Research Papers: Hydrodynamic Lubrication

Three-Dimensional Thermohydrodynamic Morton Effect Simulation—Part I: Theoretical Model

[+] Author and Article Information
Junho Suh

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: menartek@tamu.edu

Alan Palazzolo

Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: a-palazzolo@tamu.edu

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 30, 2013; final manuscript received March 17, 2014; published online April 25, 2014. Assoc. Editor: Mihai Arghir.

J. Tribol 136(3), 031706 (Apr 25, 2014) (14 pages) Paper No: TRIB-13-1151; doi: 10.1115/1.4027309 History: Received July 30, 2013; Revised March 17, 2014; Accepted March 23, 2014

The present study is focused on accurate prediction of the Morton effect problem including journal asymmetric heating and the corresponding long period amplitude oscillations using a nonlinear time transient rotor-dynamic simulation. This paper presents a theoretical model of thermal induced synchronous instability problems in a nonlinear rotor–bearing system, and suggests a new computational algorithm for the nonlinear transient analysis of the Morton effect where the dynamic and thermal problems are combined. For the analysis of the Morton effect problem, a variable viscosity Reynolds equation and a 3D energy equation are coupled via temperature and viscosity, and solved simultaneously. Three-dimensional heat transfer equations of bearing and shaft are modeled by a finite element method, and thermally coupled with the fluid film via a heat flux boundary condition. Asymmetric heat flux into the synchronously whirling rotor is solved by the orbit time averaged heat flux from fluid film to the spinning shaft surface. The journal orbit is calculated by the nonlinear transient dynamic analysis of a rotor–bearing system with a variable time step numerical integration scheme. For the computation time reduction, modal coordinate transformation is adopted in dynamic and thermal transient analysis. Thermal bow effect makes a significant change to the dynamic behavior of a rotor–bearing system, and a thermal hysteresis bode plot, that is one of the characteristics of the Morton effect problem, is presented with time varying spin speed.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Tieu, A., 1973, “Oil-Film Temperature Distribution in an Infinitely Wide Slider Bearing: An Application of the Finite-Element Method,” J. Mech. Eng. Sci., 15(4), pp. 311–320. [CrossRef]
Khonsari, M., and Beaman, J., 1986, “Thermohydrodynamic Analysis of Laminar Incompressible Journal Bearings,” ASLE Trans., 29(2), pp. 141–150. [CrossRef]
Knight, J., and Barrett, L., 1988, “Analysis of Tilting Pad Journal Bearings With Heat Transfer Effects,” ASME J. Tribol., 110(1), pp. 128–133. [CrossRef]
Earles, L., Armentrout, R., and Palazzolo, A., 1990, “A Finite Element Approach to Pad Flexibility Effects in Tilt Pad Journal Bearings—Part II: Assembled Bearing and System Analysis,” ASME J. Tribol., 112(2), pp. 178–182. [CrossRef]
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]
Gomiciaga, R., and Keogh, P., 1999, “Orbit Induced Journal Temperature Variation in Hydrodynamic Bearings,” ASME J. Tribol., 121(1), pp. 77–84. [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]
Balbahadur, A., and Kirk, R., 2004, “Part II—Case Studies for a Synchronous Thermal Instability Operating in Overhung Rotors,” Int. J. Rotating Mach., 10(6), pp. 477–487. [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]
Murphy, B. T., and Lorenz, J. A., 2010, “Simplified Morton Effect Analysis for Synchronous Spiral Instability,” ASME J. Vib. Acoust., 132(5), p. 051008. [CrossRef]
Childs, D. W., 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]
Lee, J. G., and Palazzolo, A., 2012, “Morton Effect Cyclic Vibration Amplitude Determination for Tilt Pad Bearing Supported Machinery,” ASME J. Tribol., 135(1), p. 011701. [CrossRef]
Meirovitch, L., 2010, Fundamentals of Vibrations, Waveland Press, Long Grove, IL, Chap. 7.
Inman, D. J., and Singh, R. C., 2001, Engineering Vibration, Prentice Hall, Englewood Cliffs, NJ.
Cook, R. D., 2007, Concepts and Applications of Finite Element Analysis, Wiley, New York.
Lund, J., 1987, “Review of the Concept of Dynamic Coefficients for Fluid Film Journal Bearings,” ASME J. Tribol., 109(1), pp. 37–41. [CrossRef]
Lund, J., and Thomsen, K., 1978, “A Calculation Method and Data for the Dynamic Coefficients of Oil-Lubricated Journal Bearings,” Topics in Fluid Film Bearing and Rotor Bearing System Design and Optimization, ASME, New York, pp. 1–28.
Kim, J., Palazzolo, A. B., and Gadangi, R. K., 1994, “TEHD Analysis for Tilting-Pad Journal Bearings Using Upwind Finite Element Method,” Tribol. Trans., 37(4), pp. 771–783. [CrossRef]
Gadangi, R. K., Palazzolo, A. B., and Kim, J., 1996, “Transient Analysis of Plain and Tilt Pad Journal Bearings Including Fluid Film Temperature Effects,” ASME J. Tribol., 118(2), pp. 423–430. [CrossRef]
Heinrich, J., Huyakorn, P., Zienkiewicz, O., and Mitchell, A., 1977, “An ‘Upwind’ Finite Element Scheme for Two-Dimensional Convective Transport Equation,” Int. J. Numer. Methods Eng., 11(1), pp. 131–143. [CrossRef]
De Jongh, F. M., and Van Der Hoeven, P., Eds., 1998, “Application of a Heat Barrier Sleeve to Prevent Synchronous Rotor Instability,” Proceedings of the Twenty-Seventh Turbomachinery Symposium, Turbomachinery Laboratory, Texas A&M University, College Station, TX, pp. 17–26.
De Jongh, F., Morton, P., and Holmes, R., 1996, “The Synchronous Instability of a Compressor Rotor Due to Bearing Journal Differential Heating. Discussion,” ASME J. Eng. Gas Turbines Power, 118(4), pp. 816–824. [CrossRef]


Grahic Jump Location
Fig. 1

Pad dynamic model with flexible pivot

Grahic Jump Location
Fig. 2

Thermal deformation of shaft

Grahic Jump Location
Fig. 3

Schematic diagram of shaft and pad 3D motions

Grahic Jump Location
Fig. 4

Asymmetric thermal expansion of shaft

Grahic Jump Location
Fig. 5

Thermal bending induced eccentricity (en) and phase (θn)

Grahic Jump Location
Fig. 6

Temperature and heat flux boundary condition

Grahic Jump Location
Fig. 8

Algorithm for transient Morton effect analysis

Grahic Jump Location
Fig. 11

Seven surfaces with prescribed convection or fixed temperature conditions

Grahic Jump Location
Fig. 12

Steady state analysis of rotor–bearing system with 2D and 3D energy equations

Grahic Jump Location
Fig. 13

Comparison of 2D and 3D energy equation for transient Morton effect analysis

Grahic Jump Location
Fig. 15

Hysteresis vibration amplitude at NDE bearing

Grahic Jump Location
Fig. 14

Thermal bow versus nonthermal bow model



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