Abstract
The strip with a time-dependent tension moves, namely a harmonically varying tension about a constant initial tension. The nonlinear vibration model of moving strip between two mills with time-dependent tension was established. Approximate solutions were obtained using the method of multiple scales. Depending on the variation of the tension, three distinct cases arise: frequency away from zero or two times the natural frequency, frequency close to zero, frequency close to two times the natural frequency. For frequency close to zero and away from zero and two times the natural frequency, the system is always stable. For frequency close to two times the natural frequency, the stability is analyzed respectively when the trivial solution exists and the nontrivial solution exists. Numerical simulation was made on some 1660 mm tandem rolling mill, and the stable regions and unstable regions for parametric resonance are determined with different cases. The rolling speed and the thickness of strip have strong influences on the stability of principle parametric resonances. But the distance between two mills has little influence on the stability of principle parametric resonances.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Wickert J A, Mote C D. Classical Vibration Analysis of Axially Moving Continua [J]. ASME Journal of Applied Mechanics, 1990, 57(3): 738.
Oz H R, Pakdemirli M, Boyaci H. Non-Linear Vibrations and Stability of an Axially Moving Beam With Time-Dependent Velocity [J]. International Journal of Non-Linear Mechanics, 2001, 36(1): 107.
CHEN Li-qun, YANG Xiao-dong. Steady-State Response of Axially Moving Viscoelastic Beams With Pulsating Speed: Comparison of Two Nonlinear Models [J]. Internal Journal of Solids and Structures, 2005, 42(1): 37.
ZHANG Hong-xing, ZHANG Wei, YAO Ming-hui. Experimental Research on Nonlinear Vibration of an Axially Moving Viscoelastic Belt [J]. Journal of Dynamics and Control, 2007, 5(4): 361.
Swiatoniowski A, Bar A. Parametrical Excitement Vibration in Tandem Mills, Mathematical Model and Its Analysis [J]. Journal of Materials Processing Technology, 2003, 134(2): 214.
Bar A, Bar O. Types of Mid-Frequency Vibrations Appearing During the Rolling Mill Operation [J]. Journal of Materials Processing Technology, 2005, 162(spec iss): 464.
Bar A, Swiatoniowski A. Interdependence Between the Rolling Speed and Non-Linear Vibrations of the Mill System [J]. Journal of Materials Processing Technology, 2004, 155(1): 2116.
Kim C H, Perkins N C, Lee C W. Parametric Resonance of Plates in a Sheet Metal Coating Process [J]. Journal of Sound and Vibration, 2003, 268(4): 679.
TANG Hua-ping. DING Rui, WU Yun-xin. Investigation for Parametric Vibration of Rolling Mill [J]. Trans Nonferrous Met Soc China, 2002, 12(3): 485.
Kong L, Parker R G. Approximate Eigensolutions of Axially Moving Beam With Small Flexural Stiffness [J]. Journal of Sound and Vibration, 2004, 276(1): 459.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation Item: Item Sponsored by National Natural Science Foundation of China (50875231); Great Natural Science Foundation of Hebei Province of China (E2006001038)
Rights and permissions
About this article
Cite this article
Sun, Jl., Peng, Y. & Liu, Hm. Non-Linear Vibration and Stability of Moving Strip with Time-Dependent Tension in Rolling Process. J. Iron Steel Res. Int. 17, 11–15 (2010). https://doi.org/10.1016/S1006-706X(10)60106-9
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S1006-706X(10)60106-9