Research Papers

Thermoelastic Modeling of Rotor Response With Shaft Rub

[+] Author and Article Information
S. Ziaei-Rad, E. Kouchaki

Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

M. Imregun

Department of Mechanical Engineering, Imperial College London, London SW7 2BX, UK

As shown in Figs.  29, the phase of the rotor response is defined as the angle between the unbalance force and the displacement vector at the seal location.

The peak shown in zoomed part of Fig. 6 is the initial transient, which decays rapidly because of the damping in the system.

J. Appl. Mech 77(6), 061010 (Aug 20, 2010) (12 pages) doi:10.1115/1.4000904 History: Received July 14, 2008; Revised November 27, 2009; Published August 20, 2010; Online August 20, 2010

This paper studies the effects of shaft rub on a rotating system’s vibration response with emphasis on heat generation at the contact point. A 3D heat transfer code, coupled to a 3D vibration code, was developed to predict the dynamic response of a rotor in the time domain. The shaft bow is represented by an equivalent bending moment and the contact forces by rotating external forces. The seal ring is modeled as a linear spring, which exerts a normal force to the rotor. The tangential force is then calculated as the product of the normal force with the friction coefficient. Stable or unstable spiraling and oscillating modes were seen to occur in well defined shaft speed zones. In the main, for the configurations studied, the shaft vibration was found to be unstable for speeds below the first critical speed and stable for speeds above the first critical speed. Limit cycle behavior was observed when the phase angle between the unbalance force and the response was around 90 deg. The vibration behavior with rub during startup and shutdown was studied by considering the effects of acceleration/deceleration rate, friction coefficient, and mass unbalance. It was found that friction coefficient and increasing mass unbalance amplified the rub effects while acceleration/deceleration rate reduced it.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

The contact between shaft and seal

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Figure 2

Contact forces during rub

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Figure 3

Flowchart for rotor response at each time step

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Figure 4

Geometry and dimensions for the numerical example

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Figure 5

Frequency response of the rotor with no rub to the mass

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Figure 6

Rotor response for case 1. The dotted line shows the clearance position beyond which rub occurs.

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Figure 7

Temperature distribution after 50 s

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Figure 8

Rotor response for case 2

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Figure 9

Thermal moment and mass unbalance force with its direction in below and above resonance (Fu is the mass unbalance and MT is the thermal moment)

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Figure 10

Rotor response for case 3

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Figure 11

Shaft stability in terms of phase angle

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Figure 12

Rotor response for case 4

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Figure 13

Transient response of the rotor during startup—No rub α=50 rpm/s and mass unbalance=1.1×10−3 kg m

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Figure 14

Rotor response, with rub, for startup and shutdown conditions, α=±50 rpm/s, mass unbalance=1.1×10−3 kg m, μ=0.05, and ks=500 kN/m

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Figure 15

Rotor response with and without rub (Newkirk effect) α=±50 rpm/s, mass unbalance=1.1×10−3 kg m, μ=0.05, and ks=500 kN/m

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Figure 16

Influence of angular acceleration/deceleration on rotor response. Mass unbalance=1.1×10−3 kg m, μ=0.05, and ks=500kN/m. 

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Figure 17

Influence of friction coefficient on rotor response α=±80 rpm/s. Mass unbalance=1.1×10−3 kg m, and ks=500 kN/m.

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Figure 18

Influence of mass unbalance on rotor response, α=±50 rpm/s, μ=0.05, and ks=500 kN/m

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Figure 19

The linear four-noded tetrahedral element



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