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Shock and Vibration
Volume 2017, Article ID 6837697, 10 pages
https://doi.org/10.1155/2017/6837697
Research Article

Dynamic Response of Parallel Hoisting System under Drive Deviation between Ropes with Time-Varying Length

1School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, China
2Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, China University of Mining and Technology, Xuzhou 221116, China
3School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China
4State Key Laboratory of Heavy Mining Equipment, Luoyang 471039, China

Correspondence should be addressed to Guohua Cao; nc.ude.tmuc@auhougoac

Received 12 September 2016; Revised 6 December 2016; Accepted 21 December 2016; Published 29 January 2017

Academic Editor: Carlo Trigona

Copyright © 2017 Guohua Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The dynamic responses of parallel hoisting system with time-varying length and rigid guidance under drive deviation are investigated considering tension and torsion characteristics of the ropes. The variable-domain three-node elements of rope are employed and the corresponding differential algebraic equations (DAEs) are derived using Lagrange’s equations of the first kind. The slack situation of the rope is considered, and the dynamic equations which are systems of DAEs are transformed to ordinary differential equations (ODEs). The dynamic responses of tension, torsion, and acceleration are analyzed considering radius’ error of the drums, which indicates that the drive deviation between ropes can cause large influence on the tension difference and even cause one of the ropes to slack. However, the torsion of the corresponding rope is active. And unreasonable discordance between ropes should be controlled for the design and manufacture of drum on super deep parallel hoisting system.