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Research Papers: Gas Turbines: Structures and Dynamics

Reduced Order Modeling for Multistage Bladed Disks With Friction Contacts at the Flange Joint

[+] Author and Article Information
Giuseppe Battiato

DIMEAS,
Politecnico di Torino,
Torino 10129, Italy
e-mail: giuseppe.battiato@polito.it

Christian M. Firrone

DIMEAS,
Politecnico di Torino,
Torino 10129, Italy
e-mail: christian.firrone@polito.it

Teresa M. Berruti

DIMEAS,
Politecnico di Torino,
Torino 10129, Italy
e-mail: teresa.berruti@polito.it

Bogdan I. Epureanu

Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109-2125
e-mail: epureanu@umich.edu

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 4, 2017; final manuscript received August 31, 2017; published online January 3, 2018. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(5), 052505 (Jan 03, 2018) (10 pages) Paper No: GTP-17-1273; doi: 10.1115/1.4038348 History: Received July 04, 2017; Revised August 31, 2017

Most aircraft turbojet engines consist of multiple stages coupled by means of bolted flange joints which potentially represent source of nonlinearities due to friction phenomena. Methods aimed at predicting the forced response of multistage bladed disks have to take into account such nonlinear behavior and its effect in damping blades vibration. In this paper, a novel reduced order model (ROM) is proposed for studying nonlinear vibration due to contacts in multistage bladed disks. The methodology exploits the shape of the single-stage normal modes at the interstage boundary being mathematically described by spatial Fourier coefficients. Most of the Fourier coefficients represent the dominant kinematics in terms of the well-known nodal diameters (standard harmonics), while the others, which are detectable at the interstage boundary, correspond to new spatial small wavelength phenomena named as extra harmonics. The number of Fourier coefficients describing the displacement field at the interstage boundary only depends on the specific engine order (EO) excitation acting on the multistage system. This reduced set of coefficients allows the reconstruction of the physical relative displacement field at the interface between stages and, under the hypothesis of the single harmonic balance method (SHBM), the evaluation of the contact forces by employing the classic Jenkins contact element. The methodology is here applied to a simple multistage bladed disk and its performance is tested using as a benchmark the Craig–Bampton ROMs of each single stage.

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References

Hurty, W. C. , 1965, “Dynamic Analysis of Structural Systems Using Component Modes,” AIAA J., 3(4), pp. 678–685. [CrossRef]
Craig, R. R. , and Bampton, M. C. C. , 1968, “Coupling of Substructures for Dynamic Analyses,” AIAA J., 6(7), pp. 1313–1319. [CrossRef]
Bladh, R. , Castanier, M. P. , and Pierre, C. , 2003, “Effects of Multistage Coupling and Disk Flexibility on Mistuned Bladed Disk Dynamics,” ASME J. Eng. Gas Turbines Power, 125(1), pp. 121–130. [CrossRef]
Song, S. H. , Castanier, M. P. , and Pierre, C. , 2005, “Multistage Modeling of Turbine Engine Rotor Vibration,” ASME Paper No. DETC2005-85740.
D'Souza, K. X. , and Epureanu, B. I. , 2012, “A Statistical Characterization of the Effects of Mistuning in Multistage Bladed Disks,” ASME J. Eng. Gas Turbines Power, 134(1), p. 012503. [CrossRef]
Battiato, G. , Firrone, C. M. , Berruti, T. M. , and Epureanu, B. I. , 2016, “Reduced Order Modeling for Multi-Stage Coupling of Cyclic Symmetric Structures,” International Conference on Noise and Vibration Engineering and International Conference on Uncertainty in Structural Dynamics (ISMA/USD), Leuven, Belgium, Sept. 19–21, pp. 3447–3462. https://experts.umich.edu/en/publications/reduced-order-modeling-for-multi-stage-coupling-of-cyclic-symmetr
Laxalde, D. , Thouverez, F. , and Lombard, J. P. , 2007, “Dynamical Analysis of Multi-Stage Cyclic Structures,” Mech. Res. Commun., 34(4), pp. 379–384. [CrossRef]
Laxalde, D. , Lombard, J. P. , and Thouverez, F. , 2007, “Dynamics of Multistage Bladed Disks Systems,” ASME J. Eng. Gas Turbines Power, 129(4), pp. 1058–1064. [CrossRef]
Sternchuss, A. , Balmes, E. , Jean, P. , and Lombard, J. P. , 2009, “Reduction of Multistage Disk Models: Application to an Industrial Rotor,” ASME J. Eng. Gas Turbines Power, 131(1), p. 012502. [CrossRef]
Zucca, S. , Firrone, C. M. , and Gola, M. M. , 2012, “Numerical Assessment of Friction Damping at Turbine Blade Root Joints by Simultaneous Calculation of the Static and Dynamic Contact Loads,” Nonlinear Dyn., 67(3), pp. 1943–1955. [CrossRef]
Krack, M. , von Scheidt, L. P. , Wallaschek, J. , Siewert, C. , and Hartung, A. , 2013, “Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and Its Application to Bladed Disks With Shroud Contact,” ASME J. Eng. Gas Turbines Power, 135(10), p. 102502. [CrossRef]
Chen, J. J. , and Menq, C. H. , 1999, “Prediction of Periodic Response of Blades Having 3D Nonlinear Shroud Constraints,” ASME Paper No. 99-GT-289.
Firrone, C. M. , Zucca, S. , and Gola, M. M. , 2009, “Effect of Static/Dynamic Coupling on the Forced Response of Turbine Bladed Disks With Underplatform Dampers,” ASME Paper No. GT2009-59905.
Firrone, C. M. , and Zucca, S. , 2009, “Underplatform Dampers for Turbine Blades: The Effect of Damper Static Balance on the Blade Dynamics,” Mech. Res. Commun., 36(4), pp. 515–522. [CrossRef]
Firrone, C. M. , 2009, “Measurement of the Kinematics of Two Underplatform Dampers With Different Geometry and Comparison With Numerical Simulation,” J. Sound Vib., 323(1), pp. 313–333. [CrossRef]
Schwingshackl, C. W. , Petrov, E. P. , and Ewins, D. J. , 2012, “Effects of Contact Interface Parameters on Vibration of Turbine Bladed Disks With Underplatform Dampers,” ASME J. Eng. Gas Turbines Power, 134(3), p. 032507. [CrossRef]
Gaul, L. , and Lenz, L. , 1997, “Nonlinear Dynamics of Structures Assembled by Bolted Joints,” Acta Mech., 125(1), pp. 169–181. [CrossRef]
Gaul, L. , and Nitsche, R. , 2001, “Dynamics of Structures With Joint Connections,” Structural Dynamics 2000: Current Status and Future Directions, D. J. Ewins , and D. J. Inman , eds., Research Studies Press, Baldock, UK, pp. 29–48.
Oldfield, M. J. , Ouyang, H. , and Mottershead, J. E. , 2005, “Simplified Models of Bolted Joints Under Harmonic Loading,” Comput. Struct., 84(1), pp. 25–33. [CrossRef]
Schwingshackl, C. W. , and Petrov, E. P. , 2012, “Modeling of Flange Joints for the Nonlinear Dynamic Analysis of Gas Turbine Engine Casings,” ASME J. Eng. Gas Turbines Power, 134(12), p. 122504. [CrossRef]
Schwingshackl, C. W. , Maio, D. D. , Sever, I. A. , and Green, J. S. , 2013, “Modeling and Validation of the Nonlinear Dynamic Behavior of Bolted Flange Joints,” ASME J. Eng. Gas Turbines Power, 135(12), p. 122504. [CrossRef]
Maio, D. D. , Schwingshackl, C. W. , and Sever, I. A. , 2016, “Development of a Test Planning Methodology for Performing Experimental Model Validation of Bolted Flanges,” Nonlinear Dyn., 83(1), pp. 983–1002. [CrossRef]
Firrone, C. M. , Battiato, G. , and Epureanu, B. I. , 2016, “Modeling the Microslip in the Flange Joint and Its Effect on the Dynamics of a Multi-Stage Bladed,” ASME Paper No. GT2016-57998.
Castanier, M. P. , Ottarsson, G. , and Pierre, C. , 1997, “A Reduced Order Modeling Technique for Mistuned Bladed Disks,” ASME J. Vib. Acoust., 119(3), pp. 439–447. [CrossRef]
Battiato, G. , Firrone, C. M. , and Berruti, T. M. , 2017, “Forced Response of Rotating Bladed Disks: Blade Tip-Timing Measurements,” Mech. Syst. Signal Process., 85, pp. 912–926. [CrossRef]
Griffin, J. H. , 1980, “Friction Damping of Resonant Stresses in Gas Turbine Engine Airfoils,” ASME J. Eng. Power, 102(2), pp. 329–333. [CrossRef]
Botto, D. , Lavella, M. , and Gola, M. , 2012, “Measurement of Contact Parameters of Flat on Flat Contact Surfaces at High Temperature,” ASME Paper No. GT2012-69677.

Figures

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Fig. 1

Interface and active DoF in the case of a bladed disk

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Fig. 2

h = 2 mode shape of a dummy blisk at the disk level: the displacement field at the blue circumference is described by the sum of increasing order spatial harmonics

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Fig. 3

Interstage boundary of a cyclic symmetric stage. Sectors and radial line segments are denoted by n and j, respectively [23].

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Fig. 4

1D Jenkins contact element with constant normal load N0 and tangential contact load fc acting on the ground

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Fig. 5

Multistage bladed disk full FE model

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Fig. 6

Normalized forced responses of the stage 1: α multistage ROM versus β multistage ROM

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Fig. 7

Normalized forced responses of the stage 2: α multistage ROM versus β multistage ROM

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