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TECHNICAL PAPERS

Generic Friction Models for Time-Domain Vibration Analysis of Bladed Disks

[+] Author and Article Information
E. P. Petrov, D. J. Ewins

Centre of Vibration Engineering, Mechanical Engineering Department, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

J. Turbomach 126(1), 184-192 (Mar 26, 2004) (9 pages) doi:10.1115/1.1644557 History: Received December 01, 2002; Revised March 01, 2003; Online March 26, 2004
Copyright © 2004 by ASME
Topics: Force , Friction , Motion , Stress , Disks
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References

Dahl,  P. R., 1976, “Solid Friction Damping of Mechanical Vibrations,” AIAA J., 14(12), pp. 1675–1682.
Gaul,  L., and Lenz,  J., 1997, “Nonlinear Dynamics of Structures Assembled by Joints,” Acta Mech., 125, pp. 169–181.
de Wit,  C. C., Olsson,  H., Astrom,  K. J., and Lischinsky,  P., 1995, “A New Model for Control of Systems With Friction,” IEEE Trans. Autom. Control, 40(3), pp. 419–425.
Armstrong-Helouvry,  B., Dupont,  P., and de Wit,  C. C., 1994, A “Survey of Models, Analysis Tools and Compensation Methods for the Control of Machines With Friction,” Automatica, 30, pp. 1083–1138.
Ibrahim,  R. A., 1994, “Friction-Induced Vibration, Chatter, Squeal, and Chaos,” Appl. Mech. Rev., 47, “Part I: Mechanics of Contact and Friction,” pp. 209–226, “Part II: Dynamic and Modeling,” pp. 227–253.
Griffin, J. H., 1990, “A Review of Friction Damping of Turbine Blade Vibration,” Int. J. Turbo Jet Engines, (7), pp. 297–307.
Sanliturk,  K. Y., Imregun,  M., and Ewins,  D. J., 1997, “Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers,” ASME J. Vibr. Acoust., 119, pp. 96–103.
Sextro, W., 1996, “The Calculation of the Forced Response of Shrouded Blades With Friction Contacts and Its Experimental Verification,” Proc. of 2nd European Nonlinear Oscillation Conference, Prague, Sept. 9–13.
Yang,  B. D., Chu,  M. I., and Menq,  C. H., 1998, “Stick-Slip-Separation Analysis and Non-linear Stiffness and Damping Characterization of Friction Contacts Having Variable Normal Load,” J. Sound Vib., 210(4), pp. 461–481.
Petrov,  E., and Ewins,  D., 2004, “Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks,” ASME J. Turbomach., 126, pp. 364–371.
Yang,  B. D., and Menq,  C. H., 1998, “Characterization of 3D Contact Kinematics and Prediction of Resonant Response of Structures Having 3D Frictional Constraint,” J. Sound Vib., 217(5), pp. 909–925.
Tabor,  D., 1981, “Friction—The Present State of Our Understanding,” ASME J. Lubr. Technol., 103, pp. 169–179.
Tworzydlo,  W. W., Cecot,  W., Oden,  J. T., and Yew,  C. H., 1998, “Computational Micro- and Macroscopic Models of Contact and Friction: Formulation, Approach and Applications,” Wear, 220, pp. 113–140.
Mostanghel,  N., and Davis,  T., 1997, “Representations of Coulomb Friction for Dynamic Analysis,” Earthquake Eng. Struct. Dyn., 26, pp. 541–548.

Figures

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Friction contact interaction of rough surfaces
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Motion of the asperity model along a line
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Arbitrary planar motion of the asperity model
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Effects of different choice of the constant, c: (a) on the sign function approximation; (b) on hysteresis loop shapes
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The friction force and hysteresis loops for different levels of the normal load variation: (a) fz=100; (b) fz=100+40 sin τ; (c) fz=100+80 sin τ
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Hysteresis loops for different phase values of the normal load variation: fz=100+80 sin(t+ϕ)
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Friction force with multiharmonic displacement and normal load variation
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Hysteresis loops for variable friction characteristics: (a) μ=1/3μ0(2+e−0.1τ);kt=k0; (b) μ=μ0;kt=1/3k0(2+e−0.1τ); (c) μ=1/3μ0(2+e−0.1τ) and kt=1/3k0(2+e−0.1τ)
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Vectors of the friction force for different trajectories and normal load variation: (a) a case of an ellipse with the ratio of its axis lengths 2:1; (b) a case of an ellipse with the ratio 2:0.1
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Magnitude of the friction force vector for different trajectories: (a) fz=100; (b) fz=100+60 sin τ
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Trajectory of motion and vectors of the friction force for different levels of displacements
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Magnitude of the friction force vector for different levels of displacements
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Variation of the friction force as a function of radius of the minimum curvature
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Friction forces for different orientation of anisotropy axes for the friction coefficient, μ(φ): (a) friction force vector at different points of the trajectory; (b) magnitude of the friction vector
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Finite element model of the test rig, (a); and a patch where the blades have the friction contact interface, (b)
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Variation of displacement components over the time interval considered
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Calculated friction force: (a) as functions of time; (b) hysteresis loops for the whole time range for friction force component fy

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