13. Coupled vibration of hoisting cable in cable‑guided hoisting system with different swivels

Jinjie Wang1, Guohua Cao2, Mingxing Lin3, Shanzeng Liu4

1, 2, 4School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou, China

1, 2Jiangsu Key Laboratory of Mine Mechanical and Electrical, Xuzhou, China

3School of Mechanical Engineering, Shandong University, Jinan, China

2Corresponding author

E-mail: 1wangjinjie@cumt.edu.cn, 2caoguohua@cumt.edu.cn, 3mxlin@sdu.edu.cn, 4liushanzeng@163.com

(Received 2 October 2015; accepted 10 November 2015)

Abstract. In most cases, the hoisting cable in the cable-guided hoisting system is connected to the hoisting bucket with the swivel. The coupled longitudinal-torsional responses of the hoisting cable with time-varying length are investigated. The hoisting cable and two guiding cables are discretized by employing the assumed modes method, while the equations of motion are derived using Lagrange equations of the first kind, where a coefficient  varying from 0 to 1 is introduced to represent the free spinning, proportional and self-locking swivels. The longitudinal and torsional displacements with different swivels are obtained. The results indicate the torsional displacement in the free spinning swivel is much larger than that in the proportional and there is one resonance in the former, while the longitudinal resonance in the free spinning swivel occurs earlier than that in the other two, which implies the system frequencies decrease. In addition, the presented model could also be used to describe the coupled vibration in the rigid rail‑guided hoisting system but needs more modes.

Keywords: hoisting cable, coupled vibration, swivel, guiding cable.

References

[1]        Ma C., Xiao X. M. Kinetic analysis of a multi-rope friction mine hoist under overload conditions. Journal of Vibroengineering, Vol. 15, Issue 2, 2013, p. 925‑932.

[2]        Zi B., Qian S., Ding H. F., Andres K. Design and analysis of cooperative cable parallel manipulators for multiple mobile cranes. International Journal of Advanced Robotic Systems, Vol. 9, 2012, p. 1‑10.

[3]        Zhu W. D., Ren H. A linear model of stationary elevator traveling and compensation cables. Journal of Sound and Vibration, Vol. 332, Issue 12, 2013, p. 3086‑3097.

[4]        Wang P. H., Fung R. F., Lee M. J. Finite element analysis of a three-dimensional underwater cable with time-dependent length. Journal of Sound and Vibration, Vol. 209, Issue 2, 1998, p. 223‑249.

[5]        Kaczmarczyk S., Ostachowicz W. Transient vibration phenomena in deep mine hoisting cables. Part 1: Mathematical model. Journal of Sound and Vibration, Vol. 262, Issue 2, 2003, p. 219‑244.

[6]        Zhang P., Zhu C. M., Zhang L. J. Analysis of forced coupled longitudinal-transverse vibration of flexible hoisting system with varying length. Engineering Mechanics, Vol. 25, Issue 12, 2008, p. 202‑207.

[7]        Ren H., Zhu W. D. An accurate spatial discretization and substructure method with application to moving elevator cable-car systems. Part 2: Application. Journal of Vibration and Acoustics, Transactions of the ASME, Vol. 135, Issue 5, 2013, p. 051037.

[8]        Samras R. K., Skop R. A., Milburn D. A. Analysis of coupled extensional torsional oscillations in wire rope. Journal of Engineering for Industry, Vol. 96, 1974, p. 1130‑1135.

[9]        Hashemi S. M., Roach A. A dynamic finite element for vibration analysis of cables and wire ropes. Asian Journal of Civil Engineering, Vol. 7, Issue 5, 2006, p. 487‑500.

[10]     Shao X. G., Zhu Z. C., Wang Q. G., Chen P. C., Zi B., Cao G. H. Non-smooth dynamical analysis and experimental validation of the cable-suspended parallel manipulator. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 226, Issue 10, 2012, p. 2456‑2466.

[11]     Verreet R., Ridge I. M. L. The use of swivels with steel wire ropes. OIPEEC Round Table Conference, Bethlehem, USA, 2001.

[12]     Lanczos C. The Variational Principles of Mechanics. Dover Publications, New York, 1986.

[13]     Ilchmann A., Reis T. Surveys in Differential-Algebraic Equations 2. Springer-Verlag, Berlin, Germany, 2015.