A method to predict the non-linear vibratory response of bladed disc system with shrouded dampers

Abstract

The prediction accuracy of the non-linear vibratory response of bladed disc system with shrouded dampers depends on the modelling of bladed disc system, the friction contact model for depicting the non-linear constraint force, and the solution method of non-linear vibration equations of the bladed disc system. In order to improve the computation efficiency, the bladed disc system is assumed to be tuned in this article. Under this assumption, the vibratory response of the bladed disc system can be predicted based on a sector model having the cyclically symmetric constraint. This article particularly describes the formulation of the sector model and the infliction of cyclically symmetric constraint. The proposed three-dimensional (3D) friction contact model used to depict the non-linear constrained force is a numerical method, in which the relative motion of the contact surfaces is an arbitrary complex periodical one. The hybrid frequency–time domain (HFT) method is applied to solve the non-linear vibration equations of the bladed disc system for its high computation efficiency and computation accuracy. Finally, based on the sector model, numerical 3D friction contact model, and HFT domain method, a method is developed to predict the non-linear vibratory response of the bladed disc system with shrouded dampers.

Keywords

bladed disc system shrouded blade 3D friction contact model hybrid frequency–time domain method

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References

Griffin

J. H.

Friction damping of resonant stresses in gas turbine engine airfoils. J. Eng. Power, 1980, 102, 329–333.

Griffin

J. H.

Menq

C. H.

Friction damping of circular motion and its implications to vibration control. J. Vib. Acoust., 1991, 113, 225–229.

Menq

C. H.

Bielak

Griffin

J. H.

The influence of microslip on vibratory response. Part 1: a new microslip model. J. Sound Vib., 1986, 107(2), 279–293.

Menq

C. H.

Chidamparam

Griffin

J. H.

Friction damping of two-dimensional motion and its application in vibration control. J. Sound Vib., 1991, 144(3), 427–447.

Menq

C. H.

Yang

B. D.

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

Yang

B. D.

Menq

C. H.

Modeling of friction contact and its application to the design of shroud contact. J. Eng. Gas Turbines Power, 1997, 119, 958–963.

Yang

B. D.

Chu

M. L.

Menq

C. H.

Stick-slip-separation analysis and non-linear stiffness and damping characterization of friction contacts having variable normal load. J. Sound Vib., 1998, 210(2), 461–481.

Yang

B. D.

Menq

C. H.

Characterization of 3D contact kinematics and prediction of resonant response of structures having 3D frictional constraint. J. Sound Vib., 1998, 217(5), 909–925.

Yang

B. D.

Menq

C. H.

Characterization of contact kinematics and application to the design of wedge dampers in turbomachinery blading: part 1. Stick-slip contact kinematics. J. Eng. Gas Turbines Power, 1998, 120, 410–417.

10.

Petrov

E. P.

Ewins

D. J.

Analytical formulation of friction interface elements for analysis of nonlinear multi-harmonic vibrations of bladed disks. J.Turbomach., 2003, 125, 364–371.

11.

Petrov

E. P.

Ewins

D. J.

Generic friction models for time-domain vibration analysis of bladed disks. J.Turbomach., 2004, 126, 184–192.

12.

Petrov

E. P.

Ewins

D. J.

Advanced modeling of underplatform friction dampers for analysis of bladed disk vibration. J. Turbomach., 2007, 129, 143–150.

13.

Petrov

E. P.

A method for use of cyclic symmetries in analysis of nonlinear multiharmonic vibrations of bladed disks. J. Turbomach., 2004, 126, 175–183.

14.

Siewert, C., Panning, L., Gerber, C., and Masserey, P. A. Numerical and experimental damping prediction of a nonlinearly coupled low pressure steam turbine blading. In Proceedings of the ASME turbo expo 2008: power for land, sea, and air, Berlin, Germany, 9–13 June 2008, ASME paper no. GT2008-51073 (American Society for Mechanical Engineers, Washington, DC).

15.

Siewert, C., Panning, L., Wallaschek, J., and Richter, C. Multiharmonic forced response analysis of turbine blading coupled by nonlinear contact forces. In Proceedings of the International gas turbine and aeroengine congress and exhibition, Orlando, Florida, 8–12 June 2009, ASME paper no. GT2009-59201, pp. 1–13 (American Society for Mechanical Engineers, Washington, DC).

16.

Poudou, O. and Pierre, C. Hybrid frequency-time domain methods for the analysis of complex structural systems with dry friction damping. In Proceedings of the 44th AIAA/ASME/ASCE/AHS structures, structural dynamics, and materials Conference, Norfolk, Virginia, 7–10 April 2003, AIAA paper no. 2003-1411, p. 14 (American Institute of Aeronautics and Astronautics, Houston, Texas).

17.

Chen

J. J.

Yang

B. D.

Menq

C. H.

Periodic forced response of structures having three-dimensional frictional constraints. J. Sound Vib., 2000, 229(4), 775–792.

18.

Chen

J. J.

Menq

C. H.

Periodic response of blades having three-dimensional nonlinear shroud constraints. J. Eng. Gas Turbines Power, 2001, 123, 901–909.

19.

Wang

J. H.

Chen

W. K.

Investigation of the vibration of a blade with friction damper by HBM. J. Eng. Gas Turbines Power, 1993, 115, 294–299.

20.

Sanliturk

K. Y.

Ewins

D. J.

Modelling two-dimensional friction contact and its application using harmonic balance method. J. Sound Vib., 1996, 193(2), 511–523.

21.

Gu, W. W. and Xu, Z. L. 3D numerical friction contact model and its application to nonlinear blade damping. In Proceedings of the ASME turbo expo 2010: power for land, sea, and air, Glasgow, UK, 14–18 June 2010, ASME paper no. GT2010-22292 (American Institute of Aeronautics and Astronautics, Houston, Texas).