0
Research Papers: Hydrodynamic Lubrication

Double Overhung Disk and Parameter Effect on Rotordynamic Synchronous Instability—Morton Effect—Part I: Theory and Modeling Approach

[+] Author and Article Information
Xiaomeng Tong

Mem. ASME
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: tongxiaomeng1989@tamu.edu

Alan Palazzolo

Professor
Fellow ASME
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77843
e-mail: a-palazzolo@tamu.edu

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 5, 2016; final manuscript received June 1, 2016; published online August 16, 2016. Assoc. Editor: Mihai Arghir.

J. Tribol 139(1), 011705 (Aug 16, 2016) (11 pages) Paper No: TRIB-16-1003; doi: 10.1115/1.4033888 History: Received January 05, 2016; Revised June 01, 2016

The Morton effect (ME) is a thermally induced instability problem that most commonly appears in rotating shafts with large overhung masses, outboard of the bearing span. The time-varying thermal bow due to the asymmetric journal temperature distribution may cause intolerable synchronous vibrations that exhibit a hysteresis behavior with respect to rotor speed. The fully nonlinear transient method designed for the ME prediction, in general, overhung rotors is proposed with the capability to perform the thermoelastohydrodynamic analysis for all the bearings and model the rotor thermal bow at both overhung ends with equivalent distributed unbalances. The more accurate nonlinear, coupled, double overhung approach is shown to provide significantly different response prediction relative to the more approximate linear method based using bearing coefficients and the single-overhung method, which assumes that the ME on both rotor ends can be decoupled. The flexibility of the bearing pad and pivot is investigated to demonstrate that the pivot flexibility can significantly affect the rotordynamics and ME, while the rigid pad model is generally a good approximation.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

De Jongh, F. , 2008, “The Synchronous Rotor Instability Phenomenon—Morton Effect,” 37th Turbomachinery Symposium, College Station, TX, pp. 159–167.
Dowson, D. , and March, C. , 1966, “ Paper 6: A Thermohydrodynamic Analysis of Journal Bearings,” Proc. Inst. Mech. Eng., 181(15), pp. 117–126.
Dowson, D. , Hudson, J. , Hunter, B. , and March, C. N. , 1966, “ Paper 3: An Experimental Investigation of the Thermal Equilibrium of Steadily Loaded Journal Bearings,” Proc. Inst. Mech. Eng., 181(2), pp. 70–80.
Keogh, P. , and Morton, P. , 1993, “ Journal Bearing Differential Heating Evaluation With Influence on Rotor Dynamic Behaviour,” Proc. R. Soc. London, Ser. A, 441(1913), pp. 527–548. [CrossRef]
Keogh, P. , and Morton, P. , 1994, “ The Dynamic Nature of Rotor Thermal Bending Due to Unsteady Lubricant Shearing Within a Bearing,” Proc. R. Soc. London, Ser. A, 445(1924), pp. 273–290. [CrossRef]
Larsson, B. , 1999, “ Journal Asymmetric Heating—Part I: Nonstationary Bow,” ASME J. Tribol., 121(1), pp. 157–163. [CrossRef]
Larsson, B. , 1999, “ Journal Asymmetric Heating—Part II: Alteration of Rotor Dynamic Properties,” ASME J. Tribol., 121(1), pp. 164–168. [CrossRef]
Tucker, P. , and Keogh, P. , 1996, “ On the Dynamic Thermal State in a Hydrodynamic Bearing With a Whirling Journal Using CFD Techniques,” ASME J. Tribol., 118(2), pp. 356–363. [CrossRef]
Gomiciaga, R. , and Keogh, P. , 1999, “ Orbit Induced Journal Temperature Variation in Hydrodynamic Bearings,” ASME J. Tribol., 121(1), pp. 77–84. [CrossRef]
Balbahadur, A. C. , and Kirk, R. , 2004, “ Part I—Theoretical Model for a Synchronous Thermal Instability Operating in Overhung Rotors,” Int. J. Rotating Mach., 10(6), pp. 469–475. [CrossRef]
Kirk, G. , Guo, Z. , and Balbahadur, A. , 2003, “ Synchronous Thermal Instability Prediction for Overhung Rotors,” 32nd Turbomachinery Symposium, College Station, TX, pp. 8–11.
Balbahadur, A. , 2001, “ A Thermoelastohydrodynamic Model of the Morton Effect Operating in Overhung Rotors Supported by Plain or Tilting Pad Journal Bearings,” Ph.D. thesis, Virginia Tech, Blacksburg, VA.
Murphy, B. , and Lorenz, J. , 2010, “ Simplified Morton Effect Analysis for Synchronous Spiral Instability,” ASME J. Vib. Acoust., 132(5), p. 051008. [CrossRef]
Childs, D. , and Saha, R. , 2012, “ A New, Iterative, Synchronous-Response Algorithm for Analyzing the Morton Effect,” ASME J. Eng. Gas Turbines Power, 134(7), p. 072501. [CrossRef]
Panara, D. , Panconi, S. , and Griffini, D. , 2015, “ Numerical Prediction and Experimental Validation of Rotor Thermal Instability,” 44th Turbomachinery Symposium, College Station, TX, Sept. 14–17, pp. 1–18.
Lee, J. , and Palazzolo, A. , 2012, “ Morton Effect Cyclic Vibration Amplitude Determination for Tilt Pad Bearing Supported Machinery,” ASME J. Tribol., 135(1), p. 011701. [CrossRef]
Dimorgonas, A. , 1970, “ Packing Rub Effect in Rotating Machinery,” Ph.D. thesis, RPI, Troy, NY.
Grigor'ev, B. S. , Fedorov, A. E. , and Schmied, J. , 2015, “ New Mathematical Model for the Morton Effect Based on the THD Analysis,” 9th IFToMM International Conference on Rotor Dynamics, Milan, Italy, pp. 2243–2253.
Suh, J. , and Palazzolo, A. , 2014, “ Three-Dimensional Thermohydrodynamic Morton Effect Simulation—Part I: Theoretical Model,” ASME J. Tribol., 136(3), p. 031706. [CrossRef]
Suh, J. , and Palazzolo, A. , 2014, “ Three-Dimensional Thermohydrodynamic Morton Effect Analysis—Part II: Parametric Studies,” ASME J. Tribol., 136(3), p. 031707. [CrossRef]
De Jongh, F. , and Van Der Hoeven, P. , eds., 1998, “ Application of a Heat Barrier Sleeve to Prevent Synchronous Rotor Instability,” 27th Turbomachinery Symposium, College Station, TX, pp. 17–26.
De Jongh, F. , and Morton, P. , 1996, “ The Synchronous Instability of a Compressor Rotor Due to Bearing Journal Differential Heating,” ASME J. Eng. Gas Turbines Power, 118(4), pp. 816–824. [CrossRef]
Nicholas, J. , Gunter, E. , and Allaire, P. , 1976, “ Effect of Residual Shaft Bow on Unbalance Response and Balancing of a Single Mass Flexible Rotor—Part I: Unbalance Response,” ASME J. Eng. Gas Turbines Power, 98(2), pp. 171–181. [CrossRef]
Nicholas, J. , Gunter, E. , and Allaire, P. , 1976, “ Effect of Residual Shaft Bow on Unbalance Response and Balancing of a Single Mass Flexible Rotor—Part II: Balancing,” ASME J. Eng. Gas Turbines Power, 98(2), pp. 182–187. [CrossRef]
Salamone, D. , 1977, “ Synchronous Unbalance Response of a Multimass Flexible Rotor Considering Shaft Warp and Disk Skew,” Master's thesis, University of Virginia, Charlottesville, VA.
Salamone, D. , and Gunter, E. , 1978, “ Effects of Shaft Warp and Disk Skew on the Synchronous Unbalance Response of a Multimass Rotor in Fluid Film Bearings,” ASME Fluid Film Bearing and Rotor Bearing System Design and Optimization, pp. 79–107.
API, 2002, “ Axial and Centrifugal Compressors and Expander-Compressors for Petroleum, Chemical and Gas Industry Services,” American Petroleum Institute, Washington, DC, Standard No. API 617.
Kirk, R. , and Reedy, S. , 1988, “ Evaluation of Pivot Stiffness for Typical Tilting-Pad Journal Bearing Designs,” ASME J. Vib. Acoust. Stress Reliab. 110(2), pp. 165–171. [CrossRef]
Lund, J. , and Pedersen, L. , 1987, “ The Influence of Pad Flexibility on the Dynamic Coefficients of a Tilting Pad Journal Bearing,” ASME J. Tribol., 109(1), pp. 65–70. [CrossRef]
Suh, J. , 2014, “ Nonlinear Transient Rotor-Bearing Dynamic Analysis Considering Shaft Thermal Bow Induced Instability Problem,” Ph.D. thesis, TAMU, College Station, TX.
Young, W. , and Budynas, R. , 2002, Roark's Formulas for Stress and Strain, Vol. 7, McGraw-Hill, New York.
Heinrich, J. , Huyakorn, P. , Zienkiewicz, O. , and Mitchell, A. R. , 1977, “ An Upwind Finite Element Scheme for Two-Dimensional Convective Transport Equation,” Int. J. Numer. Methods Eng., 11(1), pp. 131–143. [CrossRef]
Schmied, J. , Pozivil, J. , and Walch, J. , 2008, “ Hot Spots in Turboexpander Bearings: Case History, Stability Analysis, Measurements and Operational Experience,” ASME Paper No. GT2008-51179.
Marin, M. , 2012, “ Rotor Dynamics of Overhung Rotors: Hysteretic Dynamic Behavior,” ASME Paper No. GT2012-68285.

Figures

Grahic Jump Location
Fig. 1

Schematics of temperature boundary surfaces

Grahic Jump Location
Fig. 2

Boundary conditions for rotor thermal deformation

Grahic Jump Location
Fig. 3

Configuration for determining rotor thermal bow

Grahic Jump Location
Fig. 4

Pad boundary conditions for bearing thermal deformation modeling

Grahic Jump Location
Fig. 5

Depiction of synchronous force sources on a flexible rotor model

Grahic Jump Location
Fig. 6

Free-body diagram of the rigid pad

Grahic Jump Location
Fig. 7

Restricted DOFs of the flexible pad

Grahic Jump Location
Fig. 8

Film thickness diagram

Grahic Jump Location
Fig. 9

Film boundary conditions for the Reynolds equation and the energy equation

Grahic Jump Location
Fig. 10

Staggered integration scheme

Grahic Jump Location
Fig. 11

Rotor configuration

Grahic Jump Location
Fig. 12

(a) Second bending mode shape and (b) linear unbalance response at bearings with/without coupling

Grahic Jump Location
Fig. 13

ME hysteresis at the NDE bearing: (a) average temperature and PK–PK ΔT, (b) PK–PK vibration amplitude at the bearing with and without thermal bow, and (c) 1× vibration polar plot at the bearing

Grahic Jump Location
Fig. 14

Steady-state ME analysis of (a) PK–PK bearing vibration amplitude and PK–PK journal ΔT, (b) resultant imbalance, and (c) minimum film thickness ratio with and without the ME

Grahic Jump Location
Fig. 15

ME analysis on the NDE with various transient methods: (a) PK–PK vibration amplitude at the bearing node, (b) 1× polar plot of the bearing, and (c) PK–PK ΔT across the journal circumference

Grahic Jump Location
Fig. 16

Comparison of fully nonlinear transient method and SOWM: (a) PK–PK journal ΔT on the NDE and DE, (b)1×polar plot of the DE bearing, and (c) 1× polar plot of the NDE bearing

Grahic Jump Location
Fig. 17

Comparison of fully nonlinear transient method and SOWM: (a) PK–PK journal ΔT on the NDE and DE, (b)1×polar plot of the DE bearing, and (c) 1× polar plot of the NDE bearing

Tables

Errata

Discussions

Related

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