Time-delayed positive-position and velocity fefe edback controller to suppress the lateral vibrations in nonlinear Jeffcott-rotor system

Document Type : Original Article

Authors

1 Dept. of Physics and Eng., Mathematics, Faculty of Elect., Eng., Menoufia University.

2 Dept. of Physics and Eng., Mathematics, Faculty of Elect., Eng., Menoufia University

Abstract

Within this paper, the negative-velocity and positive-position
feedback (PPF) controllers are combined together to eliminate the
lateral vibrations of a vertically supported nonlinear Jeffcott-rotor
system. Time-delays (1 and 2 ) in the control loop are included in
the system model. The slow-flow modulating equations governing
the whole system vibration amplitudes are derived utilizing
asymptotic analyses. The maximum limits of  1 and 2 at which the
system solution remains stable are illustrated. The analyses
approved that the integration of velocity controller to the PPF one,
improves the control efficiency and stretches the stable limits of both
 1 and 2 . Finally, numerical confirmations for the obtained analytical
results are included, which are in excellent agreement with the
analytical solution

References

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[1] T. Yamamoto “On the vibrations of a shaft supported by bearings having
radial clearances,” Trans. Jpn. Soc. Mech. Eng,Vol. 103, No. 21, pp.186-
192, 1955
[2] T. Yamamoto “On the critical speed of a shaft of subharmonic oscillation,”
Trans. Jpn. Soc. Mech. Eng,Vol. 111, No. 21, pp.853-858, 1955
[3] F.F. Ehrich“Subharmonic vibration of rotors in bearing clearance,” ASME
Paper No. 66-MD-1.
[4] F. F. Ehrich “High-order subharmonic response of high-speed rotors in
bearing clearance,” ASME J. Vib. Acoust. Stress. Reliab. Des, Vol. 110,
No. 1, pp.9-16, 1988
[5] T. Yamamoto and Y. Ishida“Theoretical discussions on vibrations of a
rotating shaft with nonlinear spring characteristics,” Trans. Jpn. Soc.
Mech. Eng. Ser. C 41, pp.1374-1384, 1975. (in Japanese)
[6] R. Ganesan“Dynamic response and stability of a rotor support system with
non-symmetric bearing clearances,” Mech. Mach. Theory Vol. 31, No. 6,
pp.781-798, 1996.
[7] Y. Kim and S. Noah“Quasi-periodic response and stability analysis for a
non-linear Jeffcott rotor,” Journal of Sound and Vibration Vol. 190, No. 2,
pp.239-253, 1996.
[8] T. Kashimura, H. Yabuno, T. Inoue,and Y. Ishida“Analysis of 1/2-order
subharmonic resonance in a horizontally supported Jeffcott rotor,”
ICSV14, 9–12 July 2007, Cairns, Australia
[9] H. Yabuno, T. Kashimura, T. Inoue, and Y. Ishida“Nonlinear normal
modes and primary resonance of horizontally supported Jeffcott rotor,”
Nonlinear Dynamics Vol. 66, pp.377-387, 2011.
[10] N. A. Saeed and H. A. El-Gohary “On the nonlinear oscillations of a
horizontally supported Jeffcott rotor with a nonlinear restoring force,”
Nonlinear Dynamics Vol. 88, pp.293-314, 2017.
[11] Y. Ishida and T. Inoue“Vibration Suppression of nonlinear rotor systems
using a dynamic damper,” Journal of Vibration and Control Vol. 13, No. 8,
pp.1127-1143, 2007.
[12] N. A. Saeed and M. kamel“Nonlinear PD-controller to suppress the
nonlinear oscillations of horizontally supported Jeffcott-rotor system,”
International Journal of Non-Linear Mechanics Vol. 87, pp.109-124, 2016.
[13] N. A. Saeed and W. A. El-Ganaini“Time-delayed control to suppress the
nonlinear vibrations of a horizontally suspended Jeffcott-rotor system,”
Applied Mathematical Modelling Vol. 44, pp.523-539, 2017.
[14] N. A. Saeed and W. A. El-Ganaini“Utilizing time-delays to quench the
nonlinear vibrationsof a two-degree-of-freedom system,” MeccanicaDOI:
10.1007/s11012-017-0643-z, 2017. dth: 0px; "> [15] M.Eissa and N. A.Saeed“Nonlinear vibration control of a horizontally
supported Jeffcott-rotor system,” Journal of Vibration and Control DOI:
10.1177/1077546317693928, (2017).
[16] A. Nayfeh and D. Mook“Nonlinear Oscillations,” Wiley, New York, 1995.
[17] L. F. Shampine and S. Thompson “Solving DDEs in MATLAB,” Applied
Numerical Mathematics Vol. 37, pp.441-458, 2001.

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