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Journal of Tribology | Volume 140 | Issue 2 | research-article
Research Papers: Hydrodynamic Lubrication

Nonlinear Dynamics of Flexible Rotors Supported on Journal Bearings—Part I: Analytical Bearing Model

[+] Author and Article Information
Mohammad Miraskari

Mechanical Engineering Department,
University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada
e-mail: m.miraskari@alumni.ubc.ca

Farzad Hemmati

Mechanical Engineering Department,
University of British Columbia,
054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada
e-mail: farhemmati@alumni.ubc.ca

Mohamed S. Gadala

Mechanical Engineering Department,
University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada;
Mechanical Engineering Department,
Abu Dhabi University,
Abu Dhabi, United Arab Emirates
e-mail: gadala@mech.ubc.ca

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received November 25, 2016; final manuscript received August 14, 2017; published online October 4, 2017. Assoc. Editor: Alan Palazzolo.

J. Tribol 140(2), 021704 (Oct 04, 2017) (15 pages) Paper No: TRIB-16-1367; doi: 10.1115/1.4037730 History: Received November 25, 2016; Revised August 14, 2017
Article
References
Figures
Tables

To determine the bifurcation types in a rotor-bearing system, it is required to find higher order derivatives of the bearing forces with respect to journal velocity and position. As closed-form expressions for journal bearing force are not generally available, Hopf bifurcation studies of rotor-bearing systems have been limited to simple geometries and cavitation models. To solve this problem, an alternative nonlinear coefficient-based method for representing the bearing force is presented in this study. A flexible rotor-bearing system is presented for which bearing force is modeled with linear and nonlinear dynamic coefficients. The proposed nonlinear coefficient-based model was found to be successful in predicting the bifurcation types of the system as well as predicting the system dynamics and trajectories at spin speeds below and above the threshold speed of instability.
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References

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Figures

Grahic Jump Location
Fig. 1

The schematic of a journal inside bearing (a) and modeling the effect of journal bearings with linear stiffness and damping coefficients (b)

+The schematic of a journal inside bearing (a) and modeling the effect of journal bearings with linear stiffness and damping coefficients (b)
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The schematic of a journal inside bearing (a) and modeling the effect of journal bearings with linear stiffness and damping coefficients (b)
Grahic Jump Location
Fig. 2

Schematic of a flexible rotor supported on journal bearings (a) and the adopted coordinate system (b); OJ and OM correspond to the geometric center of the journal and the central disk, respectively

+Schematic of a flexible rotor supported on journal bearings (a) and the adopted coordinate system (b); OJ and OM correspond to the geometric center of the journal and the central disk, respectively
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Schematic of a flexible rotor supported on journal bearings (a) and the adopted coordinate system (b); OJ and OM correspond to the geometric center of the journal and the central disk, respectively
Grahic Jump Location
Fig. 3

Linear dynamic coefficients in X–Y coordinate system

+Linear dynamic coefficients in X–Y coordinate system
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Linear dynamic coefficients in X–Y coordinate system
Grahic Jump Location
Fig. 4

Nonlinear (second-order) dynamic coefficients (absolute values) in X–Y coordinate system

+Nonlinear (second-order) dynamic coefficients (absolute values) in X–Y coordinate system
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Nonlinear (second-order) dynamic coefficients (absolute values) in X–Y coordinate system
Grahic Jump Location
Fig. 5

Nonlinear (third-order) dynamic coefficients (absolute values) in X–Y coordinate system

+Nonlinear (third-order) dynamic coefficients (absolute values) in X–Y coordinate system
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Nonlinear (third-order) dynamic coefficients (absolute values) in X–Y coordinate system
Grahic Jump Location
Fig. 6

stability bounds of the flexible rotor-bearing system for a range of nondimensional shaft stiffness values (a) and comparison to experimental results of Wang and Khonsari [19] (b)

+stability bounds of the flexible rotor-bearing system for a range of nondimensional shaft stiffness values (a) and comparison to experimental results of Wang and Khonsari [19] (b)
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stability bounds of the flexible rotor-bearing system for a range of nondimensional shaft stiffness values (a) and comparison to experimental results of Wang and Khonsari [19] (b)
Grahic Jump Location
Fig. 7

Selected operating points of a fully balanced rotor-bearing system in stable and unstable regions for time integration

+Selected operating points of a fully balanced rotor-bearing system in stable and unstable regions for time integration
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Selected operating points of a fully balanced rotor-bearing system in stable and unstable regions for time integration
Grahic Jump Location
Fig. 8

Journal trajectories for the operating points within the supercritical region; point I (S = 0.5, γ = 4), before crossing the threshold speed (a), point II (S = 0.5, γ = 5.5), after crossing the threshold speed (b), and the subcritical region; point III (S = 2.5, γ = 4.5), before crossing the threshold speed (c), and point IV (S = 2.5, γ = 6), after crossing the threshold speed (d)

+Journal trajectories for the operating points within the supercritical region; point I (S = 0.5, γ = 4), before crossing the threshold speed (a), point II (S = 0.5, γ = 5.5), after crossing the threshold speed (b), and the subcritical region; point III (S = 2.5, γ = 4.5), before crossing the threshold speed (c), and point IV (S = 2.5, γ = 6), after crossing the threshold speed (d)
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Journal trajectories for the operating points within the supercritical region; point I (S = 0.5, γ = 4), before crossing the threshold speed (a), point II (S = 0.5, γ = 5.5), after crossing the threshold speed (b), and the subcritical region; point III (S = 2.5, γ = 4.5), before crossing the threshold speed (c), and point IV (S = 2.5, γ = 6), after crossing the threshold speed (d)
Grahic Jump Location
Fig. 9

Comparison of the obtained journal trajectory based on linear and nonlinear coefficient models and the force based model for operating points I (a), II (b), IV(c), and (d)

+Comparison of the obtained journal trajectory based on linear and nonlinear coefficient models and the force based model for operating points I (a), II (b), IV(c), and (d)
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Comparison of the obtained journal trajectory based on linear and nonlinear coefficient models and the force based model for operating points I (a), II (b), IV(c), and (d)

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