Abstract
Torsional vibration characteristics are important information for rotating machinery design and control. Jointed shaft is a commonly used element in drive trains of rolling mill. The torsional vibrations of one- degree -of freedom nonlinear dynamical system are controlled using active control. The multiple scale perturbation technique used to get the approximate solution of the differential equation describes the system. The worst resonance cases were deduced and the frequency response function are obtained. The stability and steady state response of the system are studied and discussed numerically. The numerical solutions are focused on both the effects of the different parameters and the system behavior at different resonance cases. To insure the validity of the results, a comparison between the numerical and analytical solution was presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Pei-ming, L. Ji-zhao, J. Jin-shui, L. Bin and H. Dongying, Nonlinear dynamics of torsional vibration for rolling mill's main drive system under parametric excitation, Journal of Iron and Steel Research, 20 (1) (2013) 7–12.
R. Zhang and C. Tong, Torsional vibration control of the main drive system of a rolling mill based on an extended state observer and linear quadratic control, Journal of Vibration and Control, 12 (2006) 313–327.
A. T. El-Sayed and H. S. Bauomy, Passive and active controllers for suppressing the torsional vibration of multiple-degree-of-freedom system, Journal of Vibration and Control (2013) 1–17.
A. F. El-Bassiouny, Vibration and chaos control of nonlinear torsional vibrating systems, Physica A, 366 (2006) 167–186.
G. Wenzhi, and H. Zhiyong, Active control and simulation test study on torsional vibration of large turbo-generator rotor shaft, Mechanism and Machine Theory, 45 (2010) 1326–1336.
M. Saigo and N. Tanaka, Torsional vibration suppression by wave absorption controller, Journal of Sound and Vibration, 295 (2006) 317–330.
S. F. Asokanthan and P. A. Meehan, Non-linear Vibration of a Torsional System Driven by a Hooke's Joint, Journal of Sound and Vibration, 233 (2) (2000) 297–310.
M. M. Kamel and Y. A. Amer, Response of parametrically excited one-degree-of-freedom system with non-linear damping and stiffness, Physica Scripta, 66 (2002) 410–416.
A. H. Nayfeh and D. T. Mook, Nonlinear oscillations, New York, John Wiley (1979).
D. J. Mead, Passive vibration control, England, John Wiley & Sons (1988).
J. B. Hunt, Dynamic vibration absorbers, London, Mechanical Engineering Publications (1979).
M. Eissa, Vibration control of non-linear mechanical system via a neutralizer, Electronic Engineering Bulletin for Faculty of Electronic Engineering Menouf in Egypt, 18 (1999) 1–20.
A. T. El-Sayed, M. Kamel and M. Eissa, Vibration reduction of a pitch-roll ship model with longitudinal and transverse absorbers under multi excitations, Mathematical and Computer Modelling, 52 (2010) 1877–1898.
A. F. El-Bassiouny and M. Eissa, Dynamics of a single-degree-of-freedom structure with quadratic, cubic and quartic non-linearities to a harmonic resonance, Applied Mathematics and Computation, 139 (2003) 1–21.
J. Kevorkian and J. D. Cole, Multiple scale and singular perturbation methods, Applied Mathematical Sciences, Springer (1996).
R. V. Dukkipati, Solving vibration analysis problems using matlab, New Age International Pvt Ltd Publishers (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editor Yeon June Kang
Y. A. Amer received his B.S. degree in Mathematics from Zagazig University, EGYPT, in 1992. He then received his M.S.c and Ph.D. degrees from Zagazig University, in 1996 and 2002, respectively. Dr. Y. A. Amer is currently an Associate Professor of Mathematics at the Department of Mathematics, Faculty of Science, Zagaziga University, Egypt. Dr. Y. A. Amer research interests include Non-linear dynamical systems, Numerical Analysis, Vibration control and Partial differential equations.
A. T. EL-Sayed received his B.S. degree in Mathematics from Zagazig University, EGYPT, in 2001. He then received his M.S.c and Ph.D. degrees from Zagazig University, in 2007 and 2011, respectively. Dr. A. T. EL-Sayed is currently an Assistant Professor of Mathematics at the Department of Basic Sciences, Modern academy for Engineering and Technology, Egypt. Dr. A. T. EL-Sayed research interests include Differential equations which simulates non-linear dynamical systems, Numerical Analysis and Vibration control.
F. T. El-Bahrawy received her B.S. degree in Mathematics from AL-Azhar University, EGYPT, in 2005. She then received her M.S.c. degrees from AL-Azhar University, in 2011. F. T. El-Bahrawy is currently an Assistant Lecture of Mathematics at the Department of Basic Sciences, Modern academy for Engineering and Technology, Egypt. F. T. El-Bahrawy research interests include Differential equations, Numerical Analysis, and Vibration control.
Rights and permissions
About this article
Cite this article
Amer, Y.A., EL-Sayed, A.T. & El-Bahrawy, F.T. Torsional vibration reduction for rolling mill’s main drive system via negative velocity feedback under parametric excitation. J Mech Sci Technol 29, 1581–1589 (2015). https://doi.org/10.1007/s12206-015-0330-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-015-0330-8