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Research Papers: Gas Turbines: Structures and Dynamics

# Overcoming of a Resonance Stall and the Minimization of Amplitudes in the Transient Resonance of a Vibratory Machine by the Phase Modulation Method

[+] Author and Article Information
J. Michalczyk

Faculty of Mechanical Engineering and Robotics, University of Science and Technology (AGH), 30-059 Krakow, Polandmichalcz@agh.edu.pl

Ł. Bednarski

Faculty of Mechanical Engineering and Robotics, University of Science and Technology (AGH), 30-059 Krakow, Polandlukaszb@agh.edu.pl

J. Eng. Gas Turbines Power 132(5), 052501 (Mar 03, 2010) (7 pages) doi:10.1115/1.3204503 History: Received November 25, 2008; Revised May 27, 2009; Published March 03, 2010; Online March 03, 2010

## Abstract

The present paper elucidates the difficulties faced in the practical implementation of phase modulation methods in the form that was presented by Wang and in the actual systems where the motor driving moment is the control value. A more general model, which takes into consideration the impact of machine vibrations on the rotor angular velocity, was developed. The modification of the phase modulation method is also proposed. The usefulness of such an approach for shaping the transient resonance of the machines with an unbalanced rotor is proven by means of a simulation and an experiment.

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## Figures

Figure 1

Calculation model; assumption for the model (a) rigid-rotor and rigid bearings producing the first rotor critical speed ωn that is substantially below a running speed and (b) one direction motion for the housing

Figure 2

The impact of the vibratory moment on the free rundown that was obtained by the numerical solution of Eq. 1 for M=0; curve a: system without a vibratory moment and curve b: system with a vibratory moment

Figure 3

The impact of the vibratory moment on the occurrence of the resonance stall during start-up (obtained for the numerical solution of Eq. 1 for curve a: M>M0−Mw and curve b: M<M0−Mw)

Figure 4

Resonance stall (obtained from numerical calculations); (a) body vibrations and (b) motor angular velocity

Figure 5

Overcoming resonance stall (obtained from numerical calculations); (a) vibrations of machine body and (b) angular velocity of motor; A is the motor disengagement instant and B is the motor engagement instant

Figure 6

View and scheme of the experimental stand; 1 is the vibratory machine body, 2 is the vibrator with constant unbalancing, 3 is the electric motor (three-phase, asynchronous, and slip ring), 4 is the changeover switch (left; stop-right), 5 is the yoke clutch, 6 is the body suspension, 7 is the vibration detector, and 8 is the HP logger

Figure 7

Machine body vibrations—full cycle of a machine motion (the result of the experiment). Start-up and stall in the resonance and passing through the stall zone as a result of the applied motor control.

Figure 8

Machine body vibrations—motor switching inappropriately performed (on purpose). The system remains in the resonance zone (the result of the experiment).

Figure 9

Passing through the resonance zone during the vibration machine start-up (obtained from numerical calculations); (a) body vibrations and (b) vibrator angular velocity

Figure 10

Dependence of the vibration maximum amplitude on the motor disengagement instant (obtained from numerical calculations). The vibration maximum amplitude without any control was equal to 0.019965 for line “a” and resonance frequency 19.23 rad/s for line “b.”

Figure 11

Determination of the motor restarting instant. The maximum mean value of the vibratory moment takes place in half of the first escalating slope of the motor angular velocity curve.

Figure 12

(a) Angular velocity of the vibrator following disengagement of the driving moment (at a frequency of 19 rad/s) and (b) change in the phase angle (defined in Ref. 10) in the resonance zone as a result of the applied control (obtained from numerical calculations)

Figure 13

Transition through the resonance zone in the course of the vibration machine start-up with the motor disengagement and engagement at the most advantageous time (obtained from numerical calculations); (a) body vibrations and (b) vibrator angular velocity

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