0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Childs, D. W. , Mclean, J. E. , Zhang, M. , and Arthur, S. P. , 2016, “ Rotordynamic Performance of a Negative-Swirl Brake for a Tooth-on-Stator Labyrinth Seal,” ASME J. Eng. Gas Turbines Power, 138(6), p. 062505. [CrossRef]
Kirk, G. , and Gao, R. , 2012, “ Influence of Preswirl on Rotordynamic Characteristics of Labyrinth Seals,” Tribol. Trans., 55(3), pp. 357–364. [CrossRef]
Sun, D. , Wang, S. , Fei, C. W. , Ai, Y. T. , and Wang, K. M. , 2016, “ Numerical and Experimental Investigation on the Effect of Swirl Brakes on the Labyrinth Seals,” ASME J. Eng. Gas Turbines Power, 38(3), p. 032507.
Kim, T. S. , and Cha, K. S. , 2009, “ Comparative Analysis of the Influence of Labyrinth Seal Configuration on Leakage Behavior,” J. Mech. Sci. Technol., 23(10), pp. 2830–2838. [CrossRef]
Pugachev, A. O. , Kleinhans, U. , and Gaszner, M. , 2012, “ Prediction of Rotordynamic Coefficients for Short Labyrinth Gas Seals Using Computational Fluid Dynamics,” ASME J. Eng. Gas Turbines Power, 34(6), p. 062501. [CrossRef]
Li, Z. G. , Li, J. , and Yan, X. , 2013, “ Multiple Frequencies Elliptical Whirling Orbit Model and Transient RANS Solution Approach to Rotordynamic Coefficients of Annual Gas Seals Prediction,” ASME J. Vib. Acoust., 135(3), p. 031005. [CrossRef]
Zhang, H. , Jia, X. Y. , Pan, X. J. , Jiang, B. , and Zheng, Q. , 2016, “ Interaction Between Rotor and Annular Seals: Interlaced and Straight-Through Labyrinth Seals,” J. Propul. Power, 32(6), pp. 1483–1493. [CrossRef]
Li, W. , Yang, Y. , Sheng, D. R. , and Chen, J. H. , 2011, “ A Novel Nonlinear Model of Rotor/Bearing/Seal System and Numerical Analysis,” Mech. Mach. Theory, 46(5), pp. 618–631. [CrossRef]
Ma, H. , Li, H. , Niu, H. Q. , Song, R. Z. , and Wen, B. C. , 2013, “ Nonlinear Dynamic Analysis of a Rotor-Bearing-Seal System Under Two Loading Conditions,” J. Sound Vib., 332(23), pp. 6128–6154. [CrossRef]
Yan, X. , He, K. , Li, J. , and Feng, Z. P. , 2014, “ Numerical Techniques for Computing Nonlinear Dynamic Characteristic of Rotor-Seal System,” J. Mech. Sci. Technol., 28(5), pp. 1727–1740. [CrossRef]
Li, Z. G. , and Chen, Y. S. , 2012, “ Research on 1:2 Subharmonic Resonance and Bifurcation of Nonlinear Rotor-Seal System,” Appl. Math. Mech., 33(4), pp. 499–510. [CrossRef]
Wang, W. Z. , Liu, Y. Z. , and Jiang, P. N. , 2015, “ Numerical Investigation on Influence of Real Gas Properties on Nonlinear Behavior of Labyrinth Seal-Rotor System,” Appl. Math. Comput., 263, pp. 12–24. [CrossRef]
Wang, W. Z. , Liu, Y. Z. , Meng, G. , and Jiang, P. N. , 2009, “ A Nonlinear Model of Flow-Structure Interaction Between Steam Leakage Through Labyrinth Seal and the Whirling Rotor,” J. Mech. Sci. Technol., 23(12), pp. 3302–3315. [CrossRef]
Wang, W. Z. , Liu, Y. Z. , Meng, G. , and Jiang, P. N. , 2009, “ Nonlinear Analysis of Orbital Motion of a Rotor Subject to Leakage Air Flow Through an Interlocking Seal,” J. Fluids Struct., 25(5), pp. 751–765. [CrossRef]
Scharrer, J. K. , 1987, “ A Comparison of Experimental and Theoretical Results for Labyrinth Seals,” Ph.D. thesis, Texas A&M University, College Station, TX.
Scharrer, J. K. , 1988, “ Theory Versus Experiment for the Rotordynamic Coefficients of Labyrinth Gas Seals—Part I: A Two Control Volume Model,” ASME J. Vib. Acoust. Stress Reliab. Des., 110(3), pp. 270–280. [CrossRef]
Neumann, K. , 1964, “ Zur Frage der Verwendung von Durchblickdichtungen im Dampfturbinenbau,” Maschinentechnik, 13(4), pp. 188–195.
Childs, D. W. , 1993, Turbomachinery Rotordynamics Phenomena, Modeling, and Analysis, Wiley, New York.
Gurevich, M. I. , 1966, The Theory of Jets in an Ideal Fluid, Pergamon Press, Oxford, UK.
Vermes, G. , 1961, “ A Fluid Mechanics Approach to the Labyrinth Seal Leakage Problem,” ASME J. Eng. Gas Turbines Power, 83(2), pp. 161–169. [CrossRef]
James, E. A. J. , 1984, Gas Dynamics, Prentice Hall, Upper Saddle River, NJ.
He, H. J. , and Jing, J. P. , 2014, “ Research Into the Dynamic Coefficient of the Rotor-Seal System for Teeth-on-Stator and Teeth-on-Rotor Based on an Improved Nonlinear Seal Force Model,” J. Vib. Control, 20(15), pp. 2288–2299. [CrossRef]
Muszynska, A. , 2005, Rotordynamics, CRC Press, Boca Raton, FL. [CrossRef]
Muszynska, A. , and Bently, D. E. , 1990, “ Frequency Swept Rotating Input Perturbation Techniques and Identification of the Fluid Force Models in Rotor/Bearing/Seal Systems and Fluid Handling Machines,” J. Sound Vib., 143(1), pp. 103–124. [CrossRef]
Childs, D. W. , 1983, “ Dynamic Analysis of Turbulent Annular Seals Based on Hirs' Lubrication Equation,” ASME J. Lubr. Technol., 105(3), pp. 429–436. [CrossRef]
Adiletta, G. , Guido, A. R. , and Rossi, C. , 1996, “ Chaotic Motions of a Rigid Rotor in Short Journal Bearings,” Nonlinear Dyn., 10(3), pp. 251–269. [CrossRef]
Nelson, H. D. , 1980, “ A Finite Rotating Shaft Element Using Timoshenko Beam Theory,” ASME J. Mech. Des., 102(4), pp. 793–803. [CrossRef]
Childs, D. W. , and Scharrer, J. K. , 1988, “ Theory Versus Experiment for the Rotordynamic Coefficients of Labyrinth Gas Seals—Part II: A Comparison to Experiment,” ASME J. Vib. Acoust. Stress Reliab. Des., 110(3), pp. 281–287. [CrossRef]
Friswell, M. I. , Penny, J. E. T. , Garvey, S. D. , and Lees, A. W. , 2010, Dynamics of Rotating Machines, Cambridge University Press, New York. [CrossRef]
Pollman, E. , Schwerdtfeger, H. , and Termuehlen, H. , 1978, “ Flow Excited Vibrations in High-Pressure Turbines (Steam Whirl),” ASME J. Eng. Gas Turbines Power, 100(2), pp. 219–228. [CrossRef]
Bachschmid, N. , Pennacchi, P. , and Vania, A. , 2008, “ Steam-Whirl Analysis in a High Pressure Cylinder of a Turbo Generator,” Mech. Syst. Signal Process., 22(1), pp. 121–132. [CrossRef]
Villanueva, J. A. B. , Aguilar, F. J. J.-E. , and Trujillo, E. C. , 2010, “ Analysis of Steam Turbine Instabilities of a 100 MW Combined Cycle Power Plant,” ASME Paper No. IMECE2010-38506.

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of the typical section of labyrinth seal

Grahic Jump Location
Fig. 2

Illustration of the rotor whirl orbit

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 3

Flexible rotor shaft and frames of reference

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 11

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

Grahic Jump Location
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

Grahic Jump Location
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)

Grahic Jump Location
Fig. 10

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

Grahic Jump Location
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

Grahic Jump Location
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

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In