Research Papers

Dynamic Behavior Analysis of a Rotor System Based on a Nonlinear Labyrinth-Seal Forces Model

[+] Author and Article Information
Enjie Zhang

School of Mechatronics Engineering,
Harbin Institute of Technology,
No. 92, West Dazhi Street, Nangang District,
Harbin 150001, China
e-mail: ejz.2007@163.com

Yinghou Jiao

School of Mechatronics Engineering,
Harbin Institute of Technology,
No. 92, West Dazhi Street, Nangang District,
Harbin 150001, China
e-mail: jiaoyh@hit.edu.cn

Zhaobo Chen

School of Mechatronics Engineering,
Harbin Institute of Technology,
No. 92, West Dazhi Street, Nangang District,
Harbin 150001, China
e-mail: chenzb@hit.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 30, 2018; final manuscript received June 25, 2018; published online July 30, 2018. Assoc. Editor: Tsuyoshi Inoue.

J. Comput. Nonlinear Dynam 13(10), 101002 (Jul 30, 2018) (12 pages) Paper No: CND-18-1043; doi: 10.1115/1.4040709 History: Received January 30, 2018; Revised June 25, 2018

Taking the flow field features of labyrinth seal into consideration, the fluid force generated from the seal cavity, which is spatially separated into two regions, is modeled with the perturbation method. The rotor orbit defined in the perturbation analysis is spatio-temporal varied, which is quite different from the usually preconditioned elliptical track. Meanwhile, the nonlinear fluid force originating from the seal clearance is delineated by the Muszynska's model. Based on the short bearings assumption, a nonlinear oil-film force model is employed. The rotating shaft is simulated by Timoshenko beam finite element with the consideration of geometric asymmetry. Applying the Lagrange's equations, the motion equations of the rotor-bearing-labyrinth seal system are derived. By means of spectrum cascades, bifurcation diagrams, Poincaré maps, etc., the numerical analysis of the system dynamic characteristics is conducted. The results show that abundant nonlinear behaviors can be triggered in the speed-up. The instability threshold and the vibration amplitude of the rotor system are, respectively, enhanced and reduced by the increasing inlet pressure. With shorter seal length, the sealing effect is decreased, whereas the system stability is improved. The fluid-whip phenomenon can be eliminated by increasing the mass unbalance eccentricity at a certain rotational speed.

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Fig. 1

Schematic diagram of the typical section of labyrinth seal

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Fig. 2

Illustration of the rotor whirl orbit

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Fig. 3

Flexible rotor shaft and frames of reference

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Fig. 4

The cross-coupled stiffness obtained by experiment [28] and theoretical method (present)

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Fig. 5

Schematic diagram and finite element model of a rotor-bearing-seal system

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Fig. 6

Vibration responses of the system simulated by different numbers of finite element unit

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Fig. 7

Dynamic responses of the rotor system (disk #2): (a) spectrum cascade, (b) bifurcation diagram, (c) elaborate spectrum cascade, and (d) rotor trajectories

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Fig. 8

Spectrum cascades and maximum radial displacement of the rotor system (disk #2) under different inlet pressures: (a) Pin = 0.139 MPa, (b) Pin = 0.18 MPa, (c) Pin = 0.4 MPa, and (d) maximum radial amplitude

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Fig. 9

Leakage performance and the dynamic responses of the rotor system with varying inlet pressure: (a) leakage and axial mean flow velocity and (b) spectrum cascade at ω = 8500 rpm (disk #2)

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Fig. 10

Variation of leakage flow rate in respect to the number of seal strips

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Fig. 11

Effect of seal length on dynamic responses of the rotor system (disk #2): (a) Nt = 5 and (b) Nt = 10

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Fig. 12

Spectrum cascades of the rotor system (disk #2) under different eccentricities and with varying eccentricity: (a) ed2 = 0 mm, (b) ed2 = 0.1 mm, (c) ed2 = 0.3 mm, and (d) ω = 13,500 rpm

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Fig. 13

Rotor orbits and Poincaré maps of the rotor-bearing-labyrinth seal system (disk #2) at ω = 13,500 rpm: (a) rotor orbits and (b) Poincaré maps



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