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Research Papers

Morton Effect Induced Synchronous Instability in Mid-Span Rotor–Bearing Systems—Part I: Mechanism Study

[+] Author and Article Information
Zenglin Guo

Gordon Kirk

Department of Mechanical Engineering,  Virginia Polytechnic Institute and State University, Blacksburg, VA 24061gokirk@vt.edu

J. Vib. Acoust 133(6), 061004 (Oct 04, 2011) (11 pages) doi:10.1115/1.4004665 History: Received January 28, 2006; Revised March 11, 2011; Published October 04, 2011; Online October 04, 2011

The Morton Effect in rotor-bearing systems may lead to an unstable operation. In Part I, the mechanism of the Morton Effect–induced thermal instability in the mid-span rotor systems is studied. First, the equivalent thermal induced imbalance is introduced and its magnitude and directions are assumed, to represent the viscous thermal effect on the rotor systems. Then, the simplified rotor and bearing models are adopted for the derivation of analytical expressions. The results show that there exists a threshold of instability due to the Morton Effect in the mid-span rotors. Based on the assumptions of linear isotopic bearing supports, this threshold speed takes a simple form, which is determined by the support stiffness and the introduced equivalent coefficient of thermal effect, for the rigid or elastic rotors, with the thermal imbalance acting in the same direction as the response displacement. The threshold of instability is also obtained for the system with the thermal imbalance acting perpendicular to the response displacement, where the supporting damping plays a role. For a perspective view of the system stability, a stability map for the damped rigid mid-span rotors with the thermal imbalance having arbitrary phase difference is generated. It shows that the stable operating regions of the system are bounded by two curves of threshold of instability, named the first and second threshold speeds of instability, respectively. The Morton Effect–induced instability thresholds are actually affected by both the magnitude and relative phase of the thermal imbalance. The mechanism of the Morton Effect–induced thermal instability of mid-span rotors supported by linear isotropic bearings can be explained through the fact that the Morton Effect introduces either negative stiffness or negative cross-coupled stiffness. In addition, the Morton Effect also has a comprehensive impact on both the amplitude and phase lag of the steady-state unbalance response. It may shift both curves in a manner dependent on the relative magnitude and direction of the thermal imbalance.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Overhung rotor with Morton Effect involved

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Figure 2

Rigid rotor with linear isotropic supports. (a) Rotor and bearing model. (b) Orbit.

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Figure 3

Operating speed regions with Morton Effect involved

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Figure 4

Elastic rotor (extended Jeffcott model) with linear isotropic supports. (a) Rotor and bearing model. (b) Orbits of journal and disk.

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Figure 5

Transient process of unbalanced response for extended Jeffcott rotor system without Morton Effect included. (a) Below threshold of instability (N = 8000 rpm). (b) Above threshold of instability (N = 9550 rpm).

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Figure 6

Transient process of unbalanced response for extended Jeffcott rotor system with Morton Effect included. (a) Below threshold of instability (N = 8000 rpm). (b) Above threshold of instability (N = 9550 rpm).

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Figure 7

Damped rigid rotor with Ut perpendicular to line of centers

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Figure 8

Rigid rotor where Ut has arbitrary phase difference from line of centers

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Figure 9

Stability map of damped rigid rotor system (At  = 0.1 and ζ = 0.2)

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Figure 10

Steady-state response (ψ = 0°)

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Figure 11

Steady-state response (ψ = 180°)

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Figure 12

Steady-state response (ψ = 90°)

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Figure 13

Steady-state response (ψ = 270°)

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Figure 14

Phase at critical speed (Ω = 1)

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