Research Papers: Gas Turbines: Structures and Dynamics

Modal Analysis Method for Blisks Based on Three-Dimensional Blade and Two-Dimensional Axisymmetric Disk Finite Element Model

[+] Author and Article Information
Wangbai Pan

Department of Aeronautics and Astronautics,
Fudan University,
Shanghai 200433, China
e-mail: 14110290001@fudan.edu.cn

Guoan Tang

Department of Aeronautics and Astronautics,
Fudan University,
Shanghai 200433, China
e-mail: tangguoan@fudan.edu.cn

Meiyan Zhang

Department of Aeronautics and Astronautics,
Fudan University,
Shanghai 200433, China
e-mail: zhangmy@fudan.edu.cn

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 December 28, 2015; final manuscript received September 1, 2016; published online December 7, 2016. Assoc. Editor: Philip Bonello.

J. Eng. Gas Turbines Power 139(5), 052504 (Dec 07, 2016) (12 pages) Paper No: GTP-15-1580; doi: 10.1115/1.4035142 History: Received December 28, 2015; Revised September 01, 2016

In this paper, a novel and efficient modal analysis method is raised to work on blisk structures based on mixed-dimension finite element model (MDFEM). The blade and the disk are modeled separately. The blade model is figured by 3D solid elements considering its complex configuration and its degrees-of-freedom (DOFs) are condensed by dynamic substructural method. Meanwhile, the disk is structured by 2D axisymmetric element developed specially in this paper. The DOFs of entire blisk are tremendously reduced by this modeling approach. The key idea of this method is derivation of displacement compatibility to different dimensional models. Mechanical energy equivalence and summation further contribute to the model synthesis and modal analysis of blade and disk. This method has been successfully applied on the modal analysis of blisk structures in turbine, which reveals its effectiveness and proves that this method reduces the computational time expenses while maintaining the precision performances of full 3D model. Though there is limitation that structure should have proper coverage of blades, this method is still feasible for most blisks in engineering practice.

Copyright © 2017 by ASME
Topics: Disks , Blades , Displacement
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Genta, G. , 2007, Dynamics of Rotating Systems, Springer Science & Business Media, New York.
Mota Soares, C. A. , and Petyt, M. , 1978, “ Finite Element Dynamic Analysis of Practical Discs,” J. Sound Vib., 61(4), pp. 547–560. [CrossRef]
Thomas, D. L. , 1979, “ Dynamics of Rotationally Periodic Structures,” Int. J. Numer. Methods Eng., 14(1), pp. 81–102. [CrossRef]
Wang, W.-L. , Zhang, J. , and Chen, X. J. , 1988, “ Natural Mode Analysis of Blades-Disk Coupled Systems—Modal Synthesis of Symmetric Structure With C-N Group,” Acta Mech. Solida Sin., 1, pp. 61–71.
Berthillier, M. , Dhainaut, M. , Burgaud, F. , and Garnier, V. , 1997, “ A Numerical Method for the Prediction of Bladed Disk Forced Response,” ASME J. Eng. Gas Turbines Power, 119(2), pp. 404–410. [CrossRef]
Tang, J. , and Wang, K. W. , 1999, “ Vibration Control of Rotationally Periodic Structures Using Passive Piezoelectric Shunt Networks and Active Compensation,” ASME J. Vib. Acoust., 121(3), pp. 379–390. [CrossRef]
Tang, G. , Ding, J. , and Xu, X. , 2000, “ A New Method for Stress Analysis of a Cyclically Symmetric Structure,” Appl. Math. Mech., 21(1), pp. 89–96.
Vargiu, P. , Firrone, C. M. , Zucca, S. , and Gola, M. M. , 2011, “ A Reduced Order Model Based on Sector Mistuning for the Dynamic Analysis of Mistuned Bladed Disks,” Int. J. Mech. Sci., 53(8), pp. 639–646. [CrossRef]
Krack, M. , Scheidt, P. V. , 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]
Georgiades, F. , Peeters, M. , Kerschen, G. , Golinval, J. C. , and Ruzzene, M. , 2008, “ Nonlinear Modal Analysis and Energy Localization in a Bladed Disk Assembly,” ASME Paper No. GT2008-51388.
Stephenson, R. , and Rouch, K. , 1993, “ Modeling Rotating Shafts Using Axisymmetric Solid Finite Elements With Matrix Reduction,” ASME J. Vib. Acoust., 115(4), pp. 484–489. [CrossRef]
Stephenson, R. , Rouch, K. , and Arora, R. , 1989, “ Modelling of Rotors With Axisymmetric Solid Harmonic Elements,” J. Sound Vib., 131(3), pp. 431–443. [CrossRef]
Loewy, R. G. , and Khadert, N. , 1984, “ Structural Dynamics of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft Motions,” AIAA J., 22(9), pp. 1319–1327. [CrossRef]
Zhang, W. , Wang, W. , Wang, H. , and Tang, J. , 1994, “ A Finite Element Approach to the Analysis of Rotating Bladed-Disk Assemblies Coupled With Flexible Shaft,” ASME Paper No. 94-GT-107.
Shen, I. Y. , and Ku, C. P. R. , 1997, “ A Nonclassical Vibration Analysis of a Multiple Rotating Disk and Spindle Assembly,” ASME J. Appl. Mech., 64(1), pp. 165–174. [CrossRef]
Lagrange, J. L. , 1853, Mécanique Analytique, Mallet-Bachelier, Paris.
Bailey, C. D. , 1975, “ Application of Hamilton's Law of Varying Action,” AIAA J., 13(9), pp. 1154–1157. [CrossRef]
Cook, R. D. , 2007, Concepts and Applications of Finite Element Analysis, Wiley, New York.
Danielson, K. T. , and Noor, A. K. , 1997, “ Three-Dimensional Finite Element Analysis in Cylindrical Coordinates for Nonlinear Solid Mechanics Problems,” Finite Elem. Anal. Des., 27(3), pp. 225–249. [CrossRef]
Chacour, S. , 1970, “ A High Precision Axisymmetric Triangular Element Used in the Analysis of Hydraulic Turbine Components,” J. Basic Eng., 92(4), pp. 819–826. [CrossRef]
Lai, J. Y. , and Booker, J. R. , 1991, “ Application of Discrete Fourier Series to the Finite Element Stress Analysis of Axi-Symmetric Solids,” Int. J. Numer. Methods Eng., 31(4), pp. 619–647. [CrossRef]
Weissman, S. L. , and Taylor, R. L. , 1991, “ Four-Node Axisymmetric Element Based Upon the Hellinger-Reissner Functional,” Comput. Methods Appl. Mech. Eng., 85(1), pp. 39–55. [CrossRef]
Swaddiwudhipong, S. , Tho, K. K. , Hua, J. , and Liu, Z. S. , 2006, “ Mechanism-Based Strain Gradient Plasticity in C 0 Axisymmetric Element,” Int. J. Solids Struct., 43(5), pp. 1117–1130. [CrossRef]
Rauchs, G. , 2016, “ Direct-Differentiation-Based Sensitivity Analysis of an Axisymmetric Finite Element Formulation Including Torsion,” Finite Elem. Anal. Des., 109, pp. 65–72. [CrossRef]
Logan, D. L. , 2011, A First Course in the Finite Element Method, Cengage Learning, Boston, MA.
Hurty, W. C. , 1965, “ Dynamic Analysis of Structural Systems Using Component Modes,” AIAA J., 3(4), pp. 678–685. [CrossRef]
Bampton, M. C. , and Craig, R. R., Jr ., 1968, “ Coupling of Substructures for Dynamic Analyses,” AIAA J., 6(7), pp. 1313–1319. [CrossRef]
Glasgow, D. A. , and Nelson, H. D. , 1980, “ Stability Analysis of Rotor-Bearing Systems Using Component Mode Synthesis,” ASME J. Mech. Des., 102(2), pp. 352–359. [CrossRef]
Craig, R. R., Jr. , 1995, Structural Dynamics: An Introduction to Computer Methods, Society for Experimental Mechanics, Bethel, CT, p. 527.
Bathe, K. J. , Ramm, E. , and Wilson, E. L. , 1975, “ Finite Element Formulations for Large Deformation Dynamic Analysis,” Int. J. Numer. Methods Eng., 9(2), pp. 353–386. [CrossRef]
Zienkiewicz, O. C. , and Taylor, R. L. , 2000, The Finite Element Method: Solid Mechanics, Butterworth-Heinemann, Waltham, MA.


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Fig. 1

Cyclic symmetric structure

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Fig. 2

(a) Blisk in cutaway view, (b) 3D finite element model of blade, and (c) 2D finite element model of disk

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Fig. 3

(a) Blade and disk model shown in the same coordinate and (b) detail information of interface of disk and blade, including joint points and offset angle

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Fig. 4

MPCs applied on the top of disk. ◇ represents joint nodes. ○ represents dependent nodes.

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Fig. 5

Three-dimensional ring of one axisymmetric element

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Fig. 6

MPCs applied on the bottom of blade. ◇ represents joint nodes. ○ represents dependent nodes.

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Fig. 7

A set of blisk containing same disk with different number of blades

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Fig. 8

MDFEM corresponding to Fig. 7

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Fig. 9

Coverage–error relationship in Table 1

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Fig. 10

Sector model of blisk

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Fig. 11

Modal shape contour plots. (a) Sector model first order by patran (1.393711 × 10+03 Hz), (b) MDFEM first order by matlab (1.393649 × 10+03 Hz), (c) sector model third order by patran (3.371681 × 10+03 Hz), and (d) MDFEM third order by matlab (3.337990 × 10+03 Hz).



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