A nonlinear, planar model of a slack cable with bending stiffness and arbitrarily moving ends is developed. The model uses the slope angle of the centroid line of the cable to describe the motion of the cable, and the resulting integro-partial differential equation with constraints is derived using Hamilton’s principle. A new method is developed to obtain the spatially discretized equations, and the Baumgarte stabilization procedure is used to solve the resulting differential-algebraic equations. The model can be used to calculate the equilibria and corresponding free vibration characteristics of the cable, as well as the dynamic response of the cable under arbitrarily moving ends. The results for an equilibrium and free vibration characteristics around the equilibrium are experimentally validated on a laboratory steel band. The methodology is applied to elevator traveling and compensation cables. It is found that a vertical motion of the car can introduce a horizontal vibration of a traveling or compensation cable. The results presented are verified by a commercial finite element software. The current method is shown to be more efficient than the finite element method as it uses a much smaller number of elements to reach the same accuracy. Some other interesting features include the condition for a traveling or compensation cable equilibrium to be closest to a natural loop and a direct proof that the catenary solution is unique.
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ASME 2010 International Mechanical Engineering Congress and Exposition
November 12–18, 2010
Vancouver, British Columbia, Canada
Conference Sponsors:
- ASME
ISBN:
978-0-7918-4445-8
PROCEEDINGS PAPER
A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables
W. D. Zhu,
W. D. Zhu
University of Maryland, Baltimore County, Baltimore, MD
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H. Ren,
H. Ren
University of Maryland, Baltimore County, Baltimore, MD
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C. Xiao
C. Xiao
University of Maryland, Baltimore County, Baltimore, MD
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W. D. Zhu
University of Maryland, Baltimore County, Baltimore, MD
H. Ren
University of Maryland, Baltimore County, Baltimore, MD
C. Xiao
University of Maryland, Baltimore County, Baltimore, MD
Paper No:
IMECE2010-39219, pp. 1137-1163; 27 pages
Published Online:
April 30, 2012
Citation
Zhu, WD, Ren, H, & Xiao, C. "A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables." Proceedings of the ASME 2010 International Mechanical Engineering Congress and Exposition. Volume 8: Dynamic Systems and Control, Parts A and B. Vancouver, British Columbia, Canada. November 12–18, 2010. pp. 1137-1163. ASME. https://doi.org/10.1115/IMECE2010-39219
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