Contents

• List of Figures
• List of Tables
  • Abstract
  • Nomenclature.
• 1 Introduction.
• 2 Parallel-lay ropes
  • 2.1 Types of rope.
  • 2.2 Uses of Parafil rope.
    • 2.2.1 Resistance to corrosion.
    • 2.2.2 Light weight.
  • 2.3 Termination design.
    • 2.3.1 Static failure.
    • 2.3.2 Spike bed-down.
    • 2.3.3 Cyclic fatigue.
  • 2.4 Abrasion data for Parafil G ropes.
  • 2.5 Summary.
• 3 Friction and abrasion of synthetic fibres.
  • 3.1 Introduction.
  • 3.2 Friction.
    • 3.2.1 Classical friction.
    • 3.2.2 Friction of polymers.
      • 3.2.2.1 Summation of friction components.
      • 3.2.2.2 Effect of spin finish on friction.
  • 3.3 Kevlar-on-aluminium friction.
    • 3.3.1 Measurement of yarn-on-capstan friction.
    • 3.3.2 Apparatus.
    • Experimental equivalent coefficient of friction, .
    • 3.3.4 Experimental coefficients of friction, A and .
      • 3.3.4.1 Expressing in terms of A and .
  • 3.4 Yarn-on-yarn friction for Kevlar 49.
  • 3.5 Abrasion of polymeric fibres.
    • 3.5.1 Experimental results on abrasion in the literature.
      • 3.5.1.1 Mechanical abrasion.
      • 3.5.1.2 Thermal failure.
  • 3.6 Yarn-on-yarn abrasion.
  • 3.7 Kevlar 49-on-aluminium abrasion.
    • 3.7.1 Apparatus.
    • 3.7.2 Contribution from the thickness to be abraded.
    • 3.7.3 Contribution from the amplitude of cycling.
    • 3.7.4 Overall lifetime equation.
  • 3.8 Summary.
• 4 Anisotropy of synthetic fibres.
  • 4.1 Introduction.
  • 4.2 Elasticity in materials.
  • 4.3 Published values for Kevlar.
    • 4.3.1 Nomenclature used here.
    • 4.3.2 Correlation of fibre and Abaqus parameters.
  • 4.4 Transverse compression of a pad of fibres.
    • 4.4.1 Sizing of rig.
    • 4.4.2 Experimental set-up.
    • 4.4.3 Observations.
      • 4.4.3.1 Speed.
      • 4.4.3.2 Calibration.
      • 4.4.3.3 Plasticity.
      • 4.4.3.4 Compression of a fibre to a rectangle using a finite element analysis.
      • 4.4.3.5 Yield line analysis of a fibre compressing to a hexagon.
      • 4.4.3.6 Young's modulus on first loading (Curve A).
      • 4.4.3.7 Young's modulus on unloading-reloading (Curve B).
  • 4.5 Values for use in the finite element model
  • 4.6 Summary.
• 5 Finite element modelling of a parafil termination.
  • 5.1 Introduction.
  • 5.2 Alternatives to finite elements.
  • 5.3 The finite element approach.
  • 5.4 An Abaqus finite element analysis of a Parafil termination.
    • 5.4.1 Introduction.
    • 5.4.2 Geometry.
      • 5.4.2.1 Spike.
      • 5.4.2.2 Barrel.
      • 5.4.2.3 Rope.
      • 5.4.2.4 Interface elements.
      • 5.4.2.5 Springs.
      • 5.4.2.6 Mesh refinement.
    • 5.4.3 Contact.
      • 5.4.3.1 Gap elements INTER3A.
      • 5.4.3.2 Interface element ISL22A and slide lines.
      • 5.4.3.3 Pressure-clearance relationship.
    • 5.4.4 Friction subroutine.
      • 5.4.4.1 Elastic stick.
      • 5.4.4.2 Slip.
    • 5.4.5 Material subroutine.
      • 5.4.5.1 Kevlar - orthotropic.
      • 5.4.5.2 Orientation.
    • 5.4.6 Verification of the subroutines.
    • 5.4.7 Establishing contact.
      • 5.4.7.1 Initial contact within the termination.
    • 5.4.8 Loading history.
  • 5.5 Summary.
• 6 Results from the finite element analysis.
  • 6.1 Introduction.
  • 6.2 Spike results.
    • 6.2.1 Relative slip between the rope and the spike.
      • 6.2.1.1 Description of the elastic slip - true slip graphs.
      • 6.2.1.2 Behaviour from initial assembly to a preload of 60%, then unloaded.
      • 6.2.1.3 Behaviour on cycling between 5% and 50%.
      • 6.2.1.4 Behaviour on loading from 5% to failure.
    • 6.2.2 Slip between the rope and the spike.
      • 6.2.2.1 Cycling.
      • 6.2.2.2 Behaviour on loading to 100%.
    • 6.2.3 Contact force between the rope and the spike.
    • 6.2.4 Force in the spike.
    • 6.2.5 Stresses in the spike.
  • 6.3 Contour plots of stress.
  • 6.4 Barrel results.
    • 6.4.1 Relative movement between the rope and the barrel.
    • 6.4.2 Friction between the rope and the barrel.
    • 6.4.3 Stresses in the barrel.
    • 6.4.4 Force in the barrel.
  • 6.5 Rope results.
    • 6.5.1 Stresses in the rope.
      • 6.5.1.1 Axial stress.
      • 6.5.1.2 Shear stress.
  • 6.6 Salient conclusions.
    • 6.6.1 Modelling.
    • 6.6.2 Observations.
      • 6.6.2.1 First-loading.
      • 6.6.2.2 Cycling the load.
• 7 Comparison between analysis and actual tests.
  • 7.1 Introduction.
  • 7.2 The strain gauging of a 60 tonne Parafil G termination.
  • 7.3 Readings from the spike.
    • 7.3.1 Nose of the spike, gauges 1 3.
    • 7.3.2 Middle of the spike, gauges 4 9.
    • 7.3.3 Base of the spike, gauges 10 12.
  • 7.4 The barrel.
    • 7.4.1 Middle of the barrel, gauges 13 24.
      • 7.4.1.1 The behaviour in the middle of the barrel.
    • 7.4.2 Base of the barrel, gauges 25 30.
  • 7.5 Asymmetry within the termination.
    • 7.5.1 Possible asymmetric distributions.
  • 7.6 Displacements.
    • 7.6.1 Bed-down.
    • 7.6.2 Force-displacement.
  • 7.7 Anomalous spike movement.
    • 7.7.1 Limiting angle of friction.
      • 7.7.1.1 Limiting contact pressure for 3.5^o spike.
      • 7.7.1.2 Limit on angle of spike.
    • 7.7.2 Viscoelasticity.
  • 7.8 Prediction of contact pressure using Lamé's equations.
  • 7.9 Lifetimes under cyclic loading.
    • 7.9.1 Predicted lifetimes for other size ropes.
  • 7.10 Summary.
• 8 Discussion.
  • 8.1 Improvements to the termination design.
    • 8.1.1 Modifications to the geometry.
      • 8.1.1.1 Adjusting the contact pressure.
      • 8.1.1.2 Adjusting the radius of spike.
      • 8.1.1.3 Improved spike design.
    • 8.1.2 Materials.
      • 8.1.2.1 Feasibility of non-metallic terminations.
      • 8.1.2.2 Reduction in weight.
      • 8.1.2.3 Improvement of lifetimes.
    • 8.1.3 Prevention of anomalous spike movement.
      • 8.1.3.1 Redesign.
      • 8.1.3.2 Loading the spike.
  • 8.2 Improvements to the finite element model.
    • 8.2.1 Extend range.
      • 8.2.1.1 Yield of aluminium.
    • 8.2.2 Range of friction measurements.
    • 8.2.3 Model yarn-on-yarn friction.
    • 8.2.4 Yarn-on-yarn abrasion.
    • 8.2.5 Hysteresis.
    • 8.2.6 Viscoelasticity.
      • 8.2.6.1 Transverse creep.
      • 8.2.6.2 Axial creep.
    • 8.2.7 Discretisation of the transverse loading curve.
      • 8.2.7.1 Stress-strain at the nose.
    • 8.2.8 Analysis of a partly abraded termination.
  • 8.3 Asymmetry.
    • 8.3.1 Future tests.
    • 8.3.2 Mechanical assembly.
  • 8.4 Summary.
• 9 Conclusions and recommendations.
• Appendix A Factors affecting the gauge readings.
  • A.1 Contact pressure on gauges.
  • A.2 Elasticity of epoxy.
• Appendix B Calculation of principal strains.
• Appendix C Strains due to bending.
• Appendix D Termination assembly.
• References.
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