Modelling, Simulation and Experimental Validation of Nonlinear Dynamic Interactions in an Aramid Rope System

Abstract:

Vibration phenomena taking place in lifting and hoist installations may influence the dynamic performance of their components. For example, in an elevator system they may affect ride quality of a lift car. Lateral and longitudinal vibrations of suspension ropes and compensating cables may result in an adverse dynamic behaviour of the entire installation. Thus, there is a need to develop reliable mathematical and computer simulation models to predict the dynamic behaviour of suspension rope and compensating cable systems. The aim of this paper is to develop a model of an aramid suspension rope system in order to predict nonlinear modal interactions taking place in the installation. A laboratory model comprising an aramid suspension rope, a sheave/ pulley assembly and a rigid suspended mass has been studied. Experimental tests have been conducted to identify modal nonlinear couplings in the system. The dynamic behaviour of the model has been described by a set of nonlinear partial differential equations. The equations have been solved numerically. The numerical results have been validated by experimental tests. It has been shown that the nonlinear couplings may lead to adverse modal interactions in the system.

• Periodical: Applied Mechanics and Materials (Volume 706)
• Pages: 117-127
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.706.117
• Online since: December 2014
• Authors: Stefan Kaczmarczyk, Seyed Mirhadizadeh
• Keywords: Elevator System, Experimental Tests, Lifting Installation, Modeling, Nonlinear Dynamic Interactions, Numerical Simulation

References

[1] S. Kaczmarczyk, W. Ostachowicz, Transient Vibration Phenomena in Deep Mine Hoisting Cables. Part 1: Mathematical Model International, Journal of Sound and Vibration 262 (2003) 219-244.

DOI: 10.1016/s0022-460x(02)01137-9

[2] Y. Terumichi, S. Kaczmarczyk, S. Turner, M. Yoshizawa, W.M. Ostachowicz, Modelling, Simulation and Analysis Techniques in the Prediction of Non-Stationary Vibration Response of Hoist Ropes in Lift Systems, Materials Science Forum, 440-441 (2003).

DOI: 10.4028/www.scientific.net/msf.440-441.497

[3] J.P. Andrew, S. Kaczmarczyk, Systems Engineering of Elevators, Elevator World Inc., Mobile, Alabama, (2011).

[4] A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations, John Wiley, New York, (1979).

[5] O.A. Goroshko, G.N. Savin, Introduction to Mechanics of One-Dimensional Bodies with Variable Length, Naukova Dumka, Kiev, (1971).

[6] Kotera, T, Vibrations of String with Time-Varying Length. Bulletin of the JSME 21 (1978) 1469-1474.

DOI: 10.1299/jsme1958.21.1469

[7] S. Marczyk, J. Niziol, Transverse-Longitudinal Vibrations of Ropes with Time-Varying Length. Engineering Transactions 27 (1979) 403-415.

[8] A. Kumaniecka, J Niziol, Dynamic Stability of a Rope with Slow Variability of the Parameters. Journal of Sound and Vibration 178 (1994) 211-226.

DOI: 10.1006/jsvi.1994.1479

[9] Y. Terumichi, M. Ohtsuka, M. Yoshizawa, Y. Fukawa, Y. Tsujioka, Nonstationary Vibrations of a String with Time-Varying Length and a Mass-Spring System Attached at the Lower End. Nonlinear Dynamics 12 (1997) 39-55.

DOI: 10.1115/detc1993-0092

[10] S. Kaczmarczyk, The Passage Through Resonance in a Catenary-Vertical Cable Hoisting System with Slowly Varying Length. Journal of Sound and Vibration 208 (1997) 243-269.

DOI: 10.1006/jsvi.1997.1220

[11] S. Kaczmarczyk, W. Ostachowicz, Non-Stationary Responses of Cables with Slowly Varying Length. International Journal of Acoustics and Vibration 5 (2000) 117-126.

DOI: 10.20855/ijav.2000.5.357

[12] W.D. Zhu and J. Ni: Journal of Vibration and Acoustics Vol. 122 (2000) pp.295-304.

[13] W.D. Zhu, J. Ni and J. Huang: Journal of Vibration and Acoustics Vol. 123 (2001) pp.347-35.