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Hydrodynamic Lubrication

Morton Effect Cyclic Vibration Amplitude Determination for Tilt Pad Bearing Supported Machinery

[+] Author and Article Information
Alan Palazzolo

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

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received January 17, 2012; final manuscript received September 11, 2012; published online December 20, 2012. Assoc. Editor: J. Jeffrey Moore.

J. Tribol. 135(1), 011701 (Dec 20, 2012) (12 pages) Paper No: TRIB-12-1011; doi: 10.1115/1.4007884 History: Received January 17, 2012; Revised September 11, 2012

This paper presents theoretical models and simulation results for the synchronous, thermal transient, instability phenomenon known as the Morton effect. A transient analysis of the rotor supported by tilting pad journal bearing is performed to obtain the transient asymmetric temperature distribution of the journal by solving the variable viscosity Reynolds equation, a 2D energy equation, the heat conduction equation, and the equations of motion for the rotor. The asymmetric temperature causes the rotor to bow at the journal, inducing a mass imbalance of overhung components such as impellers, which changes the synchronous vibrations and the journal's asymmetric temperature. Modeling and simulation of the cyclic amplitude, synchronous vibration due to the Morton effect for tilting pad bearing supported machinery is the subject of this paper. The tilting pad bearing model is general and nonlinear, and thermal modes and staggered integration approaches are utilized in order to reduce computation time. The simulation results indicate that the temperature of the journal varies sinusoidally along the circumferential direction and linearly across the diameter. The vibration amplitude is demonstrated to vary slowly with time due to the transient asymmetric heating of the shaft. The approach's novelty is the determination of the large motion, cyclic synchronous amplitude behavior shown by experimental results in the literature, unlike other approaches that treat the phenomenon as a linear instability. The approach is benchmarked against the experiment of de Jongh.

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References

Figures

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Fig. 1

Thermohydrodynamic model boundary conditions

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Fig. 2

Thermally induced rotor bend and overhung mass

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Fig. 3

First four thermal modes with normalized temperature fields: (a) mode I, (b) mode II, (c) mode III, and (d) mode IV

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Fig. 4

Verification of thermal mode approach: (a) computation domain, (b) boundary condition, (c) transient results, and (d) steady state solution

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Fig. 5

Computation time versus mode number

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Fig. 6

Flow chart for calculating time averaged journal temperatures for a given elliptical, synchronous orbit

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Fig. 7

Flow chart: (a) full time transient analysis and (b) staggered integration scheme

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Fig. 8

Journal surface temperature comparison: (a) ΔT (pk-pk) versus εf, (b) temperature distribution on the journal surface at z/L = 0, and the (c) reference results plotted versus z and α

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Fig. 9

Temperature distribution versus θ versus revolutions with a forward whirl radius ratio of 0.05

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Fig. 10

Temperature distribution in the shaft; forward whirl radius ratio (a) 0.05 and (b) 0.15

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Fig. 11

Maximum temperature difference across a journal diameter versus forward whirl radius ratio; ( ) phase angle between high spot and hot spot

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Fig. 12

FEM rotor model and test results [12]

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Fig. 13

Morton effect simulation results: (a) 7200, (b) 8000, and (c) 8500 rpm

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Fig. 14

Temperature difference versus revolutions for: (a) 7200, (b) 8000 rpm, and (c) 8500 rpm

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Fig. 15

Limit cycle at (a) 8000 rpm and (b) 9000 rpm

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Fig. 16

Effect of reducing the (a) bearing clearance (o: original system, m: modified system) or (b) lubricant viscosity

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