Analysis of dry friction hysteresis in a cable under uniform bending

  • Huang, Xiaolun (Dept. of Mechanical Engineering, The University of Calgary) ;
  • Vinogradov, Oleg (Dept. of Mechanical Engineering, The University of Calgary)
  • Published : 1994.03.25


A cable is considered as a system of helical wires and a core with distributed dry friction forces at their interfaces. Deformations of the cable subjected to a uniform bending are analyzed. It is shown that there is a critical bending curvature when a slip at the wire-core interface occurs. It originates at the neutral axis of the cross section of the cable and then spreads symmetrically over the cross section with the increase of bending. The effect of slippage on the cable stiffness is investigated. This model is also used to analyze a cable under the quasi-static cyclic bending. Explicit expression for the hysteretic losses per cycle of bending is derived. Numerical examples are given to show the influence of dry friction and helix angle on the bending stiffness and hysteretic losses in the cable.



  1. Claren, R. and Diana, G. (1969), "Mathematical analysis of transmission line vibration", IEEE Transaction on Power Apparatus and Systems, pas-88(12), pp.1741-1767.
  2. Costello, G.A. and Phillips, J.W. (1976), "Effective modulus of twisted wire cables," J. of Eng. Mech., ASCE, 102, pp.171-181.
  3. Costello, G.A. (1990), "Theory of Wire Rope," Springer-Verlag, New York, Inc.
  4. Hruska, F.H. (1951), "Calculations of stresses in wire rope," Wire and Wire Products, 26, pp.766-767, 799-801.
  5. Huang, N.C. (1978), "Finite extension of an elastic strand with a central core," J. of Applied Mechanics, ASME, 44, pp.852-858.
  6. Huang, X. (1992), "Mechanics of Cables with Interwire Friction," Ph.D. dissertation, Dept. of Mech. Eng., the University of Calgary, Calgary, Canada.
  7. Huang, X. and Vinogradov, O. (1992), "Interwire slip and its influence on the dynamic properties of tension cables," 2nd International Offshore and Polar Engineering Conference, Paper No. ISOPE-92-T5-01, SanFrancisco, USA, June 14-19.
  8. Luchansky, M. (1969), "Axial stresses in armor wires of bent submarine cables," J. of Eng. for Industry. ASME, 91, pp.687-693.
  9. Knapp, R.H. (1983), "Simple bending models for helically armored cables," Proc 2nd Int. Off-shore Mech. and Arctic Eng., New York, pp.360-364.
  10. Machida, S., and Durelli, A.J. (1973), "Response of a strand to axial and torsional displacements," J. of Mech. Eng. Science, 15, pp.241-251.
  11. Sturm, R.G. (1936), "Vibration of cables and dampers-I," AIEE Trans., 55, pp.455-465.
  12. Vinogradov, O.G., and Atatekin, I.S. (1986), "Internal friction due to twist in bent cable," J. of Eng. Mech., ASCE, 112(9), pp.859-873.
  13. Vinogradov, O. and Huang, X. (1991), "Dry friction losses in axially loaded cables," Report #462, Dept. of Mechanical Engineering, University of Calgary, Calgary, Canada.
  14. Vinogradov, O. and Pivovarov, I. (1986), "Vibration of a system with non-linear hysteresis," J. of Sound and Vibration, 111(1), pp.145-152.
  15. Yu, A. (1952), "Vibration damping of stranded cable," Proc. Soc. Exp. Stress Analysis, 9, 141-158.

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