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Research Papers

Novel Frame Model for Mistuning Analysis of Bladed Disk Systems

[+] Author and Article Information
Jie Yuan

Aerospace Engineering,
University of Bristol,
Bristol BS8 1TR, UK;
Aerospace Division,
Cranfield University,
Cranfield MK43 0AL, UK

Fabrizio Scarpa

Aerospace Engineering;Dynamics and Control Research Group,
University of Bristol,
Bristol BS8 1TR, UK
e-mail: f.scarpa@bristol.ac.uk

Branislav Titurus

Aerospace Engineering;Dynamics and Control Research Group,
University of Bristol,
Bristol BS8 1TR, UK

Giuliano Allegri

Department of Aeronautics,
Imperial College London,
London SW7 2AZ, UK

Sophoclis Patsias, Ramesh Rajasekaran

Rolls-Royce plc,
P. O. Box 31,
Derby DE24 8BJ, UK

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 9, 2015; final manuscript received May 23, 2016; published online April 24, 2017. Assoc. Editor: John Yu.

J. Vib. Acoust 139(3), 031016 (Apr 24, 2017) (13 pages) Paper No: VIB-15-1430; doi: 10.1115/1.4036110 History: Received October 09, 2015; Revised May 23, 2016

The work investigates the application of a novel frame model to reduce computational cost of the mistuning analysis of bladed disk systems. A full-scale finite element (FE) model of the bladed disk is considered as benchmark. The frame configuration for a single blade is identified through structural identification via an optimization process. The individual blades are then assembled by three-dimensional (3D) springs, whose parameters are determined by means of a calibration process. The dynamics of the novel beam frame assembly is also compared to those obtained from three state-of-the-art FE-based reduced order models (ROMs), namely: a lumped parameter approach, a Timoshenko beam assembly, and component mode synthesis (CMS)-based techniques with free and fixed interfaces. The development of these classical ROMs to represent the bladed disk is also addressed in detail. A methodology to perform the mistuning analysis is then proposed and implemented. A comparison of the modal properties and forced response dynamics between the aforementioned ROMs and the full-scale FE model is presented. The case study considered in this paper demonstrates that the beam frame assembly can predict the variations of the blade amplitude factors, and the results are in agreement with full-scale FE model. The CMS-based ROMs underestimate the maximum amplitude factor, while the results obtained from beam frame assembly are generally conservative. The beam frame assembly is four times more computationally efficient than the CMS fixed-interface approach. This study proves that the beam frame assembly can efficiently predict the mistuning behavior of bladed disks when low-order modes are of interest.

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References

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Figures

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Fig. 1

FE model of (a) a bladed disk and (b) a single blade sector

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Fig. 2

Natural frequencies versus nodal diameters (FE)

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Fig. 3

Mode shapes of the first six modes of the sector

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Fig. 4

2DOFs per sector mode

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Fig. 5

Timoshenko beam approximation based on the FE sector

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Fig. 6

Assembly of the Timoshenko beams with the coupling springs

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Fig. 7

Beam frame sector approximation based on FE sector

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Fig. 8

Auto MAC of the first six modes with ten nodes

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Fig. 9

The relative NF and MAC errors of the first five modes

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Fig. 10

The assembly of the beam frame with coupling springs

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Fig. 11

Two substructuring strategies: (a) BDA and (b) BSA

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Fig. 12

Relative NF errors of the first six flapping mode families provided by the CMS approach with two assembly approaches: (a) BDA and (b) BSA

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Fig. 13

Relative NF errors of the first six flapping mode families using CMS-based ROMs with different numbers of modes as modal bases

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Fig. 14

Relative NF errors of the first six flapping mode families using CMS-based ROMs with different numbers of master nodes as modal bases

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Fig. 15

Relative NF errors of the first six flapping mode families using CMS-based ROM with two interface methods

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Fig. 16

The modal displacement of (a) the third rotor mode at the second ND and (b) the third bladed disk sector mode

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Fig. 17

The location of the lumped mass in the representative blade

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Fig. 18

The sensitivity of NFs of the first three out-of-plane modes to the lumped mass

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Fig. 19

Distribution of lumped masses used in the five mistuning patterns

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Fig. 20

Example of loading distribution for third engine order excitation on the 24 blades

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Fig. 21

The variations of the natural frequency with nodal diameter: (a) lumped parameter model, (b) Timoshenko beam assembly, (c) beam frame assembly, and (d) FE-based CMS approach

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Fig. 22

Comparison of the maximum blade amplitude factor between the four ROMs and the full-scale FE model (fixed-interface method: 192 modes and 21 × 24 master nodes; free-interface methods: 240 modes and 21 × 24 master nodes)

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Fig. 23

Comparison of the central processing unit (CPU) time between three types of ROMs and the full-scale FE model

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