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Journal of Vibration and Acoustics | Volume 134 | Issue 2 | Research Paper
Research Papers

Force Feedback Control for Active Stabilization of Synchronous Whirl Orbits in Rotor Systems With Nonlinear Stiffness Elements

[+] Author and Article Information
M. O. T. Cole

C. Chamroon, P. Ngamprapasom

Department of Mechanical Engineering,  Chiang Mai University, Chiang Mai 50200, Thailand

J. Vib. Acoust 134(2), 021018 (Jan 26, 2012) (10 pages) doi:10.1115/1.4005021 History: Received July 05, 2010; Accepted August 16, 2011; Published January 26, 2012; Online January 26, 2012
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Synchronous vibration in rotor systems having bearings, seals, or other elements with nonlinear stiffness characteristics is prone to amplitude jump when operating close to critical speeds as there may be two or more possible whirl motions for a given unbalance condition. This paper describes research on how active control techniques may eliminate this potentially undesirable behavior. A control scheme based on feedback of rotor-stator interaction forces is considered. Model-based conditions for stability of low amplitude whirl, derived using Lyapunov’s direct method, are used to synthesize controller gains. Subsidiary requirements for existence of a static feedback control law that can achieve stabilization are also explained. An experimental validation is undertaken on a flexible rotor test rig where nonlinear rotor-stator contact interaction can occur across a small radial clearance in one transverse plane. A single radial active magnetic bearing is used to apply control forces in a separate transverse plane. The experiments confirm the conditions under which static feedback of the measured interaction force can prevent degenerate whirl responses such that a low amplitude contact-free orbit is the only possible steady-state response. The gain synthesis method leads to controllers that are physically realizable and can eliminate amplitude jump over a range of running speeds.
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Copyright © 2012 by American Society of Mechanical Engineers
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+Rotor-stator dynamic model with nonlinear interaction: (a) subsystems and (b) combined model with nonlinear feedback element
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Rotor-stator dynamic model with nonlinear interaction: (a) subsystems and (b) combined model with nonlinear feedback element
Figure 1

Rotor-stator dynamic model with nonlinear interaction: (a) subsystems and (b) combined model with nonlinear feedback element

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+Rotor-stator model involving a single nonlinear stiffness element
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Rotor-stator model involving a single nonlinear stiffness element
Figure 2

Rotor-stator model involving a single nonlinear stiffness element

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+Multiplicity of possible synchronous whirl responses can be determined from a Nyquist plot for the linear part of the model (case 1 high ks)
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Multiplicity of possible synchronous whirl responses can be determined from a Nyquist plot for the linear part of the model (case 1 high ks)
Figure 3

Multiplicity of possible synchronous whirl responses can be determined from a Nyquist plot for the linear part of the model (case 1 high ks)

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+Nyquist plot for the linear part of the model (case 2 low ks)
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Nyquist plot for the linear part of the model (case 2 low ks)
Figure 4

Nyquist plot for the linear part of the model (case 2 low ks)

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+Rotor-stator system dynamics under control with force-feedback gain matrix H
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Rotor-stator system dynamics under control with force-feedback gain matrix H
Figure 5

Rotor-stator system dynamics under control with force-feedback gain matrix H

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+Calculated unbalance response showing effect of local feedback of measured rotor-stator interaction force u=-0.7f: (a) with positive interaction stiffness k=0.02 MN/m and (b) with negative interaction stiffness k=0.01 MN/m
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Calculated unbalance response showing effect of local feedback of measured rotor-stator interaction force u=-0.7f: (a) with positive interaction stiffness k=0.02 MN/m and (b) with negative interaction stiffness k=0.01 MN/m
Figure 6

Calculated unbalance response showing effect of local feedback of measured rotor-stator interaction force u=-0.7f: (a) with positive interaction stiffness k=0.02 MN/m and (b) with negative interaction stiffness k=0.01 MN/m

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+Region for stable low-amplitude whirl: comparison of Nyquist and Lyapunov boundaries (case 1)
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Region for stable low-amplitude whirl: comparison of Nyquist and Lyapunov boundaries (case 1)
Figure 7

Region for stable low-amplitude whirl: comparison of Nyquist and Lyapunov boundaries (case 1)

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+Nyquist plot for actively controlled system (case 1) with force feedback. Results with controller gain optimized for two different frequencies are shown.
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Nyquist plot for actively controlled system (case 1) with force feedback. Results with controller gain optimized for two different frequencies are shown.
Figure 8

Nyquist plot for actively controlled system (case 1) with force feedback. Results with controller gain optimized for two different frequencies are shown.

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+Region for stable low-amplitude whirl under force-feedback control (case 1). Results with controller gain optimized for two different frequencies are shown.
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Region for stable low-amplitude whirl under force-feedback control (case 1). Results with controller gain optimized for two different frequencies are shown.
Figure 9

Region for stable low-amplitude whirl under force-feedback control (case 1). Results with controller gain optimized for two different frequencies are shown.

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+Region for stable low-amplitude whirl under force-feedback control (case 2). Results with controller gain optimized for two different frequencies are shown.
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Region for stable low-amplitude whirl under force-feedback control (case 2). Results with controller gain optimized for two different frequencies are shown.
Figure 10

Region for stable low-amplitude whirl under force-feedback control (case 2). Results with controller gain optimized for two different frequencies are shown.

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+Flexible rotor-AMB test rig: (a) photograph and (b) CAD model
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Flexible rotor-AMB test rig: (a) photograph and (b) CAD model
Figure 11

Flexible rotor-AMB test rig: (a) photograph and (b) CAD model

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+Measured rotor vibration response without control: (a) orbit amplitudes and (b) selected orbit plots
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Measured rotor vibration response without control: (a) orbit amplitudes and (b) selected orbit plots
Figure 12

Measured rotor vibration response without control: (a) orbit amplitudes and (b) selected orbit plots

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+Measured rotor vibration response with force-feedback control
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Measured rotor vibration response with force-feedback control
Figure 13

Measured rotor vibration response with force-feedback control

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