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Über dieses Buch

This book considers the modelling and analysis of the many types of ropes, linear fibre assemblies. The construction of these structures is very diverse and in the work these are considered from the modelling point of view. As well as the conventional twisted structures, braid and plaited structures and parallel assemblies are modelled and analysed, first for their assembly and secondly for their mechanical behaviour. Also since the components are assemblies of components, fibres into yarns, into strands, and into ropes the hierarchical nature of the construction is considered.

The focus of the modelling is essentially toward load extension behaviour but there is reference to bending of ropes, encompassed by the two extremes, no slip between the components and zero friction resistance to component slip. Friction in ropes is considered both between the rope components, sliding, sawing and scissoring, and within the components, dilation and distortion, these latter modes being used to model component set, the phenomenon instrumental in rope proofing. The exploitation of the modelling is closed by the suggested modelling and analysis of component wear and life limitation and also of rope steady state heating. These will require extensive experimentation to extract the necessary coefficients, achievable by parallel testing of prototypes and similar structures.

This development is focused on the modelling and analysis of ropes and other similar structures. All the modelling is based on the Principle of Virtual Work and admissible modes of deformation. Finally this book is directed towards the various industries involved in design, manufacture and use of ropes, stays and other similar structures.



Chapter 1. Introduction

This chapter, the introduces the modelling of linear fibre structure, ropes and cables firstly by outlining the structures and introducing the basics in the modelling approaches to be used.
C. M. Leech

Chapter 2. Fibre Geometry and Fibre Mechanics

Fibres and polymer fibre materials are discussed. Dimensionality is introduced as an essential component and the other assumptions then follow; axial stiffness and strength is a primary requirement and the secondary deformation modes, flexural and torsion are to a less extent important. The problems of measurement of linear structures leads to the classical textile measurements of ‘lateral dimension’ by way of weight and Tex or denier; these are carried through to the other material and component properties, typically as stiffness and strength. A detailed survey into the classification one dimensional material (fibre) properties such as viscoelasticity and anelasticity is conducted.
C. M. Leech

Chapter 3. Component Path Geometries

This chapter considers the general fibre paths and specifically helical geometry; the effect of deformation of the helix on the deformation of the constituent fibre component is analysed. Finally a comparison in the energy of extension, twist and flexure is made so that useful engineering approximations can be selected.
C. M. Leech

Chapter 4. Transversely Continuous Structures

Having dealt with the fibre as the constituent for a structure, linear structures are then examined; these include yarns, cables and ropes. In this chapter, transversely continuous structures are considered; these are structure where the constituent component are so small and so numerous that it is appropriate to consider the structure as a continuum, although in the classis sense it would be anisotropic and inhomogeneous. In this chapter the parallel assembly is also examined and the implications of variability in component length (or prestrain) are quantified.
C. M. Leech

Chapter 5. Hierarchical Structures

In this chapter the hierarchical nature of rope structures is identified for the analysis and modelling of ropes and cords and other similar structures; indeed it is indigenous in their manufacture and construction. The various terminology specific to the rope industry is detailed, and the process of structure normalisation is outlined.
C. M. Leech

Chapter 6. Transversely Discrete Structures

This chapter examines transversely discrete structures, those in which the components are easily countable and identifiable. The component (fibre, yarns, strands etc.) elements are assembled by twisting or weaving (braiding, plaiting) into another linear component whose dimensionality (L/d) is reduced from that of the constituent component. Tension and torsion behaviour are the focus, but by implication in the modelling transverse deformation is important is developing the model for the structure behaviour. This arises from the compression and distortion of components as the structure is loaded. Also in this chapter the various component nomenclatures are listed and the various component assembly configurations are described. The hierarchical nature of rope structures is important for the analysis and modelling of ropes and cords and other similar structures; indeed it is indigenous in their manufacture and construction. Finally bending of helical structures is introduced with the two extreme assumptions, no slip and zero friction.
C. M. Leech

Chapter 7. Contact Force and Friction

This chapter introduces contact forces and pressures and its modelling; consequent to this is friction as occurs within the structure and between the constituent components. Various friction or more correctly energy dissipative mechanisms are identified and are grouped into two categories; those that arise because of relative motion between components are labelled INTER modes and those that arise because of the deformation of the component are INTRA modes and dilation and distortion are in the latter category. Because of the inhomogeneous nature of the fibre structures continuum theories do not necessarily lead to the best models. The quantification of dilation and distortion is achieved through the packing factor and the shape factor. Also included in this chapter is the modelling of structure life as limited by the continued abrasion between components. This uses the friction models and various wear criteria which must be measured by testing.
C. M. Leech

Chapter 8. Component Wear, Life and Heating

In this chapter a preliminary investigation into component wear and structural heating is initiated, where the emphasis is on the wear and heating of the components due to repeated abrasion between contiguous components. This is considered by assuming that the wear and heating are related to the work done by sliding or scissoring. First the work done on the component by repeated sliding, sawing or scissoring is estimated and secondly the effect of this on the deterioration of component performance, wear is quantified. Finally the steady state thermodynamic equilibrium, due to repeated abrasion between contiguous components is determined.
C. M. Leech


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