Advertisement

A Continuum Model for the Carding Machine

  • M. E.-M. Lee
  • H. Ockendon
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 1)

Abstract

Motivated by study of fibre dynamics in the carding machine, a textiles manufacturing process, we derive a continuum model for a medium composed of entangled fibres. Extensional and shearing simulations produce promising comparisons with experimental results.

Keywords

Bulk Stress Couple Partial Differential Equation Scalar Order Parameter Shearing Simulation Braid Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ericksen, J. L. (1991), Liquid crystals with variable degree of orientation. Archive of Rational Mechanics and Analysis, 113, p92–120MathSciNetCrossRefGoogle Scholar
  2. 2.
    Hinch, E. J., Leal, L. G. (1975), Constitutive equations in suspension mechanics. Part 1. General formulation. Journal of Fluid Mechanics, 71 (3), p481–495MathSciNetCrossRefGoogle Scholar
  3. 3.
    Komori, T., Makishima, K. (1977), Estimation of fibre orientation and length in fiber assemblies, textile Research Journal, 47, p309–314Google Scholar
  4. 4.
    Lang, S., Tate, J. L. (1965), The collected papers of Emil Artin, Addison-Wesley, p446–471Google Scholar
  5. 5.
    Lee, M. E.-M. (2001), Mathematical models for the carding machine. DPhil Thesis, University of OxfordGoogle Scholar
  6. 6.
    Spencer, A. J. M. (1972), Deformations of fibre-reinforced Materials. Oxford University PressGoogle Scholar
  7. 7.
    Toll, S., Manson, J.-A. E. (1994), Dynamics of a planar concentrated fiber suspension with non-hydrodynamic interaction. Journal of Rheology, 38(4), July/August, p985–997Google Scholar
  8. 8.
    Toll, S., Manson, J.-A. E. (1995), Elastic compression of a fiber network. Journal of Applied Mechanics, 62, March, p223–226Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • M. E.-M. Lee
    • 1
  • H. Ockendon
    • 1
  1. 1.Centre for Industrial and Applied Mathematics, Mathematical InstituteUniversity of OxfordOxfordUK

Personalised recommendations