The Mathematical Institute, University of Oxford, Eprints Archive

Mathematics of crimping

Cooke, W. (2000) Mathematics of crimping. PhD thesis, University of Oxford.

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Abstract

The aim of this thesis is to investigate the mathematics and modelling of the industrial crimper, perhaps one of the least well understood processes that occurs in the manufacture of artificial fibre.

We begin by modelling the process by which the fibre is deformed as it is forced into the industrial crimper. This we investigate by presuming the fibre to behave as an ideal elastica confined in a two dimensional channel. We consider how the arrangement of the fibre changes as more fibre is introduced, and the forces that are required to confine it. Later, we apply the same methods to a fibre confined to a three dimensional channel.

After the fibre has under gone a preliminary deformation, a second process known as secondary crimp can occur. This involves the `zig-zagged' material folding over. We model this process in two ways. First as a series of rigid rods joined by elastic hinges, and then as an elastic with a highly oscillatory natural configuration compressed by thrusts at each end. We observe that both models can be expressed in a very similar manner, and both predict that a buckle can occur from a nearly straight initial condition to an arched formation. We also compare the results to experiments performed on the crimped fibre.

Throughout much of the process, the configuration of the fibre does not alter. This part of the process we call the block, and model the material in this region in two ways: as a series of springs; and as an isotropic elastic material. We discuss the coupling between the different regions and the process that occurs in the block, and consider both the steady state and stability of the system.

Item Type:Thesis (PhD)
Subjects:H - N > Mechanics of deformable solids
O - Z > Partial differential equations
H - N > Numerical analysis
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:38
Deposited By:Eprints Administrator
Deposited On:10 Mar 2004
Last Modified:20 Jul 2009 14:18

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