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Research Papers

Study on Vibration Characteristics of Fan Shaft of Geared Turbofan Engine With Sudden Imbalance Caused by Blade Off

[+] Author and Article Information
Jing Wei

State Key Laboratory of
Mechanical Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: weijing_slmt@163.com

Peixin Bai

State Key Laboratory of
Mechanical Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: baipeixin_sklmt@163.com

DaTong Qin

State Key Laboratory of
Mechanical Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: dtqin@cqu.edu.cn

Teik C. Lim

Office of The Provost,
University of Texas Arlington,
Box 19118, 701 South Nedderman Drive
Davis Hall, Suite 321,
Arlington, TX 76019
e-mail: teik.lim@uta.edu

PanWu Yang

State Key Laboratory of
Mechanical Transmissions,
Chongqing University,
Chongqing 400044, China
e-mail: yangpanwu_sklmt@163.com

Hong Zhang

Sino-European Institute of Aviation Engineering,
Civil Aviation University of China,
Tianjin 300300, China
e-mail: zhanghong.siae@hotmail.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 3, 2017; final manuscript received February 1, 2018; published online March 14, 2018. Assoc. Editor: Patrick S. Keogh.

J. Vib. Acoust 140(4), 041010 (Mar 14, 2018) (14 pages) Paper No: VIB-17-1293; doi: 10.1115/1.4039246 History: Received July 03, 2017; Revised February 01, 2018

Based on the requirements of the dynamic design of geared turbofan (GTF) engines, the vibration characteristic of the fan shaft is investigated. The effect of sudden imbalance caused by blade off, the time-varying meshing stiffness, and meshing errors on the vibration characteristics is fully considered in the dynamic model. The improved Euler–Bernoulli beam element considering the effects of shear deformation is employed and a coupled relationship between the gear–shaft–bearing–casing is established. Under windmilling condition with a single blade completely lost, the vibration characteristics of the fan shaft of the turbofan engine with and without a gearbox system are compared. The effect of the gear system on the vibration of the fan shaft under different rotating speeds is examined. The results show that the orbit of the fan shaft center in the turbofan engine with the gearbox system exhibits a multifrequency whirling motion and has a stable limit cycle. Under windmilling condition, the meshing frequency and the modal frequency have multiple intersection points. The critical speed is dense and the peak value of the transient vibration of the GTF engine gearbox shows a wave rise with an increase in speed. The results of this study could provide a reference for the parameter design and optimization of GTF engines.

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Figures

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Fig. 1

Product picture: (a) gears and (b) bearings

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Fig. 2

Simplified diagram of the gear transmission system with fan

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Fig. 3

Geometric model of the gear transmission system

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Fig. 4

Sketch of gear transmission in windmilling condition

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Fig. 5

Simple shafting unit model

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Fig. 6

Improved Euler–Bernoulli beam element

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Fig. 7

Dynamic model of gear pairs: (a) dynamic model of the double helical gear pair, (b) dynamic model of sun–planet i pair, and (c) dynamic model of ring–planet i pair

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Fig. 8

Node model of the gear transmission system

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Fig. 9

Schematic diagram of the assembly rules of the overall system

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Fig. 10

Nonuniform cantilever beam model of a gear tooth

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Fig. 11

Mechanical model of imbalance

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Fig. 12

Single blade residue: (a) residue 10%, (b) residue 40%, (c) residue 70%, and (d) residue 100%

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Fig. 14

Time-varying meshing stiffness: (a) time-varying external meshing stiffness and (b) time-varying internal meshing stiffness

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Fig. 15

Time-domain graph of radial vibration without gearbox: (a) bearing 1 in the X-direction and (b) bearing 1 in the Y-direction

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Fig. 16

Frequency-domain graph of radial vibration without gearbox: (a) bearing 1 in the X-direction and (b) bearing 1 in the Y-direction

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Fig. 17

Time-domain graph of radial vibration with gearbox: (a) bearing 1 in the X-direction and (b) bearing 1 in the Y-direction

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Fig. 18

Frequency-domain graph of radial vibration with gearbox: (a) bearing 1 in the X-direction and (b) bearing 1 in the Y-direction

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Fig. 19

Time-frequency graph of the meshing force: (a) time-field graph of the meshing force and (b) frequency-field graph of the meshing force

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Fig. 20

Shaft orbit of the system without gear

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Fig. 21

Shaft orbit of the GTF engine system: (a) orbit of shaft center before sudden imbalance, (b) shaft orbit of the GTF engine system with gear, and (c) orbit of shaft center after sudden imbalance

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Fig. 22

Impact factor of key nodes

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Fig. 23

Systematic Campbell chart

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Fig. 24

Peak value of the bearing 1: (a) peak value of the bearing 1 in the X-direction and (b) peak value of the bearing 1 in the Y-direction

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Fig. 25

Transient response in the X-direction: (a) sun gear in the X-direction, (b) ring gear in the X-direction, (c) bearing 1 in the X-direction, and (d) fan shaft front end in the X-direction

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Fig. 26

Steady peak after sudden imbalance in the X-direction: (a) sun gear in the X-direction, (b) ring gear in the X-direction, (c) bearing 1 in the X-direction, and (d) fan shaft front end in the X-direction

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Fig. 27

Transient response in the Y-direction: (a) sun gear in the Y-direction, (b) ring gear in the Y-direction, (c) bearing 1 in the Y-direction, and (d) fan shaft front end in the Y-direction

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Fig. 28

Steady peak after sudden imbalance in the Y-direction: (a) sun gear in the Y-direction, (b) ring gear in the Y-direction, (c) bearing 1 in the Y-direction, and (d) fan shaft front end in the Y-direction

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