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A new approach to geometrically nonlinear analysis of double cable system with a movable guide pulley

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Abstract

Double cable system (DCS) with a movable guide pulley (MGP) is a common component in many mechanical equipment. It is difficult to calculate the unstressed length of cable under a preload, and the form-finding analysis after obtaining the unstressed length. To solve this problem, a method of establishing double-layer nonlinear equations for calculating the unstressed length of cable under a given preload is proposed. For the inner single cable, a new cable element is presented based on Hermite interpolation. Later, initial cable form is obtained by approximating catenary as a three-point parabola, and the initial values for the nonlinear equations are derived. For the outer double cable, unstressed length is a descriptive variable of the DCS. In view of the constraints on a single cable posed by the guide pulleys, corresponding constraint equations are obtained by introducing the angle of rotation of the MGP, which is a process variable. Under a given preload at an end of single cable, equations for the DCS with a MGP are constructed. Moreover, the tangent stiffness matrixes are derived for quick solution, and unstressed length for the DCS is obtained. On this basis, by changing the partial constraint equations of the DCS, the form-finding analysis of the cable can be achieved. A few numerical examples and comparisons demonstrate the reliability of the proposed new approach for geometrically nonlinear analysis of cables.

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Acknowledgments

This work has been supported by the National Natural Science Foundation of China (Grant No.11872137 No.11802048 and No.91748203).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Jinshuai Xu, Zhaohui Qi, Yingpeng Zhuo & Tianjiao Zhao

  2. School of Mechanical Engineering, Dalian University of Technology, Dalian, 116024, China

    Rumin Teng

  3. Chair of Materials Handling, Material Flow, Logistics, Technical University of Munich, Garching, 85748, Germany

    Lingchong Gao

Authors
  1. Jinshuai Xu
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  2. Zhaohui Qi
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  3. Yingpeng Zhuo
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  4. Tianjiao Zhao
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Correspondence to Jinshuai Xu.

Additional information

Jinshuai Xu received his B.S., M.S. degrees in Department of Mechanical Engineering from Dalian University of Technology, China, in 2006 and 2009, respectively. He has been engaged in product design for seven years in the field of engineering machinery design, and has become a senior engineer at the same time. In 2016, he entered the Department of Engineering Mechanics of Dalian University of Technology to study for a Ph.D. His main research interests include structural geometric nonlinearity and dynamic calculation of mobile cranes.

Zhaohui Qi received his Ph.D. in Department of Engineering Mechanics from Jilin University of Technology, China, in 1994. He is a Professor of the Department of Engineering Mechanics at Dalian University of Technology. His research interests include dynamics of multibody and complex mechanical systems.

Yingpeng Zhuo received his M.S. degree in Department of Engineering Mechanics from Dalian University of Technology, China, in 2020, and continue study for a Ph.D. in Dalian University of Technology. His research interests include dynamics of multibody and slender nested systems.

Rumin Teng received his Ph.D. in Department of Mechanical Engineering from Dalian University of Technology, China, in 2012. He is an Associate Professor of the Department of Mechanical Engineering at Dalian University of Technology. His research interests include control strategy of construction machinery and modern design theory and method of heavy equipment.

Tianjiao Zhao received his M.S. degree in Department of Engineering Mechanics from Dalian University of Technology, China, in 2017. In 2017–2019 previously worked on the design of trains and their computational analysis. He is currently studying at Dalian University of Technology for a Ph.D. His research interests include dynamics of rope pulley and truss systems.

Lingchong Gao received his B.S., M.S. degrees in Department of Mechanical Engineering from Dalian University of Technology, China, in 2012 and 2015, respectively. He is studying for a Ph.D. in Institute of Material Handling, Material Flow, and Logistics at Technical University of Munich, Germany. His research interests include dynamic analysis and control of slender structures in construction machinery.

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Xu, J., Qi, Z., Zhuo, Y. et al. A new approach to geometrically nonlinear analysis of double cable system with a movable guide pulley. J Mech Sci Technol 37, 5263–5280 (2023). https://doi.org/10.1007/s12206-023-0928-1

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  • DOI: https://doi.org/10.1007/s12206-023-0928-1

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