplatform dampers for turbine blades: theoretical modelling, analysis and comparison with experimental data. Journal of Engineering for Gas Turbines and Power. 123(4): 919–929.

20.

Siewert C, Panning L, Wallaschek J and Richter C (2009) Multiharmonic forced response analysis of a turbine blading coupled by nonlinear contact forces. In Proceedings of ASME Turbo Expo 2009: Power for Land, Sea and Air, Orlando, FL, June 8–12. GT2009–59201.

21.

Sinclair

Cormier

(2002) Contact stresses in dovetail attachments: physical modelling. Journal of Engineering for Gas Turbines and Power. 124: 325–331.

22.

Szwedowicz J, Gibert C, Sommer TP and Kellerer R (2008) Numerical and experimental damping assessment of a thin-walled friction damper in the rotating setup with high pressure turbine blades. Journal of Engineering for Gas Turbines and Power 130(1): 012502 (10 pages).

23.

Yang

Menq

(1998a) Characterization of contact kinematics and application to the design of wedge dampers in turbomachinery blading: part 1 - stick-slip contact kinematics. Journal of Engineering for Gas Turbines and Power. 120: 410–417.

24.

Yang

Menq

(1998b) Characterization of contact kinematics and application to the design of wedge dampers in turbomachinery blading: part 2 – prediction of forced response and experimental verification. Journal of Engineering for Gas Turbines and Power. 120: 418–423.

25.

Yang

Menq

(1998c) Characterization of 3D contact kinematics and prediction of resonant response of structures having 3D frictional constraint. Journal of Sound and Vibration. 217(5): 909–925.

26.

Yang

Chu

Menq

(1998) Stick–slip– separation analysis and non-linear stiffness and damping characterization of friction contacts having variable normal load. Journal of Sound and Vibration. 210(4): 461–481.

27.

Zucca S, Botto D and Gola MM (2008) Range of variability in the dynamics of semi-cylindrical friction dampers for turbine blades. In Proceedings of ASME Turbo Expo, Berlin, Germany, July 9–13. GT2008–51058.