Coupled vibrations of rope-guided hoisting system with tension difference between two guiding ropes

Abstract

The flexibility of the guiding rope and the tension difference between two guiding ropes cause the lateral and torsional vibrations of the hoisting conveyance in the rope-guided hoisting system, respectively, which are theoretically investigated with two different cases in this paper. The assumed modes method is used to discretize the hoisting rope and two guiding ropes, and Lagrange equations of the first kind is adopted to derive the equations of motion, while the geometric matching conditions at the interfaces of the ropes are accounted for by the Lagrangian multiplier. Considering all the geometric matching conditions are approximately linear, the differential algebraic equations are transformed to a system of ordinary differential equations. The current method can obtain not only the accurate lateral displacements of two guiding ropes, but also the constraint forces between the hoisting conveyance and two guiding ropes. Further, the current method is verified by the ADAMS simulation. Finally, the effects of various parameters on the lateral and torsional vibrations of the hoisting conveyance are analyzed and results indicate that the appropriate tension difference and distance difference could decrease the maximum lateral displacement, which is useful to design super deep rope-guided hoisting system for the decrease of the vibration.

Keywords

Hoisting rope guiding rope coupled vibration Lagrange’s equations

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References

Wang

Kang

Sun

et al.

Modeling and parameter analysis of in-plane dynamics of a suspension bridge with transfer matrix method. Acta Mech 2014; 225: 3423–3435.

Qian

Ding

et al.

Design and analysis of cooperative cable parallel manipulators for multiple mobile cranes. Int J Adv Robot Syst 2012; 9: 1–10.

Bao

Cui

. Stiffness and dexterous performances optimization of large workspace cable-driven parallel manipulators. Adv Robot 2014; 28: 187–196.

Arrasate

Kaczmarczyk

Almandoz

et al.

The modelling, simulation and experimental testing of the dynamic responses of an elevator system. Mech Syst Signal Process 2014; 42: 258–282.

Wang

Zhang

. Effect of terminal mass on fretting and fatigue parameters of a hoisting rope during a lifting cycle in coal mine. Eng Fail Anal 2014; 36: 407–422.

Shao

Zhu

Wang

et al.

Non-smooth dynamical analysis and experimental validation of the cable-suspended parallel manipulator. Proc IMechE, Part C: J Mechanical Engineering Science 2012; 226: 2456–2466.

Zhu ZC. Mine elevator. Patent WO2013007059, China, 2013.

Deb

. Dynamics of a string and an elastic hammer. J Sound Vib 1975; 40: 243–248.

Fung

Lin

Yao

. Vibration analysis and suppression control of an elevator string actuated by a PM synchronous servo motor. J Sound Vib 1997; 206: 399–423.

10.

Zhu

. Vibration of elevator cables with small bending stiffness. J Sound Vib 2003; 263: 679–699.

11.

Kaczmarczyk

Ostachowicz

. Transient vibration phenomena in deep mine hoisting cables. Part 1: Mathematical model. J Sound Vib 2003; 262: 219–244.

12.

Kaczmarczyk

Ostachowicz

. Transient vibration phenomena in deep mine hoisting cables. Part 2: Numerical simulation of the dynamic response. J Sound Vib 2003; 262: 245–289.

13.

Kaczmarczyk

Picton

. The prediction of nonlinear responses and active stiffness control of moving slender continua subjected to dynamic loadings in a vertical host structure. Int J Acoust Vib 2013; 18: 39–44.

14.

Zhu

Chen

. Theoretical and experimental investigation of elevator cable dynamics and control. J Vib Acoust Trans ASME 2006; 128: 66–78.

15.

Kimura

Ito

Fujita

et al.

Forced vibration analysis of an elevator rope with both ends moving. J Vib Acoust Trans ASME 2007; 129: 471–477.

16.

Zhu

Zheng

. Exact response of a translating string with arbitrarily varying length under general excitation. J Appl MechTrans ASME 2008; 75: 1–14.

17.

Andrew

Kaczmarczyk

. Rope dynamics. Elevator World 2011; 59: 45–56.

18.

Bao

Zhang

Zhu

et al.

Transverse vibration of flexible hoisting rope with time-varying length. J Mech Sci Technol 2014; 28: 457–466.

19.

Zhu

Ren

Xiao

. A nonlinear model of a slack cable with bending stiffness and moving ends with application to elevator traveling and compensation cables. J Appl Mech Trans ASME 2011; 78: 1–13.

20.

Zhu

Ren

. A linear model of stationary elevator traveling and compensation cables. J Sound Vib 2013; 332: 3086–3097.

21.

Sandilo

Horssen

. On variable length induced vibrations of a vertical string. J Sound Vib 2014; 333: 2432–2449.

22.

Sandilo

Horssen

. On a cascade of autoresonances in an elevator cable system. Nonlin Dyn 2015; 80: 1613–1630.

23.

Zhu

Chen

. Forced response of translating media with variable length and tension: Application to high-speed elevators. Proc IMechE, Part K: J Multi-body Dynamics 2005; 219: 35–53.

24.

Bao

Cui

et al.

Dynamic analysis of cable-driven parallel manipulators with time-varying cable lengths. Finite Elem Anal Des 2012; 48: 1392–1399.

25.

Wang

Fung

Lee

. Finite element analysis of a three-dimensional underwater cable with time-dependent length. J Sound Vib 1998; 209: 223–249.

26.

Cui

Bao

et al.

Dynamic analysis of cable-driven parallel manipulators using a variable length finite element. J Comput Nonlin Dyn 2015; 10: 1–7.

27.

Zhu

Ren

. An accurate spatial discretization and substructure method with application to moving elevator cable-car systems-part I: Methodology. J Vib Acoust 2013; 135: 1–10.

28.

Ren

Zhu

. An accurate spatial discretization and substructure method with application to moving elevator cable-car systems-part II: Application. J Vib Acoust 2013; 135: 1–21.

29.

Hurty

. Dynamic analysis of structural systems using component modes. AAIA J 1965; 3: 678–685.

30.

Greenway

. Lateral stiffness and deflection of vertical ropes with application to mine shaft hoisting. Aust J Mech Eng 2008; 5: 59–70.

31.

Wang

Cao

Zhu

et al.

Lateral response of cable-guided hoisting system with time-varying length: Theoretical model and dynamics simulation verification. Proc IMechE, Part C: J Mechanical Engineering Science 2015; 229: 2908–2920.

32.

Dvorak

Freistetter

. Chaos and stability in planetary systems, Berlin: Springer, 2005.

33.

Lanczos

. The variational principles of mechanics, New York: Dover Publications, 1986.

34.

Ilchmann

Reis

. Surveys in differential-algebraic equations II, Berlin: Springer, 2015.

35.

Wang

Cao

Wang

et al.

A novel driving strategy for dynamic simulation of hoisting rope with time-varying length. Int J Model Simul Sci Comput 2013; 4: 1–17.